University of Alberta

Productivity Studies Using Advanced ANN Models

B Y

Ming Lu @

A thesis submitted to the Faculty of Graduate Studies and Research in p h a l fdultillment

of the requirements for the degree of Doctor of Philosophy

in

Construction Engineering and Management

The Department of Civil and Environmental Engineering

University of Alberta

Edmonton, Alberta, Canada

Spring 2001

National Library Bibliathèque nationale du Canada

Acquisitions and Acquisitions et Bibliographie Services services bibliographiques

395 Wellington Street 395. rue Wellington Ottawa ON K1A ON4 Ottawa ON KI A ON4 Canada Canada

Your file votre rëférence

Our fi& Notre rdfdrence

The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, ioan, distribute or sell copies of this thesis in rnicroform, paper or electronic formats.

The author retains ownership of the copyright in this thesis. Neither the thesis nor substantial extracts fkom it may be printed or otherwise reproduced without the author's permission.

L'auteur a accordé une licence non exclusive permettant a la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/fih, de reproduction sur papier ou sur format électronique.

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

Estirnating labor productivity is one of the most difficult aspects of prepming an

estimate, or a control budget based on the estimate for labor-intensive activities in

construction. The primary objective of research is deveioping artificial neural neavork or

ANN based C$i.Kna~g tools CO offer estimators valuable information about labor

productiviv in bidding nem jobs.

In conjunction with a major Canadian industrial contractor, the thesis research

presents case studies on the theoretical basis and practical considerations for m e a s k g

and analyzing labor productivity in industrial construction. Two important activities of

process piping mere investigated: pipe installation in the field and spool fabrication in the

fabrication shop. Emerging cornputer modeling techniques such as data warehouses and

ANN were researched fiom an academic perspective and irnplemented in industry to

meet the challenges in productivity studies. The thesis research has addressed: (1) how to

quannfv labor productivity in indusmal construction Erom a contractor's point of view;

(2) how to measure actual labor productivity in industrial construction based upon on-

site control practices; and (3) how to utilize ANN to analyze the vmiability of actual

labor production rates and the sensitivity of idensed influencing factors.

Using actual data, the proposed ANN models were proven to be effective in

both risk analysis and sensitivity analysis of construction labor productivity. The

developed data warehouses and -W-based decision-support tools have been

lmplemented or are in the process ofimplementation at the involved Company. The h a 1

results of the research not only assist estîmaton to improve the accuracy of e s t i m a ~ g

labor production rates for studied activities in biddlig new jobs, but also offer the

management a precise and integrated view of corporate productiviq information

spanning across many business divisions. The esperience and lessons levned Gom the

successful, productive and rnumally beneficial collaboration benveen academh and

industry in the diesis research wX potentialiy benefit other universiq-indusq joint

research projects in the hture.

This thesis is organized in a paper format, consishg of five main chapters and

five appendices. Every chapter is an independent paper and c m be read separately.

However, î11 the chapters are logically coherent and pertinen~ to the theme of thesis.

Each ;ippendix is a user manual for one computer program that was developed in house

in the thesis research. Chapter 1 o v e ~ e w s the mhole thesis by introducing background

information, problem statements, research objectives, methodologies used, and

contributions achieved. Chapter 2 discusses a case study of industrial construction Iabor

productivïty, which depicts the settings of the research. Chapter 3 presents a

probabilistic neural nenvork classification model along with its application in estimating

the production rates of field pipe installation. Chapter 4 presents a sensitivity analysis

method of back propagation neural networks along with its application in estimating the

production rates of shop spool fabrication. Chapter 5 surnmarizes what has been done

thus far and recomrnends what to do in the future research. Appendk A is for the PINN

trainer program based on the mode1 described in Chapter 3. Appendis B is for the

FabMaster program, which is the data marehouse for the fabrication facilities. Appendis

C is for Fab-OLAP, which is an on-line analytical processing program in cornpanion

wïth FabMaster. Appendïx D is for the PipinghIaster program, whïch is the data

warehouse for the field construction systems. Appendks E is for the SensitiveNN

program based on the model as described in Chapter 3.

First and siacerely, 1 would like to thank my universitg adssor, Dr. S. bI.

AbouRizk, mithout whose visions, guidance and encouragement this academic

achievement would not have become a redty.

Especially, 1 would like to ha& my industry advisor, b k U. H. Hermann of

PCL, whose professionalïsm and enthusiasm have set the pace and the standard for the

mhole work. 1 am exaemely gratefd to PCL Industriai Constructors, Inc. for s p o n s o ~ g

the research hnancially and allowing me to use its actual data for developing problems

and validaMg solutions diroughout the thesis.

Findy, 1 wodd like to dia& my wife, Duojia, for her understanding, love and

assistance in making this thesis fiom thoughts to finish. 1 dedicate this work to her and

o u arriving W u a n Hum.

Table of Contents

CHAPTER 1 INTRODUCTION ................................................................................................................. 1 BACKGROUNDS .......................................................................................................................................... 1

Industrial Construction ....................................................................................................................... 1 3 Prodrictivity Strtdies .............................................................................................................................. -

Prodrictiviry Modeis ............................................................................................................................. 3 An@cial Neural Nehvorks .................................................................................................................... 5

.............................................................................................................................. PROBLEM STATEMENTS 8 Procirictivity Stridies .............................................................................................................................. S

........................................................................................................................................ A NN Models 13 RESEARCH OBJECI-IVES ............................................................................................................................ 15

............................................................................................................................ Prodrictivity Strtdies 16 ............................................................................................. Probnbilistic Neural Network Modeling 16 .............................................................................................. Sensitivity Analysis of Neural Nehvorks 16

M ~ O D O L O G E S ..................................................................................................................................... 17 Reviewing Literatrtre to Recognize Issues ........................................................................................... 17 Identihing Factors froni Brairlstorrriing by Donrairz Erperts .............................................................. 17 Using Data Warehorlse tu Qrrantitative Data ..................................................................................... 18 Qriestionnaire Srirvey .......................................................................................................................... 19 Cornputer Progrnmniing ..................................................................................................................... 2 1

..................................................................................................................... AcADEMIC CONTR[B UTIONS 21 INDUSTRIAL CONTRBUTIONS ................................................................................................................... 22 CONCLUS~ONS .......................................................................................................................................... 23 REFRENCE~ ............................................................................................................................................... 23

CHAPTER 2 A CASE STUDY OF INDUSTRIAL CONSTRUCTION LABOR PRODUCTIVITY ..................................................................................................................................... 28

INTRODUCTION ......................................................................................................................................... 28 .................................................................................................................... INDUSTRIAL CONSTRUCTION 30

FIELD PIPE INSTALLATION ........................................................................................................................ 32 ................................................................................................................. Prodrictivity Qiianrificcntion 33 .................................................................................................................. Producrivity Measrrrerrtenr 34

....................................................................................................................................... Input Factors 36 ............................................................................................... Probabilistic neriral nenvork trrodeling 40

....................................................................................................................... SHOP SPOOL FABRICATION 42 ................................................................................................................. Prodrictivity Quantification 43 .................................................................................................................. Prodrtctivity Measurernent 46

lnprit Factors ....................................................................................................................................... 47 ......................................................................................... Sensitivity Analysis of Ittflrienci~zg Factors 51

CONCLUSIONS .......................................................................................................................................... 57 REFRENCES ............................................................................................................................................... 58

CHAPTER 3 ESTIMATING LABOR PRODUCTIVITY USING PROBABILITY INFERENCE NEURAL NETWORK ........................................................................................................................... 6 0

....................................................................................................................................... INTRODUC~ION 6 0 ................................................................................................................................. Probleni Dorrlairz 61

.................................................................................................................. Review of NN Applications 64 ..................................................................... P R O B A B ~ ~ INFERENCE NEURAL L'WWORK ( P I W ) MODEL 64

Introduction of the PINN Mode1 ......................................................................................................... 64 Overview of the PlNN Topology and Process ........................ ... ...................................................... 67 Data Pre-Processing ........................................................................................................................... 70 Orrtpilt Zone Setzip ............................................................................................................................... 74 Processing Elements (P E) crt Kotionen Layer ................................................................................... 74

.......................................................................................................................... NN Learning Process 75

List of Tables

Table 2-1: Sample of pipe installation unit labor rates ............................................................. 33

Table 2-2: Input factors to pipe installation productioi~ ...................................................... 39

Table 2-3: Sample of degree-of-difficulty factors for converting welds into units ............... 4 4

Table 2-4: Explanatory factors ro spool fabrication productivity ........................................... 50

Table 3-1: Input Factors and Data Type of PINN Mode1 ...................................................... 72

Table 3-2: Inpur Data Sample of PINN Mode1 ......................................................................... 73

Table 3-3: Scaled Input Vector and Initial Weight Vectors ................................................... 78

Table 3-4: Updating Kreight Vectors in Firs t Leaming Stage .................................................. 79

Table 3-5: Updathg Weight Vectors in Second Leaning Stage ............................................... 81

Table 3-6: Trained PINN Ready to Recd for A Given Input Vecmr ............................... .... 85

....................................................................... Table 3-7: Recall Calculations at Bayesian Layer 86

Table 4-1 : Data Set for Testing BPNN and Regression Analysis ......................................... 117

aN1 Table 4-2: Pan5al Derivative (Slope) (-) at Four Input Points ...................................... 119 NP

aN. Table 4-3: Statisucs of Partial Derivative (Slope) Values: (-) ........................................ 119 ~ S P

Table 4-4: Input Factors of Spool Fabrication Labor Productivity .................................. 128

Table 5-1: PINN vs . BP NN ...................................................................................................... 144

Table B-1: Size Range Codes ...................................................................................................... 159

Table B-2: Material Type Codes ................................................................................................. 160

Table B-3: Item Codes for Spool Level Data Compilation ................................................... 160

Table B-4: Sarnple cf Fabhlaster Outputs ................................................................................ 170

................... Table D-1 : Sample of Quantity Calculation Summary Table in PipinghIaster 190

List of Figures

Figure 1-1: Sample Quesho~a i r e for Findïng Facts about Spool Fabrication .................... 20

Figure 2-1: Output interface of PINN recall program ............................................................. 41

Figure 2-2: Sensitivity Analysis of Spool Fabrication BPNN Mode1 .................................... 51

Figwe 2-3: Tes ting Sensitivity of BPNN to Matenal Type ...................................................... 57

Figure 3-1: Topology of PINN Mode1 ........................................................................................ 66

Figure 3-3: Operations at Bayesian Layer in Recd ................................................................... 80

Figure 3-3: Cornparison of PINN and Back Propagation NN .......................................... 88

Figure 3-4: PINN Output for the Base Case Scenario ............................................................. S9

Figure 3- 5: PINN Output for Scenario 1 .............................................................................. 91

Figure 3-6: P W Output for Scenario 3 ................................................................................... 92

Figure 4-1: Stnicme of Back-Propagation NN Mode1 .......................................................... 103

Figure 4-2: Illustration for Node and Laper Representations ................................................ 108

Figure 4-3: Distributions for Input Sensitivity ..................................................................... 120

Figure 4-4: Sensitivity Analysis of Spool Fabrication BPNN Mode1 .................................... 123

Figure 4-5: T e s ~ g Sensitivïty of BPNN to Material Type .................................................... 132

Figure A-1 : Select an identifier key of one previous mal ........................ ...... .................. 147

Figure A-2: User selects data table .... .. ....................................................................................... 149

Figue A-3: Flag status of records .............................................................................................. 150

Figure A-4: Setup structure and leaming parameters for PINN .......................................... 152

Figure A-5: SpecZy training iteraüons and train- test PINN .................................................. 153

Figure A-6: Check training results ............................................................................................. 151

. . Figure A-7: Detected noise m training data .............................................................................. 155

Figure A-8: Global report for a train-test t r ia l ........................................................................ 156

Figure A-9: PINN Trainer on-line help .................................................................................... 157

...................................................................... Figure B-1: Program Flow Chart of FabMaster 165

........................................................................ Figure B-2: Main User Interface of FabMaster 128

......................................................................................................... Figure C-1: Select one ratio 181

.......................................................... Figure C-2: T d on "number of pipe pieces per foot" 182

........ ....................................................................................... Figure C-3: View details of data .. 183

Figure D-1: S t r u c ~ e s of Raw Data Tables for A Project ..................................................... 185

Figure D-2: Main user interface of FabMaster ........................................................................ 186

Figure D-3: Handikg: S-Reference Information Inte@o/ Check ....................................... 188

Figure D-4: Welding: X-Re ference Information In t e g i t y Check ....................................... 189

.................................................. Figure D-5: Productivity Analvsis Page for Pipe HandlLig 191

Figure D-6: Sample of Pipe Handling Ques tiomaire ............................................................. 192

Figure D-7: Program Flow Chart of Pipinghfas ter ................................................................. 193

............................................................... Figure E-1: Splash Screen of SensitiveNN program 195

............................................................................................. Figure E-2: Program Switchboard 197

Figure E-3: Open FFBPNN-mdb First ..................................................................................... 197

Figure E-4: Select data source table ........................................................................................... 198

Figure E-5: Examine details of data and edit record s tatus ................................................... 199

Figure E-6: Program main interface of SensitiveNN ............................................................. 2 0 1

Figure E-7: Check leaming results when NN training temiinates ........................................ 202

Figure E-8: Check s Input Sensitivitp for each input-output pair ........................................ 204

Chapter 1: Introduction

Indus trial Construction

Barrie et al (1992) described industrial construction as:

"Indusmal construction covers a wide range of construction projects that

are essential to our ualities and basic industries, such as petroleum rehenes and

petrochemical plants, synthetic fuel plants, fossil fuel and nuclear power plants,

off s bore oil/gas production facilities, cryogenic plants etc. Indus trid

construction generalIy Çeatures large amounts of hghly cornples process piping,

mechanical, electrical, and instrumentation mork; bo th design and consuuction

require the highes t level of engineering expertise Gom multiple disciplines."

In particular, the installation of process piping systems in indusuial construction

is selected for productivïty studies because it accounts for the bulk of direct labor hours

of an ind~soial contractor. Process piping is used to transport fltids between storage

tanks and processing units. Instdation of piping systems generally consists of nvo

processes: (1) spool fabrication in a commercial pipe shop; (2) pipe installation in the

field. Although the trvo processes are inseparable and can be integrated to optimize the

econornics of a particular situation, they are treated independent of each otl~er in the

thesis because of the cuxent estimaMg and control practices of the involved company.

The productivity studies described in the thesis are conducted to support the

management's decision-rnaliing in the context of the company's m e n t management

systems, as opposrd to radically changing these systems.

Productivity Studies

In a construction task that is performed by hand labor, productivity is commonly

espressed as the labor production rate (man-hours per installed unit), which measures a

key dimension of performance and is a critical factor to estimating, scheduling and

control of the project (hlfeld, 1988). Little information could be found in literature on

the theoretical basis and practical considerations for measuring and analyzing labor

productivity of indusmial construcuon. In conjunction wïth a major indusnial concrac tor

(refened to as "the company" hereafter), productivity smdies were conducted for tsvo

Lnportmt activities in industeid construction: pipe installation in the field and spool

fabrication in the fabrication shop.

In general, productivity studies encompass three tasks: (1) developing special

methods and techniques to quanti@ labor productivity for e s ü m a ~ g , and to measure

actual labor productivïty for on-site control, (2) identifjmg input factors that cause the

vmiability in productiviq, and (3) analy zing the relations hips benveen input factors and

productivitg to enhance the accuracy of productivity estimating or Mprove the on-site

performance dkectly. The focus of investigation is the average labor production rates

(man-houn per unit) of these activities 3t the end of a project, rather than the d d y hbor

production rates, because the primary objective of reseaech is developing ANN-based

estimating tools to offer estimators valuabie information about labor productivity in

bidding new jobs, rather than assessing and improving the crem performance in the field.

Produc tivity Models

Several established models for studying productivity cm be found in the

literature, including work s tudy techniques, expectancy model, action-response model,

regression model, expert systems, and arnhcial neural networks (NN).

Work-study techniques were adopted in a nurnber of productivity models, in

which only a fenr factors related to work method were included (Thomas and D d y ,

1983). Such work-study models cannot be used to model esternai and management

factors. Thomas et al. (1990) and Thomas et ai. (1991) discussed additional drawbacks of

work-study techniques for construction productivity modeling.

The Espectancy model and action-response rnodel are tsvo alternative techniques

proposed to exphin variations in construcuon productivity. In the elrpectancy model, the

effort that an individual is &g to evert accounts for the ciifferences in job

performance or productivity (Maloney and McFillen 1985). The action-response model

graphically depicts the interaction of a number of factors that lead to the loss of

productiviq- (Halligan et. al. 1994). Both models contribute to understanding the

variations in productivity; however, neither can be used to quanufy the influences of

multiple factors on construction productivity (Sommez and RoMngs, 1998).

Sanders and Thomas (1993) developed an additive linear regression model to

study the effect of sis project-related variables on masonry productivity based on data

obtaioed fiom 11 projects. Eight binary variables mere used in the model to represeat

the variations in productivity due to temperature and hurnidity. The effect of crew size

was also taken into account in the model. The results of this regression model suggested

higher productiviq rates for crew with femer members. Thomas and Sakarcan (1994)

conànued the reseaxch of Sandea and Thomas (1993) by developing the additive Linear

regression model for the purpose of forecasckg labor productivity. They only included

job condition variables chat describe the work content and the physical components of

the work. The focus of both studies was to determine the coefficient of condition

variables, or the effect of a present condition on the activity productiviry rate based on

the results of historical study; such coefficients were derived independendy of other

inputs vithout accounting for combined effects. In addition, the determined coefficients

are constants based upon the average values of historical data, and do not reflect the real

situations in wiiich the values of such coefficients may vary with the specific job

conditions.

Esqxrt systems is another technique applied co model labor productivity in trvo

studies found in literature. Hendnckson e t al. (1 987) developed an hvo-stage espert

system named ''MASON" to estimate acuvity durations for m a s o q construction. First,

the maximum espected productivity was estirnated. Nest, this rate was adjusted for

various characteristics of job or site. The masimum productivity estimates and the

followhg adjustments mere based on the knowledge obtained Erom interviews with a

professional mason and a supportkg laborer. Christian and Hachy (1995) developed an

esTert system to estimate the production rates for concrete pouring. The expert system

relied on the knowledge extracted Erom experts and data coLlected £rom seven

construction sites. The user simply queried the expert system for an estimate through a

ques tion-and-ansmer routine. In both e-upert sys tems, productiviq mas es timated

through previously dehned decision d e s obtained from domain experts. Because the

nature of forrnulating rules is subjective, the resultant rules may be inconsistent.

h o t h e r disadvantage of analyzing productivirp based on expert systems is expert

systems do not perforrn Functional input-output mapping, i.e. quantitative evaluation of

the impact of job condiuons on productivity.

In the follow-.ï.ng subsection background information about r \NN models d be

introduced and the technique of modeling productirity using IWN d be discussed.

Artificial Neural Networks

htïficial Neural Networks (ANN) research involves multiple disciplines

including biology, xtificial inteiligence, cornputer science, and mathematics and evolves

with the developments in each related discipline. Kohonen (1995) dehned MJN as "

massively pardel htercomected network of simple (usudy adaptive) elements and their

hierarchical organizations, intended to interact with the objects of the real world in the

same way as the biological nervous systems do." Sirnply put, an A N N mode1 is an

analytical mode1 that sirnulates the cognitive learning process of the huma . brain, and is

automaticdy constructed feom leaming esamples or data by ttid and error Gthout

heuiristic design or other human intervention.

ANN deds effkctively mith ill-structured problems, in which the algorithms

required to solve them CaMOt be given in a precise and explicit fashion, or the data for a

partïcular problem are either not complete or cannot be s p e d e d preasely (Widman et.

al., 1989). ANN has been found to be capable of perfomilig pardel computations on

different tasks, such as pattern recognition, 1inea.r optimization, speech recognition, and

predicuon (Mukhe jee and Deshpande 1995). In short, the s p e d leaming algonthms of

ANN are capable of performing .gh dimensional, non-lineu input-output mapping and

extracMg hidden patterns and predictive information from observing the leuning

esamples.

In recent years, ANN has been rescarched and applied as a convenient dedsion-

support tool in a rarieq of application areas in civil engineering, including modulv

consmiction decision making &Iurt;iza and Fisher, 1993), s t n i c ~ a l analysis (Flood and

Katirn, 1994), e s t i m a ~ g construction productivity (Portas and AbouRizk, 1997), mode

choice analysis of beight mansport market (Sayed and Razavi, 1999), construction

m&p estünating (LI et al 1999), measurkg organizauonal effecùveness (Sinha and

hfcI<im, 2000), and predicbng setdement durkg tunneling (Shi, 2000).

In o u research, ANN was selected as the main methodology and utilized to

analyze the varGbility of actual labor production rates and the sensitivicy of identified

influencing factors due co two reasons.

Fkst, construction labor productivity is influenced by a variety of factors. bIodel

fit-ting based on construction labor productivity data requires quantification of the effects

of factors on labor productivity and quanacation of the interactions among the factors.

The task of hding a mapping hinction h m the independent variables to the dependent

variable is analogous to that performed by some of the neural netrvork models such as

back propagation (Sonmez and Rowïngs, 1998). In statistics, regression analysis is the

most common method to explore this relationship; in particular, the objectives and

operations of nonlinear regression analysis are comparable to back propagation neural

nenvorks. Homever, regression models requke the user to define a priori the parametric

expression for the model (lïnear, quadratic, etc.). In the case of modeling productivity,

the user is mainly concemed wïth what the productivity dl be for any given set of work

conditions, and may not necessarily be interested in the parametrïc expression of the

model, for instance, a highly complex nonlinear hnctional equation. On the other hand,

ANN is capable of nonlinear mapping for most complicated problems such as modeiing

productivity; the modeler does not need to esert much effort to decide on the class of

relationships in a precise and e,uplicit fashion.

Secondly, one of the amactive properties of ANN is th& capacity for tolerating

moderate amouncs of noise in the data. In many real applications, the quantity and

quality of the avdable data for modehg labor productivity rnay not support the fitting

of a regression model. In such cases, ANN may be applied to generalize the knowledge

from incomplete or noisy data and provide good solutions the problem.

Moselhi et al. (1991) pointed out the possible use of ANN for construction labor

producüvi~ modeling. Portas and AbouRizk (1997) developed an M N model to

estimate construction productivity for concrete formork msk. The rnajority of data

used in the study mas collected by questiomaires on a project basis. The prediction of

the ANN model was compared wïth that of senior estbators for a single project.

Sonmez and RoMngs (1998) developed ANN models for quantitative evaluation of the

impact of multiple factors on productivity in concrete pouring, fomwodc, and concrete

anishing tasks, using data compiled fiom eight building projects. Their study also

compared regression models induding the pure Linev regression rnodel, the regression

models rvith interaction and nonlinear tenns Gth ANN models, and concluded, " the

use of neural networks helped the overd modeling process. Neural networlcs have

shown potential for quantitative evaluation of the effects of multiple factors on

productivity, especially when interactions and nonlineu relations mere present-"

The problems to be solved in the thesis research were identified dirough

invest iga~g the m e n t eshmating and control practices of the involved Company and

reviewing the established -!INN models and applications as found in the litetanire. Placed

into civo different perspectives, i.e. productivity studies and A N N models, the d e h e d

problems can be stated as follows:

Productivity Studies

EstunaMg labor production rates for field pipe instdation commences Mth

establishing base production rates for various work items. Base production rates reflect

the contractor's present labor productivity level under normal rvorlc conditions that are

most ofien encountered in the field. The installation location is one of the major

considerations for an estimator to d e h e a classification of work conditions. For

example, the base produccion rates of pipe installation are valid for the conespondlig

base classification only, in which the installation location is above ground up to 12 fi

hgh. fm estimator determines a degree-of-difficulty factor (often referred to as

c'multiplier" in the company) for each non-base classif5cation to adjust the base rates up

or down in order to reflect the unfavorable or favorable work conditions for the job

bWig estimated. This is a subjective detision process, requiring substantial esperience

and skill on the part of the estimator to determine realistic production rates for the work

conditions to be encountered. Empirical degree-of-difficul~ factors for each

classification of work conditions based on the installation location serve as a guide or

tool to assist in decidïng on such factors and can be found in the company's business

manual. For example, the degree-of-difficulty factor for underground pipe installation (3

to 10 ft deep) is about two times the factor for aboveground pipe installation (up to 12 f i

high), while the factor for pipe installation inside building at over 10 fi of height is about

~ v o Mies the factor for underground pipe installation (4 to 10 ft deep).

Historical piping productivity data of 66 projects mas coliected Erom the

company and compiled into numerïc format for andysis. The folIowing hvo

observations mith regard to the actual degree-of-difficulty factors can be made Erom the

histoncd dam of the company: (1) the degree-of-ciifficulty factor for one classification of

installation location may reveal a widespread distribution instead of a constant value as in

the company's business manual; and (2) different ciassifications of installation location

may end up with veq- close values of the degree-of-difficulty factor, not as distinguished

as in the cornpany's business manual.

The above obsemations are not iniaally e-xpected and the e-uplanation c m be

attributed to the fact that more factors esist, other than the location of installation,

which contribute to the variability in labor productivity. In practice, an estünator rnay

adjust the value of degree-of-difficulty factor iri the business manual on a job based on

es~erience and specific job conditions, and subjected to the approval of senior

management. Barrie et al (1992) found that construction hbor productivity may fluctuate

d d l y due to nurnerous factors that affect it, and many are highly qualitative in name,

including the effect of location and regiond v ~ u o n s , the learning c u v e , work schedule

and work d e s , environmental effects, crew eqerience and management factors.

Identification of input factors in the study of field pipe installation productivity was

mainly based on Knowles (1 997). A total of 36 input factors are considered relevant and

used to redehe the classi6cation of pipe installation. Those factors include bath global

project-level information and specific activity-level information.

To estimate a fabrication project, a speual "unitization" scheme is applied to

quanti$ the various work items uniformly into an abstract unit of measure cded

"fabrication unit" or "unit" by weighting them for their degree of difficulty. A degree-of-

difficulty Factor is empirically determined for each weld, taking into account pipe

diameter, mall thickness of pipe, weld type putt weld, socket weld, saddle and lateral

welds) and the time required to lay out and perfom the weld. Quantity of non-welding

work items such as cutting, beveling, handling pipe and fittings, i n s t a h g supports are

also converted into "units" by appIying conesponding degree-of-difficuly factors in the

scheme-

Once the total "units" for a project are detemilied, the focus of productiviq

study in spool fabrication is on the production rate directly (man-hour/unit). Sirnilar to

deciding on the degree-of-dïffiultg factor for a classification of work conditions in field

pipe installation, deuding o n unit tabor rate for spool fabrication requires the esperience

and judgment of the estünator. The environmental effects and management factors aïe

noc considered as sgnïficant factors, as in the field productivïty studies, because of the

controlled shop environment, consistent policy and management personnel d h g the

period of investigation. h totd of 29 input factors are identified as affecting labor

productivi~ of shop spool fabrication based on consultation -5th expenenced estimators

and shop superintendents in the Company.

It is not straightfomasd to create a conventional andytical model so as to

accommodate the impacts of numerous factors on the mget xsky variable - degree-ol-

difficdty factor or production rate. It takes yevs of site ex~erience and eshat ing

practice for an estimator to develop his/her own mental model. The decision process

relies heavily on individuaïs experïences and the results are often inconsistent r e f l e c ~ g

the experience and disposition of the estirnator.

ANN has becn proposed by many as an alternative to streamllie the e s t ï m a ~ g

process and reduce the subjective nature of the work.

ANN Models

The classic Back Propagation NN predicts a single value without gi~ing any

bacbvp infornation on the risks of taking thïs value as correct. Observing the acmal

values for the degree-of-difficulty factors of field pipe instaliation indicates that the

target nsby variable lies over a relatively wide range. The result from an informal end-

user s w e y showed that estimators are more cornfortable to accept a deûsion support

model \.th the capability of analyzing the uncenainty of its outpur. Thus, a probabilistic

NN modeling approach that c m predict a distribution or probability densitg h c u o n

over the output range is preferred ar,d has been researched.

Portas & AbouRizk (1997) proposed a feed fonvard baclc propagation neural

network model for estimating construction production rates of formwork. The nenvork

outputs a single point prediction dong wi& a number of output zones, with equal

Iikelihood of the production rate being in any one zone. The output zones are

symrnemc and divided evenly across the range of likely production rate values. D k g

training, the output zone with the output that coincides with the actual production rate is

remarded with a prirnary score of 1.0, representing strong certaliv. A certain degree of

fuzziness is considered by remarding the 2 adjacent output zones with secondary scores

of 0.5, representing weak certainty. iV1 the other output zones are assigned a score of O.

Once the hW is trained and inputs are entered, the NN d predict a point value as weU

as the likelihood of production rates being within the output zones. This model achieved

lïmited success due to the fact that the adopted back-propagation N N mode1 is long on

non-linear regression, but short on &ssi£ication.

Specht (1 99 1) revisited Probabilis tic Neural Network (PNN) and General

Regression Neural Nenvork (0 algorithms wïth the objective of i n t e g r a ~ g

statistics and neural training. GRNN/PNN is a memory-based feed fomrard neural

network mode4 mhere the training is performed in one pass, thus requiùng less training

&ne. GRNN/PNN is able to identify a posterior distribution over the NN meiglit

vectors and a point-value prediction is generated based o n the predicted distdbution.

However, based on experhentations and observations, GRNN/PNN is not quite

tolerant of noisy data (inaccurate or incomplete records) and imposes a demandlig

standard of data quality that is hard to achieve in reality. The memory demand and

cornpuMg t h e for GRNN/PNN increase very rapidly when the dimension of input

vector and the quantity O E training samples increase.

