research article inverse analysis and modeling for...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 975703 9 pageshttpdxdoiorg1011552013975703

Research ArticleInverse Analysis and Modeling for Tunneling Thrust onShield Machine

Qian Zhang12 Yilan Kang1 Zheng Zheng1 and Lihui Wang3

1 Key Laboratory of Modern Engineering Mechanics Tianjin University Tianjin 300072 China2 State Key Laboratory of Shield Machine and Boring Technology China Railway Tunnel Group Co Ltd Zhengzhou 450001 China3Department of Military Vehicle Academy of Military Transportation Tianjin 300161 China

Correspondence should be addressed to Yilan Kang tju ylkangtjueducn

Received 7 October 2013 Accepted 1 November 2013

Academic Editor Cheng Shao

Copyright copy 2013 Qian Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

With the rapid development of sensor and detection technologiesmeasured data analysis plays an increasingly important role in thedesign and control of heavy engineering equipmentThe paper proposed amethod for inverse analysis andmodeling based onmasson-site measured data in which dimensional analysis and data mining techniques were combined The method was applied to themodeling of the tunneling thrust on shield machines and an explicit expression for thrust prediction was established Combinedwith on-site data from a tunneling project in China the inverse identification of model coefficients was carried out using themultiple regression methodThe model residual was analyzed by statistical methods By comparing the on-site data and the modelpredicted results in the other two projects with different tunneling conditions the feasibility of the model was discussed The workmay provide a scientific basis for the rational design and control of shield tunneling machines and also a new way for mass on-sitedata analysis of complex engineering systems with nonlinear multivariable time-varying characteristics

1 Introduction

With the rapid development of sensor and detection tech-nologies the on-site measurement of large engineeringequipment can now provide extensive and real-time massmeasured data which include the evolution information ofthe key control variables during equipment operation andother main influencing factors Determining the internalrelation among these main influencing factors in miscel-laneous and noisy data and building an evolution modelthat can represent the inherent law are significant to thedesign control and safe operation of complex engineeringequipment

Data mining technology has provided technological toolsfor the analysis and modeling of mass engineering data andhas been effectively applied in measured data analyses invarious fields such as product and process design equipmentcontrol and fault detection [1] The common data miningtools used in engineering data analysis at present includestatistical (regression analysis correlation analysis cluster

analysis etc) and artificial intelligence methods (fuzzy the-ory rough set neural network genetic algorithm etc) Theregression analysis method which is characterized by higherror-tolerant ability transparent mining course and highcontrollability has an important function in the modelingand mining of the law between variables in continuousmass engineering data [2] Moreover some new methodsin artificial intelligence pattern recognition and machinelearning have been introduced in many engineering dataanalyses [3ndash5]

Shield tunneling machine a kind of typical equipmentutilized in underground engineering is characterized by acomplex structure and a heavy-duty mechanismThis equip-ment has a significantly high requirement for safe operationand control because it operates in complex geological con-ditions and extreme multifield underground environmentsTunneling thrust is the most important control variable ina shield tunneling machine which reflects the geologicaladaptability of the equipment The thrust value can directlyaffect the tunneling status and efficiency of the equipment

2 Mathematical Problems in Engineering

The composition of the total thrust is very complex andusually includes dozens of components which are closelyrelated to the geological condition the equipment structureand operating statusHowever the influence laws between thethrust and those factors remain unclear Therefore analyzingthe effective information in mass tunneling data recorded bythe equipment airborne system and studying the correlationamong the major control parameters are important for thesetting and control of the tunneling thrust and for ensuringsafe and efficient construction

The classic Krause empirical formula is currently themain formula adopted to estimate the shield tunneling thrust[6] Krause a German engineer proposed an empiricalformula 119865 = 1205731198632 (119863 is the diameter and 120573 is the empiricalcoefficient) through the statistical analysis on engineeringdata from hundreds of shield machines [7] This empiricalformula describes the power relation between the thrust andthe equipment diameter However all the other factors suchas construction geological conditions andmachine operatingstatus are included in the wide-range empirical coefficient120573 as shown in Figure 1 In the early stage of thrust design600 kNm2 was used as the experience thrust value on unitarea of the tunneling interface [8] Besides Zhang et al [9]developed a linear regression model based on experimentaldata analysis which took the thrust the cutterhead rotatingspeed and the chamber pressure as independent variablesand the advance rate as the dependent variable Ates etal [10] discussed the statistical relationships between TBMdiameter and installed thrust capacity nominal cutterheadtorque capacity total weight maximum rotational speed ofcutterhead and number of disc cutters based on a databaseincluding 262 TBMsrsquo design parameters Hassanpour et al[11] proposed a performance prediction model which con-sidered two rock characteristic parameters as independentvariables through regression data analysis Yagiz et al [12]carried out a regression model of the advance rate consid-ering five geological parameters in which four independentvariables have a linear relationship with the advance rateexcept one Grima et al [13] presented a similar model ofthe advance rate using the neural-fuzzy method Zhang et al[14] proposed a regression model of the energy consumptioncombined with mechanical analysis Gong and Zhao [15]analyzed the on-site data from a project in Singapore todiscuss the relation between the rock brittleness and thetunneling performance Hamidi et al [16] discussed themapping relation between rock properties and the advancerate through Rock Mass Rating sorting technique Benardosand Kaliampakos [17] established a neural network model ofthe penetration considering rock property parameters thethrust force of single cutter the cutter dimension and therotating speed Zhou et al [18] proposed a prediction modelfor the air chamber pressure control in slurry shield tunnelingthrough the PSO-based Elman neural network method

Data mining technology has been gradually applied inthe analysis of mass measured data to extract the importantrelation among the parameters contained in shield engineer-ing However many problems remain in the actual use ofthis technology First most of the regression models built

180000

135000

90000

45000

0

Tota

l thr

ust (

kN)

F = 120573D2

120573 = 1200

120573 = 500

2 4 6 8 10 12

Diameter (m)

Figure 1 Predicted thrust range by Krause empirical formula

for the above mentioned work are linear or quasilinearregression models which exhibit difficulty in recognizingthe nonlinear structure as a explicit model Recognizingand building a explicit function expression with a definitephysical connotation and control law from the seeminglyldquoblack boxrdquo mass data are the difficult points Second exist-ing research lacks the internal-mechanism-analysis-basedtheoretical direction in the selection and representation ofengineering parameters and cannot effectively describe theinternal relation among core factors Lastly no instructivemodeling standard exists for the equal treatment and directadding of independent variables in different classes anddimensions during the modeling of multivariable problemsThese problems are difficult to be solved only relying onthe development of mining technologies The nature andcharacteristics of specific project objects for research mustbe combined With the development of data inverse analysisresearch problem-based internal mechanism analysis anddata mining technology need to be combined to facilitatethe application of the measured data analyses in complexengineering system modeling

This paper aims to conduct a systematical analysis ofmass on-site data from the airborne recording system ofshield machines in order to identify and build an explicitfunction expression for tunneling thrust Dimensional anal-ysis method is integrated with the regression and residualanalysis technologies used in modeling A systematic masson-site data inverse analysis method is then establishedThe influencing factors of the thrust are detailed analyzedA mechanical model of tunneling thrust is built and theeffectiveness of the model is discussed with on-site data fromseveral project cases

2 Mechanical Characteristic Analysis andModeling of Tunneling Thrust

A shield machine which is usually composed of severalparts can perform integrated-underground constructionincluding excavation deslagging and lining Figure 2 gives

Mathematical Problems in Engineering 3

CutterheadSubsequentequipment

Chamber

Rotating electricalmachine

Thrust jackShield shell

Figure 2 Schematic of a shield tunneling machine

a schematic description of a shield machinersquos complex struc-ture Each part of the equipment generates constant complexmechanical effects on the surrounding ground which con-tributes to the tunneling thrust Therefore the total thrustcan include up tomore than a dozen components and changein real time with several geological and control parameterswhich present difficulties in the analysis and modeling

To analyze the main factors influencing the tunnelingthrust they can be described by three kinds of parametersincluding operating parameters geological parameter andstructural parameter as shown in Figure 3 In the tunnelingprocess of a shield machine some thrust components arerelatively stable and are not influenced by tunneling speedsuch as the earth pressure at rest the groundwater pressurethe shield shell friction and subsequent equipment tractionSome others are directly related to tunneling speed such asthe thrust acting on the cutterhead which will increase whenthe machine tunneling fast Considering these characteristicsof the tunneling thrust the paper divides it into the externalthrust and the operating thrust which can be expressed as