Kohonen proposed tmo speùal NN models, namely Self-Orgking Map (SOM)

in the late 1980s and Leaming Vector Quantization (LVQ) in the rniddle 1990s. SOM

performs unsupervised classification and clusteàng to represent high-dimensional,

nonlinearly related da ta items in an illustra tive, O ften nvo-dirnensiond dis play. LVQ

combines unsupervised and supervised leaning and is recornmended for statistical

pattern recognition problems. in LVQ, "deusion surfaces, relating to those of the

Bayesian classinec, are defined by neares t-neighbor classification mith respect to sets of

codebook vectors assigned îo each class and describing it" @<ohonen, 1995). It is noted

that the predicted result O E LVQ and SOM is detenninis tic, being classiEied into one of n

predehned clusters or classes.

IGiowles and AbouRizk (1997) presented a tmo-stage NN model in p r e d i c ~ g

pipe-installation labor productitity. The input factors are used to invoke a LVQ

classification process, follomed by a predictive one. With the classification, the mode1

predicts whether the output is likely in a cypical or non-typical range. The proper feed-

fomard back-propagation network is then esecuted. The drawback of this method is

that a build-up of errors occurs when the classification fails. For instance, if the

classification accuraq is 90% at the hrst stage of NN, and the prediction accuracy at the

second stage of NN is 85'10, the prediction accuracy of the whole 1W is only 76.5%

(90% &es 85Yo)-

In c o n a s t mith a rather wïde distribution of the actual production rate in field

pipe installation, the actual labor production rates for shop spool fabrication are

bounded within a relatively narrom range. Thus, the NN modeling of hbor productivity

in the shop puts more emphasis on the sensitivity analysis of influenchg factors based

upon the classic back propagation N-N model, as opposed to the uncertaincy analysis of

cspected production rate.

However, leamuig algorithms such as BPNN do not attempt to infer causality,

hence, classification or prediction is based on b h d coirelation of new examples nrith

previously analyzed examples, mithout giving information on the effect of each input

parameter or influencing variable upon the predicted output variable. In the reported

NN applicatioions, model validation has thus far relied upon measuring accuracy of the

calibrated netrvork to an independent testing data set that are hidden fiom the neural

nenvork in learning. The modelfs sensitivity to changes in its parameters is generally

probed by t e s ~ g the response of a manire neturork on various input scenarïos. In short,

a NN model h c t i o n s like a "black boxf' package, giving no clue on how the answers or

model outputs are obtained, or how the input parameters affect the output.

Widman et. al (1989) pointed out that the credibility of an AI program

Gequently depends o n its abiliq to explain its condusions. Lack of interpretability is a

p i t f d of the neural netmork models recognized by many and has inhibited NN fiom

achieving its fidl potential in real-morld applications. Dhar and Stein (1997) argued that

because NN algorithms such as the back-propagation NN are non-linear, high

dimensional hinctional equations f e a h g paralle1 distebuted data processing, it is liard

to esplicidy hterpret mhich parameters cause what behavior in the NN model. YVhile

mathematical and operational methods do esist for the analysis of neural nenvorks, die

methods are fairly in~olved, and are less than satisfyuig because of their theoretical

assumptions. They stated that "unlike most statistical methods, it can be difficult to say,

even in general, mhich variables are significant in what respect." (Dhar and Stein 1997)

The ultimate goal of the thesis research is to hnd better neural nework modeling

approaches to predicting production rates and productivity indices. When applied in

industrial construction estimahng as decision-support tools, the dereloped ANN-based

models for analyzing productivity should be acceptable and effective to offer estimators

valuable infomiaàon about labor productivity in bidding nem jobs. To amin this

ultimate goal, the follonrulg objectives are d e h e d in regard to three aspects:

Productivity Studies

Investigate the cuirent estimating and ou-site control practices for industrial

construction as applied to the involved Company, in order to advance the theoretical

basis and practical considerations for measuring and analpzing labor productivity in

indusrrial construction.

Probabilistic Neural Network Modeling

Building upon the previous developments achieved b y O thers, es tablis h a more

effective NN approach that suits the needs of estimating indusmal construction projects,

which requires the recreation of a new training acd r e c d algonthm that combines the

hctionality of probabilistic classification and prediction in one integrated neural

netsvork.

Sensitivity Analysis of Neural Nerworks

Define the input sensitivicg. of a NN mode1 in mathematical terms, and establish

a method of i n t e r p r e ~ g the relevance and impact of NN &put parameters on the

predicted output variable so as to gain insighr into the rationale by which NN reason and

make decisions.

Main

folloming.

methodologies udized to fulhll the abore research objectives include the

Reviewing Literature to Recognize the Issues

A compreheasive literature review was conducted in regard to the established

A I N models, productivity studies, ANN applications in the problem domain,

optimization, statistics, and industtial consmction. Literature covers a wide range of

joumals, books, and reports, which document the latest academic developments and

industrial applications in the related areas. Licerature review helps recognize the issues to

be addressed in the thesis, namely, how to get data k o m ïndusuy in modeling labor

productivity, how to analyze the uncertainq of the output from an ANN-based

productivity model, and how analyze the sensitivity of the input for an ANN-based

productivity model.

Identifying Factors fiom Brainstorming by Domain Experts

The senior management and domain expens at the Ïnvolved Company including

superintendents, production engineers, consmiction engineers, drafking supe~tendents,

quality control superintendents, and melding foremen were convened for a

bralistomiing exercise to identifV the factors that influence productivity of the studied

activities. It should be noted that those factors as identified to influence labor

productivitg holds only midiLi a specifïc setting and over a specific period. The input

factors may need adjusmient by adding relevant ones and deletlig inelevant ones when

the setting of application changes to a different contractor, or a different penod, even if

the consauction process being studied remains the same.

Using Data Warehouses to Gather Quantitative Data

Idenufgrng relevant factors and gatherïng )ueh quality data for those factors are

crucial to the success of modehg labor productivity using XNN. Fouonring

identification of factors, data needs to be coilected.

The collaborative company (PCL Industrial) provided us with access to its

business data for validation of ANN models and development of ANN-based decision-

support tools. Although the company has invested resources in management information

systems at various business divisions, those systems mere developed and implemented

separately. Productivity studies using ANN require vast amounts of data fiom different

information management systems. A corporate data warehouse is "a process by which

related data korn many operational systems is merged to a single, integrated business

information view that spans many business divisions" F a n g , 1997). With the support of

the company's management, tsvo data marehouses, namely, PipuigbIaster and FabMaster,

were custom-developed for field pipe installation and shop spool fabrication respectively

to integrate the corporate management sys tcms of es timating, production resources

planning, quality control, and labor cost control. Validating and processing of

quantitative data were automated through cornputer programming within data

marehouses. The developed data warehouses provide solid platform of integrated

historical data from which to validate the ANN models and develop ANN-based tools

for productivity analysis.

If data for some factors is not recorded in the elasting management systems,

questionnaire surveys were carefully designed and personnel at the cornpnny were

i n t e ~ e w e d to collect the needed data.

Questionnaire Survey

With the heIp of domain experts, questions and descriptive idormaiion of

choices for ra t ine on a 6ve-point scale mere f o d a t e d into a questionnaire format

with the objective of reducing ambiguities and confusions. It is worth mentioning that

such questionnaire smrey for modehng productivity using ANN is intended to fînd facts

of the past projects only. BasicaUy, in conducting the quest io~aire survey, no persond

judgment or opinion about the relationships between the facts and the results is

involved. Questions of "What" type mere asked about the factors affecting productivity

only, and no questions of "Why" and "How" types were asked about the relationships

between the factors and the productivity. In k t , i\NN would sort out the relationslups

between the facts and the results on its own through an iterative leaming process based

on e x p l o ~ g sample data. Intelligence emerges mhen ANN hnds the input-output

patterns or relationships hidden Ln the data. This feanire draws a distinct line betsveen

A m approach and other intelligent modeling approach such as expert systems: ANN

relies on facts and data, but requires less direct input fiom domain experts (Dhar and

Stein, 1997). In short, modeling productivity using ANN is relatively an objective

approach compared to expert systems. Figure 1-1 shows the questioanaire designed for

fïnding additional facts about spool fabrication.

PCL INDUSTRIAL CONSTRUCTORS INC: Fabrication Facility Productivity Questionnaire

General:

Reported By

Report Date

r

Bob Smith FabMaster Processed Flag

Project #

Project Name

Schedule:

1700204

Gas Plant & Piperack Process Modu

How busy was the shop? (Based on shop workload in ternis of units and concurrent jobs processed)

- -- -- - 1 Very Slow Relatively Slow 9 Normal Relatively Busy Very Busy I Were there rnany rushed spools?

.- - None a Relatively Few 12 Normal Relatively Many Li Many (30% plus)

(5% less) (1 0%) (20%)

.---- Engineering:

What was the rework percentage due to drawing changes?

7

None fl Relatively Few Normal Relatively Many Many (30% plus) 1 (5% less) (1 0%) (20%) 1

Were there any late drawing issues?

g Relatively Few i-~ Normal Relatively Many 7 Many (30% plus) (5% less) (1 0%) (20%)

i I What was the drawing revision rate?

Materials:

Were there rnany material shortage problems that impacted production?

1 None Relatively Few Ci Normal Relatively Many Many 1 Figure 1-1: Sample Questionnaire for Finding Facts about Spool Fabrication

Foilowhg the formulation of a questionnaire, superintendents, project managers

and estimators who were involved in the past projects were interviemed to compile facts

and gather the needed information. The interview process was straightfonvard; the

domain e-xperts had no difficulty hnding the records or recalling the facts on the projecrs

that they maaaged.

Cornputer Programming

Mcrosofi Visual Basic, Visual Basic for Application, and Access svere found to

be flesible and powerful in handling large amounts of data and comples programming

logic, hence, were selected as cornputer programmhg tools to develop both the data

warehouses and ANN models in the thesis research. hli the programs in d i s thesis

research including data ~varehouses, ANN trainers, and ANN recall programs were

developed in house without third-party sohvare and hac-e been utilized in the involved

Company.

The solutions to the identified problems, which are provided through the thesis

research, d contribute to the general knowledge of productivity srudies and ANN

modeling in regard to:

Advancing the theoretical basis and practical considerations for measuring and

analyzing labor productivity in industriai construction, which has been documented

in a paper entitled "A case study of industrial construction Iabor productivity" and

has been submitted for publication in the Journal of Consmiction Engineering and

Management, ASCE;

Devising a new neural netrvork scheme to meet the requirements in modeling Iabor

productiviq of indusnial construction, and is termed the Probability Inference

Neural Network (PNN). P m T is a dassihcation-prediction combined neural

nemork mode1 based on I<ohonenYs LVQ concept (Kohonen, 1995), but integrated

\.th a probabilistic approach, which has been documented in a paper entitled

" E s t k n a ~ g labor productiviv using probability inference neural nenvork" and is

published in the October/2000 issue of the Joumal of Cornputhg in C i d

E n g i n e e ~ g , Vol 14(3), pp 341 -338, ASCE;

EstabEshing a simulation-based method of ïnterpreting the relevance and impact of

back propagation NN input parameters on the predicted output variable so as to

gain insight into the rationale by which back propagation NN reason and make

decisions, mhich has been documented in a paper entided "Sensitivity anaiysis of

neural nenvorks in spool fabrication productivity studies" and has been submitted

for publication in the Journal of Computing in Civil E n g i n e e ~ g , ASCE.

The developed data warehouses and ANN-based decision-support tools have

been irnplemented or ate in the process of implementation at the involved Company.

The hnal results of the research not only assist estimators in irnproving the accuracy of

e s t i m a ~ g labor production rates for studied activities in biddlig new jobs, but dso offer

the management a precke and integrated view of corporate producavity infomiation

spanning across rnany business divisions. The experience and Iessons learned fiom the

successful productive and m u d y beneficial collaboration betsveen academia and

industry in the thesis research d potentially benefit other university-industry joint

research projects in the future.

The problems addressed in the thesis research were idenufled through

inves t iga~g the curent estimating practices in indusq and understanding the real

concems of industry prokssionals. Emerging compter-modeling techniques such as

data warehouses and ANN were researched Gom an academic perspective in order to

meet with the challenges in industry. The proposed novel ANN models and developed

decision suppoa tools were proven to be effective in both uncertainty mdysis and

sensitivïty arialysis of construction labor productiviq; they were validated using real data

Gom industry and successfully applied to assist esùmators in deciding on labor

production rates for new jobs.

Alfeld, L. E. (1 9 88). Constndon prodi~~~ivity - on -site mea~~zfnmetzt and nzmzcrgenzeizt.,

McGraw-Hill, New York, NY.

Bmie, D. S., and Paulson, Ir., B. C. (1 9%). Pmjë~siona/ com-hzccion management,

incl~ding CJW., deng~i-conrtnict, aodgenerd contrachg. 3" ed, McGram- W, New York, NY.

HaLligan, D- W., Demsets, L- A., Brown, J. D., and Pace, C. B. (1994). "Action-

response models and loss of productivity in construction." joz~rnuf of Com-tr/~~-tion

Engizeeniig andManagement, ASC E, 1 20(1), 47-64.

Li, Y., Shen, L. Y., and Love, P.E.D. (1999). "MN-based mark-up estimation

s ys tem with self-e-uplanatory capabilities ." Joz~n~cd Comtni~.tion Engieenig m d

&lanagcme)zt, ASCE, 125(3), 185-189.

M a l o q , W. F-, and McFiUen, J. (1985). "Valence of and satisfaction with job

outcomes ." ]ozmai of Corn-tntction Etzgineerirrg and Management, ASCE, 1 1 1 (1) , 5 3-73.

Mukherjee, A., and Deshpande, J.M. (1995), 'SvIodeling initial design process

using d c i d neural networks", Joumaf Coqûzhzg i11 Cid Engineering, ASCE, 9 (3), 1 9 4

200.

Murtaza, MB., and Fisher, D.J. (1993), 'Tu-euromex: Neural Network System for

Modular Cons tmction D ecision Making'', Jorrmal Comptïi~zg ~ I I Ch7 Enginecnk& ASCE,

8(2), 221 -333.

Sander, S. R., and Thomas, H. R. (1993). "blasonry productivity forecasting

model." Jounmi of Constnicr'on Engineering ami Ma~zagemelrï, AS CE, 1 1 9 (1 ) , 1 63- 1 79.

Saped, T., and Razmi, A. (1999). "Cornparison of neural and conventional

approaches to mode choice analysis" Jozmzai of Compziïing itz Civil Engi~teebng ASCE, 14(1),

23-30.

Shi, J. (2000). "Reduüng prediction enor by trans forming input data for neural

networks", ]ozcnzuL Coqûzhng in Cid Engineenhg, ASCE, 1 4(2), 109-2 15.

Sinha, S. K. and Md(im, RA. (2000). c c 4 M c i a l neural netmork for measuüng

organiza tio na1 e ffec tivenes s .", Jotcri~nI Compting in Cid Engzheenhg, AS CE, 1 4(l), 9 - 1 4.

Sonmez, R and Ronings, J. E. (1998). "Consmiction labor productivity

rno deling mith neural netmorks ." JozîmaI of Con~tmctioiz Engineering mzd ~tlanngeme~zt, AS C E,

l23(6), 498-504.

Thomas, H. R. and Sakarcan, AS. (1994). "Forecas~g labor productivity using

factor model." JotimaLof Con~~n~ciio~i Eirgineenhg a n d ~ u ~ z a g e ~ e / ~ t , ASCE, 120(1), 228-239.

Thomas, H. R. (1991). "Labor productiviy and work sampling: the bottom line."

JozmiaI of Co~zsfmction Engince* and Marzugement, ASCE, 1 17 (3), 423-444.

Thomas, M. R., bfaloney, M.F., Horner, R.M., Smith, G.R., Handa, V.K., and

Sanders, S.R. (1990). "Modehg construction labor productivity." ] o z d of Consindoil

Engineering und lUziiagemerz~, ASCE, 2 16 (4), 703-725.

Thomas, H. R., and Daily, J. (1983). "Crew performance measurement via

activity sampling." J o j m d of Constmction E ~zgineeritg min Mmzagen~e~zi, AS CE, 1 09 (3), 3 09 -

320.

Wang, C., B. (1997). Techno Viaoiz II, McGraw-Hill, New York, N.Y.

Widman, L-E., and Loparo, KA (1989). " A r t i E d intelligence, Simulation, and

modeling: a critical swey" , Artff;n'aL inteIhgence, dation, and modebrzg- L.E.Widman, K.A.

Loparo, and N.R. Nielsen, eds., John Wiley & Sons Ltd, New York, NY, 1-45.

Chapter 2: A Case Study of Industrial

Construction Labor ~roductivity'

In a construction task that is performed by hand labor, the labor production rate

(man-hours per uistalled unit) measures a key dimension of performance and is a cntical

factor to estimating, scheduling and control of the project (Alfeld, 1985).

Thomas et d (1999) identi6ed the

management as nvo factors that affect

complexity of the design and the project

labor productivïty and invesügated the

measurements of daily labor productivity in building conspuction including masonr)-

cons tniction, concrete fomwork construction, md s t r u c ~ a l s tee1 erection. Thep found

that good project management and consis tency

constant d d y labor production rates.

in design complexity result in relatively

1 A version of this chapter has been submitted for publication. ASCE, Journd of Consuuction Engineering and Management.

A good conelauon was also found benveen the final curmhtive production rate

(an index of the average iabor performance over the entire project penod) and the

variance of daily production rates. For instance, theit study of m a s o q construction

observed "high vuiability in daily production rates on the poor perfomiing projects due

to disruptions in the work resulting from congestion, sequencing, lack of materiais, etc"

(Thomas et al, 1999).

Little information could be found in literature on the theoretical basis and

practical considerations for measwïng and analyzing labor productivity of industriai

consrmction. In conjunction with a major industrial contractor (refened to as "the

company" hereafter), we conducted a productivity case study for nvo important activities

in indusnial consmiction: pipe installation in the field and spool fabrication in the

fabrication shop. The focus of investigation is the average labor production rates (man-

hours per unit) of these acbvities at the end of a project, rather than the daily labor

production rates as in Thomas 1999, because die prirnary objective of research is

developing ANN-based eStiIIIa~g tools to offer estimators valuable information about

labor productivity in bidding new jobs rather than assessing and improving the crew

performance in the field- This paper intends to address: (1) hom to quana$ labor

productivity in indusmal construction fiom a contractor's point of view; (2) hom to

measure actual labor productivity in indusmal construction based upon on-site control

practices; and (3) how to ualize Artifïcial Neural Nenvorks (MN) to analyze the

variability of actual labor production rates and the sensitivity of identXed influenclig

Çac tors.

The paper is

construction pertinent

Constructionyy section.

organized as folloms: important characteristics of industrial

to productivity studies are hrst discussed in the "Indusmal

Next, the "Field Pipe Xnstallatioa" section reviews the curent

e s t i r n a ~ g method, the present reportïng and accounthg systems for field pipe

insrdation in the Company, and summarkes the techniques for quantification and

measurement of field pipe installation productivity. Further, the input factors that cause

the variability in the productiviv of field pipe installation are discussed, and a

probabilistic neural network approach to modeling pipe uistdation productivity is

o v e ~ e w e d . The subsequent section "Shop Spool Fabrication" shifts the focus of

productivity studies to the fabrication faalities of the Company, and summarizes the

techniques for quantification and measurement of spool fabrication productivïty. The

input factors that affect the production rate of spool fabrication are identified, and an

NN-based sensitivity andysis appraach to modeling spool fabrication productivity is

presented.

Barrie et al (1992) described industrial construction as:

"Indusmal construction covers a wide range of construction projects d ia t

are essential to o u utilities and basic industries, such as petroleum rehneries and

petrochernical plants, synthetic fuel plants, fossil fuel and nuclear power plants,

off shore oil/gas production fadties, cryogenic plants etc. Industeal

construction generdy features large amounts of highly complex process piping,

mechanical, electrïcal, and instrumentation work, both design and construction

require the highes t Ievel of engineering e&xpemse kom multiple disciplines."

In particular, the installation of process piping systems in indusEal construction

is selected for productivïq studies because it accounts for the buLk of direct labor hours

of an industrial contractor. Process piping is used to transport fluïds benveen storage

tanks and processing units. Installation of piping systenis generally consists of tnro

processes: (1) spool fabrication in a c o m m e r d pipe shop; (2) pipe installation in the

field (Germin, 1996). hlthough the nvo processes are Liseparable and can be integrated

to optimize the econornics of a partïcular situation, they are treated independent of each

other in the paper because of the current estïmating and control practices of the

involved Company. The productiviq studies described in this paper are conducted to

support the management's decision-making in the contest of the company's curent

management sys tems, as opposed to radically changing these sys tems.

Parker et al (1984) dis~guished industrial construction from heavy constniction

in that indusmal construction does not require fleets of construction equipment and

plant (such as scrapers, loaders, cranes and trucks etc) to handle basic materials (such as

e d , rock, concrete and asphdt etc). They M e r pointed out that industrial

constniction "tends to be much more labor-intensive, though some of the largesr

hoisting and materials-handling equipment is also required" (Parker et al, 1984). An

industrial contractor usudy owns the equipment or rents it fiom a long-terrn supplier,

thus, the technology and machinery adopted in consuuction can be considered invariable

for a relatively long period of time. This feature lends the producnvity studies of

indusmal construction to the unit-cost estïmating method, mhich is cornmonly applicabIe

to labor intensive work where 'labor production rates must be independent of

equipment use and vary among projects only because of differences in labor

productivitf (Parker et. al., 1984). For instance, considering the bid item "Pour

Concrete Floor" in building constniction, to estimate the total cost in terms of Iabor

hours, work quantities are taken off in square meters of floor, then multiplied by a labor

production rate, i.e., the labor hours required on one square meter of floor. Analogously,

for field pipe installation in indusmd construction, the amount of work-in-place is

usually counted in pipe footage; field productivity for pipe installation is measured in the

form of unit rate, i.e. manhours per foot of installed pipe.

Pipe installation in the field involves "the physical placement of pipe / pipe

subassemblies, valves, and other specialty items in their required final location relative to

pumps, heat exchangers, turbines, boilers, and other processing units" (Genvin, 1996)

Productivity Quantification

In practice, pipe is customarily identified by diameter of pipe (dehned by

nominal pipe ske) dong mith \vaU thickness of pipe (dehed by schedule nurnber).

Hence, the production rate of pipe installation can be detemiined by the diameter and

mall thickness of pipe; the Iarger the diameter and the thicker the pipe, the more Iabor

hours is required 10 install one foot of pipe. Table 2- 1 shows samples of the labor rates

for handling and erecting stright run pipe (mm-hours/ft) as found in the public source

(Page and Nation, 1982).

Table 2-1: Sample of pipe installation unit labor rates (Source: Page and Nation, 1982)

Nominal Pipe Size (Diameter)

Schedde Number (Wall

Thickness)

Base Labor Rate (MWFt)

Estimating labor production rates for field pipe instdlztion starts with

establishing base production rates for various work items. Base production rates reflect

the contractor's present labor productivicy level under normal work conditions that are

most oftea encountered in the field. The installation location is one of the major

considerations for an estimator to d e h e a classification of work conditions. For

esample, the base production rates of pipe installation are valid for the conesponding

base classihcation only, in which the installation location is above ground up to 12 ft

high. An estimator detemiines a degree-of-difficulty factor (&en referred to as

c'multiplier" in the company) for each non-base classification to adjust the base rates up

or down in order to reflect the unfavorable or favorable work conditions for the job

being esàtnated. This is a subjective decision process, requiring substantial expenence

and skill on the part of the estimator to determine realistic production rates for the work

conditions to be encountered. Empiücal degt-ee-of-difhculty factors for each

classficaüon of work conditions based on ihe installation location serve as a guide or

tool to assist in deuding on such factors and can be found in the company's business

manual. For esample, the degree-of-difficultp factor for underground pipe installation (4

to 10 ft deep) is about two t h e s the factor for aboveground pipe installation (up to 12 ft

high), wMe the factor for pipe installation inside building at over 10 fi of height is about

two &es the factor for underground pipe installation (4 to 10 ft deep).

Productivity Measurement

In the contest of pipe installation, keeping uack of piping labor by individual

fittings and pipe sections is economically impractical, if not impossible, to implement in

the curent field reporting system of the company. Alfeld (1 9 88) argued that measuring

labor producüvïty requkes grouping similar accomplishrnents and separating dissimilm

accomplishment on the job site. The cost control practice of the company for field pipe

installation is descnbed next.

At the end of a day, the foremen tum in time cards for th& crews, charging the

number of labor hours to a series of cost codes. The cost codes of field pipe installation

for a particdzu project separate pipe fitters' hours by classihcations of installation

location. Thus, the total labor houts of pipe installation at vmious locations for one

project can be readily remieved fi-om the field labor cost control system of the company.

Homever, this is not the case for the amount of work accomplished. Large amounts of

various work items dong -sith variations in size and wall thickness of pipe cause the

inclusion of details of work accomplished in the foreman's t h e cards to be impractical,

34

such as the amount of work-in-place counted in footage by diameter and mail thickaess

of pipe, the saew joint or bolt-up connections and the valves and supports installations

associated mith the installed pipe. Fortunatelp, the detailed records about the amount of

work accomplished can be obtained indirectly h-orn the company's quality control system

and estimating system. Thus, we can match the actual manhours mith the work

accomplished for one classifxation of installation location, in order to compute the

actuai degree-O f-dificuls. factor (@) as gken in Equation (1):

Where H is the actual labor hours charged to pipe installation in one

class~cation of installation location,

N stands for the total number of work items contained in one classification of

installation location,

P, is the base labor rate for the iCh work item,

And Qi is the actual quantity accomplished for the ch work item

Note that the estïrnabng process desuibed in the preceding subsection is actualiy

to transform Equation (1) to compute the labor hours 0, simply by plugglig the

quantity take-off as read from construction &anrings into the quantity terni (QJ in (1).

Hence, the task of estimakg labor productivity boils down to detennining the degree-

of-difficulty factor (@) accutatelv for a future project scenario. It is e-xpected that a

constant value of the degree-of-difficul~ factor (or at least a nanom range) could be

found for each classi&ation From the company's bistoncal records and shodd be close

to the empirical value in the business manual.

Input Factors

Kistorical piping producticity data of 66 projects was collected Erom the

Company and compiled into numeric format for malysis. Because data is not well

formatted or readily accessible, a data marehouse was developed first to integrate the

conuactor's e s t i r n a ~ g system, quality control system and hbor-cost control system in

order to ease the burden of data collection and ensure the high quality of collected data.

The follonring tmo observations wïth regard to the actud degree-of-difficulty

factors can be made from the histoecal data of the Company:

The degree-of-difficulty factor for one classification of installation location rnay

reveal a widespread dismbution instead of a constant value as in the company's

business manud;

Different classifications of installation location may end up with very close values of

the degree-of-difficulq factor, nor: as distinguished as in the company's business

manual.

The above observations are not initidly expected and the explmation can be

attributed to the fact that more factors esist, other than the location of instailauon,

mhich contribute to the variability in labor productivity. In practice, an estïmator rnay

adjust the value of degree-of-difficulty fzctor in the business manual on a job based on

experience and job conditions, and subjected to the approval of senior management.

Barrie et al (1992) found that construction hbor productivicg may fluctuate d d l y due to

numerous factors that affect it, and many are highly qualitative in nature, induding the

effect of location and regional variations, the learning cuve, work schedule and work

d e s , environmental effects, crem esperience and management factors. Portas and

AbouRizk (1997) determined seven categories of activity factors and five categones of

project performance factors to be relevant to the labor production rate of concrete

formwork constxuction. Thomas et al (1999) identihed the complesiq of the design and

the project management as nvo major categories that affect labor productivity of

masonry construction. In regard to industrial construction, Knomles (1997) invescipted

a specmim of e-xplanatory factors to idenufy those that affect the productivity of pipe

installation and pipe welding in the field.

Identification of input factors in this study was based on Knowles 1997, with die

addition of t h e more factors, i.e. the contract type (lump sum or reimbursable),

installation of miscellaneous fittings (flanges, specïals, elbows etc.), and the on-site labor

charging errors between the cost code of pipe installation and that of pipe welding (since

pipe fitters and welders mostly work side by side). A t o d of 36 input factors are

considered relevant and used to redehe the classification of pipe installation. Those

factors include both global project-level information and specific acctivity-level

information, as shown in Table 2- 2. Aside hom location of instdation, more activity-

s p e d c factors are considered such as material type of pipe, the installation of non-pipe

cornponents (valves, supports, and rnisceUaneous items), non-weld joints in ins tailation

(screw joints, bolt-ups), the quantities of installed pipe at different size ranges ( s m d

bore, medium bore, and large bore), the leaming c u v e factor (total quantity of installed

pipe in footage), the crew elrperience etc. Factors pertinent to project are also included,

such as the effect of location and regional variations (project location, province/state),

project type variations @roject dehnition, contract type, and prefabrication percentage),

mark schedule and mork rules (overtime and unionized), environmental effects

(seasonal), management factors (superintendent and project manager) etc.

Table 2-2: Input factors to pipe installation productivity

Projea Location Administration

Y- of Construction Province/State Contract Type

Client Engineering Fimi Project Manager

Superintendent Project Definition

\Vork Scope Project Type

Prefab/Field Work ,iverage Crew Size

Peak Crew Size

Uninized

Equipment & Material Estra Work

Change Order Drawing & Specs Qualiqr

Location Classification Total Quantity (Learnuig)

Installation Quanti ties &Taterial Type

hIethod Of Installation Pipe Supports

Boltups Valves

Screwed Joints

hfisc. Components Welding Impact

Season Crew Ability

Site Working Conditions Inspection, Safety & Quality Overd Degree of Difficulty

Urban, Rural, Camp Job General E-xpense

89-93,93-93,95-96,97-99 M, SI<

Reimbersable, Lump Sum an indes derived &oui historical data

an indes derived Gom his torical data an index derived fi-om historicd data an indes derived from histoicicd data Chernical, Cryogenic, Gas, Refining

Confiaed / Scattered Upgrade Shutdown, Grass Root etc.