119865 = 119865119900+ 119865119890 (1)

119865119900= 119891 (119882 V 120596) (2)

119865119890= 119892 (119882119863119867119867

1015840) (3)

where119865 is the total tunneling thrust119865119900is the operating thrust

which ismainly influenced by themachine advance rate V thecutterhead rotating speed120596 and the ground bearing capacity119882 119865119890is the external thrust which is mainly influenced by

the shield diameter 119863 the ground bearing capacity 119882 thedepth of overburden 119867 and the groundwater level 1198671015840 119891()and 119892() represent the functional relation among parametersModeling for the tunneling thrust is to determine the specificfunction expressions of 119891() and 119892()

The advance rate of the machine V (mmin) and the rotat-ing speed of cutterhead 120596 (revmin) are the core parametersto describe the operating status of the machine The paperintroduces the tunneling penetration 120575 (mrev) which is thecutting depth that the cutterhead completes in every circle ofrotation The value of the tunneling penetration equals theratio of the advance rate and the rotating speed

120575 =V

120596 (4)

The tunneling penetration reflects the influence of boththe advance rate and the cutterhead rotating speedTherefore

Geologicalcondition

Equipmentfeature

Rotatingspeed

Advancerate

Adjust of o

peratin

g

paramete

rs

Change of geology

Over-burden

Geologicalcategories

Operatingstatus

Effect of shield

diameter

-waterVariationspace ofthrust

Ground

Cutterhead

Figure 3 Analysis on main factors influencing tunneling thrust

it may be used as the comprehensive characteristic index ofthe operating status Equation (2) can be simplified as

119865119900= 119891 (119882 120575) (5)

Considering that the chamber support pressure is relatedto earth pressure at rest and groundwater pressure and theacting pressure is basically in the balance status on tunnelinginterface the chamber support pressure 119875 (kPa) may be usedas an approximate substitute for the influence of both theearth pressure at rest and the groundwater pressure Equation(3) can be simplified as

119865119890= 119892 (119882119863 119875) (6)

Basic physical laws and the dimensional analysis methodare adopted in this study to determine the specific functionexpressions of 119891() and 119892() Dimensional analysis methodreveals the physical essence of the problem through thedimensional attribute analysis of parameters thereby provid-ing an effective tool for the research on complex engineeringproblems According to the dimensional analysis theory onlythe physical variables with the same dimension can be addedThen the specific functional relation of 119891() and 119892() can bedetermined based on dimensional analysis combined withthe mechanical analysis for the shield tunneling process

119865119900prop 119882119886120575119887

119865119890prop 119875119888119863119890+119882119889119863119890

(7)


Then the thrust model can be expressed as

119865 = 119865119900+ 119865119904= 1205731119882119886120575119887+ (1205732119875119888+ 1205733119882119889)119863119890 (8)

where12057311205732 and120573

3are the undetermined coefficients whose

values are related to the specific project condition and canbe identified by on-site data analysis 119886 119887 119888 119889 and 119890 are theundetermined exponents which can be determined throughdimensional equilibrium principle

The functional relation among variables in (8) needs tosatisfy the principle of dimension consistency The dimen-sional expression of tunneling thrust is [119872][119871][119879]minus2 Thephysical variables in the operating thrust 119865

119900and the external

thrust 119865119904can be expressed using three basic dimensions

namely length [119871] mass [119872] and time [119879] The dimensionof the ground bearing capacity119882 and the chamber supportpressure 119875 is [119872][119871]minus1[119879]minus2 and that of the penetration 120575and the diameter 119863 is [119871] Equation (8) can be expressed indimensional form as follows

[119872] [119871] [119879]minus2= [119872]

119886[119871]minus119886[119879]minus2119886[119871]119887

[119872] [119871] [119879]minus2= [119872]

119888[119871]minus119888[119879]minus2119888[119871]119890

+ [119872]119889[119871]minus119889[119879]minus2119889[119871]119890

(9)

The dimension consistency principle requires that thedimensions on the two sides of (9) be equal thus theundetermined exponents are 119886 = 119888 = 119889 = 1 119887 = 2 and119890 = 2 The general formula of the tunneling thrust withdimensionless undetermined coefficients 120573

1 1205732 and 120573

3are

then obtained as

119865 = 12057311198821205752+ (1205732119882+ 120573

3119875)1198632 (10)

Equation (10) gives the basic architecture of the shieldtunneling thrust model in which the relation between themain factors including the operating status the geologicalconditions and the equipment structure and the tunnelingthrust is presented If the geological parameter 119882 is smallthe required tunneling thrust is also small Under similargeological conditions the increase in the tunneling thrustis related to the square of the penetration when tunnelingfast If the equipment tunnels with a large overburden thetotal thrust will also increase In (10) the tunneling thrusthas a square relation with the equipment diameter whichis consistent with the balance relation in mechanics and thethrust-diameter relation provided in the Krause empiricalformula

3 Inverse Identification of Shield TunnelingThrust Based on Mass On-Site Data

The inversion identification of the dimensionless unde-termined coefficients in the general formula (10) can beconducted based on specific engineering data and with themultiple regressionmethodThemultiple regressionmethodone of the basic methods in data mining can be used todetermine the explicit function relation of the two groups of

Table 1 Basic statistical characteristics for the data

Minimum Maximum Average Standarddeviation

Thrust (kN) 1043607 1744065 1337689 132127Advance rate(mmmin) 2486 4589 3638 566

Rotating speed(revmin) 090 110 102 007

Penetration(mmrev) 2276 4589 3591 589

Pressure inchamber (MPa) 019 030 023 0017

Ground bearingcapacity (kPa) 7283 9046 8337 597

variables In the method the target variables are dependentand the physical variables that cause constant changes in thedependent variables are independent The analysis aims todetermine the quantitative relation between the dependentand independent variables through constant iterative compu-tation and result judgment

The project used in the regression analysis is the 700-ringconstruction area of the Tianjin Metro Line 9 from ShiyijingLu Station to Dazhigu Xilu Station in China Komatsu Ltd isselected to provide TM634PMX earth pressure balance shieldwith a diameter of 634m The tunnel has an overburden ofabout 8ndash11m The main geological strata concerned includemucky soil silty clay silt silty sand and so forth Thegeological parameters involved in the analysis were adoptedaccording to the actual situation of engineering which wasprovided through in situ geotechnique tests The operatingand control parameters used were recorded in real time bythemachine duringworkingThe on-site data out of 350 ringsof this project is used as training sample and the data of theother 250 rings will be reserved as testing sample The basicstatistical characteristics of the data is given in Table 1

Based on the least square method the professional statis-tical analysis software SPSS (Statistical Product and ServiceSolutions) is used to complete the regression computationThe optimal values of the undetermined coefficients are thendetermined and the specific expression of the tunnelingthrust is obtained as (11) The significance of the regressioncomputation is preliminarily verified through the combina-tion of 119865- and 119905-tests

119865 = 18 times 1041198821205752+ (12119882 + 079119875)119863

2 (11)

The statistical testing results of the regression computa-tion are shown in Table 2 The linear correlation coefficientreflects the level of linear correlation of the variables whichis between 0 and 1 A large value of the coefficient indicatesobvious linear correlation This coefficient can be used todiscuss the rationality of the regression model structure 119865-test is adopted to analyze the overall regression effect and119905-test is employed to determine the significance of everyregression coefficient The closer the computed result of theassociated probability (the value of Prob in Table 2) is to


Table 2 Statistical testing results of the regression computation

(a) Linear correlation coefficient

Compositional independent variable 1198751198632 1198821198632 1198821205752

Correlation coefficient 0996 0992 0967Prob 0000 0000 0000

(b) 119865-test

Model 119865-test 1198772

119865 Prob0994 17310787 0000

(c) 119905-test

Model 119905-test Regression coefficient 119905 Prob1205731

18383878 9800 00001205732

1179 7877 00001205733

0792 13268 0000

0 the better regression effect it indicates According to theresults in Table 2 the dependent variable 119865 has a close linearcorrelation with 1198821205752 1198821198632 and 1198751198632 indicating that thenonlinear structure of the regression model is rational The119865- and 119905-tests also show that the regression effect reachedsignificant levels

The above analysis shows that the tunneling thrustmodel built based on mechanical characteristic analysis anddimensional analysis methods reflects the influence of majorfactors and the internal relation among different parametersThe model can also provide a description of the changeof tunneling thrust in relation to the geological conditionsand operating status A set of curves that describe thechange between tunneling thrust under different geologicalconditions and tunneling penetration is illustrated in Figure 4based on (11)