Percentages for Prefabrication <25,25-50,50-100, >IO0

<25,25-50,50-100,100-150, >150

Yes, No

Equip.& Mat1 Cost/ Direct MH Original Project Cost/Final Projeject Cost No. of Change Orders/Total Direct blH)

1 Poor 3 Average 5 Escelient U/G on Site, Fab Shop, A/G on Site etc-

Total Quanuty In DiaInFt Qty for Size Ranges, <2", 2"-IG", >TG"

Moy,Carbon Steel, FRP/PVC,etc.

Percentages of Hand Rigging No. of Pipe Supports/Foot of Pipe

No. of Boltups/Foot of Pipe No. of Valves/Foot of Pipe

No. of Screwed Joints/Foot of Pipe Instail i1lïsc.Components hfH/Foot of Pipe

LVelding Multiplier (hliscoding on Site)

Percentages of Winter & Summer Work 1 Very Low, 3 Average 5 Vesy High

1 Esmeme Problems - 5 No Problem 1 Estremely Detailed - 5 Highiy Tolerant

1 Very Lom 3 Average 5 Very High

It should be mentioned that a questionnake survey was careWy designed and

conducted to collect some qualitative information that is not obtainable Erom the

company's reporting and accounting systems. Such information mas converted into

numenc fonriats for the foUoMng NN analysis (See Lu et al, 2000 for derails).

Probabilistic Neural Network Modehg

ANN has been proposed by many as an alternative to streamline the eshmating

process and reduce the subjective nature of the work The dassic Back Propagation NN

predicts a single value without giving any backup information on the rislcs of taking this

value as correct. Observing the actual values for the degree-of-difhculty factors of field

pipe installation indicates chat the target r isky variable Lies over a relatively nride range.

The resulr from an informal end-user survey showed that eshators are more

cornfortable to accept a decision support model with the capability of analyzing the

uncertainty of its ourput. Thus, a probabilistic NN modehg approach that can predict a

distribution or probability density hnction over the output range is preferred and has

been researched.

A nem neural network scheme was devised to meet the requirements in modehg

labor productivity of industrial constniction, and is termed the Probnbility Inference

Neural Network (PINN). PINN is a chssihcation-prediction combined neural nenvork

model based on I<ohonenYs LVQ concept (Kohonen, 1995), but integrated with a

probabilistic approach. Because the response of PINN is in the form of a probability

density funciion (distribution) at the output range, an estimator be able to decide on

the degree-of-difficulty factor for a future scenario by cornbining the PINN7s

recommendation with personal judgment.

In the PlNN model, the actual output range of the target nsky variable is divided

into a number of output zones or sub-ranges wïth an equal width. Output zones are

actuaUy some discrete dusters wïth c o n ~ u o u s boundaries. For field pipe installation,

the hrgher the value of the degree-of-difficulty factor, the higher the value of labor

production rate, hence, the more difficult and more demanding the job is. Thus, each

output zone gives an indication of the relative wotk cbfficulty and productivity levei; for

instance, output zone (0-0.71 stands for easier mork and higher productivity level

NN Recall Probability Density Graph

1.0

compzuing with output zone (0.7-1-41. The median of each sub-range can be used to

represent the typical value for each output zone and to derive a predicted vahe in

addition to the predicted dismbution, such as mode and meighted average value.

Portable computer software was developed to implement the training and testing

of the PINN model on real historical productivity data of field pipe installation at the

company. The model was validated based on an independent data set resemed for

testing. Sensitivïq malysis of the model was perfonned bjr obserping the PINN's output

in response to controlled changes in inputs and comparing PINN's output a@st that

of a n es~erïenced estimator. FoUowing satisfactory t e s ~ g and sensitivity analysis, a

r e c d program based on the traïned PINN model was irnplemented as a deasion support

tool for estirnating the degree-of-difficulty factors of held pipe installation at the

company. Figure 2- 1 shows the output interface of the recd program, indicating the

predicted probabilit)' density function over the output range, and the likelihood of the

degree-of-difficulty factor f d h g into each sub-range. Those mho are interested in the

topology and algorithm of the PINN model, and the effectiveness of applying PINN to

e s h a t e labor productivity in the contest of field pipe installation may refer to Lu et al

2000.

Spool fabrication in a commercial pipe shop involves "the cutting, bending,

tacking, and welding of individual pipe components to each other and their subsequent

heat treatment and nondestructive esamination to fonn a pipe subassembly or spool for

installation" (Gervin, 1996). A pipe spool is a portion of piping system consisting of

various piping components, such as h g e s , elboms, reducers, tees, supports, and pipe.

These components are prefabricated into distinct assemblies that are later assembled as

part of an industeal plant or production skid/module. Such prefabrication is usudy

performed under coatrolled shop envixonment located away from the job site, which

allows for bettes productivity and quality control, and heace cuts the field labor costs.

Major spool fabrication processes, such as cut, bevel, fit, weld, and handle

sections of pipe and firtings, also tends to be labor-intensive. Productiiig- data is

coIlected fiom the fabrication shop of the Company for 63 projects completed fiom

1995 to 1999, duriag which period the technologies and machines for welding and

cutchg in the shop eemain relatively stable. Like field pipe installation discussed

previously, the productbity study of spool fabrication is suitable to the unit-cost

esùtnating method-

Productivity Quantification

Alfeld (1988) pointed out the labor production rate in the shop could not be

quantified with the same units as in the field - man-hours per foot of Listded pipe,

because the shop does not install the pipe but cuts, fits and welds spools; other units of

rneasure such as spool counts and pipe sections do not satisfy the needs of quantifjing

the work accomplished in the shop either, because (1) each spool varies so much in

components, size and configuration that a simple count ofspools would be misleading;

and (2) large-size pipe requixes far more manhours to cut and weld than do the smaLl-size

pipe. Weld-inch was uàlized as a unit of rneasure to quannfy the accomplishrnent in a

fabrication shop and Table 2- 3 shows saniples of the degree-of-difhcultp factors for

convemng various butt welds into weld inches as found in Mfeld, 1988.

Table 2-3: Sample of degree-of-dititiculty factors for converthg welds into u n i t s (Source: Alfeld, 1988)

Nominal Pipe

Size

(Diame ter)

Circumference Fab. Units Weld

Type

(3)

Butt

Butt

Butt

Butt

Weighting

Factors

Similar to the concept in hlfeld 1985, in the fabrication shop of the Company, a

special "unitization" scheme is applied to quanrifv the various work items u n i f o d y into

an abstract unit of measure c d e d "Fabrication Unit" or "Unit" by w e i g h ~ g them for

their degree of difficulty. The "unitkation" is a conversion based on a standard diameter

inch dong the circurnference of a weld. A degree-of-difficulty factor is empirically

decemùned for each weld, t z h g into account pipe diameter, wall thickness of pipe, weld

type @utt weld, socket weld, saddle and laterd welds) and the time required to lay out

and perforrn the weld. Quantity of non-melding work items such as cutting, bevelulg,

handling pipe and fitnngs, lastalling supports are also converted into "Units" by appljing

corresponding degree-of-difficulty factors in the scheme.

A commercial fabrication shop usually handes several jobs simultaneously so

that it is efficient for the crew to set up and do ail the sarne size pipe fiom dïfferent jobs

at the same tirne. In the fabrication shop of the Company, it is difficult enough keeping

nack of the manhours charged to each individ~d job in the shop floor control systems.

Charging labor hours to each individual pipe section or fitüng is considered impractical

and ineffiaent in hght of the curent control technologies and management systems in

the fabrication shop.

The basic formula for spool fabrication eshating is shown in Equation (2):

VVhere H is the total manhours charged to one job,

P is the production rate (?vIf-I/Unit) for the job,

N stands for the total number of mork items (\veld or non-weld) contained in the

Subscript i stands for the P work item in the job,

@; is the degree-of-difficulty factor for the ih work item in the job,

Qi is the quanticg for the ih work item in the job in its onginal unit of measure

such as the meld counts for an weld work item, e.g. the weId count for "G Nominal Pipe

Size (Diameter), 40 Schedule Number F a l l Thickness), Butt-\Veld Type" weld is 20.

Prodiictivity Measurement

g(@i * ~ i ) in Equation (2) is actually the total quantity of

i=l fabrication mork in Units for the job. The hrst step in esthnating a spool fabrication job

is a process c d e d "uni&ation" for computing the total units of one job. The es t-cor

reads the quantity takeoff fiom spool drawulgs and look up the degree-of-difficulty

factor for each work item. This task is straightfomard but tedious because the amount

of work items in a job is usudy large; for esample, several jobs the Company completed

contain over 1,000 spools, over 10,000 welds and over 10,000 pipe sections and fittings.

The difference in the degree-of-difficultg factor benveen field and shop should

be noted:

First, the degree-of-difficuiq~. factor in ihe case of shop spool fabrication

corresponds to each work item rather than a classification of grouped work items as

in field pipe installation.

Second, the degree-of-difficulty factors in the case of shop spool fabrication are held

constant in the "unitization" scheme rather than variables as in field pipe installation.

Hence, the focus of productivity study in spool fabrication is on the production

rate directly, i-e. the P term in (2) or man-hour/unit. Dedding on P requites the

expexience and judgment of the estimator. Similar to the productivity study of field pipe

installation, a data warehouse was builr up to integrate the reporting and a c c o u n ~ g

systems in the fabrication shop in order to obtain labor hours and quantity of fabricauon

mork on each job. The data warehouse also contains a built-in computer progam,

developed to automate the tedious task of quantifping about 63 fabrication jobs into

"units" in a preüse and consistent may. Actual production rates over the penod of

investigation mere observed for W e r analysis.

Input Factors

Xfter consdting with e-xperienced estimators and shop superintendents in the

Company, a number of quantitative and qualitative factors are considered relevant to the

shop labor productivity, such as:

The m a t e d components in fabrication, Le. the percentage of non-carbon steel

(stainless, aluminurn, d o y steel etc.) units over the total units, because non-carbon

steel spools require extra care and more tirne in storage, handling and welding

cornparhg Mth carbon steel spools;

The average length of pipe sections in a spool, indicated by in-Line fittings (pieces)

per foot of pipe in spool. In-Le fitangs, such as unions, couplings, swages, reducer

etc are used to connect pipe sections in a saaight line without tums o r branches.

The complexity of spool configuration, indicated by non in-line fittïngs (pieces) per

foot of pipe in a spool, valves/supports /~ges (pieces) per foot of pipe in a spool;

The stengency of quality control, indicated by the non-destructive test requirement,

which is a percentage mith respect to weld couats according to the client's specs.

The quality of spool drawing indicated by the drawing revision rate.

The shop workload, indicating shop's state of being busy or slow, and number of

concurrent jobs handled at one time;

The effect of double handliog spools between weld stations, ùiciicated by the

percentage of multi-station roll meld inches over total roll mell inches. A meld may be

done on more than one station by different welders in the shop, depending on the

welding process and the welder's quaL6cation. It requires estra time to move spools

benveen melding stations and lay out a weld nt different stations.

The effects of rushed spools due to client's priority, late drawing issues fiom the

client, and material supply problems

The amounts of night s hift and overtime, and estra mork in tems of labor hours;

The es~erience and profiuency of crem, indicated by apprentice ratio, repair rate and

rem-orked spools.

The environmental effects are not considered as signihcant factors, as in the field

productivity studies, because of the conaolled shop enwonment. A couple of

management factors that mere initially included n-ere dropped out of analysis after

esarnining the collected data, in mhich slighr variations were observed due to the

consistent management policy and management personnel dueing the 5-year period of

investigation. It should also be mentioned that another factor describing the complexiq

of spool configuration was idenafied by domain er;perts, i.e. the number of pipe pieces

per foot of pipe in spool. The sensitivity analysis results based on coilected data reveal

that the effect of the number of pipe pieces is very similar to that of the number of in-

h e fitnngs. Such strong conehtion generalized by ANN model from the actual data is

presented to dumain experts and hnds esplanations from domain experts: pipe sections

in a spool are mostly c o ~ e c t e d by in-iine fittings such as unions, couplkgs, mages,

reducer etc; both ratios, narnelp, in-line fittings (pieces) per foot and pipe pieces per foot,

indicate the average length of pipe sections in a spool. To simpliQ the inputs of model,

the ratio of pipe pieces per foot mas dropped out of analysis, as agreed by domah

exTerts. Eventually, nineteen input factors that affect labor productivity of shop spool

fabrication are identified as listed in Table 2- 4.

Table 2-4: Explanatory factors to spool fabrication productivity

NN Input Factor (2)

:n Line Fitting @CS) per Foot of ?ipe in Spool \Ton In Line Fitting @CS) per Fooî >EPipe in Spool Jdve @CS) per Foot of Pipe in ;pool Support @CS) pet Foot of Pipe in ;pool ?lange @CS) per Foot of Pipe in ;pool liIulti-Station Roll CVeld Inches / rotal Roll Weld Inches Lepair Rate Ldbgraphy Test Requirement 'lon CS Units / Total Units

;hop Work Load

Drawïng Revision Rate

Prionty Rushed Spools

Rework Spools

Material Shortage Problems Late Drasving Issues

Night Shih MHs / Total MHs Over Time hMls / Total hEIs Extra Work hHs / Total MHs Apprenticeship b M s / Total h H s

Remarks (3)

.i ratio iadicating the average length of pipe sections n spool .\ ratio indicating complexiv o f spool confïguation

i ratio indicating comple'ÿty of spool configuration

i ratio hdicating cornplexity of spool configuration

i ratio i n d i c a ~ g compleldty of spool configuration

Multi-S tation Roll Weld requires extra handling Demeen weld stations in indes of crew's pro ficiency ln indes of quality control strïngency by specs. \Jan CS component in fabrication requires estra care n storage, handling and wvelding i 5-point rathg based on shop worliload in units ind no. of concurrent jobs indicating honr busy the ;hop was. A 5-point rating based on percent of revised spool drawings indicating dranring quality A 5-point rating based o n percent of mshed spool due to client priority indicating shop work schedules.

&

A 5-point raMg based o n percent of reworked spools due to drawing enors and quality defects

L

A 5-point ratïng on efficiency of material supply A 5-point raMg based on percent of late spool draning issuance by client that impacts fabrication Night Shift affects labor productivity Orer T h e affects labor productivity Estra Work affects labor productivity Welder a u ~ c a t i o n system affects labor

I

productivity: Apprentice os. Joumeyman

Data for the idenuhed factors is collected fiom the company's various

management s ys tems including labor cos t tracking svs tem, wveld tracking sys tem, payroU

system, matenal tracking system. Because data is unavailable in cunent systems of the

Company for such factors as the material shortage problems, quantity of reworked

spools, quantity of rushed spools due to pnoriq, shop workload etc., a questionnaire

survey was csrefdly designed and conducted wïth the suppott of the compmy

management The key personnel involved in the projects including shop

supe~tendents, project managers and coordinators, QC staff, and welding foremen

were interviewed to help recall sorne facts and gather the needed information.

Sensitivity Analysis of Influencing Factors

In contrast with a rather wide distribution of the actual production rate in field

pipe installation, the actuai labor production rates for shop spool fabrication are

bounded Nithin a relatively narrow range. Thus, the NN modehg of labor productivity

in the shop puts more emphasis on the sensitivity anaiysis of i n f l u e n ~ g factors based

upon the classic back propagation NN mode4 as opposed to the uncertainty analysis of

espected production rate based on the PZNN model.

L e h g algorithms such as back-propagation NN do not gïve information on

the effect of each input parameter or influencing variable upon the predicted output

variable. The NN model's sensitivity to changes in its input factor is generdy probed by

t e s ~ g the response of a mature nenvork on various input scenarïos. The relationships

between an output variable and an input parameter were sorted out based on the NN

algonthm so as to define the input sensitivity of a back-propagation NN model in esact

mathematical ternis in light of both normalized data and raw data (Lu et al, 2000). For a

three-layer BPNN using Siaomoid transfer hcr ions and linear normdkation procedures,

' N n R

the input sensitivity with respect to the change of 10°/o input relevant ranges (- ) is as,

R aNn - - - MAX, -MIN, - 2 ~ W - N c t ( l - N c l ) * N , ( l - N , ) 3% 10

FI =ln i=I

Where, subscript p stands for a node in die input lager of the network;

Subscript c stands for a node in the middle layer of the network; C stands for the

total nurnber of nodes in the middle layer;

Subscript n stands for a node in the output layer of the nenvork.;

Wii stands for the weight of connection benveen node i and node j;

S stands for the input signal to a node;

N stands for the output signal fkom a node;

hW& is the maximum value in the data set corresponding to output node n;

MIN, is the minimum value in the data set corresponding to output node n.

From Equation (3), for a mature network, the sensitivity of an input parameter

over an output variable is dependent on the curent input values. A Monte Carlo

simulation can be performed at the NN input space in order to observe the statistics of

input sensitivity. In our research, s taus tical analysis of simulation resulrs involves

calculating 5 percentiles of the slope variable for each input parameter, i.e. the loch, 25",

52

50", 75", and 9 0 ~ . The input sensitivitg of all input parameten is summarized and

presented in a tornado-like graph as illustrated in Figure 2- 2 for the piping fabrication

labor productivity NN model. The horizontal a'ris represents the relative input sensiwty

as detennined by (3), i.e. output response (negative or positive) nrith a change of 10°/o

relevant range in an input parameter. The vertical avis is the baseiine conespondkg to

no output response or zero change in output. Five short vertical bars correspond to each

input parameter, representing respective. the five percendes fiom left to right in an

ascending order and reflecting the central trend, the spread, and the shape of the

observed slope data distribution fiom simulation. In short, statisticd analysis of input

sensitivity based on Monte C d o simulation enables the modeler to understand the

rationale of NNYs reasoning and have pre-knomledge about the effecüveness of model

implementation in a probabilistic fashion, as illustrated by the spool fabrication

productivity model next.

A total number of 70 records mere compiled and used to train a NN model with

19 input nodes at the input layer correspondlig to 19 input parameters, 19 hidden nodes

ac the middle layer, and 1 output node at the output layer that is the unit labor hours.

The number of hidden nodes can be determined based on mals; NN learning is found to

be wusceptible mhen to the number of hidden nodes is close to the number of input

nodes. The learning rate is 0.4, the momentan is 0.1, and sigmoid transfer hrnctions are

used in hidden and output nodes. After satisfactory training (standard enor of the output

is 0.00143), the Monte Carlo based sensitivity analysis is performed on the rnamed

nenvork for 10000 simulation runs.

I In Line Fitting per Ft

!, Non In Line Fitting per Ft

i. Vaive per Ft

C. Support per Ft

i- Flange per Ft

i. Mlt Stn RW %

'. Repair Rate

I. RT Rate

). Non CS % (Un)

IO. How Busy

1 , Drawing Revision

12. Priority Rushed Spools

3 . Reworked SpooIs

14. Material Problems

5. Drawings Late

6. % night shift

'7. % overtime

8. % extra

9. % apprentices

Figure 2-2: Sensitivity Analysis of Spool Fabrication BPNN Mode1

Several independent Mals from NN training to the sensitivity andysis mere

conducted o n the sarne data set. The best mal, in which the input sensitivity of most

hctors followed the same trends, as detennined by esperienced domain e'lperts, is

shovm in Figure 2- 2. An esamination of Figure 2- 2 reveals the relationships berneen

the influencing factors and the fabrication productivity, which me generalized by NN

through obserrring historical project data in the past 5 years. For example, factor 1 is

about in line fitang pieces per foot of pipe in spool, st-hicb indicates the average length

of pipe sections in spool. According to our domain experts, in h e fittings, such as

unions, couplings, smages, reducer etc are used to connect pipe sections in a straight line

without nirns or branches. Thus, the more in line fitting pieces in spools, the more s m d

sections of pipe in spools, and the easier to handle the work. From Figure 2- 2, BPhW

determines the chances to decrease hbor hours per unit wirh the increase of this ratio are

about 78% and agrees with the &end identified by domain experts. Factors 2 to 5 are

four ratios i n d i c a ~ g the complesity of spool configuration. By our domain esTerts, the

higher such ratios, the more comples the spools' configuration, and the tougher to

hbncate the spools. From Figure 2- 2, the dominant trends of the four ratios are all on

the plus side, which matches the judgment of our domain experts. It is also observed

from Figure 2- 2 that factor 18 (extra work percentage) is relatively tighdy enveloped

around the baseline, which indicates that extra work is not as dominant as other factors

in c o n t r i b u ~ g to the variance in unit Iabor rates. The e-xplanation c m be partly

atmbuted to the fact that the amount of extra work impacts the efficiency of

administration or management more directly chan the productiviq of crew on the shop

floor. Other input factors can be interpreted and validated in a similv muiner, and are

not elaborated further due to space limit.

In particular, the effect of m a t e d type of spool fabrication on the labor

productivity was tested based on the BPNN model, because m a t e d type (carbon steel,

stainless steel, aluminum etc.) is a major consideration of an lndustnal estimator in

adjuscing unit labor hours of spool fabrication. The labor rate of non-carbon steel

fabrication is empiticaUy 1.5 Urnes the rate of carbon steel in the company's business

guideline. 24 records in the data set wïth OO/o non-catbon steel component (100% carbon

steel fabrication) were selected as t e s k g records. Nest, for each t e s h g record, the input

parameter of non-carbon steel component mas changed fiom 0% to 100%, with odier

parameters intact. Those testing records were fed to the netsvork and let NN recd the

output, i.e. the unit labor rates for non-cubon steel fabrication. n i e output fkom NN

was compared agauist the onginal output of each record, i.e. the unit kbor rate for

carbon steel fabrication. Based on the test results in Figure 2-3, NN increases the unit

labor hours on 75% of the records; the amount of decrease for 5 records, i.e. No. 1,2, 5,

6, 9, is rehtively smalI c o m p a ~ g mith the amount of increase for others. If the sample

size is large enough, the percentage should corne close to about 90%, as observed fkom

Figure 2- 2 for factor 9. On average, the ratio of non-carbon steel Iiibor rate over carbon

steel labor rate is 1.4, which is dose to 1.5 as in the guideline.

Test NN Sensitivity By Changing Material Component from 100% CS to 100% Non-CS: 75% 1 Records increase, Avg. Ratio 1.38

1 +Actual (100% CS, 0% Non-CS) 0 NN Output (0% CS, 100% Non-CS) )

O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Rec. No.

Figure 2-3: Testing Sensitivity of BPNN to Material Type

that the guideline gives

only, while NN is able to

an average nurnber (1.5) in consideration of

figure different numbers for different scenarios

taking into account 19 relevant factors. In short, such a NN-based decision support tool

d be more sophisticated and intelligent than the traditional business guideline to assist

estirnators in deùding

CONCLUSIONS

on the labor production rate of spool fabrication.

Special methods are utilized in practice for the quantihcation and measurement

of labor productivity in indus td construction. Estirnating labor productivity is one of

the most difficult aspects of preparhg an esàmate, or a control budget based on the

estimate for labor-intensive activities in indusnid consrnction. ihtifïcial neural nenvoks

are capabIe of sorüng out hidden patterns and estracting predictive information from

comples data sets, and are proven to be effective in both uncertainty analysis and

sensitivity analysis of construction labor productivity. The NN-based decision support

tooIs are developed to assist estimators in deciding on labor production rates for new

jobs; such tools can be more sophisticated and intelligent than traditional business

manuals or guidelines.

Meld, L. E. (1 9 8 8). Corn-tn~ction prodz~cfi~ity - on - d e rnensireme~zt md rnnn~zgemerrt.,

PvlcGraw-HiU , New York, NY.

Gerwin, E. (1992). "Fabrication and installation of piping systems". P@hg

Hdbook, uth ed., Nayyar, M L. eds., McGraw-W , New York, NY, 297-361.

Knowles, P. (1 9 9 7). Predicting L b o r Prodz~ctiuip U~it'g Arez~rid Netlvo r k ~ hLas ter of

Sciences Thesis, University of Alberta, Edmonton, AB.

Lu, M., AboURizk, S.M. and Hermann, U.H. (2000). "Estimating labor

productivity usuig probability inference neural nebvorks.", J. oJ Corzïpthng i f1 Cid

Engineenkg, ASCE, 14(4), 241-248.

Page, J.S. and Nation, J.G. (1 982). Edinoloor'r p@ing man hout- manrral, 3d ed., Gulf

Publishing Company Book Division, Houston,.

Puker, AD., Barrie, D. S., and Snyder, R. M. (1984), Pfamrig rzm? Estimuti~rg

Hemy Cot;l~'tna*tr;?n, McGraw-Hill, Inc., New York, NY.

Portas, J., and AbouRizk, S.M. (1997). N e d Netmork Mode1 For Estimating

Construction Product i~v . 1- of Con.r/r. Engrg. e9iVlgmt-, ASCE, 123(4), 399-410.

Thomas, H. R., and Zaorsia, 1. (1999)- "Consmiction baseline productivity:

theory and practice." J. Consk Engg. Ami hlgmt., ASCE, 125 (S), 295-303.

Chapter 3: Estimating Labor Productivity Using

Probability Inference Neural Networkl

Estirnating labor production rates (m-hr/unit) is both an m and a science. In

generd, the estimator develops the rate for a given project by s t k g wïth a "base rate"

and modifying it to reflect the speüfic conditions he/she expects to encounter in the

project being estimated. The base-rate is often detemiined statisticdy from past

historical data, or fiom industry standards. In the context of indusmd productivïty

e s t b a ~ g , the estimator accordingly adjusted the rate up or down by applying a

d i f f i c d ~ multiplier to reflect overall favorable or unfavorable conditions. In determinhg

the difhculty multiplier, consideration is only given to a couple of major factors that are

thought to affect job productivity, such as installation location of pipe (inside a

fabrication shop or on the job-site), and material type of melduig (e.g. carbon steel or

s tainless steel).

1 ,A version of this chapcer has been published. ASCE, Journai of C o m p u ~ g in Civil Engineering, October/2000, Vol 14(4), pp 241 -218.

The chalienges of this approach include the fact that it is not straightformard to

create a conventional mathematical model so as to accommodate the impacts of

numerous factors on the target rishy variable. The deasion process relies heavilv on

individual's e'rperiences and the results are often inconsistent refleckg the esperience

and disposition of the e sha to r .

Llrti&d neural nenvorks have been proposed by many as an alternative for

sneamiining the process and reducing the subjective nature of the work. Most models,

however, were based on point predictions of production rates wïth which estimators

were uncornfortable. The point prediction by NN can be d e h e d as a single value

predicted by neural nenvork models wïthout any b a c h p information on the nsks of

taking chis value as correct. The new NN model presented in this paper aises out of the

need for accurate prediction in the form of a distribution at the output range. The

estimators dl be able to make a decision for a h t u r e scenario based on the results

recded by the NN model and personal preferences and esi-eriences.

In the folloming section, previous NN applications in the problem domain are

k t reviewed.

Review of NN Applications

Mosehi, Hegazy, and Fazio (1990) cite the prediction of a realistic productivity

ievel for a certain trade as an aspect of constniction that can be modeled +th neural

nenvorks. Factors such as job size, building type, overtime work and management

conditions are typically considered by an estimator and can easily be manipulated for use

as neural network inputs.

k s h e n a s and Feng (2 992) analyzed earth-movïng equipment produccivity with

a neural network application. ,A modular neural nent-ork structure was used to m&e it

possible to add specikations of new equipmeat mith only a brief training session. Each

module represents a distinct type of equipment that w-as trained with trvo inputs, four

hidden nodes, and one output within a back propagation training algorithm.

Wales and AbouRizk (1993) used neural networks as a rneans of applying the

effects of environmental site conditions to the labor production rate on an activity.

Daily average ternpeIatue, precipitation, and cumulative precipitation over the previous

seven days were identified as three key environmental site conditions and used as inputs

uito a feed forward back propagation neural nemork training algorithm. The output was

a productivity factor such thac a value larger than 1.0 indicates that environmental site

conditions produce a greater than average productivity. On the other hand, a

productivity Factor of less than 1.0 indicates that the environmentai site conditions resdt

in below average productivity.

Chao and Skibniewski (1994) performed a case smdy in which a neural network

was used to predict the productivity of an escavator. They idenafied IWO main factors

that affect an escavator's productivity: job conditions and operation elements. Job

conditions include the characterisucs of the environment such as soil conditions, and

speufic characteristics of the excavator and excavation such as the vertical position of

the cutting edge. Operational elements, in contrast, include characteristics not directly

related to the escavating operation; for esample, the effect of wait time for trucks and

e'rtra tasks other than excavating. Two neural networks mere used for the purpose of

this case study. The hrst was used to estimate the excavator cyde time. Four key factors

were identihed as having an influence: cycle time (including swing angle), horizontal

reach, vertical position, and soi1 type (job conditions). The output of the hrst nenvork

was then incorporated into the second nenvork, which esamined the effect of the

operational elements on the productiviq.

Portas & AbouRizk (1993 proposed a feed fonvard back propagation neural

nenvork model for estimating construction production rates of formork. The network

outputs a single point prediction dong Mth a nurnber of output zones, with equd

likelihood of the production rate being in an); one zone. The output zones are

symmetric and divided evenly across the range of likely production rate values. During

training, the output zone whose output coincides mith the actual production rate is

remarded with a primary score of 1.0, representing strong certainty. A certain degree of

fuzziness is considered by remarding the 2 adjacent output zones mith s e c o n d q scores

of 0.5, representing weak certainty. LU the other output zones are assigned a score of O.

Once the NN is trained and inputs are entered and the NN ~viü predict a point value as

well as the likelihood of production rates being within the output zones. This mode1

achieved limited success and its limitation was overcome by the work discussed next.