4 Residual Analysis and Verification ofthe Shield Tunneling Thrust Model

Themeasured value of the tunneling thrust and that predictedby the model are quantitatively compared The difference inthe two is defined as the model residual as follows

119890119899= 119865measured minus 119865predicted (12)

where 119890119899is the model residual which is related to the

tunneling ring number Figure 5 presents the curves of theon-site measured values and the predicted values by (11)of the shield tunneling thrust changing with the numberof rings The measured values and the predicted valuesare consistent in terms of change trend Moreover Figure 5shows that the residual curve basically fluctuates around 0indicating that themodel has included themain parts and thecore influencing factors of the tunneling thrust Besides thefluctuation of the residual curve shows a little change trendwhich shows that someof the secondary influencing factors ofthe thrust may still be in the model residual The stationarityand randomness of the model residual data series are further

Penetration (mmrev)

Tunn

elin

g th

rust

(kN

)

30000

25000

20000

15000

1000030 40 50 60 70 80 90 100

W = 100KPaW = 80KPaW = 60KPa

Figure 4 Curves of the thrust changing with the penetration underdifferent geological conditions

Table 3 Stationarity analysis of the model residual

Phillips-Perron test statistic PP-Stat Probminus13947 0000

analyzed to discuss the applicability of the shield tunnelingthrust model

The PP statisticalmagnitude [19] is adopted to analyze thestationarity of the model residual This statistical magnitudecan describe the overall fluctuation of the residual data withthe change in the ring number Assuming that the residualdata are a nonstationary series the result (the value of Prob inTable 3) shows that the associated probability of accepting thenull hypothesis is approximately 0 Therefore the calculatedresidual of the model is a stationary series which indicatesthat the model has included the major influencing factorsof the tunneling thrust The 119876 statistical magnitude [20] isadopted to analyze the randomness of the model residualThis statistical magnitude can describe the relevance of theresidual data If the magnitude has a relatively large valuea law must be followed in the residual data Assuming thatno tunneling thrust influencing factor exists in the residualdata that is the residual data are a pure random series theresults (the values of Prob in Table 4) show that the associatedprobability of accepting the null hypothesis is approximately0 This finding means that the residual data of (11) does nottotally randomly fluctuate but has some secondary factorsexisting in it

The residual analysis above indicates that the model (11)reflects the influence of the main parts and the core param-eters of the tunneling thrust In addition some secondaryfactors and errors still exist in themodel residualThepossiblereasons may include the following First the geological dataadopted in the analysis is from geological borehole mea-surement Considering that the data obtained from a limited


30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings

Predicted valueMeasured valueResidual

(a)

200

150

100

50

0

Freq

uenc

y

lt5 lt10 lt15 lt20 lt25

Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)

Training dataDiscrepancy () = absolute value [(model value ndashmeasured value)measured value]

(b)

Figure 5 Residual analysis of the tunneling thrustmodel (a) Comparison between the predicted thrust and themeasured value (b) Statisticalhistogram of the residuals

Table 4 Randomness analysis of the model residual

Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000

number of geological boreholes cannot accurately reflect thegeological information of all the tunneling sections an errormay occur in the predicted results when the geological datais used in the model Second the effects of key geologicalparameters are considered in the model However given thatthe parameters considered are limited an error may alsooccur in the predicted value Third noise exists in some on-site measured data

The 250-ring measured data that were not involved inthe modeling process are reserved as a testing sample forthe model verification This group of independent data issubstituted in (11) and the predicted result of testing sampleis obtained Comparing the predicted value and the on-sitemeasured value of the tunneling thrust Figure 6 shows thatthey are basically accordant reflecting the rationality andeffectiveness of the inversion analysis and modeling methodbased onmassmeasured data proposed in the paperThe flowchart of the method is shown in Figure 7

5 Engineering Applications of the ShieldTunneling Thrust Model

The tunneling thrust model built based on mechanical anddimensional analyses reflects the essential characteristics ofthe equipment during construction as well as the internalinfluence law among the core control parametersThis modelcan be applied in the prediction and control of the tunnelingthrust in shield engineering under different engineer con-ditions Equation (10) provides the general formula of themodel which should be subjected to specific projects in itsapplicationThe engineering applications of the model undertwo typical geological conditions namely sandy pebblegeology and rock-soil mixed geology were illustrated in thepaper to discuss and verify the effectiveness of the model