Knowles (1 997) ~resented a wo-s tage NN model in predicting pipe-ins da t ion

labor productivity. The input factors are used to invoke a LVQ classification process

and then a predictive one. With the classification, the model predicts whether the output

is likely in a cppical or non-typical range. The proper feed-formard back-propagation

netmork is then esecuted- The drawback of this method is that a budd-up of errors

occurs when the dassification fails. For instance, if the classScation accuracy is 90% at

the Fust stage of NN, and the prediction accuracy at the second stage of NN is 8S0/o, the

prediction accuracy of the whole NN is only 76.5% (90% times 85%)- This problem

motivated the development of the model descsbed in chis paper by t;iliiog a different

probabilistic approach, mhich is more direct and more meanligfd in texns of giving a

point prediction and quantifymg its assouated probability.

Introduction of the PINN Model

Specht (1991) revisited Probabilistic Neural Network (PNN) and Generd

Regession Neural Netwoïk (GRNN) dgonthms with the objective of integrating

statistics and neural training. GRNN/PNN is a memory-based feed fonvard neural

nenvork model, where the training is performed in one pass, thus requiring less training

tirne. GRNN/PNN is able to identify a posterior distebution over the NN weight

vectors and a point-value prediction is generated based on the predicted dkmbution.

However, based on es,-perimentaÜons and observations, GRNN/PNN is not quite

tolerant of noisy data (inaccurate or incomplete records) and imposes a demanding

standard of data qu;ility that is hard to achieve in realiry. The memory demand and

cornputing time for GRNN/PNN increase very rapidly when the dimension of input

vector and the quantitg of training samples increase.

The PlBN model uses similm topology as the GR.NN/PNN model but is a

rehement of i t This is because PINN generalizes the underlying statistical patterns

\vivithin training data and codes those pattems into a lLnited number of weight vectors

through iterative l e h g . As a result, the number of weight vecîors d not

propomondly increase with the increase of dimensionaiity and quantity of ualliLig data.

Weighred Average

Pro bability Density Graph

Figure 3-1: Topology of PINN Mode1

The PINN mode1 imbeds the output zone concepts described in Portas &

AbouRizk (1997). In the application domain of industrial labor productiviry estimating,

the profile of acnial historical productivity data reveals a spread range. The range of NN

output value, i.e. the production rate multiplier, is evenly divided into a number of sub

ranges, or output zones, which are actually some discrete clusters with continuous

boundarïes. The higher the multiplier value, the more diEhcult and more demanding the

job is, and the Iowa the productivity for the job. Thus, each output zone gives an

indication of the relative mork difficulty and productivity level, for instance, output zone

[O-0.q stands for easier mork and higher productiviq level cornparhg with output zone

p.7-1.41. The median of each sub range can be used to represent the spical value for

each output zone and to derive a NN predicted value.

The PLNN uses the same strategy as the model desaibed in -\bouRizk e t al.

(1999) by incorporating 1<ohonenys LTTQ in NN learning. The main difference is that the

classificarion and prediction networks are combined in an integrated netsvork, which

required the development of a different aalung and recall algorithm. M m z a and Fisher

(1993) unlized Kohonen's unsupervised learning algorithm called self-organiung map or

SOM for modular construction dedsion making. Kohonen's L e d g Vector

Quantization (LVQ) combines unsupervised and supervisecl leaning and is

recomrnended for statistical pattern recognition problems (Kohonen, 1995). Three

options for the LVQ-algorithms (LVQ1, LVQ?, and LVQ3) mere proposed. ICo honen's

research shows that each of the three LVQ variations yields simiTar accuracy in most

staüstical pattern recognition tasks, although a different philosophy underlies each

algorithm. LVQl was utilized in the l e d g process of the PINN model.

O v e ~ e w of the PINN Topology and Process

The topology of PINN model is &en in Figure 3- 1. It is composed of four

iayers. The middle layers are a Kohonen classifier and a Bayesien Iayer. The outcome of

the PINN model at the output layer is a probability density function or a distribution

r e f l e c ~ g the Likelihood of the target variable occurring in a given zone- The mode of

the distnbution and its mean can serve as point predictions.

The PINN process consists of four stages as follow:

(1) Preparation, mfiich deals with

Scaling data at the input layer, which d be discussed in the subsection tided

"Data Pre-Processing";

Setting up output zones at the Kohonen layer, which d be addressed in the

subsection titled "Output Zone Setup"; and

What are Processing Elements and how they h c t i o n at the Kohonen Iayer,

mhich d be discussed in the subsection titled 'Trocessing Element at the

Kohonen Layer".

(2) LeamLig, which takes place between the Input layer and the Kohonen layer uslng the

LVQ algorithm. This does not involve the Bayesian layer or the Output layer. This

di be discussed in the subsection "NN Learning Process".

Once leaming is achieved, the input-output patterns are coded into the weight

vectors of the processing elements at the Kohonen layer.

(3) Investigating whether the neural network has been successhlly uained. This is

accomplished through the followïng steps:

Feed the input vectors of the training and t e s ~ g records into the input layer of

the PINN model.

Project the input vector of one record onto the Kohonen layer by using the

results of stage (3). The Eudidean distances between each processing element's

weight cector and the scaled input vector are caiculated.

-ln in-zone cornpetition occurs wïthïn every output zone at the Kohonen layer,

which is detailed in the subsection titled "In-Zone Cornpetition Stcitegy ar

Kohonen Layer". The processing element wïth the minimum Euclidean distance

value nruis.

Project the minner PE at the Kohonen layer onto the Bayesian layer. The

Bayesian layer holds a probabiliy deasity hncuon (PDF) approsimator. The

Euclidean Distance d u e s of the winner PEs are the inputs to the PDF

approlrimator. The folloMng subsection of 'TDF .ippro'dmator at Bayesian

Layer" discusses the components and operations in more details.

The output is mapped fiom the Bayesian layer and presented in the f o m of a

probability density function at the output layer. Two point predictions are

calculated in addition to the probability density hinction namely, the mode and

the weighted average. The subsection "Outputs at the Output Layery' Licludes

details about die NN outputs.

Check the NN outpua against the achial outputs of the training and teshng

records. If the results are satisfactoq-, then the neural network is dzclated to have

been trained; othernrise, repeat stage (1) using different panmeters at each layer.

(4) Recd. Once the model calibration is done, the nemal nework can be used to r e c d

the output value for any given input vector, mhich is similm to stage (3) usiag the

h a l results detemiined in stage (2) and (3). A sample cdcuiation is given in the

subsection "Sample of R e c d Process".

Data Pre-Processing

At the input layer of the PINN model (shown by Figure 3- l), the number of

input nodes corresponds to the dimension of the input ~~ector . The dimension of the

input vector depends on the number of input factors and the input data types. Three

input data q.pes are used to d e h e NN input factors, i.e. "Raw", "Rank", and "Bina.$"'

"Rad ' is used sirnplv for quantitative input factors, like general espense ratios, winter

construcüon percentages, or quantities of work. " R d ï " is used to conven subjective

factors, like crem abiliq rabngs, into numeric format. And "Binary" is used to group

testual factors into numeric formats, lilie material type and project dehnition. It shodd

be noted an input hctor of the "Raw" or "Rank" type corresponds to one input node at

the input layer, while an input factor of the "Binary" type corresponds to a number of

input nodes depending on the number of groups for the factor. For illustration, input

factors and data types for the "Pipe Installation" neural neworlc mode1 are listed in

Table 3-1. A sample record for the "Pipe Instdation" NN training is also listed in Table

3-2 showing both the ram data and conrerted NN input data. The NN input data is

norrnalized and scaled betsveen O and 1 at the input layes. These scded inputs dl be

passed fornard Fur NN training. At the Kohonen layer all weight vectors are rmdornly

initiillized betnreen O and 1.

Table 3-1: Input Factors and Data T n e of PINN Mode1

NN Input Factor

Project Location Adminis mauon Year of Construction Proxrince/S tate Contract Type Client Engineering Firm Pro j ect Manager Superintendent Project Definition Work Scope Project Type Prefab/Field Work Average Crem Size Peak Crew Size Uninized Equipment & Ma tend Estra Work Change Order Drmring & Specs Quality Location Classification Total Quantiy (ZearnLlg) Installation Quantities Matenal Type Method O f Installation Pipe Supports Bolmps Valves Screm-ed Joints bfisc. Components Welding Impact Season Crew Ability Site Working Conditions Inspection, Safety & Quality Overall Degree of Difaculty

Data Type

(2) Binary Raw

Binary Binary Binary Raw Raw Raw Raw

Binary B inary Binary Raw

Binary Binary B i n q Raw Raw Raw Rank

Binary Raw Raw

Binary Raw Raw Raw Raw Raw Raw Raw Raw Rank Rank Rank Rank

Options & Remarks (3)

Urban, Rural, Camp Job General Ex~ense 89-92,73-94,75-96,97-79 M3, SK Reirnbersable, Lump Sum an index derived fiom historical data an index derived kom historical data an index derived from historical data an index derived from histoncal data Chernical, Cryogenic, Gas, Refining Confincd / Scattered Upgrade Shutdown, Grass Root etc. Percentages for Prefabrication <25,25-50,50-100, >IO0 <25,25-50,50-100,100-150, >250 Yes, Ko Equip.& Mat1 Cost/ Direct MH Original Project Cost/Final Projeject Cost No. of Change Orders/Total Direct MH) 1 Poor 3 Average 5 Excellent U/G on Site, Fab Shop, .i/G on Site etc. Total Quantity In DiaInFt Qty for Size Ranges, <Y, 2"-16", >16" .ilioy,Carbon Steel, FRP/PVC,etc. Percentages of Hand Rigging No. of Pipe Supports/Foot of Pipe No. of Bolmps/Foot of Pipe go. of Valves/Foot of Pipe 90. of Screwed Joints/Foot of Pipe [nstall hfisc.Components MH/Foot of Pipe Welding Multiplier (bfiscoding on Site) Percentages of Winter & Summer LVork I Very Low, 3 Average 5 Trery High L Extreme Problems - 5 No Problem L Extremely Detailed - 5 Highly Toleranr 1 Very Low 3 Average 5 Very High

Table 3-2: Innut Data SamtAe of PINN Mode1

NN Input Factor

(1)

Project Location Admi& tra tion Requiremen t Year of Construction Province/S tate Contract Type Client Engineering Firm Pro ject Manager S u p e ~ t e n d e n t Project Dehnition Work Scope Project Type Prefab /Field Work Average Crew Size Peak Crew Size Uninized Equipment & M a t c d Extra Work Change Order Dra~ving & Specs Quality Ac tivity Location Classification Total Quantity (Learniflg) Installation Quantities Material Type Method O f Installation Pipe Supports Boltups Valves Screwed Joints h/lisc. Components LVelding Impact Season Crew Abiliq Site Working Conditions Inspection, Safety & Quality Ove rd Demee of DXficdtv

Raw Data

R u a l 0.235 91-95 Alberta

Reirnbersable S hell Colt

John Doer Bob Smith Chernical

Confhed to Speci£ic Area PIant Upgrade No Shutdown

10°/o, 90°/o, 0% 25-50 50-100

Yes 9 -4

0.661 0.029

Excellent Inside <loft E-Figh

6055 210,905,4940 Carbon Steel

Hand Rigging0/0, Machine Rigging '/O 0.45 4.77 1.59

O 3.18 1.25

WinterO/o, SumrnerO/o Average

Many Problems De tailed

Low

NN Input Data

(3)

Output Zone Setup

-1s discussed in the section "Introduction of the PINN rnodel", the likely range

of output values is evedy divided into a number of output zones. The output zone

boundary semp is important for PINN l e d g and recall. \Vide zones are generally not

helpfd to the decision-maker and hence should be aroided. Zones that are unacceptably

tight may prevent PINN h m l e d g . It requires some aials to obtain reasonable

output zone boundaries and the following two aspects should be considered:

1. Preüsion requirement of the user, i.e. the zone width or sub-range that suffices for

the user to make dedsions.

2. Dismbution of actual output data over the output zones. h uniform distribution of

actual output data over aU zones generaily yields better results.

Processing Elements (PE) at Kohonen Layer

At the Kohonen layer, each output zone contains an equal nurnber of processing

elernents. Each processhg element is associated with a weight vector (also referred to as

a codebook vector (Kohonen, 1995)).

Visually, a weight vector is a set of links that emanate Lom one processing

element and end at each input node as illustrated in Figure 3- 1. Thïs the dimension of a

weight vector is equal to that of the input vector (the number of input nodes). An output

zone at Kohonen layer can be visualized as a chip containing a number of pins (PEs).

DuPng NN trnining the orientation of those pins is gradually he-tuned to capture the

underlying s taustical patterns Mthin the training data (Kohonen, 1995).

Our expenence uidicates that the nurnber of processing elements nssigned to

each class should be close to the average frequency in the histogram of training data

output values, i.e. the average number of naiaing samples in one output zone.

NN Leaming Process

Data of a l l the training records is scaled at the input hyer. The scaled input data

is fed into the mode1 to calibrate the weight vectors of the Processing Elements (PE) at

the Kohonen layer, using the LVQ aIgorithrn suggested by Kohonen (2995).

The leaniing process involves a number of iterations, each of which is

comprised of the following:

1. The Euclidean distances between the input vector of a training record and each PE's

weight vectors are calculated. The PE that has the smallest Euclidean distance vdue

is declared to be a global winner. If the global \vinner PE does not belong to the

same output zone that the actual output value of this training record Falls into, the

weight vector of the global Ninner PE is pendized according to the Foliowing

equation (1):

RR stands for "Repulsion Rate", which is a Ieaming rate to penalize the global

winner PE;.

X, is the input vector of the training record, and

Wii is the m e n t weight vector of the global mnaing PE,.

Wii' is the updated weight vector of the global w h i n g PE,.

The repulsion rate is iniaally set berneen O and 1, and is reduced gradually und it

approaches O at the end of learning.

2. Followhg the global competition, an in-zone competition among processïug

elements occurs only at the output zone into whkh the acnial output value of the

training record fds. Prior to the Li-zone competition, a "conscience" value is added

to each PE's Euclidean distance and adjusted over the learning iterations, so as to

effecuvely prevent one PE nithin a specific output zone from whing all the cime

and activate as many PEs as possible in the leaming process. The formulas to

calculate the conscience Euclidean distance c m be found throughout the pertinent

literature. The interested readers can refer to Appendk II for details.

The

The

method we adopted is as Follosvs:

cc conscience" Euclidean distance between each PE's weight vector and the

input vector is calculated. The PE wîth the shortest "conscience" Euclidean distance

value is declared to be an in-zone m e r . Onlp the in-zone minner PE is remarded u s h g

equation (2):

Where:

AR stands for "-Attraction Rate", which is a leaming rate to remard the in-zone

+er PEi-

X, is the input rector of a training record, and

W, is the current weight vector of the in-zone %&mer PE,.

W,' is the updated weight vector of the in-zone whing PE,.

Wie the repulsion rate, the attraction rate is initially set benieen O and 2, and is

reduced gradua* u n d it approaches O at the end of l e k g iterations.

-1 sample calculation of one learning iteration is presented nest to illustrate the

learning process.

As shomn in Figure 3- 2, the dimension of input vector is 12, and the output

range ([O*]) is divided into 1 output zones, Le. [O-11, [l-21, [2-31, [3-4-1. Each output zone

contains 3 processing elements. Note that this sample is a simple mode1 and serves for

illustration. Problems encountered in a r ed situation, wliich are suitable for the PINN

mode1 to solve, are mostly high dimensional; the number of input nodes mav esceed

100.

The input vector of a training record is scaled benveen O and 1, and the weight

vector of a processing element nt the Kohonen layer is randomly initialized between O

and 1. Table 3-3 shows the input vector XI and the meight vectors of the 3 processing

elements in zone 1.

Table 3-3: Scded Input Vector and Initial Weight Vectors

Input Vector

The Euclidean distance (ED) is calculated berneen the input vector X, and each

weight vector Wi, as ED,; = 1.4163, ED2, = 1.5746, and ED,, = 1.2963. Suppose that

PE3 in zone 1 is the global e e r PE among d the processing elements, svhich gives a

minimum ED value of 1.2963. If the actual output of this training record does no t Ed

into zone 1, i.e. outside the sub-range [O-11, then the meight vector of PE, (W,,) is

updated by equation (1) as shown in Table 3-4. Notice that the Repdsion Rate is set to

be 0.8 at the staa of learning in the sample calculation. Kohonen (1995) recommends

smaller initial value such as 0.06 for the Repulsion Rate and -Attraction Rate for obtaining

better resdts.

Table 3-4: Updating Weight Vectors in First Learning Stage

Input Vector

If the actual output of this training record does fd into zone 1, i.e. nrithin the

sub-range [O-21, then no weight vector is updated in the global cornpetition. The learning

process steps into the second phase.

In the hrst training iteraàon, the conscience value for every processing element

in zone 1 is detemiined to be equal to O (see hppendk I). So the "consuence" Euclidean

Distance value is equal to the onginal Euclidean Distance value. PE3 is the in-zone

Figure 3-2: Operations at Bayesian Layer in R e c d

competition b e r , which gives the minimum "conscience" ED value of 1.2963, and its

weight vector W3, is updated by equation (2) as shown in Table 3-5.

Table 3-5: Updating Weight Vectors în Second Leaning Stage

Input Vector

The above learning process d iterate through al1 the training records for a

suffiuent number of m s . Notice that during the leaming process the Repulsion Rate,

Attraction Rate, the conscience value are dynamically updated to calibrate the weight

vectors.

In-Zone Cornpetition Strategy aï Kohonen Layer

The in-zone cornpetition at the Kohonen layer occurring in the recd stage

differs from that o c d g in the leaming stage. Once adequate trainhg is complete, the

PINN is capable of mapping the input ont0 the output. At the Kohonen layer, for one

output zone, the PE that has the shortest global Euclidean distance (no conscience

value) between its meight vector and the input vector is declared to be an in-zone wïnner

PE. Only the in-zone ber PE advances to the Bayesian Iayer.

UnWre the GRNN/PNN, which takes the average of PE's Euclidean distance

within one output zone as the panmeter to pass fornard (Specht 1988), PINN takes the

minimum of the PE's Eudidean distance wïtbin one output zone as the parameter to

pass Çonvard. The reason for the difierence is that in GRNN/PNN, each PE

corresponds to one training record, and differenc numbers of PEs Lie in different output

zones. In the proposed PINN, the PE does not match the training record, and an equd

nurnber of PEs dwell in each output zones and mode together in the Kohonen layer of

PINN to generalize the underlying patterns within the 6 n i n g records by ïmplementing

LVQ.

PDF Approximator at Bayesian Layer

As illustrated in Figure 3- 2, at the Bayesian layer each output zone only contains

the minner PE feom the in-zone competition at the Kohonen Layer in the recall stage.

The main components at the Bayesian layer are a kernel function and a SoÇtmas

Activation fùnction that are used co approximate the probability density of one input

vector being wvithin each output zone in the steps as ÇoIlow:

1. The square of Euclidean distance value of the minner PE from each zone is passed

into the kemel function, which is the Gaussian hinction of Bayesian methods in

sratistics as described in Specht (1988) and shomn in equation (3). If the number of

output zones is N, then for each input vector Xj, the kernel function is evduated for

N times and output one "q" value for each zone.

where: i =1,2,3,. . .N, N is the nurnber of output zones;

Xj is one input vector fed into PINN at the input layer;

(QUii-XJT(~,,-X,) is the square of the Euclidean distance value between the input

vector X, and the winner PEys meight vector Wii in the output zone i, i =1, 2,3,. . . >N.

(T is a smoothing factor, and is the only adjustable parameter of the Gaussian

h c t i o n (3) and controls the shape of the probability density hc t ion . The grearer a,

the more dispersed the probability density graph. CT is critical to PINN1s predicting

capability and can be detemiined through iterative adjustments. In regard to industrial

productivity application, 0 should fd in the range between 0.8 and 1.2.

The Sofmia-u Activation function (Sarle, 1997) as shomn in equation (4) makes

the surn of the calculation results (q values) from (3) equal to one, so that the final

output Erom the Bayesian layer can be inrerpreted as posteior probabilities ("p" values).

where: qi is the output value 6om Gaussian h c t i o n (3) for output zone output

zone i, i =l, 2,3,. . .,Ne

N is the nurnber of output zooes.

Outputs at Output Layer

At the output layer, the probabiliq distribution predicted by the PINN is

presented in the form of a Probabiliy Density Function graph, which portrays the

uncertainq of the output value.

In addition to the predicted distribution, PINN calculates two point prediction

values:

1) Mode value: the median of the output zone or sub-range that has the greatest

probability.

2) Weighted .Average Value: the sum product of the median and the probability of each

output zone. The user should neat thïs point-value prediction carefully by checking

the probability density hinction grap h.

Sample of R e c d Processing

h sample PINN recall calculation is given in the folloming sections for

iuus tration:

Suppose that the NN is mained and ready to recall the output for an input vector.

A s shomn in Figure 3- 1, the dimension of input vector is 12, and the output range ([O-

41) is divided into 4 zones, ie. [O-11, [l-21, [2-31, (3-41. Each zone contains 3 processing

elements.

Table 3-6 lists the scaled input vector X, and the weight vectors of the 3

processing elements in zone 1.

Table 3-6: Trained PINN Ready to Recail for A Given Input Vector

Input Vector

The Euclidean distance (ED) values between the weight vectors and the input

vector are calculated as ED,, ~0.9513, ED2, = 1.1670, ED,, = 1.3249.

At output zone 1, processing element PE, with a minimum ED value (0.9513) is

the in-zone cornpetition whner, and proceeds to the Bayesian layer.

Suppose the b e r PEs fiom the other 3 zones are also detemiined in the

similar manner and proceed to the Bayesian layer. Table 3-7 lists their Euclidean distance

values and outputs fiom the Gaussian function and the Sofïma-.: function.

Table 3-7: Recail Calculations at Bayesian Layer

From Table 3-7, the probability of output being within zone 1 is 0.731, hence the

mode output value is found to be the median of zone 1, i.e. 0.5. The weighted average

output value is obtained by calculating the sum-product of the Sofmiax output @ values)

and median of each output zone, i.e.

Values for Each Zone

(1)

Median

Winner PE's ED

Gaussian Output q:

Sofmna,~ Output p:

IMPLEMENTATION OF THE PIPIN MODEL

Cornputer s o b a r e based o n the PINN mode1 is developed for learning and

testing in the environment of MS Access 97 and Visual Basic for .ipplications. Historical

Zone 1

(2)

0.500

0.951

0.636

0.731

Zone 4

(5)

3.500

3.922

0.014

0.016

Zone 2

(3)

1.500

2.567

0.037

0.043

Zone 3

(4)

3.500

1.843

0.183

0.210

piping productivity data of 66 projects resulciog in 119 records of a construction

Company mas collected and compiled into N N input data for three Iabor-intensive

activities, i.e. pipe installation, pipe welding and pipe hydro-testing. In the following

sections, pipe installation is used to illustrate the testing and validation of the PINN

model.

The PINN model for "pipe installation" has a total number o f 81 input nodes.

(The input factors and a sample data are shomn in Table 3-1 and 2). The output range is

divided into 20 output zones with an equal width of 0.72. 10 processing elements are

assigned to cach output zone. The attraction rate and repulsion rate are both equal to

0.06. The srnoothing factor of the kemel function is equd to 0.8.

One hundred one records are used for PTNN leaming, while 18 records are

reserved to test the calibrated model. The learning process takes 300 iterations.

Validation of the PINN Mode1 on Testing Data

The testiog of the calibrated nemork on the 18 unseen records was surnmarked

in Figure 3- 3. Measured agahst the actual output values of the test data, for the mode

value, the average absolute error is 0.57, and the rn~uimum absolute error is 2.02; for ehe

weighted average value, the average absolute enor is 0.75, and the maximum absolute

error is 2.23. Considering a wide output range of about 15, the error is reasonable and

acceptable.

To compare the PINN model Mth a back propagation neural network, the same

training records were used to train a thee layer feed fonvard back propagation neurai

87

network, mhich has 81 input nodes at the input layer, 40 hidden nodes at the middle

layer and 1 output node at the output layer. The ~aining parameters are l e d g rate

equal to 0.8, momentum rate equal to O.+ the transfer h c t i o n is symmemc logisac

£Ùnction. Afier training was completed, the tesMg set of 18 records preriously used to

test PINN mas fed into the model. The tesüng resdts of the back propagation NN

model comparing with that of the PINN are shown in Figure 3- 3. From Figure

observed that the PINN rnodel outperforms the back propagation NN model

of point prediction accuracy, coming closer to the actual output values.

PINN VS FF BP NN

+PINN (Mode) 7 1 - -A - FFBP NN

in terms

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Test Record #

Figure 3-3: Comparison of PINN and Back Propagation NN

Figure 3-4: PINN Output for the Base Case Scenario

Sensitivity Analysis of the PINN Model

A recd program based on the trained

developed so as to d i d a t e its effectiveness

PENN model for pipe

and accuracy in the

installation was

contest of the

application domain. "What if' scenarios are tested o n the NN model

input factors in order to understand the impact of such changes on

by changuig some

the output values.

The response of the NN model is compared against chat of an expenenced estimator at

the participakg consmction Company for the purpose of model validation-

The base case scenatio is taken from one testing record. The acnial difficulty

multiplier for this scenario is 1.24. The mode value predicted by the PINN model is

1.181, giving an absolute enor of ( 1 1.181 - 1.24 1 = 0.059); and the weighted average

value is 1.313, giving an absolute error of ( 1 1.313 - 1 .X 1 = 0.073)- Figure 3- 4 shows

the predicted probability h c t i o n or distribution, the chance of output f&g into zone

2 (10.8-1-51, median = 1.181) is 69O/0.

In the following validation tests, the acmai values remain unknown, so the

responses of the estimator based on personal experiences and common senses serve as a

benchmark to measure the performance of the PINN model. The esümator responds

widi a trend or direction insread of a precise number because there are so other input

factors to take into account.

The location of pipe installation is a major consideration when the esperienced

estimator detemiines the pipe installation productivity. The instahtion location for die

base case scenario is "Piping nrithin a fabrication shop", what if the location is changed

to "Operating plant installation on the site"? The esperienccd estknator responds by

increasing the difficulcy multiplier to a certain estent to reflect the unfavorable job

conditions. Response of the PINN model is shomn in Figure 3- 5. It is observed the

mode value increases to 1.903 and the weighted average value increases to 1.983; the

chance of the output value falling into zone 3 (l1.5-2.31, median = 1.903) increases fiom

13% in the base case scenario to 78%. The PINN

estunator in the decision process for this scenmio.

has taken the same direction as the

In the base case scenario, the job is done 100% in the winter in Alberta. m a t if

NU RecaIl Probability Density Graph

1 .O

Figure 3- 5: PINN Output for Scenario 1

the job is done 100% in the summer? The estbator anticipates a reduction for the

diffidty multiplier, mhich rneans an increase of productivity level. Response of the

PINN mode1 is shown ui Figure 3- 6. It is observed the mode value rernains 1.181,

homever, the weighted average value decreases to 1.151. The chance of the output value

falling into zone 2 ([0.8-1.51, median = 1.181j decreases significantly from 69% to 44Y0,

while the chance of the output value falling into zone 1 ([0.2-0.81, median = 0.5)

increases si@cantly from 15% in the base case scenarïo to 40°/o. Again the PINN

chooses the sirriilar course of action as the estimator in the decision process for this

s cenario.

NN Rewl! Probabifity Demity Graph

i .O

Figure 3-6: PINN Output for Scenario 2

The PINN model creates a meaningful representation of a comples, real-Me

siniaaon in the problem domain and is effective in dealing with high dimensional input-

output rnapping mith multiple influentiai factors in a probabilistic approach. The

application of the PTNN model in indusmial labor production rate e s t i m a ~ g helps the

estimator choose a course of action by gïving a better understanding of the project

information available and the possible outcomes that could occur. Bccause the

probability densicy of each output zone is provided, the predicted dismbution and point-

prediction values give the estimator much more confidence in the predicted result. In

combination of the personal esperiences and preferences labor production rate for a new

project can be deterrnined.

Chao L.C., and Skibniewski, M.J. (1 993). "EstirnaMg Construction Productivity:

Neural-Network-Based Approach." Joumal of C O ~ ~ U M ~ in Civil Engineering, ,lSCE,

8(2), 234315

Hermann, R. and Lu, hl. (1997) "-ipplication of Neural Networks in Industrial

Estimating", Proceedings of the 27& Canadian Society of Civil Engineers -innual

Conference, Edmonton, AB, 15-35.

IKnowles, P. (1797). " P r e d i c ~ g Labor Productivity Using Neural Nenvorh."

Mas tcrs of Science Thesis, University of Alberta, Edmonton, AB.

Karshenas, S. and Feng, X.( 1992) "Application of Neural Networks in

Earthmoving Equipment Production EstimaMg." Cornputhg in Civil Engineering,

Proceeding of Eghth Conference, Dallas, Texas, 841-847

Kohonen, T. (1 995). "Self-Organiziag Maps", Springer Series in Information

Sciences, S p ~ g e r , London, U.K.

Moselhi, O., Hegazy, T., and Fazio, P. (1990 ) 'Tùeural Newodc as Tools in

Consmichon." Journal of Construction Engineering and Management, -ASCE, 117(4),

606-623

Murtaza, M.B., and Fisher, DJ- (1993), "Neuromes: Neural Neîsvork System for

Modular Consmction Decision Making", Journal ComputGig in C i d EngineeSng,

,%SCE, 8(2), 221-333.

Portas, J., and AbouRitk, S.M. (1997), c%Jeucal Nenvork Model For Estimating

Construction Productivity." J. of Constr. Engrg. & hlgmt., ASCE, 123(4), 399-410.

Sarle, W.S., ed. (1997), Neural Network F-IQ, part 1 of 7: Introduction, penodic

posting to the Usenet newsgroup comp.ai.neur-al-ne ts, URL:

fip://ftp.sas.com/pub/neural/FAQQhtrriI

Specht, D. F. (1 988). Trobabilis tic Neural Networks for Classihcation,

Mappings, or =lssociative Memory." IEEE International Conference on Neural

Nenvorks, 1988,1,525-532.