The first project discussed is 700-ring section betweenFengtai Dongjie Station to Fengtai Beilu Station of BeijingMetro Line 9 in China An EPB shield tunneling machinemanufactured by JTSC Company in Japan was used witha diameter of 614m The tunnel has an overburden ofabout 8ndash11m The construction area studied mainly runsthrough sandy pebble The range of the advance rate is 12ndash82mmmin and that of the rotating speed of cutterheadis 08ndash10 revmin The penetration is changed from 14 to92mmrev The pressure inside chamber is adjusted in therange of 40ndash130 kPa

The other project discussed is 400-ring section betweenXiang Mihu North Station to Xiang Mei North Station ofShenzhen Metro Line 2 in China An EPB shield tunnel-ing machine manufactured by NFM Company in Francewas used with a diameter of 628m The tunnel has anoverburden of about 9ndash12m The construction area studiedmainly runs through plain fill hard plasticmoldable gravellysand silty clay completely weathered granite and stronglyweathered granite The advance rate varies in the range


20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)

On-site measured thrust (kN)

Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)

Testing dataDiscrepancy () = absolute value [(model value ndashmeasured value)measured value]

(b)

Figure 6 Independent data test of themodel (a) Cross-correlation graph of the testing data (b) Statistical histogram of the prediction errors

Residualrequirement

Analysis for main factors and mechanical characteristics

Independent on-sitemeasured data

Model predictedvalue

Comparison

Yes

No

Improve

External + operatingthrust

Dimensionalanalysis

Mechanical modeling

Coefficient identification

Multipleregression

Residual analysis

Stationarityrandomness

Thrust model


Chamber

Rotatingelectricalmachine


Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad

Variationspace ofthrust

Mod

el p

redi

cted

thru

st (k

N)

On-site measured thrust (kN)Testing data

Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000

Testing dataDiscrepancy () = absolute value [(modelvalue ndash measured value)measured value]


Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring

Training dataOn-site value

Residual

Predicted value

300020001000

0minus1000minus2000minus3000

0 50 100 150 200 250 300 350

Figure 7 Flow chart for the mechanical analysis and modeling method based on mass on-site data

of 12ndash60mmmin The rotating speed of the cutterhead is10ndash14 revmin The excavating depth per revolution is 11ndash54mmrev The pressure inside chamber is 113ndash220 kPa

The first 100-ring data of the two projects is used todetermine the coefficients in the general formula (10) fromwhich the specific function expression of the two projectsabove can be obtained as shown in Table 5 The predictedvalue and measured value of the tunneling thrust in the two

projects are quantitatively compared and the predicted errorsare statistically analyzed as shown in Figure 8 The predictederrors of 80 data points in both of the two projects areless than 30 As the proposed model effectively extracts thecore characteristics of the thrust variation the predicted valuecan be consistent with the measured value thereby providingan important reference for the prediction and control of thetunneling thrust on shield machines

8 Mathematical Problems in EngineeringFr

eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70

0lt10 lt20 lt30 lt40 gt40

140

120

100

80

60

40

20

0

Beijing metro line 9Discrepancy () = absolute value [(model value ndashmeasured value)measured value]

(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)

lt10 lt20 lt30 lt40 gt40

140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0

Shenzhen metro line 2Discrepancy () = absolute value [(model value ndashmeasured value)measured value]

(b)

Figure 8 Statistical histogram of the model prediction errors (a) Beijing Metro Line 9 (b) Shenzhen Metro Line 2

Table 5 Engineering applications of the shield tunneling thrustmodel

General formula of themodel 119865 = 120573

11198821205752+ (1205732119882+ 120573

3119875)1198632

Thrust expression ofBeijing Metro Line 9 119865 = 91 times 10

31198821205752+ (061119882 + 039119875)119863

2

Thrust expression ofShenzhen Metro Line 2 119865 = 89 times 10

31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions

A new method for the mass on-site data analysis and mod-eling of complex engineering equipment is proposed in thisstudy which integrates the mechanical dimension analysisand the regression analysis First the engineering variableswere evaluated according to the mechanical equilibrium andthe deformation compatibility the primary and secondaryinfluencing factors were then distinguished Second theinternal interaction laws among different variables weredetermined through the dimensional analysis method Thebasic architecture of themodel was identified and the generalformula for themodel was establishedThird themodel coef-ficients were determined and specific function expressionswere provided through multiple regression analysis methodin consideration of on-site data from specific projects Lastlythe effectiveness and applicability of the model were verifiedthrough the residual analysis