Specht, D. F. (1991) "Generd Regression Neural Nenvorks.'' IEEE T.cansactions

on Neural Netsvorks, Nov. 1991,2, 535-5176.

"Conscience" Euclidean Distance is defined as (5):

Di' = Di + Ci

Where:

Di is Euclidean distance,

and Ci is conscience value (6):

Ci =cf x ~ x ( n x w f -1)

Where:

D is the rn~&um Euclidean distance out of the global cornpetition in the

previous s u p e ~ s e d leamhg stage,

cf is a Conscience Factor, mhich is initially set berneen O and 1 by the user,

and n is the number of PEs per output zone,

wf is dehned as "Win Frequency", and the initial estimate of the Win Frequency

value (do) is set to the reciprocal of PE Number per Output Zone for dl the PEs, i.e.

1 /ne

With NN learning ongoing, both Conscience Factor (cf) and Frequency

Estimate (fe) are reduced graduaiiy und it rpproaches O at the end of leaming.

During the u n s u p e ~ s e d l e h g stage, for the in-zone whner PE, its mf value is

updated as (7):

For the in-zone loser PEs, th& mf values are updated as (8):

Basically, the above formulas are intended to increase the wf values for the

wimer PE and hence increase its conscience value so that the whmer PE d l have less

chances to again than the other loser PEs in the following learning iterations.

A r t i f i d neural netrvorks (NN) mimic the cogniuve learning process in the

human brain, and deal effectively wïdi dl-stmctured problems, in which the algorithms

required to solve them cannot be given in a precise and e~;pliut fashion, or the datx for a

particular problem are either not complete or cannot be specified precisely (Widman et.

al., 1989). NN has been found to be capable of performing parallel computations on

different tasks, such as pattern recognition, Lnear optimization, speech recognition, and

prediction @Iukherjee and Deshpande 1995).

A version of this chapter has been subtnitted for publication. ASCE, Journal of Computiag in Civil Engineering.

In recent years, Back Propagation NN (BPNN) has been researched and applied

as a convenient decision-support tool in a variety of application areas in civil eng inee~g ,

induding moduIar construction decision making (Murtaza and Fisher, 1993), structural

analysis (Flood and Kath , 1994), e s t k a ~ g construction productivity (Portas and

AbouRizk, 19977, mode choice analysis of fieight transport market (Sayed and R a z a i

1999), construction m d x p estïmating (Li et al 1999), measuring organizational

effectiveness (Sinha and blcI(im, 2000), and predicting settlement during runneling (Shi,

2000). The speud l e d g aigorithms of BPNN are capable of perfonriing high

dimensional, non-linear input-output mapping and e s t r a c ~ g hidden patterns and

predictive information from observing the l e d g esamples.

However, Leamkg algonthms such as BPNN do not attempt to infer causality,

hence, classification or prediction is based on blind correlation of new esamples with

preriously analyzed esamples, nrithout giving information on the effecr oE each input

parameter or inauencing variable upon the predicted output variable- In the repoaed

NN applications, model validation has thus far relied upon measuring accuraq of the

calibrated network to an independent testing data set that are hidden from the neural

nenvork in learning. The model's sensitivity to changes in its paramerers is generally

probed by t e s ~ g the response of a mature nenvork on various input scenarios. In short,

a NN mode1 funcrions like a "black box" package, giving no clue on (1) how the ansmers

or model outputs are obtaked; (2) how the input parameters affect the output.

Widrnan et. al (1989) pooulted out that the credibiliry of an AI program

frequently depends on its ability to explain its conclusions. Lack of interpretability is a

pi t fd of the neural netmork models recognized by many and has inhibited NN from

achieving its full potential in real-world applications. Dhar and Stein (1997) argued that

because NN algonthms such as the back-propagation NN are non-linear, high

dimensional fimctional equations feaniring pardel distributed data processing, it is hard

to e-xplicitly interpret which parameters cause what behavior in the NN model. i'vhile

mathematical and operational methods do esist for the analysiç of neural networks, the

methods are fairly involved, and are Iess than satisfping because of th& theoretical

assumptions. They stated that "unlike most statistical methods, it can be difficult to say,

even in general, which variables are signrficant in what respect." (Dhar, et.al. 1997)

Our research intends to address the idenfied issue by concent ra~g on

sensitiviy analysis of BPNN. Similar to regression analysis, the sensitivity of an NN

input pxrameter could be expressed as the hrst-order partial derivative benveen an NN

output variable and the input paiameter. In the "Literanire RevieW" section, we bnefly

introduce several related methods for knodedge eirplanaaon and factor analysis of NN

found in iiterature. In the section entitled "BPNN Algorithm and Input Sensitivity", the

back-propagation NN algorithm is described kst, followed by the derivation of

mathematical relationships between an hTN output variable and NN input space in lighr:

of both normalized data and original data. The follonring section "BPNN vs. Regression

Analysis" discusses the difference between BPNN and regression analysis of statistics

and demonstrates the sophistication and superi~rity of BPNN over regression analysis in

a case study based on a s m d data set. Nest, statisücd analysis of input sensitivity based

on Monte C d o simulation is described in the section entitled "Statistical Analysis of

Input Sensiüvity" to understand the rationale of BPNN's reasoning and the effectiveness

of model implementation in a probabilisuc fashion. In the "Industrial Application"

section, the new approach is applied to estimate the labor productivity of spool

fabrication in an industnal setting, and important aspects of the application including

problem definition, factor identification, data collection, and the tesbng resuln bascd on

real data set are discussed and presented.

Li et al (1999) realized the inability of BPNN to provide e.xplanations on its

output negatively affects the user-acceptance of BPNN. ï k e y investigated the use of

KT-1 method for automatically estlacting d e s from a mature BPNN in an atternpt to

explain why and how BPNN makes a p a r t i d u recommendation in developing a

decision support tool to e s h a t e the consmiction markup. KT-1 method is a heuristic

approach to generating conhmüng/disconfimiing d e s fiom each hidden or output

node based on the weighted connections and the threshold value of each node, and is

constrained by the complesiv of network structure. As pointed out by the authors, such

automatic de-extraction systems as KT-1 cannot marrant a N y informative

euplanation faality because KT4 lacks the associative knowledge (Le. cornmon sense,

professional knomledge etc.) in its de-esnacting process (Li, et. al., 1999).

Sinha and bIcIGn (2000) utilized BPNN to measure organizational effectiveness

of construction h s . They have applied statistic analysis methods, such as Principal

Component Analysis (PCA), stepwise regression and conelation analysis on n BPNN

model in an attempt to identify the dominant factors that influence the target output

variable, and further to reduce the dimension of input space. Homever, the theoretical

underpinning of such statistical techniques requires carehil study of rheir applicability in

sotring real problems. For instance, lacking în amareness of the assumptions of least

squares regression (nomality, homoscedasticityy independence of errors, and linearity)

may cause the rnisuse of regression and correlation analysis (Levine et. al, 1998); use of

PCA, which assumes linear relationships betsveen variables, Wht bias the selection of

deteminant factors bp escludïng those that have non-linear relationships with the target

output variable @Zefenes, et. a1.,1995).

Alternative approaches to factor analysis include using auto-associative back-

propagation neural nenvorks to perfonn non-linear dimension reduction and sensitivity

analysis (Cano1 and Ruppert, 1988). The neural nemork has one hidden layer mith k

hidden processing elements, where k is less than the dimension of input space IZ. The

output space is a repiica of the input space. Analogous to the rationale of PCA, this

method is to compress data by representiog many variables by a few components: if we

can reproduce the input space using k (k < n) hidden processing elements nrithout loss

of information, then the activation values of the 6 processing elements in the hidden

layer d compute the 6rst k principal components at the input space, under appropriate

conditions. One pidall of this method obseïved by Refenes et. al (1995) is that the

stochastic nature of the data-generating process at the neural nenvork input space may

cause high variance in the analysis results. It is also noted that the output variable is

excluded from the auto-associative neural network analysis, hence, such analysis of input

parameters or influenchg factors does not take into account the relationships behveen

the input parameters and the output variable.

Explanations on the importance of input parameters can also be obtained by

examinkg the weights of a mature network so as to chwacterize the strengths of the

relationship betmeen inputs and outputs. Knowles and AbouRizk (1997) added up the

absolute value of weights from one input node to every hidden processing element in a

trained BPNN model wïth only one hidden layer for esUmating pipe installation

producuvity. The total weight vdue of an input node may iadicate the intensity of the

connection from the input node to the hidden layer of the nemork; the higher the sum

value, the more signihcant the input parameter is. rilthough this heuristic approach is

straightfonvard to understand and easy to use, the resdts may bc unstable or inaccurate

due to the fact that it fails to take into account the c o ~ e c t i o n s between the hidden layer

and output layer. In modeling the behavioral mode choice of the US. Geight transport

market, Sayed and Razavi (1999) combined the leaniiag abilitp of BPNN and the

transparent nature of hzzy logic in order to explain the knowledge contained in a

BPNN model, which is stored in the form of a weight ma& that is hard to interpret.

The neuroftxzzy rnodel Ocilitates the selection of sipficant variables that affect the

output and displays the stored knowledge in terms of hzzy linguistic rules (Sayed and

Razati, 1999).

Based on the above methods found in literanire, the effect of each input

parameter on the output variable in t e r m s of magnitude and direction sd i remaïns

unknown, i.e. the input sensitivi~. In the follonring section the algoPthmic aspecrs of the

BPNN model are studied in order to d e h e the input sensitivïq in an exact mathematical

term.

Figure 4-1: Structure of Back-Propagation NN Model

BPNN ALGORTTHM AND ~[NPuT SENSITMTY

Frorn the biological perspective, BPNN is origindy proposed as an AI model to

simulate the cognitive Ieataiag process in human brain, in which millions of murons are

ktercomected and interact with one and another through cornplex electrochemical

reactions and signal processing. An d c i a l NN model such as BPNN is merelv an

over-simpEed representation of the real NN in tems of mechanism and structure. h

typicai BPNN has a multi-layer structure. Each layer contains a number of processing

elements (PE) or nodes, mhich are M y interconnected bemieen layen (Figure 4-1). The

ïntensity of connection betmeen trvo processing elements is represented using a weight.

Put into the perspective of mathernatics, BPNN is essentially a gradient-decent

optimization algorithm to search for the optima in a high-dimensional weight space with

the objective of minimizing the global eirror benveen NN output values and acmd

output values. An iterative weight-adjus~g scheme is used to modiq the weights of alI

the connections in the NN structure in a stepwise fashion.

BPNN Aigorithm

The basic formulae to describe signal processing of a PE in BPNN are simply as:

Where:

Subsaïpt c stands for a processing element in the hidden laper or output iayer of

BPNN;

Subscnpt i is the node index at the previous Iayer of BPNN;

W, stands for a weight value betnreen node i and node c;

S stands for the input signai to a node;

N stands for the output signal from a node.

Equation (1) shows that a processing element receives a weighted linear

combination of input signals £rom the previous layer. Equation (2) is Sigmoid (iogistic)

h c t i o n and is the most comrnonly used transfer (squashg) h c t i o n in BPNN,

through which a processing element transforms the input signal into an output signal.

Note that a bias node Mth constant input value -1 Erom the previous laper is aiso

connected to a processing element and involved in the calculation, representing the

activation threshold of a processing element (Figure 4-1).

The digital s b a l s flom through the BPNN foilowing (1) and (2) from layer to

layer und the output layer is reached.

The global error (E) of the BPNN optimization search is expressed in (3):

Where:

N stands for the output signal Gom BPNN;

D stands for the target d u e ;

Subsaipt i is the index of records in the training data set and T stands for the

size of training data set.

The weight of the BPNN is adjusted using the delta d e to move to the opposite

aE direction of - as (4):

awpc

aE = - h . N .- as,

h is a gain ratio in (0,1), also called learnulg rate, which sets the pace of BPNN

Iearning;

Subscrip t p stands for a processing element in the previous layer of the nenvork;

Subscript c stands for a processing element in the m e n t layer of the network.

For a processing element

For a processing element

at the output Iayer of BPNN,

at the hidden layer of BPNN,

T --

In (6), subscript n is the index of processing elements in the nest layer, and J is

the to tai number of processing elements in the nest layer.

Usudy, a momentum tenn is added to the weight adjusting scheme to take into

account the meight change in the previous step as shomn in (7).

dE ?

AW,, =-A- N O-

P as, +CL * q c

9

AWpc ïs the weight change in the previous step, and p is the momennun ratio

vhich is usudy less than h .

BPNN adjusts meights following (7) by observing the training data set repeatedly,

until the global error E is reduced to an accepted l m 1 to declare the BPh'N to be

crained.

The BPNN shodd have at least three layers: the input layer, one hidden Inyer,

and the output layer. The three-layer-strucnired BPNN ~vith Sigmoid transfer functions

has been found by many to be adequate in solving non-linear op timization problems. In

the following sections, we use the three-layer Sigrnoidal BPNN to illustrate the

mathematical inferences of input sensitiviq for simpliciq- of representation. However,

interested readers can readily estend the derived input sensitiviq to BPNN with more

comples structures and other trans fer hmctions.

Input Sensitivity Based on Normalized Data

Based on the BPNN algorithm presented in previous sections, me can soa out

the relationships between an output variable and an input parameter to de hne the input

sensitivity of BPNN in an esact mathematical tenn.

Notations used in the followkg mathematical formulae are lis ted as belom:

Subscript p stands for a node in the Previous layer of the netntork-

Subscnpt c stands for a node in the Current layer of the nemork; C stands for the

total number of nodes in the cunenc layer.

Subscript n stands for a node in the Nest layer of the network.

LVii stands for the weight of connection between node i and node j.

S stands for the input signal to a node.

N stands for the output signal from a node.

If the curent node is an input node (in the hrst layer of the nenvork), S is the

normalized input data in range (0,l).

Previous Layer Curren t Layer Next Layer

Figure 4-2: Illustration for Node and Layer Representations

If the curent node is not an input node (in a hidden layer or an output layer),

Note thac equation (9) is the same as (1) escept thac (9) d i s~guishes one node or

processing element p fiom others n t the previous layer. The relationship betrveen the

output signal N, and the input signal Sc is defined in (2), fiom which, we have:

As shown in Figure 4-2, in the three-Iayer BPNN, node p is an input node in the

input layer, node c is a hidden node in the middle layer, and node n is an output node at

the output layer. The focus of BPNN sensitive analysis is on investigating the &SE-order

partial derivative of the output signal Erom node n (Nd over the input signal to node p

(SJ. By (8), we have S, = Np.

fiom (IO), we know,

From (1 l), we know,

So, (12) cari be expressed as:

Because more than one processing element exists in the current Iayer (hïdden

Iayer), assume, the number of processing elements at layer c is C. A general form of

input sensiuviry for BPNN is then expressed as (1 4):

Input Sensitivity based on Original Data

In daivuig (13), me assume aIl data including inputs and outputs has already

been normalized in the range (0,l). From the perspective of real applications, usually it is

convenient and straightfomard to probe the sensitivity of BPNN based on the original

or raw data instead of scaled data.

Various linear or non-linear normahation methods can be used to uansfonn

raw data- Shi (2000) retiewed the established data transformation methods for BPNN

and proposed a new one calIed ccdisaïbution transformation", which fits statistical

distributions to raw input data and ualizes the resdtant Cumulative Densiq Functions

(CDF) to scale inputs to [0,1]. The theoretical underpinning of such transformation is

relativdy weak as pointed out in Shi, 2000, but such transformation does complicate the

application of NN. The conclusion about the superiority of ccdistribution

transformation" scenario over the traditional linear transfomation scenmio is b v e d at

ernpiricdy based on independent esperiments on each method. Due to a number of

variable factors (such as learning rates, momennuri) and stochastic phenornena (such as

the initialization of network weights and the esistence of multiple local optima in the

searching space), the improvement of netnrork performance may not be attributable or

only p d y attributable to the input transformation methods.

The non-hear mapping capability of BPNN is mainly owhg to the non-linear

transfer functions in hidden and output PE S. Xccording to our experiments on BPNN,

a good selection of hidden layer smctures and transfer functions based on mals

generally results in improvement of BPNN's performance. Thus, we recornmend using

such robust, undistorted and simple data normalizabon methods as h e a r transformation

to normalize both inputs and outputs in BPNN and satisfy the neural cornputauon

requirements. The simpliaty of BPNN will be maintained wïthout sacrihcing its

fwictionality, mhich can be M e r demonstrated £rom sensit ivi~ analysis of BPNN in

the following sections.

If we take into consideration the data normalizauon procedure, the simplest and

most comrnonly used one is a linear process as folloms:

(UB - LB) (Sp-MINp)+LB

Np = (MAX, -MINp)

Where, I23 is the upper bound of the nomalùed interval (LB,UB), and LB is the

lower bound, for sigrnoid transfer function, usudy LB = 0, and UB = i;

b L L 2 is the maximum value in the data set corresponding to input node p or

parameter p;

MIN, is the minimum value in the data set conesponding to input node p or

parame ter p.

A formula similar to (15) is applied to normalize the output data, in order to

match the output range of the trmsfer h c t i o n s in BPNN, i.e. (0,l) for Sigrnoid uansfer

functions. If we take N, as the raw output data, there is a scale-back process involved at

the output layer, which w d cancel out the UB (1) and LB (O) in combination with the

scaling process at the input layer. So w e can arrive at a more general form of (14) based

on linear norrnalization procedures as:

JN, - MAX,-MIN, -- . ~ W , , W , , - N , ( l - N c , ) - N n ( l - N n ) (W as, MAX, -MIN, i=i

This slope or partial derivative is dehned as absolute input sensitivity and

represents the expected change in output variable N,, per unit (1) change in input

parameter S,, holding the other input parameters constant. In a red-wodd problem, each

input parameter may have different unit of measure, and hence various relevant range,

which encompasses dl values from the s n d e s t to the kges t used in training the model.

Simily to regression analysis, it is important for BPNN to interpolate nrithin ùie range

rather than estrapolate beyond the mage in order to make sensible predictions. For one

input parameter ranging from 1 to 20000, one unit change is too s m d to be considered

mhile for another input parameter ranging from 0.1 to 0.6, one change is too big to

occur. Thus, it is more appropriate to use a relative one-unit (such aslOO/o of relevant

ranges) as the basic unit change in input parameters instead of an absolute one-unit (1).

Through such transformation, the input sensitivity is undistorted and more meaningful

in terms of comparing the effect of different input parameters upon the output variable.

The relative input sensitivity is dehed as (1 7):

relevant ranges i.e. 10% Bmes ~ ~ Y , - MINJ. Note that die input sensitiviq is

independent of the relevant ranges of input parameters and represents the amount that

output variable N, changes (either positive or negative) for a particular unit change in the

input parameter S,, i-e. the 10% of its relevant range.

BPNN vs. REGRESSION ANALYSIS

The above sensitivity analysis of BPNN is analogous to the dassic multiple

regression analysis in statistics, mhich predicts the values of response or dependent

variable based on the values of multiple e.<planatory or independent variable and c m be

dehned as (1 8):

Where B,, is an intercept representing the average value of N,, when ail the

es~lanacory variables S , are equal to zero, i =l to M, M is the total number of

a N n explanatory variables. - is a slope for the i" esplmatory variable and its dehiniaon as pi

is identical to the input sensitivity of BPNN as above. However, ody by esamliing the

difference between BPNN and regression analysis c m the sophisucation and supedoety

of BPNN over regression analysis be demonsaated, as discussed neat.

aNn in BPNN is An examination of Equation (16) indicates that the value of -

dependent on severd factors:

1. The interna1 structure of BPNN, i-e. the number of hidden nodes and number of

hidden layers.

2. The BPNN data set, i-e. the relevant range of each input parameter and output

variable,

3. The weight values of BPNN, i.e. the intensitg of c o ~ e c u o n among processing

elements Erom the input layer to the output layer. This is actually the result of

BPNN maining, and hence dependent on the training data set.

4. The cunent input values loaded at the input nodes. From (l), (2), and (1), it is

evident N, and N, are hincuons of the cunent input values at the input layer and

the weight values of BPNN.

We can also observe that once a BPNN is trained on a data set, the &sr three

factors (BPNN smicture, meights and training data set) are &ed, so the sensicivis. of an

input parameter over an output variable is totally determined by the fou& factor, i.e. die

cunent input values. If we treat the current input values as the coordinate values of an

input point at the BPNN input space, the dimension of nihich is equal to the number of

input parameters, me can conclude that, for a trained BPNN,

-- - F(1nput - Po int) as,

Here, F stands for a fuaction.

Indeed, BPNN perfoms a multiple Iineaï regression analysis at each individual

data point to fit a non-lineu high dimension hyperplane to the training data set. The

slope value dong each dimension, dong mirh the intercept value P,,, varies Erom data

point to data point, in contrast with being constant in regression analysis. Simply put in

tnro dimension space, BPNN is capable oE fitting a flexible cuve and ail the observed

data points fidi on the line; while regression analysis can only approiamate a straight h e

chat strings up the data points with the m i a i m u amount of deviation based on least

square method.

Aside from above discussions, three other advantages of BPNN over regression

analysis are worrh mentioning:

(1) BPNN poses no theoretical constraints on data in contrast .Nith the assumptions of

least square regression and the required residual analysis in regression analysis

(Levine et al, 1997).

(2) BPNN supports more than one output in input-output mapping in conttast with

only one output in regression anaiysis.

(3) BPNN reLz~es the requirements of data in terms of both quantity and quality in

contrast with regression analysis. That means BPNN is capable of non-linear

mapping with only a very limited quantitg of obserc-ed data points and is tolerant of

noisy data (inaccurate or incornplete data).

Table 4-1: Data Set for Testing BPNN and Regression Analysis

Output

In order to illustrate the cornparison of BPNN and regression analysis, we

studied the input sensitivity of BPNN trained on an &cial data set with 4 inputs, 1

output and only 10 records as shomn in Table 41. The BPNN mode1 has four input

parameters, 1 output variable, and one hidden layer with three hidden nodes, wliich is

detemiined based on trials. The leaming rate is 0.8 and the momenturn is 0.3. Standard

Error of the estimate in regression analysis is a measure of variation around the fitted

line of regression and is cdculated as a measurement of accuracy to compare the

performances of tmo techniques. Standard Error is actudy a slight variant of the global

enor tenn E in BPNN as (3). After achieving satisfactory training (standard error of the

NN output is reduced to 0.00158), we calculated the partial derivative values of the

output variable over each input parameter using (16) at various input points. n i e results,

as shown in Table 4-2, indicate that for a specific input parameter, the slopc value over

the output variable varies svith the input points. In order to analyze such variation, a

Monte Carlo stmulation is performed at the BPNN input space to observe the statistics

aNn value for each input parameter. In each simulatioa w, an input point is of -

randomly generated in the BPNN input space and triggers a BPNN r e c d process. A

slope value of each input parameter over the output variable is calculated. If the number

of simulation runs is large enough, we c m assume we d traverse the entire BPNN

input space by interpola~g. A program in MS VB and Access is developed to perform

the Monte C d o simulation exi~eiiments for 1000 iterations. The resultant Probability

Density Functions (PDF) of slope values for the four input parameters are shown in

Figure 4-3 and the statis tics ;ire sumrnarized in Table 4-3.

aN, Table 4-3: Statistics of Partial Denvative (Slope) Values: (-) ~ S P

3Nl Table 4-2: Partial Derivative (Slope) (-) at Four Input Points at NP

BPNN Input Space

Input Factor

Index @)

(9 1

7 - 3

4

Input Factor

Index @)

(1)

1

7 - 3

4

Point

(0.5,0.5,0.5,0.5)

(2)

-0.1594

0.8915

-0.1685

0.9974

Point

(0.9,0.9,0.9,0.9)

(4)

0.22 69

0.3267

-0.31 69

0.2878

Point

( 0 1 , 0 1 0 1 0 1 )

(3)

-0.3057

0.26 1 3

-0.0398

0.4799

Maximum

(2)

0.9797

1.9502

0.4833

2.2255

Point

(0.2,0.4,0.6,0.8)

(5)

0.1115

0.3917

0.3302

O.1G11

Average

(4)

-0.01 51

0.5769

-0.2678

0.6365

Minimum

(3)

-1 .O366

0.0042

-2.1053

0.003 1

Std. Dev.

(5)

0.3863

0.4038

0.5489

0.5064

95% Confidence

Interval

(6)

-0.0390 - 0.0089

0.5518 - 0.6019

-0.3018 - -0.2338

0.6051 - 0.6679

Figure 4-3: Distributions for Input Sensitivity

A regression analysis is conducted on the same data set of 10 observations in MS

Excel. The results are that the slope of the tirst input parameter is 0.1217, the slope of

the second input parameter is 1.0141, the dope of the third input parameter is minus

0.5925, and the slope of the fourth input parameter is 0.5509; the intercept is minus

0.03054. Note that those slope values are constants in contrast with distributions as

obtained &om BPNN. The standard error based on the outputs of regression analysis is

as high as 0.1285 compared Mth merely 0.00158 of BPNN.

In short, BPNN outperforms regression analysis by a significant mugin in our

experiments, which agrees with the previous analysis and comparisons.

The simulation results reveal disuibutions of slope data for BPNN, which take

various shapes (Fig. 3). If the actual distribution of input sensitivïty to be encountered in

operations is available, cornparison of the actual distribution nrith the conesponding

Monte C d o distribution obtained from BPNN can serve as an effective means for

mode1 validation. However, in most real BPNN applications quantitative information is

unavailable to fit such actual distributions of input sensitivïty due to the complesity of

the engineering or management problems being solved. This is also the reason of

choosing BPNN insiead of other conventional mathematical models in the £ k t place.

An experienced domah expert may also have difhculty figuring out such distributions of

input sensitiviv on a subjective basis, because the deusion process generally relies on

assessrnent of the entire input scenario and there are so many interacting factors. The

domain experts may share some cornmon hunches about the probability of increasing or

decreasing the output variable mith a certain adjusanent of an influencing factor. But the

amount of adjusment is generally very subjective depending on the lapur scenario and

persond e-xperience and temperarnent.

Therefore, instead of fitang distributions, statistical analysis of simulation resdts

involves calculatlig 5 percendes of the slope variable for each input parameter, i.e. the

lochh, 2Sh, 5oLh, 75th, and 90". The input sensitivity of di input parameten is summarized

and presented in a tornado-fie graph as ilIustrated in Figure 4-4 for the piping

fabrication labor productiviq BPNN model. The horizontal asis represents the relative

input sensitiviy as d e t e k e d by (17), i.e. output response (negative or positive) nith a

change of 10% relevant range in an input parameter. The vertical mis is the basellie

coreesponding to no output response or zero change in output. Five short vertical bars

correspond to each input parameter representing respecuvely the five percentiles f?om

left to right, reflecting the central trend, the spread, and the shape of the obsenred slope

data dismbution from simulation. The guidelines for i n t e r p r e ~ g the graph and

sim-dation resulcs are listed as below:

The leftmost bar ( lOh percentile) being to the left of baseline represents that the

chance of the slope value for the corresponding inpur parameter being posiave is

above 90%, or with increase of the input value the probability for the output value to

increase is 90%.

10. How Busy

1 1- Drawing Revision

12. Priority Rushed Spools

13. Reworked Spools

14. Material Problems

15. Drawings Late

16. % night shift

17. % overtime

18. % extra

19. % apprentices

1 - - - - - - - - - - - - - - - - - - -l--.l--l -#- - - - - - - - - - - - - - - - - - - - - - - - -

1 - In Line Fitting per Ft

Non In Line per Ft - - - - - - - - - - - - - - - - - - - - - - - - - I-i--t . . . . . . . . . . . . . . . . . . . .

- - - - - - - - - - - - - - - - - - - - - - - - - q ( - i -1- - - - - - - - - - - - . - - - - - - - . -

Figure 4-4: Sensitivity Analysis of Spool Fabrication BPNN Mode1

l - per - - - - - - - - - - - - - - - - - - - - - - - , - 4. s ~ p p o n per ~t

- - - - - - - - - - - - - - - - - - - - - - - - - 5. Flange per Ft

1 1 - 1 - -1 - - - - - - - - . - - . . . . - -

-11 -1- -1- -1- - - - - - - - - - - . - - - - - - -

- - - - - - - - - - - - - - - - - - - - - l - - 1- .l- -1- - - - - - - - - - . . - . - - - - - - - - - 6. Mlt Stn RW %

The rïghmiost bar ( 9 0 ~ percentile) being to the rïght of baseline represents that the

chance of the slope value for the conesponding input parameter being negative is

above 90°/o, or mith increase of the input value the probability for the output value to

decrease is 90%.

The 25& and ~5~ percentiles can be explained in a simiL21: manne= as the 1 O I h and 9oKh

percentiles according to the relative positions of the conesponding bars to die

baseline in the graph.

The middle bar (50th percende) riding on the baseline represents chat the chance for

the output variable to increase or decrease is 50%.

An input parameter with a dope dismbution clustering around the basellie has less

effect on the output variable than that with a slope disuibution distant &om the

baseluie. Thus, the magnitude of input sensiüvïty can be inferred Erom obsenvlg the

absolute values of percentiles as well.

Note that the statistical descriptors (percentiles) are based on simulation samples

rather than the entice population. However, the sample size is assumed to be large

enough (10000 runs to draw Figure 4-4) to traverse the input space of BPNN, and

the confidence interval estimates are rather tight, hence the statistical descriptors

based on the samples can represent those for the population.

The proposed sensitivity analysis method is of stochastic nature because of

independent mals for BPNN aainlig (such as initialization of network parameters,

hidden layer structure, and local optima) and Monte Cado process. If BPNN training

is achieved and the simulation iteration is large enough, the results for most input

parameters are stable in temis of direction and magnitude of input sensitivity, escept

for a couple of input parameters smapping sides nrith respect to the baseline fiom

trial to trial. 4 semi-optimal BPNN mode1 can be determined by selecbng the nial in

mhich input sensitivity of major input panmeters makes sense o r is agreed upon by

the domain e-xpert.

In case b a t the sensitivity of one input parameter dways takes the opposite direction

in the tomado graph comparing against domain es~ert 's esperience or common

sense, the dehi t ion and data collection procedures for the input parameter dong

mith the data itseli shouid be carefdy reexamined for s h o n f d s before the input

parameter is dropped out of BPNN analysis.

The sensitivïty analysis of BPNN as described in the previous sections is applied

to andyze a BPNN mode1 for esthating labor production rate o f pipe spool fabrication

in the fabrication facility of PCL Indusuial Constructors Inc, mhich is one of the largest

and most modem pipe fabrication and module facilities in Western Canada.

Spool Fabrication Basics

A pipe spool is a portion o f piping system consiseng of various piping

components, such as flanges, elboms, reducers, tees, supports, and pipe. These items are

prefabricated into d i s ~ c t assemblies thar are later assembled together as part of an

industnal plant or production skid/module. Such prefabrication is usuallp performed

under controlled shop environment iocated away fiom the actual project site, which

doms for better productivity and quality control, and hence cuts the field labor costs.

Major spool fabrication processes, such as cut, bevel, fit, weld, and handle

sections of pipe and fitthgs, tends to be labor-intensive. Productivitg dam is coUected for

63 projects completed 6-om 1995 to 1999, d k g which period the technologies and

machines for welding and cutang in the shop remain relativelv stable. The productivky

studies of spool fabrication is suitable to the unit-cost estimating method, in which labor

production rates must be independent of equipment use and v q among projects o d y

because of differences in labor productivity (Parker et. al., 1984).

Due to the variation in size, wall thickness and con£iguration of each individual

spool, a special unitkation scheme is utilized in the Company to quanti9 the various

work items uniformly into an abstract unit of measure called "Fabrication Unit" or

"Unit" on the basis of weld inches of standard wall thichess pipe. Quantity of non-

welding work items such as cutting, bevehg, handling pipe and fittings, installing

supports are also converted into "Units" by applying corresponding empirical factors Ui

the scheme.

Factor Identification and Data Collection

The labor hours per fabrication unit become the focus of investigation, wtJch

ranges L-orn 0.1 MH/Un.it to 0.5 h~fH/Unit in the collected historical data. The unit labor

hous fluctuate from job to job due to a number of quantitative and qualitative factors,

indudiig the complelacg of spool confguration, the material components in fabrication,

the stringency of quality control, spool dra~ving qualiq~, the amounts of night shift yid

ovenime, extra work, crem esperience etc. The environmental efçects and management

factors are not considered as significant factors because of the connolled shop

environment and consistent policy and personnel of management during the period of

inves~ation. 19 input parameters are idenaed as listed in Table 4-4.

Table 4-4: Input Factors of Spool Fabrication Labor Productivity

NN Input Factor (2)

In Line Fitting @CS) pe Foot of Pipe in Spool Non In Line Fitting @CS per Foot of Pipe in Spool Valve @CS) per Foot O

Pipe in Spool Support @CS) per Foot O

Pipe in Spool Flange (pcs) per Foot O

Pipe in Spool CIIulti-S tauon Roll Welc inches / Total Roll Welc Inches Repair Rate Radiograp hy Tes, Requirement Non CS Units / Tota Units

<hop Work Load

Drawing Revision Rate

Prioritg Rushed Spools

Rework Spools

lulaterial Shortage Problems Late Drawing Issues

Night Skift hWs / Total blHs 3ver Time bfHs / Total bfHs Zxtra Work MHs / Total rvms Qpprenticeship MHs / rotal MHs

Data Source (3)

M a t e d Track. sys.

Material Track. S YS.

Material Track. sys.

Material Track. sys.

Material Track. sys.

Weld Track. Sys.

Weld Track. Sys. Weld Track. S y s ,

Weld Track. & Matenal Track.

S YS.

Questionnaire

Questionnaire

Ques tiomake

Questionnaire Quesuonnaire

Payroll Sys.

Payroll Sys.

Payroll Sys.

Payroll Sys.

Remarks (4)

h ratio indicatkg the average length of pipe sections in spool h rauo b d i c a ~ g comple'üty of spooi c o n w a tion h ratio indicating complesity of spool configuration h ratio indicating complexity of spool configuration A ratio indicating comple-uty of spool configuration Multi-Station Roll Weld requires extra handling between weld stations

An index of crew's proficiency A n indes of qualis. control sbingenq by specs.

Non CS component in fabrication requires estra :are in storage, hancilhg and weldïng

A 5-point rathg based on shop workload in lnits and no. of concurrent jobs indicating how 3usy the shop was. A 5-point ratbg based on percent of revised

4 5-point ratkg based on percent of rushed ipooi due to client pnoety ~ i d i C a ~ g shop work jchedules. 1 5-point rating based on percent of reworked ;pools due to drawing errors and quality defects i 5-point 1 a ~ g on efficient); of material supply i 5-point rating based on percent of late spool irawhg issuance by client that impacts kbncâtion Gght S M affects labor productivity

3ver Time affects labor productivity

3 m a Work affects labor productivity

Velder qualification sys tem affects labor xoductiviq: Apprentice vs. Journeyman

Data is collected fiom the company's various transaction systems induding labor

cost tracking systern, weld aacking system, pagroU system, material tracking systern. In

order to ease the burden of data gathering and ensure high quality of data, a histoncal

project data marehouse is custom-developed using Mcrosofi hccess and VBA to

integrate ram data Erom different transaction systems and automate the validation of raw

data and the calculauon of productivity in£ormauon. Because data is unavailable in

cunent transaction systems of the Company for such factors as the draming revision rate,

late drawing issuance, materid shortage problems, quanticy of remorked spools, quantity

of nished spools due to prioriy, shop work load data, a questionnaLe survey is carefully

designed and conducted nrith the support of the Company management. The key

personnel involved in the projects UicludLig shop supe~tendents, project managers and

coordinators, QC staff, and welding foremen are interviewed to help recall some facts

and gather the needed information.

BPNN Training and Sensitivity Analysis

A total number of 70 records are compiled and used to train a BPNN mode1

nrith 19 input nodes at the input layer correspondïng to 19 input parameters, 19 hidden

nodes at the middle layer, and 1 output node nt the output layer that is the unit labor

hours. The number of hidden nodes can be detemJned based on trials; BPNN learning

is found to be unsusceptible mhen the number of hidden nodes is close to the number of

input nodes. The leamïng rate is 0.4, the momenturn is 0.1, and sigmoid transfer

h c t i o n s are used in hidden and output nodes. After satisfactory training (standard enor

of the output is 0.00143), the Monte C d o based sensitivitg anaiysis is performed on the

matured network for 10000 simulation runs. Note that Equation (17) is used to

determine the input sensitivity, which is based on the change of 10% of relevant input

range.

Several independent tnals fiom B P N N training to the sensiuvïtp analysis are

conducted on the same data set. The best trial, in which the input sensitivity of most

factors folloms the same trends, as determined by ex~erienced domain e-xperts, is shomn

in Figure 4-4. An examination of Figure 4-4 reveals the relationships berneen the

influencing factors and the fabrication productivity, mhich are generahed by BPNN

through obserring histoncal project data in the past 5 vears. For exarnple, factor 1 is

about in line f i b g pieces per foot of pipe in spool, which indicates the average length

of pipe sections in spool. According to our domain esperts, in line f i d g s , such as

unions, couplings, swages, reducer etc sre used to connect pipe sections in a straight line

without nims or branches. Thus, the more in line fitting pieces in spools, the more smali

sections of pipe in spools, and the easier to handle the work. From Figure 4-4, BPNN

detemiines the chances to decrease labor hours per unit mith the increase of this ratio are

about 78% and agrees with the trend identiiied by domain esperts. Factors 2 to 5 are

four ratios indicating the complesity of spool configuration. By our domain esTerts, the

higher such ratios, the more comples the spools' configuration, and the tougher to

fabricate the spools. From Figure 4-4, the dominant trends of the four ratios are all on

the plus side, *ch matches the elrperience of our domain experts. It is also observed

fiom Figure 4-4 that factor 18 (extra morli percentage) is relatively tightly enveloped

around the baseline, which indicates that estra work is aot as dominant as other factors

130

in conmbuting to the variance in unit labor rates. The explanation cm be pardy

attributed to the fact that the arnount of estta work more directly impacts the efhciency

of administration or management than the producàvity of crem on the shop Boor. Other

input factors can be interpreted and validated in a similar marner, and are not elaborated

further due to space limit.

Model Testing and Validation

In particular, the effect of matend srpe of spool Fabrication on the labor

productivï~ is tested based on the BPNN model, because material s.pe (carbon steel,

stainless steel, alumïnum etc.) is a major consideration of an industtial estimator in

adjusting unit labor hours of spool fabrication. The labor production rate of non-carbon

steel fabrication is ernpirically 1.5 àmes the rate of carbon steel in company's business

guidelule. 24 records La the data set wïth 0% non-carbon steel component (100% carbon

steel fabrication) are selected as testkg records. In the nest step, for each testing record,

only the input parameter of non-carbon steel component is changed Erom 0% to 100%

mith other parameters intact. Those testing records are fed to the nemrork and let BPNN

recall the output, i-e. the unit labor rates for non-carbon steel fabrication. The output

Erom BPNN is compared against the original output of each record, i.e. the unit labor

rate for carbon steel fabrication. Based on the test results in Figure 4-5, BPNN increases

the unit labor hours on 75% of the records; the amount of decrease for 5 records, i.e.

No. 1, 2, 5, 6, 9, is rektively small compaEng with the amount of increase for othee. If

the sample size is luge enough, the percentage should corne close to about 9O0/0, as

obsemed bom Figure 4-4 for Factor 9. O n average, the ratio of non-carbon steel labor

Test NN Sensitiviîy By Changing Material Component from 100% CS to 100% Non-CS: 75% Records increase, Avg. Ratio 1.38

1 + Actual(100% CS. 0% Non-CS) a NN Output (0% CS. 100% Non-CS) 1

O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Rec. No-

Figure 4-5: Testing Sensitivity of BPNN to Material Type

rate over carbon steel labor rate is 1.3, which is close to 1.5 irr the guïdeline.

Note that the guideline gives an average number (1.5) in consideration of

matenal type only, mhiIe BPNN is able to figure different numbers for different

scenarios taking into account 19 relevant factors. In short, a BPNN-based decision

suppoa tool d be more sophisticated and intelligent than the uaditiond business

guideline.

The model validation approach of BPNN based on the proposed sensitivity

analysis is superior to the conventional validation approach of testing the mature

nenvork with an independent data set, in that such sensitivity analysis enables the

modeler to understand the rationale of BPNNYs reasoning and have a pre-knowledge

about the effectiveness of model implementation in a probabilistic fashion.

The insight into the BPNN model gained h-om the proposed sensitivity anaiysis

method gives the user more confidence in the BPNN's prediction, hence faciLitates the

implementation of BPNN-based decision support tools. The success of our indusmd

application in estïmating labor productivity of spool fabrication esceeded our initial

expectations. Not only does this new method prove to be effective in addressing

problem domains in which BPNN has been applied, but also it potentially malces BPNN

app ealing to new engineering or business applications.

Carrol, R.J. and Ruppert, D. (1 988). TranJfomntion alrd EVe&hting in Regssion,

Chapman & H d , New York, NY.

D har, V. and Stein, R. (2 997). Inte/hgent De~ikon SIlpport Sy~tems: The S~ieim of

Kplowlec&e IVork. Upper Saddle River, Prentice-Hall, Inc., New Jersey.

Flood, I., and Kartarn, N. (1994). "Neural networks in civil engineering: systems

and applications ." 3. Const~. Engrg. And~\/rgm&., ASCE, 124(1), 18-33.

Knomles, P. (1 997). Pr*icting L b o r Pmdztctiui. Using Nermd Ne~works. Mas ters of

Science Thesis, University of Alberta, Edmonton, AB.

Levine, D. My Berenson, M. L., and S tephan, D. (1998). Statihir )r Ah~zugcr~

zmkg L V I ~ ~ J - O ~ EXCEL, Prentice-Hall, Inc., Upper Saddle Rive, New Jersey.

Li, Y-, Shen, L. Y., and Love, P.E.D. (1999). ''ANN-based mark-up estimation

syscem nrith self-esqhnatory capabilines." JomvaI of Corirtn~ctian Engizeeting U I I ~

fVImagenzent, ASCE, 125(3), 155-189.

bfukherjee, A., and Deshpande, J.M. (1995), "hlodeling initial design process

using yàftcial neural nenvorks", joz~maI Conputing in CIMI Engimenig, ASCE, 9(3), 1 9 4

200.

Murtaza, M.B., and Fisher, D.J. (1993), 'Weuromes: Neural Nemork Systern for

EvIodular Construction Decision Making'', jo t~r~zd Co7rpzlcing NI Civil Eemering, AS CE,

8(2), 221-233.

Shi, J. (2000). "Reduüng prediction error by transfomiing input data for neural

networlis", Jouniai C o m p u ~ g in Civil Engineering, ASCE, 14(2), 109-1 15.

Sinha, S. K. and M c I b , R A . (2000). "Artifidai neural network for measuPng

organizational effectiveness.", Journal C o m p u ~ g in Civit Engineering, ASCE, 11(1), 9-

14.

Parker, AD., Barrie, D. S., and Snyder, R. M. (1984), Planning and E s t i r n a ~ g

Heavy Construction, McGraw-Hdl, Inc., New York, NY-Portas, J., and AbouRizk, S.M.

(1997). Neural Netsvork Modd For EstunaMg Construction Productivity. J of Corn-t~

Engrg. dN Mgmt., ASCE, 123(4), 399-410.

Refenes, AN., Zaprnis, AD., Connor, J.T. and Bunn, D.W. (1995). "Neural

Netsvorks in Invesment bIanagement". IfzteZhgerzt Systestns for Finance m d Bz~s~Iz~J'J', S.

Goonadake, and P. Treleaven, eds., John Wiley & Sons Ltd, , Chichester, EngIand,

177-209.

Sayed, T., and Razavi, A. (1999). "Cornparison of Neurd and Conventional

hpproaches to Mode Choice Analysis" Joiird oJ Compz~ling in Cid Enginehg, ASCE,

14(1), 23-30.

Widrnan, L.E., and Loparo, KA (1989). " i M ü a l intelligence, Simulation, and

modeling: a critical survey", Art@&/ inteihgence, nimztiatio~ and modeLing. L.E.Widman, I<.A

Loparo, and N.R Nielsen, eds., John Wilev & Sons Ltd, New York, NY, 1-45.

Chapter 5: Conclusion and Recomrnendation

In conjunction with a major indusuial contractor of Canada, the thesis research

conducted case studies on the theoretical basis and practical considerations for

measuring and analyzing labor productivity in i n d u s d consmction. Two important

activities of process piping were investigated: pipe installation in the field and spooI

fabrication in the fabrication shop. The p r i m q objective of research iç developing

ANN-based esha t ing tools to offer estirnators valuable information about labor

productivity in bidding new jobs, because estimating labor productivity is one of the

most difficult aspects of preparing an estimate, or a control budget based on the estimate

for labor-intensive activities in industrial construction. ArtXcial neural netsvorks are

capable of sortkg out hidden patterns and e s l x a c ~ g predictive information from

cornplex data sets, and nrere proven to be effective in both uncertaïnty analysis and

sensitivity analysis of coosttuction labor productivity in the research. The thesis research

has addressed: (2) how to quanti* labor productivity in industrial construction fiom a

contractor's point of view; (2) how to measure acmd labor productivity in industrial

construction based upon on-site control practices; and (3) how to ualize M c i d Neural

analyze the labor production rates and the

sensitivity of identifïed influenckg factors.

Productivity Studies and Data Collection

The thesis research reviewed current estimating practices as applied to the

involved Company and generalized special methods utiIized in practice for the

quantification and measmement of labor productiviq in industrial construction. The

input factors that cause the varkbility in the productivity for studied activities were

identified through literature review and consultation with es~enenced domain experts at

the involved Company. With the support of the company's management, two data

nrarehouses were custom-developed for field pipe installation and shop spool fabrication

respectkely to iritegrate the corporate management systems of e s t ima~g , production

resources pIanning, quality control, and labor cost control. It should be mentioned that

questionnaire surveys were carefdy designed and conducted to collect some qualitative

and desuïptive information that is not obtainable Ecom the company's reportkg and

a c c o u n ~ g systems. Eqerienced supe~tendents, project managers and eschators of

the involved Company mere interviewed to help recall some facts and gather the needcd

information. The data warehouses provide solid platforni of integrated h i ~ t ~ a d data

from which to validate novel ANN models and develop ANN-based tools for

productivity analysis.

Probabilistic Neural Network Modeling

The thesis research derived a probabilistic neural network classil5cation model

cded the Probability Inference Neural Network (PINN), mhich is based on the same

concepts as those of the Learning Vector Quantkation (LVQ) method combined with a

probabilistic approach. The PINN model was intended to overcome limitations of other

137

neural netmork models and mas developed for predicting labor production rates for

indusmal consmcüon. The thesis presented and explained the topology and algorithm

of the PINN rnodel in details. Portable computer sofnvare was developed to impiement

the aWiing, t e s ~ g and recall for P m . PINN was tested on real historicd productivity

data at the involved Company to analyze the degree-of-difficuly factor of field pipe

installation productivity and compared to the classic feed fonvard back propagation

neural netmork model; thïs showed marked improvement in performance and accuracy.

The PLNN model creates a meaningful representation of a comples, real-life situation in

the problem domain and in general is effective in dealing with high dimensional input-

output mapping with multiple influential factors in a probabilistic approach. The

application of the PINN model Ln industrial labor production rate e s t k a ~ g gives an

estirnator a better understanding of the project information available and the possible

outcomes that could occur. Because the response of PINN is in the form of a

probability density h c t i o n (dismbuuon) a t the output range, an estirnator WU be able

to deüde on the degree-of-difficulty factor for a future scenarïo by combining the

PINN's recommendation with personal judgment.

Sensitivity Analysis of Back Propagation Neural Networks

Validation of a NN model has thus far relied upon measuring accuracy of the

calibrated netsvork to an independent testing data set that are hidden Erom the neural

nenvork in leaming. A NN model's sensitivity to changes in its parameters is generally

probed by t e s ~ g the response of a mature necwork on various input scenarios. The

thesis research also investigated the classic back propagation NN algorithm to study the

effect of each input parameter or influencing variable upon the predicted output variable.

The input sensitiviv of back propagation NN is defïned in esact mathematical terms in

Light of both normalized data and ram data. The diffe~ence betmeen back propagation

NN and regression analysis of statistics is discujsed and the sophistication and

superioriv of back propagation NN over regression analysis is h t h e r demonstrated in a

case study based on a smail data set In addition, statisticai analysis of input sensitivity

based on Monte Carlo sirnulauon enables the modeler to understand the rationale of

back propagation NN reasoning and have pre-knomledge about the effectiveness of

model implernentation in a probabilistic hshion. The sensitivity analysis of back

propagation NN was successfully applied to analyze the labor production rate of pipe

spool fabrication at the involved Company. Important aspects of the application

lnduding problem defkition, factor identification, data collection, and model testing

based on real data were discussed and presented in the thesis. The model validation

approach of back propagation NN based on the proposed sensitivity andysis is superior

to the conventional validation approach, in which the mature nemrork is tested with an

independent data set and the modei's sensitivity is probed through obserwig the output

with respect to changes in input based on a lirnited nurnber of scenzuios. The insight into

the back propagation NN model galied from the proposed sensitivicy analysis method

gives the user more confidence in the back propagation NN's prediction, hence

facilitates the implementation of back propagation NN -based deùsion support tools.

Not only does this nem method prove to be effective in addressing problem domains in

which back propagation NN has been applied, but also it potentidy makes back

propagation NN appealing to new engineering or business applications.

Conclusion

The problems addressed in the thesis research were idendied through

investiga~g the m e n t estimating pracuces in industly and understanding the real

concems of indusw professionals. Emerging computer modeling techniques such as

data marehouses and ANN mere researched Erom an academic perspective and

implemented in industry to meet mith the challenges. The proposed novel ANN models

and developed decision support tools nrere validated using real data from indus- and

s u c c e s s ~ y applied to assist estimators in deading on labor production rates for new

jobs. The esperiences and lessons learned h m the successful, productive and mutudy

beneficial collaboration betnreen academia and industry throughout the thesis research

dl potentidy serve as a mode1 to guide other university-industry joint research projects

in the future.

There are a number of issues that need to be addressed in greater detail in the

fu tue,

Quantification of Textual / Descriptive data

Three input data types are used to define NN input factors in the thesis, i.e.

"Rad', "Rank", and "Binary". "Raw" is used sïmply for quantitative input factors, like

general expense ratios, winter construction percentages, or quantities of work. "Rank" is

used to conven subjective factors, like crew ability raùngs, into numeric format. And

"Binary" is used co group texmal or descriptive factors into numenc fonnats like matenal

1.10

type and project defuition. It should be noted XI input factor of the "Ram" or "Rank"

tppe corresponds to one input node at the input layer, while an input factor of the

"Binary" type corresponds to a number of input nodes depending on the number of

groups for the factor. %Binary" data -pe satisfies the cornputing requirements of neural

netmorks for converting textual or descriptive data, however, some disadi-antages

associated mith "Binaxy" data may affect the performance and sensitivity analysis of

neural networks.

First, increased dimension of NN input space caused by "Binary" data type

increases the complesity of network smicture and the quantity of netrvork parameters.

Based on experimentations and observations, the PINN mode1 is not very susceptible to

the increase of the N N input space dimension, homever back propagation NN does

suffer in terms of leaming t h e and generalization ability Nith the increase of input

dïmensionality. The generalization ability is not guatanteed to irnprove, but chances are

very high that the learning Üme wilI increase considerably.

Secondly, the input sensitivity of back propagation neural nenvotlcs is de6ned for

each NN input node. A change for an input factor of '%inary" data type entails changes

in more than one input nodes of NN. Thus the input sensiuvity for an input Factor of

"Binary" data type must take into account the combination effect of involved input

nodes. What input nodes are involved depends on hom the change is made. For

esample, suppose four different material w e s are considered, conespondmg to four

NN input nodes, a change kom type 1 (1000) to type 2 (0100) trïggers changes in the

fïrst and second NN input nodes; while a change Lom type 1 (1000) to type 3 (0010)

%ers changes in the hrst and thitd N N input nodes. Note tliat the input sensitivity of

back propagation hW for one input node is not a constant value but a distribution, such

combination effect makes it difficult to esp1,a.h the sensitivity of an "Binarp" type factor.

Fortunately, there is no such "Binary" type factor in spool fabrication

productiviq analysiç where the sensitivity andysis was tested. For the field pipe

installation productivïtg analysis, an esperïment was conducted to treat such "Binary"

factors such as material type and project type as "Rank" factors. Various groups in each

factor were ranked on a 5-point scale by their relative difficulty based on the judgment of

domain expert such that a unit increase in the corresponding NN input node codd

represent the increase of degree-of-difhnilty factors. The results of the esperknent are

satishctoiry and the input sensitivity follows the correct direction for most factors.

However, the dran-back of such a heuristic method is that sometirnes even the domain

esTerts found it hard or impossible to weight the relative difficulty and rank each group

in a factor in a sensible way.

In short, more sophisticated methods such as &zzy set theory may be researched

and introduced into NN to convea textual or descriptive factors into numeSc formats.

Optimization of NN Structure

NN structure m d y concerns with the middle layers, for instance, the number

of hidden layers and number of hidden nodes in each for a BP NN; the number of

processing elements assigned to each output zone at Kohonen layer and the setup of

output zones for a PINN model. The determination of NN sarucme relies heavily on a

mal-and-enor based process, in which cornparhg the NN's outputs nrith actual outputs

on an independent tesMg data set serves as a yardstick for ju s t iwg the structure. Such

optunization of NN structure tends to be hampered due to factors such as the stochastic

processes involved in NN leaming, the existence of multiple local optima in search of

the NN intemal parameters, noise mithin leamïng data set, values of leaming rates and

m e s of data transfer functioas

One appealing solution is to obtain the acnial distribution of input sensitioiv for

key input factors (if not dl) to be encouncered in operations. Matching the

conesponding Monte Cario distributions obtained fiom BP hW to the actual

distributions can seme as an effective means for optimization of the NN structure, in

addition to validation of the NN model as discussed in Chapter 4. Hence, gathering

quntitative information to fit actual disnibutions of input sensitivity could be included

as part of data collection for NN applications in the future if both data and resources are

available.

Sensitivity Analysis of PINN Mode1

In the thesis, the PINN model's sensitivity to changes in its parameters is sâll

probed by tesMg the response of a manire n e ~ o r k on various input scenarios. One

approach that have been tried is to take advantage of the sensitivity- analysis method for

BP NN as proposed in the thesis to infer the input sensitivitg for a PINN model under

the following conditions:

1. The BP N N and PINN are trained with the same leaming data set and tested with

the same t e s k g data set, and both models are satisfactorily trauied;

2. And the point-value predictions of the BP NN and those of the PINN mode1 for the

testing data set are very close.

Thus, it can be assurned that the tnro models would "think alike" and have

common input sensitivity for a pa15cular input factor.

Table 5-1 shows the resulrs of five teshng records based on the training data for

spool fabrication product i~ty after PXO models have satisfied the abore conditions.

Table 5-1: P ï N N vs. BP NN

It is noted that the &st condition is not hard to satisfy, but the second condition

rnay oot be readily met The BP NN and PINN may require to be trauied repetitively

using different smictures and leaming parameten in order to satisfy both conditions.

BPNN

0.239

O. 156

0.221

0.1 57

0.286

In the hure, it would be perfect if an independent approach could be found to

explain the input sensitivity of the PINN mode1 analyticaily.

PINN

(Mode)

0.205

0.145

0.235

O. 1 45

0.265

The applications of AI\TN in e s t i t n a ~ g labor productivity of indusnial

consmiction prove that -ANN is effective in addressing the complesity and requiremenrs

in the problem domain. It is hoped that the contributions made in the thesis research

m d l make MW appealing to more engineering or business applications in the hture.

&PEND= A: USER'S MANUAL FOR PINN TRAINER

Probabilistic Inference Neural Nenvork (PINN) trainer is a genenc neural

nenvorli training and testkg program developed based on a new NN scheme as

proposed in Chapter 3 of the thesis.

Step 1. Prepare data and import data into trainer

The last column in a data table must be named as "Status", which hgs the

training/testing statu for each record. Status 1 stands for a training record, and Status 2

for a testing record, and Status O for an ignored record. The nest-to-last column in a data

table must be named as "Output", storing Actual Output Values of the target nsLy

variables such as actual production rates. Ali the rernaining columns in a data table d

be the input factors and no requirements are imposed on the narnes and relative order of

columns. The trainer nrill automatically count the number of total inputs and read in

data.

The prepared data table for PINN must be imported to the database file

'T1INN.mdb7'.

Step 2. Give a unique identifier key for a new training-testing trial

A unique identifier key is used to dis~guis1-i each training-testing scenario or

trial, whïch is de6ned by the data source table to use, training / testing records within

the data, the setup of the output zones, trnining parameters, and number of training

iterations. hTaming convention requires no space in the key and numbers and short tests

are dowed such as cc081899aWeld".

For a previous trial, user can pick out the identifier key hom the drop-domn List.

Next, user may click the buttons on the switchboard to check trzining results

Figure A-1: Select an identifier key of one previous trial

("Check-Train" button), check t e s ~ g result ("Check-Test" button), and check global

report about training and testing ("Global Report" button) as shown in Figure A-1.

For a new &al, user needs to in a new idenfier key in the Identifier Key bos

first. And then click "T~ain-Test" button on the switchboard to activate the program.

Step 3 Select data table, edit training / testing status and setup output

zones

- -

Figure A-2: User select~ data table

User selects one data table fiom the &op-dom list of "Data Table Name" &sst

(Figure A-?), and clicks the "Edit Stanis: Trah or Test" button to Bags training and

r e s ~ g records (Figure A-3). The trainer d read in data and display the maximum and

minimum of the output values for user to setup the output zones.

Figure A-3: Flag status of records

Setting up the output zones properly- and adequately is crucial to PlNN's

performance. Too wïde zone widths won't be adequate to help user make deasion, while

too nanom zone midths d probably sacrifice the accuracy of PINN's prediction. The

Çollowing two issues should be taken into account:

- Pression requirement of user. Here is a heuristic fonnula to appro-uuriate zone

wïdth:

Zone Width= 0.4*0utpurRange*Ac~~1:aqThreshold

- Distribution of actual output values over the output zones. A uniform distribution

generally yields better results.

Two approaches are avdable to set up the output zones:

1. User speuhes the number of output zones only. The trainer will evenly divide

the actual output range into the number of output zones as user has specified, and

automaticdly determine lower bound, upper bound, and mid value for each output zone.

2. User speuhes the lower and upper bounds of the output range and the width

of each zone as well. The trainer d start from the lower bound of output range and

detemine the boundaries of each output zone, und the upper bound of output value

range is esceeded.

Step 4. SpeciQ structure and learning parameters for PINN

Following the setup of output zones, user shifts focus to the next page to speÙS

a number of structure and leaming parameters for PINN iccluding the scale max and

151

min, the number of processing elements per output zone, the attraction rate and

repulsion rate and conscience hctor for leanllng, the smoothing factor for kemel

hc t ion , and the accuracy threshold for performance rneasurement Figure A-4 shows

the program screen, user may take the default values or set new values for those

parameters. Refer to the technical paper and online help for detailed explanatioas of

Figure A-4: Setup structure and learning parameters for PINN

those parameters-

Step 5 Speciw training itetations and train-test PINN

Folloming settïng the PLNN parameters, user shifts to the nest page to spec*

Figure A-5: Specify training iterations and train-test PINN

the training irerations by enterkg the "No. of Train Epochs", as shown in Figure A-5.

Step 6 Investigate whether the PINN mode1 has been successfully

trained

FoUowing training and testkg, user clicks the "Check-Train" button and the

"Check-Test" button on the switch board to view the results for maining data and

'1 Training Data: Actuaï VS N N -Rediction

f Training Records Probabiliîy Density Graph

10 . Mode Avg E I ~ 1 0 1 5 1

I

Figure A-6: Check training results

testkg data respectively and investigate whether the neural netmork has been

successEully trained-

The majority of training records should indicate a centralized trend and the

dismbution generated by PINN f d s in the correct output zones for their actual output

values, as shown in Figure A-6. Othemvïse, user should repeat fiom step 2 and perform

another trial using different network structure and learning parameters, or increase

leamïng iterations. Note that on the *ht side of Figure A-6, the accuracy scatistics of

point predictions are also induded for user to judge the model' performance or maturity.

User observes the tesàng data in a very sirnilar manner. Testing data speaks more in

iaining Datas Actual VS N N Prediction

. .

Training Records Probability Oensiîy Graph to

Figure A-7: Detected noise in training data

j u d p g the nenvotk's performance thaa training data because the traines bas not seen

the t e s ~ g records in the learning process.

In case that after a nurnber of different train-test m a l s , for a pmxicular training

record, the PINN indicates a very Çar-off point prediction value (mode) comparing wïth

the actual output value, or die PINN demonstrates a very dispersed dismbution as

shown in Figure A-7, such a record is likely tu be noise in the data and the data of the

record should be esarnined for errors.

Step 7 RecaU based on a trained PINN mode1

Once satisfactory results are obtained for both training and testing data, the

Figure A-8: Global report for a train-test trial

PINN mode1 is dedared to be crained and ready for developing a recd program. User

clicks the "Global Report" button to review the infomiation about this trial as shown in

Figure A-8.

If user does not want to keep a trial any more, select the identifier key for the

trial and click the "Delete Key" button on the switchboard to delete alI the data related

to the trial.

An on-Iine help is dso developed givïng details about how to use the crainer

output

M ode

m Weiphted

Average

Probabiiity

Distribution

Figure A-9: PINN Trainer on4ne help

program dong mith some technical descriptions about the PINN mode1 as shown in

Figure A-9. By selecting a category, related topics are fîltered out; user chooses one topic

of interes& the description d be automatically displayed-

APPENDIX B: USERS' MANUAL FOR FAISMASTER

FabMaster is a histoncal project data warehousing system customized for the

Fabrication Facilities of PCL Industrial Constructors, Inc. It is a n automated data

processing tool to estract raw data Gom Fabrication Resources Planning System, Wcld

Tracking System, Labor Cost Contxol System, and conven raw data into aggregate

quantiq data at spool level and various ratios of productivity, quality control and

configuration complexity at cost-center level. A cost center, d e h e d by project number,

material type and size range of spools, is the level of detail that actud labor hours were

tracked in the corporate labor cost control systern. Two levels of compilation are

involved in FabMaster to convert raw data into item-coded productivity information, i.e.

the spool level and the cost-center level. The codiag systems for material type and size

range of spools used in the Company and Fabbhstrr are shown in Table B-1 and B-2.

The item codes for spool level compilaaon arc shown in Table B-3.

Table B-1: Size Range Codes

ID

1

7 - G

16

30

O

Description

< 2"

- 7 -4"

6-14"

16-34"

30-48"

To td

Table B-2: Material Type Codes

Table B-3: Item Codes for Spool Level Data Compilation

ID Description

Iescrip tion

JO. of pipe pieces

'ootage of pipe pieces

liameter Inch Fr of pipe pieces

'ons of pipe pieces

cio. of pipe pieces longer han G ft

'ootage of pipe pieces longer than G ft

>iaIriT;t of pipe pieces longer than G ft

'ons of pipe pieces longer than G ft

JO. of Stub Ends

JO. of Branches (Olets)

JO. of Caps/Plugs

\io. of EIbows

JO. of Swages

\To. of Blind Flanges

<o. of Dummy Legs

JO. of S'&'/TH Couphgs

JO. of Lap Joint Flanges

h. of hnchors/Shoes/Slider Supports

\To. of Nipples

go. of O s c e F h g e

\io. of Reducers

\30. of Slip-on/SW/TH FLznge

<o. of Tees

\To. of Unions

L'o. of Vdves

<o. of Weld Neck F h g e s

\To. of Laterds

\To. of Pvlisc Items

No. of Flanges

No. of In-Line Fittings

No. of Out-Line Fitrings

No. of Supports

No. of Design \Velds

Diamecer Inch of Design Welds

Equivalent Diameter Inch of Design Welds

1 ItemCode 1 Description

Volume of Design \Vdds

No- of BW Design \Velds

Diameter Inch of BW Design \Velds

Equivdent Diameter Inch of B\V Design Welds

\'olume of BW Design \Velds

No. of S\V Design \Velds

Diameter Inch of S\V Design \Velds

Equivalent Diameter Inch ofS\V Design \Velds

Volume of SW Design \Velds

No. of OL Design \VeIds

Diameter Inch of OL Design \Velds

Equivalent Diameter Inch of OL Design \Velds

IToIume of OL Design \Velds

No. of Pressure Amchmena in Design Welds

Diameter lnch of Pressure Attachments in Design Welds

Equivdent Diameter Inch of Pressure Attachments in Design \Velds

CToIurne of Pressure Artachments in Design LVelds

No. of Non Pressure Attachments in Design \Velds

Diameter Inch of Non Pressure ,-îmchments in Design \Velds

Equivalent Diameter Inch of No Pressure ,.\mchrnents in Design \Velds

Volume of No Pressure Attachments in Design \Velds

No. of Positon Welds in Design \Velds

Diameter Inch of Positon \Velds in Design \Velds

Equivaient Diameter Inch of Positon \Velds in Design \Velds

\'olume of Positon \Velds in Design \Velds

No. of hidu-station Roii Welds in Design \Velds

Diameter lnch of MuIti-staaon Roll \Velds in Design \Velds

Equivalent Diameter Inch of hlulti-station Roll \Velds in Design \Velds

Volume of hiulti-station Roii \Velds in Design \cVelds

Volume ofTig Process in Design welds

Volume of &Lig Process in Design \Velds

Volume of FCAW Process ia Design \Velds

Volume of Stick Process in Design \Velds

VoIume of SubArc Process in Design Welds

Volume of Rotoweld Process in Desiga \Velds

No. of Reworked Welds

3iameter Inch of Remorked \Velds

3quivaient Diameter Inch of Reworked LVelds

Description

Volume of Reworked Welds

No. of Cut Sheet Revisions

Spool LVeight in Tons

RT percenc per Spec

MT percent per Spec

M' percent per Spec

Phi1 percent per Spec

P K " 1 /O per Spec

FT percent per Spec

BHN

\T percent per Spec

UT percenc per Spec

No. of Accepted Weids

\Veld Units in SpooI

Weight of Non-pipe in Spool

No of Spools in a matenal-size group

Step 1 Download Raw Data from Corporate Management Systems into FabMaster

S i - raw data tables of a project required for FabMaster to process are dkectly

downloaded Erom the corporate databases of various management systems in electronic

formats, namely RD-BranchPlant-SP (Spool) and RDBranchPlant-MT (Pieces) Grom J. D .

Edsvards matcrial resources planning sys tem, plus RDBranchPlant-DG (Dra\ving),

RD-BranchPlant-SC (Spec) , RDBranc hPlant-WD (Weld De tails) and

RDBranchPlant-WW Weld Welders) Gom WeldTrack quality control sys tem, as s homn in

the program flow chart of FabMas ter (Figure B-1).

User enters the project number and clicks the "Lïnk RD Tables" to import raw data

tables. If al! needed tables are in phce, user kicks off the program Bow by hitting die

'Trocess if' button.

JDEdwards RD-B ranchPlant-SP (SpooI) RDBranchPht-MT (Pieces)

based on 23

Pass aU checks- 1st level cornpihaon & deril-ed qcy cdcuhtion

2nd level compilation based on Spool Item Code Structure

3rd level compilation based on Job-Material-

Cost Code Structure

Figure B-1: Program Flow Chart of FabMaster

Step 2. Data Validation Based on Pre-defined Rules

The foIlowing d e s were programmed in FabMaster to detect abnormalities and

prompt user to scrub raw data of errors prior to processing.

1. No blank is dowed in ptem Number] in RD-BranchPlanthfT.

2. No blank is allowed in p e l d Process] in RD-BranchPlant-WD.

3. PVeld Process] in RDBranchPlant-\JCTD must be a known process-combination in table

LP~WeldProcessCombo.

4. No blank is aliowed in goint Type] in RDBranchPlant-W.

5. (loint Type] in RDBranchPlantWD must be a known type in table

LP-Join tType-PANP .

6. No blank or O is dowed in p e l d Size] in RDBranchPlant-W.

7. [Weld Size] in RD-BranchPlant-WD m u t be a known s i x in table LP-PipeOD.

8. No blank or O is allowed in p e l d Thickness] in RD-BranchPlant-\W.

9. No redundant spool is dowed to exist in RDBranchPlant-SP.

10. No blank or O is allowed in [Spool Weight] in RDBranchPlant-SP.

11. No blank or O is allowed in [Spool Units] in RDBranchPlantSP.

12. No blank or O is allowed in [Size Group] in RD-BrmchPlant-SP.

13. [Size Group] in RD-BranchPht-SP must be a h o w n one in table tP-SizeGroup.

14. No blank or O is allowed in p la te rd Group] in RDBranchPlant-SP.

15. platerial Group] in RDBranchPlant-SP must be a h o w n one in table

LP-LateridGsoup .

16. [Spool Nurnber] in RDBranchPlant-SP must have a corresponding record in

RDBranchPlantDG.

17. No blank is allowed in [Spec] in RDBranchPlant-SC.

18. [Spec] in RDBranchPlant-DG rnust have a corresponding reference in

RDBranchPlantSC.

19. [Spool Number] in RDBranchPlant-SP must have a corresponding record in

R D B ranchPIant-MT.

20. PVeld Thichness] in RDBranchPlant-Cm like 3000/6000 must be able to be converted

to inches by tinding a reference Li LP-PipeThickness.

21. p e l d Thichness] in RD-BranchPlant_WD must not be abnormaily large (greater than

5").

22. PVeld Size] in RDBranchPlant-WD must be able to be converted to Equivalent

Diameter Inches by hnding a reference in LP-PipeThickncss based on size and

thickness.

23. For an Olet type weld, a reference in LP-OletDkn based on weId size must be found.

. .- - , - . . . . ,

- - _ r - .

Ënter Branch Piant Nor . - 11 709286 ~hadc Q W ~ ~ M ~ T T , ~

- - - - - - - - - - - . - - - . -- - - - - - - -- -. .. - . . . , . .

Figure B-2: Main User Interface of FabMaster

FabMaster d hint user about the detected problem records, violated d e s and

solutions (either update cross-reference tables or correct ram data tables) in its progress

monitor mindows as showo in Figure B-2. To resume the program flow after hxing

problems, user needs to hit the "process it" button again to continue the process from

where it paused 1s t time.

Step 3 Unithe a project and perform spool Ievel compilation

Once dl the checks on raw data are passed, FabMaster runs its built-în prograrns to

automatically unitize a project into "Fabrication units", compute the quantities of various

work items in pre-specihed units of measure, and store the resdts into four temporaq

268

tables, namely RD-Spool, mePiece, RDÇomection, and RD-Weld. The hrçt level

compilation is conducted based on those temporary tables to generate the item-coded

aggegate data for each spool and appended to spool s u m r n q table "SMJternQty-SP".

Step 4. Compile data at cost centet level and compute ratios

The cost-center level data compilation and ratio computation follows the spool lerel

data processing and the resdts d be appended to tmo surnmarg tables "SM-ItemQty-CC"

for aggregate quantities, and "SM-ItemQy-RT" for final rsrios. Table B-4 shows samples of

Sh.I_ItemQty-RT" based on one small project nrith one materid type and one size range

only. A big project often has more than one material types and size ranges of spools.

FabMaster d generate valid ratios only for a speufic project and automaticdy handle the

roll-up of ratios to various total levels.

Table B-4: Sample of FabMaster Outputs

Matctial

To t d

To ta1

To td

To tal

Total

Tom1

Total

Total

Total

Total

Total

Total

T o d

T o d

Total

Total

To ta1

Total

Total

Total

To tal

Total

Total

Total

Total

Total

Total

T o d

Total

T o d

Totd

Total

To t d

Total

- Size

T o d

Total

Total

Total

Total

Total

Total

Total

Total

To ta1

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

T o d

Total

Total

Total

To ta1

Total

Total

Total

T o d

To ta1

To ta1

To ta1 -

Ratio Description

Total hfanHours / DiaIn*Ft

Total LLfanHours / Equiv.DiaInrFt

Total h l d o u r s / Equiv-DiaIn

Totd M d o u r s / Volume

Total PvfanHours / Unit

No. of Pipe Pieces / Footage

No. of Pipe Pieces / DhInFt

No. of Pipe Pieces / Ton

No. of Pipe Pieces / Unit

No- of Pipe Pieces Over 3 ft / Footage

No. of Pipe Pieces Over 3 fr / DiaInFt

No. of Pipe Pieces O v e 3 ft / Ton

No. of Pipe Pieces over 3 ft / Unit

No. of m g e s / Footage

No. of Flanges / DhlnFt

No. of Fianges / Ton

No. of k n g e s / Unit

No. of In-Liae Fittings / Footage

No. of In-liae Fittings / DiaInJ3t

No. of In-Line Finings / Ton

Yo. of In-line Filtings / Unit

No. of Non-In-Line Fittings / Foomge

No. of Non-In-Line Fimings / DiaInFt

'JO. of Non-In-Lide Fittbgs / Ton

go. of Non-In-Line FilMgs / Unit

'JO. of Valves / Foomge

So. of Valves / DiaInFt

'To. of Ir&-es / Ton

%o.ofVdves / Unit

%o. of Supports / Footage

go. of Supports / DialnFc

30. of Supports / Ton

Vo. of Supports / Unit

No. of PrLisc. / Footage

Ratio

Material

Total

T o d

To ta1

Total

Total

To td

Total

'Fod

Total

Total

T o d

Total

Total

Total

Total

Total

Total

Total

Total

Total

T o d

Total

T o d

Total

Total

Total

Total

Total

To ta1

To ta1

Total

Total

Total

Total

Total

Total

To ta1

Total

To ta1

Size

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

T o d

Total

Total

T o d

To ta1

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

To ta1

Toul

Total

T o d

Total

Total

Total

Total

T o d

T o d

Toral

Total

Total

Ratio Description

No. of hkc. / DidnFt

No. of LLLISc. / Ton

No-ofhlisc. / Unit

Pipe LVeight / Spool Weight

Non-Pipe \Veight / Spool LVeight

No. ofConnections (Design LVeIds) / Footage

No. of C o ~ e c a o n s (Design \Velds) / DiaInFt

No, of Comecuons (Design \Velds) / Ton

No. of C o ~ e c u o n s (Design \Velds) / Unit

No. of Multi-Station ROLL \Velds / Footage

No. of hldti-Station Roll \Velds / DiaInFt

No. of Mda-Station Roll CVelds / Ton

No. of Mda-Station Roll \Velds / Unit

No. of Repaired Welds / Footage

No- of Repriired \Velds / DiaInFt

No- of Repaked \Velds / Ton

No. of Repair \Velds / Unit

B\V DiaIn / Design \Vdd DiaIn

B\V Equiv-Dan / Design \Veld Equiv-DiaIn

BQ' Vol. / Design \Veld Vol.

SV D d n / Design \Veld DiaIn

SV7 Equiv-DiaIn / Design Weld Equiv-DiaIn

SW' 1'01. / Design \Veld Vol.

3L DiaIn / Design Weld DiaIn

3 L Equiv.DiaIn / Design \Veld Equüv.DiaIn

3 L lrol. / Design \Veld lTol.

Pressure Atmchment / Design \Veld DiaIn

Pressure Anachrnent / Design \Veld Equiv.DiaIn

Pressure Anachment / Des& \Veld Vol-

Xon Pressure At tachent / Design \Veld DiaIn

Non Pressure Attachment / Design \Veld Equiv.DiaIn

%on Pressure Amchment / Design \Veld Vol.

Position Weld / Design \Veld DiaIn

Posiaon \Veld / Design \Veld Equiv-Ddn

Position \Veld / Design Weld Vol.

holl Weld / Design \Veld DiaIn

boll Weld / Design Weld Equiv-DiaIn

Kou \Veld / Design Wdd Vol.

khlti-Sraaon Roll Weld / Design Weld DiaIn

Ratio

9.232899E-05

0.0583273

5.403945E-04

0.9404383

5.956174E-02

5.786802E-O1

9.647334E-03

6.095 192

5.6471 22E-02

2.353484E-01

3.923557E-03

2.478906

2.296676E-02

3.322566E-03

5.539 139E-04

0.3499632

3.342367E-03

0.9782972

0.9782972

0.994041 3

1.335559E-O2

1 -335559E-02

3.170402E-O3

t3.34724GE-03

8.34734GE-03

2.78841 GE-03

0.9866444

0.986644

0.9968396

1.335559E-02

1 -335559E-02

3.1704OE-O3

O

O

O

Material

Total

Total

Total

Totd

T o d

Total

Totai

Total

Total

Total

Total

Total

Total

TGLZ

Total

Total

Total

Total

To td

Total

Total

To ta1

Total

Total

To ta1

Total

Total

Total

Total

Total

To-d

To td

Total

Total

Total

Total

Total

Total

Total

Size - T o ta1

Total

Total

T o d

Total

Tord

Total

Total

Tod

Total

Total

T o d

T o d

To tai

Total

T o d

To ta1

To ta1

Total

To ta1

Total

Total

Total

Total

6- 14"

6-14"

6- 14"

6-14"

6-14"

6-14"

6- 14"

6-14"

6-14"

6-14''

6-14"

6-14"

6-1 4"

6-13"

6-14" -

Ratio Description

Mulu-Station Roll \Veld / Design \Veld Equiv-DiaIn

hfuIu-S tation Roll \Veld / Design Weld VOL

Single-Station Roii \Veld / Design WeId DiaIn

Single-Station Roii \Veld / Design \Veld Equk-.DhLn

Single-Station Roli \Veld / Design \VeId Vol.

Ti Process iveid / Design \Veld Vol.

hLig Process Weld / Design \Veld Vol.

F U \ V Process \Veld / Design \Veld VoI.

Stick Process \Veld / Design Weld Vol.

SubArc Process Weid / Design \Veld Vol.

Rotoweld Process Weld / Design \Veld 1'01.

Repair Rate (No. of R / R+A)

No. of Cut Sheet Revision / No. of Spool

RT rate /Spool

MT rate /Spool

P T rate /Spool

PMI rate /Spool

P\VHT rate /Spool

Fï rate /Spool

B K N rate /Spool

V T rate /Spool

UT rate /Spool

Non-Welded Spool/\VeIded Spool (Weight)

Non-LVelded Spool/WeIded Spool pnits)

No. of Pipe Pieces / Footage

'io. of Pipe Pieccs / DiaInFt

'JO. of Pipe Pieces / Ton

Xo. of Pipe Pieces / Unit

?JO. of Pipe Pieces Over 3 ft / Footage

'JO. of Pipe Pieces Over 3 ft / DiaInFt

Yo. of Pipe Pieces Over 3 ft / Ton

30. of Pipe Pieces over 3 ft / Unit go. of FLmges / Footage

go. of Flanges / DiainFt

90. of FIanges / Ton

30. of Fianges / Unit

30. of In-Line Fittings / Footage

90. of l n - h e Fitnngs / DiaInFt

30. of In-Line Fittings / Ton

Ratio

0.4257095

0.432653

0.5742905

0.5742905

0.567347

0.106721 1

0

0

0.893279

0

0

2.933985E-O2

0

100

100

0

1 O 0

1

0

100

100

100

0

0

5.3 1 61 OSE-02

8.812613E-03

5.59941 1

5.187787E-02

5.0669 13E-02

8.M7 187E-03

5.336939

4.944609E-02

5.53761E-03

9-33 1899E-04

0.583272

5.303945E-03

l.lO752Z-O3

1 -84638E-04

0.1166544

Material

Total

Total

T o d

Tord

Total

Total

Total

Total

Total

Total

Total

Total

Total

T o d

Total

T o d

To ta1

Tord

Tord

Total

Total

Total

Tord

To ta1

Total

Total

Total

T o d

To ta1

Total

Tord

Total

To ta1

To ta1

To td

Total

Total

Total

Total

Ratio Descripaon

No. of In-Line Filtings / Unit

No. of Non-in-Le Fittings / Footage

No. of Non-In-Le Fittings / DiaInFt

No- of Non-In-Line Fitüngs / Ton

No. of Non-ln-Le Filtings / Unit

No. ofTrdves / Footage

No. of lrdves / DiaInFt

No. of Vaives / Ton

No-of Valves / Unit

No. of Supports / Footage

No. of Supports / DiaInFt

No. of Supports / Ton

No. of Supports / Unit

No. of blisc. / Footage

No. of Ilfisc. / DialnFt

No. of blisc. / Ton

No-of blisc. / Unit

Pipe Weight / Spool LVeight

Non-Pipe LVeight / Spool Weight

No. of Connections (Design \Velds) / Footage

No. of Connections (Design \Velds) / DiaInFt

So. of Connections (Design \Velds) / Ton

30. of Connections (Design \Velds) / Unit

No. of Mulu-Station Roll \Velds / Footage

30. of hlulti-Station Roll \Velds / DiaInFr

No. of Mulu-Station Roll !Velds / Ton

No. of blulti-Scation Roll Welds / Unit

%o. of RepaLed \Velds / Footage

'sio. of RepaLed \Velds / DidnFc

go. of Repaired Welds / Ton

I\To. of RepaL Welds / Unit

3W DiaIn / Design Weld DiaIn

3\V Eq~~iv.DhIn / Design Weld Equiv.DiaIn

3W Vol. / Design Weld Vol.

SW DiaIn / Design Weld DiaIn

;W Equiv.DkIn / Design Weld Equiv.DiaIn

337 Vol. / Design Weld Vol.

3L Didn / Design Weld DiaIn

3L Equiv-DiaIn / Design Weld Equiv-DiaIn

Ratio

1.080789E-03

5.2053536-02

8-6779856-03

5.482757

5.079708E-02

0

0

0

0

0

0

0

0

5.5376 lE-04

9.23 1899E-05

0.0583272

5.403945E-04

0.9404383

5.956 174E-02

5.786802E-02

9.647334E-O3

6.095 192

5.64712Z-O2

2.353484E-03

3.923557E-03

2.478906

329667GE-03

3.333566E-03

5.539139E-04

0.3499632

3.242367E-03

0.9782972

0.9782972

0.9940413

1.335559E-02

1.335559E-02

3.170402E-O3

8.347246E-03

8.347246E-03

Material

T o d

T o d

Total

Tord

Total

Total

Total

Total

Totaf

Total

Total

Total

Tord

Total

Tocd

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

To ta1

Total

Total

Total

Total

Total

Total

Total

Total

Toul

Total

T o d

Total

AS W O Y )

Ratio Description

OL Vol. / Design LVeld VOL

Pressure Attachment / Design \Veld D d n

Pressure Amchment / Design Weld Equk.DiaIn

Pressure +.\nachment / Design Weld VOL

Non Pressure Amchment / Design Weld Didn

Non Pressure Attachment / Design Weld Equiv-Dialn

Non Pressure Atmchment / Design \Veld Vol.

Position \Veld / Design Weld DiaIn

Position \Veld / Design LVeld Equk-Dialn

Posiuon \Veld / Design Weld VOL

Roll Weld / Design Weld DiaIn

Roll LVeld / Design \Veld Equiv-DiaIn

Roll \Veld / Design Weld Vol.

Multi-Station Roll Weld / Design \Veld DiaIn

blulti-Station RoU [Veld / Desip WeId Equiv-DiaIn

Mula-Smtion RoU \Veld / Design T'Veld Vol.

Single-Station Roll Weld / Design \Veld DiaIn

SingIe-Station RoU Weld / Design Weld Equiv-DiaIn

Single-Station Roll Weld / Design \Veld 1'01.

T'ig Process Weld / Design \Veld 1'01.

Mig Process Weld / Design \Veld Vol.

FCAW Process Weld / Design Weld Vol.

Stick Process \Veld / Design Weld 1'01.

SubAxc Process \Veld / Design \Wd 1'01.

Rotoweld Process [Veld / Design Weld TToL

Repair Rate (No. of R / R+A)

NO. of Cut Sheet Revision / No. of Spool

R T rate /Spool

MT rate /Spool

P T rate /Spool

PMI rate /Spool

PWWT rate /Spool

FI' rate /Spool

B H N rate /Spool

VT rate /Spool

U T rate /Spool

%on-Welded Spool/\Velded Spool (Weight)

Son-Welded Spool/Welded Spool (Units)

rotal bIaaHours / Di;iIn*Ft

Ratio

2.78841 6E-03

0.986644

0.986644

0.9968396

1 -335559E-02

1 -335559E-02

3.170402E-O3

0

0

0

1

1

1

0.4257095

0.4257095

0.432653

0.5742905

0.5742905

0.567347

O. 106721 1

0

0

0.893279

0

0

2.933985E-O2

0

1 O0

1 O0

0

1 O0

1

0

1 O0

1 O0

100

0

0

1 -705658E-04

Material

AS (MoY)

AS (Moy)

AS (Moy)

AS (,.Vloy)

AS (AUoy)

*AS (.!!oy)

AS (Moy)

AS (MOT)

AS (-Uoy)

AS (hlloy)

AS ( M ~ Y )

-1s (,-Uioy)

AS (Alloy)

-AS (-Moy)

AS (Aüoy)

AS (Mo);)

AS (Moy)

AS (Ailey)

AS (AUoy)

*AS (.Woy)

-4s (Moy)

AS (Alloy)

AS (Moy)

AS (Moy)

AS (Alloy)

AS (AUoy)

AS (ruloy)

AS (Alloy)

-4s (-Uoy)

AS (Moy)

AS (Moy)

AS cMoy)

-AS (May)

.!AS (-Uoy)

AS W O Y )

AS W ~ Y )

AS ( M ~ Y )

AS (Moy)

AS W ~ Y )

Size

Total

Total

Totd

Total

Total

T o d

T o d

Total

Total

Total

Total

To td

T o d

T o d

Totai

Total

Total

Total

Total

Total

Tom1

To ta1

Tocal

Total

Total

Totai

To td

Total

Total

To td

T o d

Total

Total

Total

Total

Total

Total

T o d

T o d

Ratio Description

Total hfanHours / Equiv.Ddn*Ft

To td hlaaHours / Eqvlv-DiaIn

Total hianHours / Total ManWours / Unit

No. of Pipe Pieces / Footage

No- of Pipe Pieces / DiaInFt

No. of Pipe Pieces / Ton

No. of Pipe Pieces / Unit

No. of Pipe Pieces Over 3 ft / Footage

No. of Pipe Pieces Over 3 €t / DiaInFr

No. of Pipe Pieces Over 3 ft / Ton

No. of Pipe Pieces over 3 ft / Unit

No. of Fimges / Footage

No. of b g e s / DtaInFt

No- of b g e s / Ton

No. of b g e s / Unit

No. of In-line Fittings / Footage

No. of In-Line Fittings / DiaInFt

No. of In-line Fittings / Ton

No. of In-Line Filtings / Unit

No- of Noa-In-Line Fittings / Footage

No. of Non-ln-Line Fittings / DiaInFt

No. of Non-In-Line Fittings / Ton

No. of Non-In-Line Filtings / Unit

No. of Valves / Foomge

No. of Valves / DhInFt

No. of lrdves / Ton

No-of Valves / Unit

No. of Supports / Footage

No. of Supports / DiaInFt

No. of Supports / Ton

No. of Supports / Unit

No. of bLisc. / Footage

No. of blisc. / DhInFt

No. of PvL-c. / Ton

No-of PvLisc. / Unit

Pipe Weight / Spool LVeight

Yon-Pipe Weight / Spool Weight

30. of Connections (Design Welds) / Foomge

Ratio

1 -705658E-04

0-6 160267

2.657094

0.1394056

5.316105E-03

8.863633E-03

5.59941 1

5.1 87787E-02

5.0663 13E-02

8.U7 187E-03

5.336939

4.9UG09E-02

5.5376 1 E-03

9231899E-04

0.583272

5.103945E-O3

1 .IO7533E-O3

1 -84638E-O4

0-1 166544

1 -080789E-03

5205353E-02

8.677985E-03

5.482757

5.079708E-02

O

O

O

O

O

O

O

O

5.53761E-04

9.232 899E-O5

0.0583772

5.403945E-04

0.9404383

5.956174E-O2

5.786803E-02

Material

As (MoY) AS (Moy)

AS W o y )

AS (Moy)

AS (-Uoy)

AS (MoY)

AS (Alloy)

AS (MoY)

AS (Moy)

AS (Moy)

AS (Mol-)

AS (Moy)

AS (Moy)

AS (UOY) AS (-Uoy)

AS (Moy)

AS (rUoy)

AS (Moy)

AS (Noy)

-4s (i-uloy)

AS (Moy)

AS (Moy)

AS (iUoy)

AS (*AlIo).)

AS (hlloy)

AS (Alloy)

AS (LUoy)

AS (-Uoy)

AS (-AUoy>

AS (Moy)

AS (Moy)

-AS (rvloy)

AS ( M ~ Y ) AS (Moy)

AS W o y )

AS (May) -4s (Moy)

AS (Ailey)

AS (Moy)

Size - Total

Total

Total

Total

Total

Total

T o d

T o d

Total

Total

Total

Total

To tai

Total

Total

Total

T o d

Total

T o d

Total

Total

T o d

Total

T o d

T o d

To ta1

Totai

Total

Total

Total

Total

Total

T o d

Total

Total

Total

r o ta1

Total

rotal -

Raào Description

No. of Connecuons (Design LVelds) / Dk-JInFt

No- of C o ~ e c t i o n s (Design \Velds) / Ton

No. of C o ~ e c ü o n s (Design Welds) / Unit

No- of Multi-Station Roll Welds / Footage

No- o f Pvfulti-Station Roll WeIds / D d n F t

No. of Mulu-Station Roll LVelds / Ton

No. of Mulu-Station Roll [Velds / Unit

No. OF Repaired !Velds / Footage

No. of Repaired Welds / DiaInFt

No. of Repaired Welds / Ton

No. of Repair \Velds / Unit

BW' DiaIn / Design Weld DiaIn

BW Equiv-Diain / Design Weld Equiv-DiaIn

BK' Vol. / Design WeId Vol.

SLV D a n / Design Weld DiaIn

S\V Equiv-DiaIn / Design \Veld Equiv-DiaIn

SV7 1'01. / Desiga Weld Vol.

OL DiaIn / Design Weld Diah

OL Equiv-DiaIn / Design \Veld EquivDkIn

OL Trol. / Design Weld Vol.

Pressure At tachent / Design \Veld DiaIn

Pressure Attachment / Design LVeld Equiv-DhIn

Pressure Attachment / Design \Veld Vol.

Son Pressure Amchment / Design \Veld DiaIn

Non Pressurc Attachment / Design Sreld Equiv-DiaIn

Non Pressure Attachment / Design \Veld Vol.

Posiüon \Veld / Design \Veld DiaIn

Position \Veld / Design \Veld Equiv-DiaIn

Position \Veld / Design Weld Vol.

Roll Weld / Design \Veld DiaIn

Roll Weld / Design Weld Equiv.DiaIn

Roll Weld / Design Weld Vol.

Mulu-Staaon Roll Weld / Design \Veld DiaIn

bluia-Station Roll 'LVeld / Design WeId Equiv-DiaIn

Uula-Station Roll Weld / Design Weld Vol.

Single-Station Roll Weld / Design Weld DiaIa

Single-Station Roll Weld / Design Weld Equïv.DiaIn

Single-S tauon RolI \Veld / Design \Veld TroL

ï'ig Process Weld / Design WeId Vol.

Ratio

9.647334E-03

6.095 192

5.647 133E-02

2-353484E-O2

3-923557E-O3

2.478906

2296676E-02

3.333566E-03

5.5391 39E-04

0.3499633

3.2423G7E-03

0.9782972

0.9782972

O.9WO413

1.335559E-03

1.335559E-02

3.170402E-03

S.34724GE-03

8.347246E-03

2.78841 GE-O3

0.9866-l-N

0.9866CW

0.8968296

1.335559E-02

1.335559E-02

3.1 70402E-03

O

O

O

1

1

1

0.4257095

0.4257095

0.432653

0.5743905

0.5742905

0.567347

0.206721 1

Material

AS (Moy)

AS (Noy)

AS W o y ) AS (Moy)

AS (Mo).)

AS (Mo).)

AS (Moy)

AS (rvloy)

AS (Moy)

AS (Aioy)

AS (Moy)

AS (Noy)

Lis (Moy)

AS (-Uoy)

Lis (hlloy)

Lis (Moy)

AS (Uoy)

AS (rvloy)

AS (Moy)

AS (Noy)

AS (May)

AS (Moy)

AS (May)

,AS (Moy)

AS (Moy)

AS (Moy)

AS W ~ Y )

AS (AUoy)

AS (Moy)

AS (ALioy)

AS (LUloy)

AS (Alloy)

AS (Alioy)

AS (Uoy)

AS (May)

AS (Alloy)

AS P ~ Y )

AS (Aiioy)

AS (Alloy)

Size - To tai

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

Total

6-14"

6-14"

6-14"

6-1 4"

(5-14"

6- 14"

6-14"

6-14"

6-14"

6-14"

6- 14"

6-14"

6- 14"

6- 14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

Ratio Description

Mig Process \Veld / Design Weld Vol.

F=\V Process Weld / Design Wdd Vol-

Stick Process !Veld / Design Wdd Vol.

Subhrc Process \Veld / Design Weld VOL

Rotoweld Process Weld / Design Weld 1701-

Repait: Rate (No. of R / R+A)

No. of Cut Sheet Revision / No. oESpool

RT rate /Spool

MT rate /Spool

PT rate /Spool

Ph11 rate /Spool

PWHT rate /Spool

FT rate /Spool

B H N rate /Spool

''T rate /Spool

U T rate /Spool

Non-LVelded Spool/Welded Spool (Weiglit)

Non-LVelded Spool/LVelded SpooI (Units)

No. of Pipe Pieces / Footage

No. of Pipe Pieces / DialnFt

30. of Pipe Pieces / Ton

No. of Pipe Pieces / Unit

No. of Pipe Pieces Over 3 Ft / Footzge

'JO. of Pipe Pieces Over 3 ft / DïaInFt

No. of Pipe Pieces Over 3 Ft / Ton

So. of Pipe Pieces over 3 ft / Unit

Mo. of Fianges / Footage

'To- of Fhnges / DiaInFr

30. of Fhnges / Ton

No. of Fhnges / Unit

Mo. of In-Line Fitlingj / Footage

No. of In-Line Fittings / DialnFt

No. of In-line Fittings / Ton qo. of In-Line Piltings / Unit

go. of Non-In-Lïne Fitaogs / Footage

qo. of Non-la-Line Fittligs / DiaInFt

go. of Non-In-Line Fittings / Ton

go. of Non-In-Line Filtings / Unit \JO. of Valves / Footage

Ratio

Materid

AS (Moy)

AS (Moy)

AS (Alloy)

AS (Ailey)

AS (r\Uoy)

AS (AlIoy)

AS (Moy)

AS (,-Vloy)

AS (~Uoy)

AS (AUoy)

AS (,-Vloy)

AS (Alloy)

AS (Moy)

AS (-Uoy)

AS (Moy)

-4s (Alloy)

AS (-Uoy)

AS (Moy)

AS (Auoy)

AS GWoy)

AS (Moy)

AS (Moy)

AS (AUoy)

AS (Alloy)

AS (,illoy)

AS (Moy)

AS (Moy)

AS Woy)

AS (Alloy)

Lis (Auoy)

AS (Lüioy)

AS WOY) AS (,.Vloy)

AS P O Y ) AS (Moy)

AS Woy) AS (Mo y)

AS (May)

AS (May)

Size - 6-14"

6-14"

6- 14"

6-24"

6-14"

6-14"

6-14"

6-1 4"

6-14"

6- 14"

614"

6-14"

6-14"

6-14"

6-14"

6-14"

6- 14"

6-1 4"

6-24"

6- 13"

6-14"

6-13"

6-1 4"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14''

6-14"

6-14"

6-13"

6-13"

6-14"

6-14''

G- 14"

6-14"

6- 14"

G- 14"

Ratio Description

No. of Valves / DialnFt

No. of Valves / Ton

No-of Trdves / Unit

No. of Supports / Footage

No. oESupports / DiaInFt

No. of Supports / Ton

No. of Supports / Unit No. of Mise. / Foomge

No. of hlisc. / DiaIf i t

No. of bLisc. / Ton

No-of hiisc. / Unit

Pipe Weight / Spool Weight

Non-Pipe \Veight / Spool LVeight

No. of Connections (Design \Velds) / Foocage

No. ofcomections (Design \Velds) / DiaInFt

No. of C o ~ e c t i o n s (Design \Xelds) / Ton

No. of Comrctions (Design Welds) / Unit

No. of hldti-Station Roll \Velds / Foomge

No- of bfulu-Scation Roll \Velds / DiaInFt

No. of Mdt i -kaon RoU \Velds / Ton

No. of hfulu-Station Roll \Velds / Unit

No. of Repaired \Velds / Footage

No. of RepaLed Welds / DiaInFt

No. of Repaired \Velds / Ton

No. of RepaL \Velds / Unit

B\V DiaIn / Design \Veld DiaIn

B\V Equiv-DiaIn / Design \Veld Equiv.Dia1n

B\V Vol. / Design \Veld Trol.

S\V DiaIn / Design \Veld DiaIn

SW Equiv.Didn / Design Weld Equiv-Ddn

S\V Vol. / Design \Veld Vol.

OL DiaIn / Design \Veld DiaIn

OL Equiv.DiaIn / Design Weld Equiv.DiaIn

OL Vol. / Design \Veld Vol.

Pressure At tachent / Design Weld Dialn

Pressure Attachment / Design Weld Equiv.DiaEn

Pressure Attachrnent / Design \Veld VOL

Non Pressure Attachmenr / Design 'WeId DiaIn

Non Pressure Attachment / Design WeId Equiv.Dialn

Ratio

Material

AS (LLUoy)

AS (U~OF)

AS (Moy)

AS (Moy)

AS (MoY)

AS (Uloy)

AS (Moy)

A4S (,.Ulo:.)

AS (Moy)

AS (AUoy-)

-4s (-Uoy)

-4s (Moy)

AS (+Uoy)

AS (Uloy)

AS (Moy)

AS (-Uoy)

-4s (Moy)

AS (,-Uioy)

AS (Uoÿ)

AS (Alloy)

'4s (*Uoy)

AS (Moy)

AS (Noy)

AS (Alloy)

AS (Alloy)

AS (-Uoy)

AS (Noy)

,AS (Mo).)

'4s (-Uoy)

AS (-Uoy)

AS (Moy)

AS (floy)

Size - 6-14"

6-14"

6-14"

6- 14"

6-14"

6-14"

6- 13"

6-14"

6-14"

6-14"

6-14"

6-14"

6- 14"

6-14''

6- 14"

6-13"

6- 14"

6- 14"

6-14"

6-14''

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

6-14"

G-14"

Ratio Description

Non Pressure Attachent / Design \Veld Vol.

Position !Veld / Design \Veld Diain

Position LVeld / Design Weld Equiv-DiaIn

Position \Veld / Design \Veld Vol.

Roll \Veld / Design \Veld D d n

RoU \Veld / Design LVeld EqukDiaIn

Roll Weld / Design \Veld VOL

blulti-Station Roll \Veld / Design \Veld DiaIn

hlulti-Staaon Roll \Veld / Design Weld Equiv-DiaIn

hlulti-Station Roll Weld / Design \Veld Vol.

Single-Station Roll \Veld / Design \Veld DiaIn

Single-Station Roll \Veld / Design Weld Equiv-Dialn

Single-Station RoU \Veld / Design \Veld Vol.

rig Process Weld / Design \Veld Vol.

4% Process Weld / Design Weld Vol.

FCALV Process \Veld / Design Weld VOL

Stick Process \Veld / Design \Veld Vol.

SubArc Process \Veld / Design Weld Vol.

Xotoweld Process Weld / Design \Veld Vol.

XepaL Rate (No. of R / Rt-\)

go. of Cut Sheet Revision / No. of Spool

XT rate /Spool

b1T rate /Spool

?T rate /Spool

'MI rate /Spool

?\VHT rate /Spool

T' rate /Seo01

3HhT rate /Spool

4T rate /Spool

JT rate /Spool

\ion-Welded Spool/CVelded Spool (YVeight)

\ion-ivelded Spool/Welded Spool (Uni=)

Ratio

3-170402E-03

O

O

O

1

1

1

0.1257095

0.4257095

0.432653

0.5742905

0.5732905

0.567347

0.106721 1

O

O

0.893279

O

O

2.933985E-02

O

100

100

O

1CO

1

O

100

1 O0

100

O

O

FabMaster processed project data individually and warehoused the item-coded

project information in an easy-to-access format. Fab-OLAP provides the functionaliq

of vieming and analyzing productiviq-related information across dl projects that have

been processed bp FabMaster. Fab-OLAP is an O n - h e Andytical Processing System

custom-developed for the Fabrication FaUlities of PCL Indusmal Constructors, Tnc. The

system feanires dynamic query, graphic presentation, and the functionality of statistical

anaiysis on 105 ratios of labor productivity/spool configuraton compleSq/qualiq

control. It is an advanced decision-support tool for management to grasp the trend in

the historical project data and identifg exceptional problems in the work at hand.

Figure C-1: Select one ratio

Step 1. Load the program and select one ratio

User selects one ratio from the "Select Ratio" dropdomn Est, which includes all

the 105 ratios computed in FabMaster, as shown in Figure C-1.

Step 2. Apply Filters on Material Type and Size Range

Fab-OLAP uses the standard codes of the Company for the material types and

size ranges. Fab-OWP helps user e-xplore data in decision-oriented mays and allows

user to view data and get at them fomi different perspectives dong the dimension of

181

Figure C-2: Trial on ccnumber of pipe pieces per foot"

material and size. The histogram dong &th ~ t a t i ~ t i d analysis results for the selected

ratio is presented on screen and updated automatically. Figure C-2 shows the nial based

on "carbon steel 6-14 inch spool, nurnber of pipe pieces per foot of pipe".

Step 3. Drill into details of data

Fab-OUP doms user to drill dom to details of data by clicking the T i e w

Data" button. Figure C-3 shows the data behind the selected ratio.

1 7ûû250 / CS (Carbon] 6-1 4" j No- af Pipe Pieces / Footage i 0.13346798! - 1 700204j CS (Carbon] 6-1 4" I + No. of Pipe Pieces / Footage : 3.660536~-02;

1 7002551 CS [Carbon) 1 6-1 4" i No- af Pipe Pieces / Faotage 1 O.OU4265;

1 7002651 CS (Carbon) 1 6-1 4" !No. of Pipe Pieces / Footage ' 4.8767 1 7E-02;

17002341 CS (Carbon) 1 6-1 4" 1 No. of Pipe Reces / Foatage 0.0488468 3 17004781 CS (Carbon] 16-1 4" No. of Pipe Pieces / Foatage 6.061 01 9E-M!

I

1 700205; CS (Carbon] / 6-1 4" ' No. of Pipe Pieces / Footage O. 0656395 3 i 1

' 1 700474[Cç [Carbon] 6-1 4" j No. of Pipe Pieces / Footage p 6.587098~-021 1

17004621 CS [Carbon] 6-1 4" : l No. of Pipe Pieces / Footage 16.762063E-021

1700466 j CS [Carbon] 6-1 4" i No. of Pipe Pieces / Footage 7.231 822E-Mf

1 700242! CS [Carbon) / 6-1 4" i No. of Pipe Pieces / Fooiage / 7.61 0802E-021

1700206j CS [Carbon] 1 6-1 4" b No. of Pipe Pieces / Footage 7 ï2931 4~-021 1

1700481 j CS [Carbon) i 6-1 4" No. af Pipe Pieces / Footage 7.750466E.O2] '

1700211 i CS [Caban) j 6-1 4" No. af Pipe Pieces / Fmtage .8.051168E-021 i

1700464 [ CS [Cabon) 1 6-1 4" 'No. of Pipe Pieces / Footage 8 496705E-Mi

1700491 ! Cç (Carbon) 1 6-1 4" ' No. of Pipe Pieces / Footage 8 67351 4E-02: 1

1 70021 3; CS (Caban] 16-14'' :No. of Pipe Pieces / Footage 1 8.859606E-021

Figure C-3: View details of data

Step 4. Prht out the trial and statistical analysis resdts

User clicks the 'Trint out" button to psint a hard copy of the current trial and

stausticd analysis results including the histograrn for record.

&PENDIX D: USER'S MANUAL FOR PIPINGMASTER

PipingMaster is a historical project data =-arehoushg system customized for the

field construction systems of PCL Industrial Constructors, Inc. It is an automated data

processing tool to estract ram data from Labor Cost Control System, Estimating System,

and Quality Contcol Spstem, and convert raw data into useful pruductiviq information

based on embedded expert d e s . Pipe handling and welding are processed by

Pipinghlaster independendy, but in simila fashions including the user interfaces and

prograrn logic. Thus, Pipe handling is selected to illustrate the program flow in the

following steps.

Step 1. Impoa raw data in standard format

User irnports three ram data tables for each project into the database manudy to

d o w for PipingMaster to calculate the quantity of piping work, namely,

RDJroject#Hand table for pipe hanrlling, RD-Project#Detl for pipe work

components, RD-Project#Weld for pipe melding. The table structures are shown in

Figure D-1.

RD-Pro j#Hand

Project #

Nominal Size

Schedule

Ciassifïcation

hhterial Type

Length (fi)

Es tUnitPvLH

RD-Pro j#Detl

Project #

Detl Type

Nominal Size

Classifïca tion

Mzterial Type

Quantity

RD-Pro j#Weld

Project #

Nominal Size

Schedule

Joint Type

Classification

Material Type

# \cVelds

Es tUnitlhIH

Figure D-1: Structures of Raw Data Tables for A Projcct

The detailed quantity take-off (in footage) for pipe handling of one project is

available in the project estimate only. L'sually information is known and complete o n the

size, the thickness, the material tgpe, and the location classification of each individual pipe

section.

The detailed quantity take-off in number of welds for pipe melding of one project is

availaole either in the project estimates or in the field quality control system. In most cases

the pipe ske, pipe thickness, pipe material type, location classification and meld joint type are

knomn for each individual weld.

Installation of other piping moxk components (or piping details) includes pipe

supports, bolt-ups, valces, screw joints, and misceUaneous items like flanges, specialties,

185

elbows, cuts and bevels. The number and type ofwork components and estimated unit man-

hours for one project me available in the project estimates. However, information on the

size, material type, location dassihcation may not be found in the estimate. Therefore, we

need to check the ram data integrïty of the piping work components prior to processing.

Step 2 Raw Data Integrity Check

The raw data integrity check is controlled by the entered project setting regarding the

raw data integiq and methods of actual mm-hour cost coding as shown in Figure D-2. User

Matuid Type

- ---- Sue R a g e [<TT'-16'>16'1 y= OIoaae Ho If Co& To Total ri NO Lwd

Figure D-2: Main user interface of FabMaster

enters the project number to be processed and answer a number of Yes/No questions about

the project Nesq user clicks "Check Raw Data Integritg" button to s t m the program. User

dl be prompted to correct any problems due to failure to pass the checks.

The PipingMaster is capable of identïfyïng missing data or incorrect data in the raw

data tables. For esample, if actual labor hours in the labor cost system were tracked to the

level of various classifications of location, then a null in the "Classihcation" field of the raw

data tables d be detected as invalid data and must be corrected for W e r processing.

Three valid types ofmeld joinh i.e. BW putt Weld), SW (Socket Weld), OL (Olet Weld) and

five valid types of piping work components are allowed lo the RD-Project#Ded table, 1.e.

bolt-up, valve, screw joint, support, and misc.

Step 3 Check cross-reference Data for Quantity Calculation

User hrst chooses one of four options and then click the "Check Cross Reference

Integriy" button to perform the check for the selected option. Four options should be

checked through one by one. User d be prompted to correct raw data or update cross

reference tables in case Pipinghlaster finds a problem. The "Action" button d only be

activated when aLi the ram data checks and cross reference checks are passed.

In PipingMaster, a number of cross-reference tables are involved to caldate the

quantitg in various units of measurement, i.e. five units of measurement for pipe handling:

DiametePLength (Tnch*Feet), Equivalent Diameter*Length (Inch*Feet), Length (Fee t),

Weight (p.lI.T), and Base Manhours (MH); five units of measurement for pipe welding:

Diameter (Inch), Equivalent Diameter (Inch), Volume (Cubic Inch), Volume/Thickness

(Square Inch), and Base bfanhours ($El). Cross-reference integrity check is performed to

ascertain that each record in the raw data table can h d the needed information in the

conesponding cross-reference tables so as to calculate accurate quantities. The forrnulae

187

used are commonly found in an industriai maoual or piping handbook- The relationships

between raw data tables and cross-reference tabIes are shomn in Figure D-3 and Figure D-4.

NominalSize Schedule

RD-Proj#Hand Project # Nominal Size Schedule Classiacation M a t e d Type Length

OuterDiameter (inch)

Figure D-3: HandLuig: X-Refercncc Information Integrity Check

Schedule Thicknes (inch)

Project # Nominal Size Schedule Joint Type Classification Ma terid Type # Welds Es tUnitkfH

-1 Schedule

JT 1s OL tblOletDim Nominal Oudet

Dimension B

Figure D-4: Welding: X-Reference Information Integrity Check

Step 4 Generate Aggregate Cost Codes and Calculate Quantities

User hits the "Action" button to generate aggregate cost codes to the level of project

nurnber, classi£ication of location, material type, size range, activity, and unit of measure. The

total quantities and quantities breakdown for size ranges, dong with the generated cost

codes 1 . be appended a summary table called "tblQuanutyLMaster". Table 1 shows sample

records in the summary table for one relatively s m d job.

Table D-1: Sample of Quantity Calculation Surnmary Table in PipingMaster

Pro ject# Material

CS

CS

CS

CS

AS

AS

SS

SS

TOT

TOT

Class

41 0

41 0

460

460

460

460

460

460

31 O

460

CostCode Description

Welding Total

Volume/Thickness

Handling Total Feet

Handiing Total Feet

Welding To ta1

Volurne/Thickness

Handling Total Feet

Welding Total

Volume/Thickness

Handling To tal Feet

LVeIdrng To tri

Volurne/Thickness

Hand Tot Mati Tot Size Ft

Hand Tot M a t l Tot Sizc Ft

Step 5 Enter ActuaI Hours and Compute Actual Degree-of-difficulty Factors

Folloming generating the cost codes and calculating the quantities, PipingbIaster

Show Gnnpïkd Records aid A d ln Actual Mhs h m LCS Report Proje& 1 Materiaflypa 1 Classification 1 CostCode 1 QtyTotal 1 BaseMH 1 Adual Mhn 1 Statris [

Shan U35 Act MHr la Girrcnt Roiect

Show Campikd Han- MuPipiicrt: 1 Proje- lateria4 Classl CostCode 1 QtyBetow2 ( Qty2TolS 1 QtyAbovelS 1 QtyTotal 1 ES!MUI~ M u l t l Statur 15L30486 CS 410 302151-02 11 5623 O 5634 100 388 No

Figure D-5: Productivity Analysis Page for Pipe Handiing

sliifis focus to productiviry analysis page as shown in Figure D-5. User reads acrual

manhours and enters into the "actuai manhours" column for corresponding records. Nesr,

user hits the "Analyze" button to let PipingMaster figure out the actud labor hours for pipe

handling based on the project setting about actual labor cost t r a c h g practice and the

ernbedded espert d e s for handling different scenarios. Evennidy, the acmal degree-of-

difficulty factors are computed for each record and listed against the factors estimators have

used for comparison. After comparison, user decides on which records are valid for NN to

use by switching the status of one record from No to Yes.

Step 6 Make Questionnaires for Valid Records

T L INDUSTRIAL CONTRACTORS INC. Pipe Handling Report

Prtpaied By: I # i t d i Sotaert Report Date: 15/7/59

1 .Handling Job Group by Prqect # 1500484_007 CosiCode: m-

Figure D-6: Sample of Pipe Handling Questionnaire

PipingMaster m&es questiomaires for those valid records as conhmied by user.

Figure D-6 shows a sampIe questionnaire.

Followïng the above six steps, Pipïngbkister processes one project and convert ram

data into accurate cost-coded productiviy information for f5uther productivity analysis.

Figure D-7 shows the flom chart of the whole program.

1 Check Raw Data Intecgrity 1 [ Correct Missîng/

Compile Estimated Man- hours for Pipe

Work Component from

the Raw Data

N 1 Incorrect Data 1s Data Complete and

Correct?

\1/ Prorate

Estimated Man- hours for Pipe

Work Component

Based On Pipe

A

1s Piping Work Component included in the "Pipe Install~' Cost Code?

N

Cost-Coded MA-hours & Genqrate Indices

Extract Es timated Man- hours fcom "Pipe Instd"

1s Output Data Valid?

Y

Y k/ v

<

Generate Historical Cost / Codes/Qty for NN

Y I

Quantitative Input and 1 Questiomakes for 1

1 Subjectivq Data CollecMg 1

1s ~ o c a t i & Classification, Matenal Type, and Size

Ranges Known For Piping Work Component?

9 Feed Valid Data To NN for

Training I

Figure D-7: Program Flow Chan of PipingMaster

N Generate Indices for Piping \Vork

Components

APPENDIX E: USER'S MANUAL FOR SENSIT~VENN

SensitiveNN is a back propagation Neural-Network based system to analgze the

sensitivity of input factors in some comples engineering and management problems that

are not amenable to analy-sis ushg conventional mathematical models- The sensitivity

analysis method is proposed in this thesis.

Step 1 Prepare data for SensitiveNN

The last column in a data table must be named as "Status", which flags the

teaining/testing status for each record. Status 1 stands for a training record, and Status 2

for a tesring record, and Status O for an ignored record. The nest-to-last N columns in a

data table contain Actual Output Values of the target nsky variables such as actual

nroduction rates, N being the number of outputs. rill the remaining columns in a data

table will be the input factors. There are no requirements imposed on the column names.

The trainer dl count the number of inputs and outputs according to user's setup of the

netsvork, which is discussed in Step 3.

Figure E-1: Splash Screen of SensitiveNN program

The prepared data table for PINN must be imported to the database file

"FE3PNN.mdb" prior to analysis, which is instded nrith the program and by default

under the program folder.

Once the data table is imported, user can s ta r t up the program

"SensitiveNN.exe". The splash screen shows up as in Figure E-1. By hittïng the forin,

user proceeds to &.e nest step.

Step 2 Link SensitiveNN to data tables and select the one for analysis

Figure E-2 shows the switchboard of the program. User needs to link to

"FFBPNN.rndb" h s t in order to load up data. By clicking the "Link FFBPNN.mdb"

button, an "Open File" dialog form pops up as show in Figure E-3.

NOTE TO USERS

Page(s) missing in num ber only; text follows. Page(s) were microfilmed as received.

196

This reproduction is the best copy available.

* - . _ _ - . - .- . - .

-linport& .-. - -

~ h e ~ ~ a t a set fa NN Anabsis shdd have been lmportedinto - FFEPNN;mdb ih theformat of a Table with a Status Field!

Figure E-2: Program Switchboard

, . . r Open aspad-only

Figure E-3: Open FFBPNN-mdb Fust

Once FT;SPNN.mdb is linked, all the data tables are listed in a combo bos for 197

user to select the one for analysis. AU the M d s in the selected table are numbered and

Listed in the list box captioned "Field List of Selected Datay', as shonm in Figure E-4. By

diclckg the "Show Datayy button, user can examine the details of data and edic the

train/test status for each record, which is shomn in Figure E-5.

- .

Show Data

Enter 1

Importa&

T ~ - D & 'Set for NN Analpis .should have been Irnported ïnto . FFBPNN.mdb h the Format of a Table wth a S tatus Field!

Fiold List of Selected Data. -

Figure E-4: Select data source table

. . . . ..

Figure E-5: Examine details of data and edit record status

Step 3 Set up NN structure and Iearning parameters to train-test BP NN

Followkg linktng to the data source, user click the "Enter" button on the

switchboard to enter the main interface of the program, as shown in Figure E-6.

User enters the tüal ID, the leaming rate, the momentum rate, the number of

inputs, the number of hidden processing elements in the rniddle layer, the number of

outputs, the training iterations, and the threshold of global error to terminate learning. Ir

is important to match the number of inputs and outputs with the number of columns of

the linked data table in the previous step. User may revert to the switchboard (Figure E-

4) m y t h e for double check bp clicking the "Exit" button, and clicks the "Enter" button

on the switchboard to restore the main interface. The mal ID is used to identify a

spedfic tnin-test trial and store the n e ~ o r k parameters and weights.

I 1

f tain 'n Test - - I

Figure E-6: Program main interface of Sens itiveNN

User may refer to the pertinent paper for details of those NN parameters.

Once the network is set up, click the "Train n Test" bunon to start the leaming

peocess, mhich can be monitored through a progress bar. The current iteration and

global error are also shonm at the top and bottom of the progress bar dynamically during

the leaming.

Step 4 Training tenninates and investigate leamîng results

Figure E-7: Check learning results when NN training terminates

The trainkg process terminates when any of the foilowing conditions is satisfied:

1. The current training iteration hits the uses-specified total iterations.

2. The current global enor is lomer than the user-specified threshold of global error.

3. User hits the "Stop" button.

When training terminates, user investigates the leaming results by checking final

global enor and compwing the actual outputs against the NN outputs for both training

and testing data as shown Li Figure E-7. Note that the average absolute errors for both

training data and leaming data are cornputed and shown in the screen as well. If the

average absolute enors for both training data and lemming data are reasonably small, the

netwolk is declared to be crained and the program flow moves to the next step.

Othernrise, repeat step 3.

Step 5 Perform Monte Carlo simulation to analyze the sensitivity of input factors

Based on a mature network obtained from Step 4, user spedies the total number

of simulation nrns in the left lower corner of the main interface and clicks the

"Sensitivity Analysis Simulation" button. m e n the simulation is done, the statisticai

analysis results of simulation about the input sensiavity berneen each input-output pair

are shown on screen as in Figure E-8- X tab-delimited test 6le called "SenNNFile-txt" is

also generated in the program folder recording the simulation results, mhich can be

imported to Excel for p l o t ~ g . Note tiiat the text H e ~vill be erased nest tkne the

simulation is perfomed, thus user should back it up if iieeded.

Step 6 Save a trial

User cari Save a mal including the network structure, l e d g parameters and

final weights of trained netsvork by clicking the "Save Trial" button. The trial ID d be

the key for access the network at later times, hence must be remembered.