The method proposed was applied to analyze and modelthe tunneling thrust in shield engineering determine theinternal law of effect between the tunneling thrust and thecore parameters (eg geological equipment operating andstructural parameters) and build an explicit general tun-neling thrust model The model coefficients were identifiedthe thrust function expression of the specific project was

provided and the effectiveness of the model was verifiedbased on the mass on-site data of Tianjin Metro Line 9Furthermore the model was also applied to two otherengineering cases with different geological characteristicsBeijing Metro Line 9 and Shenzhen Metro Line 2 to evaluatethe applicability of the model

This work can serve as a theoretical basis for the thrustdetermination in the forward design and construction con-trol of shield tunneling machines It may also offer newresearch concepts for mass measured data analysis andmodeling of complex engineering equipment characterizedby nonlinearity multiple influencing factors and multifieldcoupling

Acknowledgments

This work was supported by the State Key Laboratoryof Shield Machine and Boring Technology the NationalBasic Research Program of China (973 Program Grant no2013CB035402) and the National Natural Science Founda-tion of China (NSFC Grant no 11127202)

References

[1] A K Choudhary J A Harding andMK Tiwari ldquoDataminingin manufacturing a review based on the kind of knowledgerdquoJournal of Intelligent Manufacturing vol 20 no 5 pp 501ndash5212009

[2] S Chatterjee and A S Hadi Regression Analysis by ExampleJohn Wiley amp Sons Hoboken NJ USA 2012

[3] J Zhao P Witold and S Sabrina ldquoData mining and knowledgediscovery in industrial engineeringrdquoMathematical Problems inEngineering vol 2013 Article ID 790160 2 pages 2013

[4] P Z Lu S Y Chen and Y J Zheng ldquoArtificial intelligence incivil engineeringrdquo Mathematical Problems in Engineering vol2012 Article ID 145974 22 pages 2012


[5] W Li K Huang D Zhang and Z Qin ldquoAccurate countingbloom filters for large-scale data processingrdquo MathematicalProblems in Engineering vol 2013 Article ID 516298 11 pages2013

[6] L T Wang G F Gong H Shi and H Y Yang ldquoModelingand analysis of thrust force for EPB shield tunneling machinerdquoAutomation in Construction vol 27 pp 138ndash146 2012

[7] T Krause Schildvortrieb mit flussigkeits- und erdgestutzterOrtsbrust vol 24 Mitteilung des Instituts fur Grundbau undBodenmechanik 1987 (German)

[8] BMaidlMHerrenknecht and L AnheuserMechanised ShieldTunneling Ernst amp Sohn Berlin Germany 1996

[9] H Zhang XWu andW Zeng ldquoStudy on tunneling experimentandmathematical model of EPB shieldrdquoChinese Journal of RockMechanics and Engineering vol 24 no A02 pp 5762ndash57662005 (Chinese)

[10] U Ates N Bilgin and H Copur ldquoEstimating torque thrustand other design parameters of different type TBMs withsome criticism to TBMs used in Turkish tunneling projectsrdquoTunnelling and Underground Space Technology vol 40 pp 46ndash63 2014

[11] J Hassanpour J Rostami and J Zhao ldquoA new hard rock TBMperformance predictionmodel for project planningrdquoTunnellingand Underground Space Technology vol 26 no 5 pp 595ndash6032011

[12] S Yagiz C Gokceoglu E Sezer and S Iplikci ldquoApplication oftwo non-linear prediction tools to the estimation of tunnel bor-ingmachine performancerdquoEngineeringApplications of ArtificialIntelligence vol 22 no 4-5 pp 818ndash814 2009

[13] M A Grima P A Bruines and P N W Verhoef ldquoModelingtunnel boring machine performance by neuro-fuzzy methodsrdquoTunnelling and Underground Space Technology vol 15 no 3 pp259ndash269 2000

[14] Q Zhang C Qu Y Kang G Huang and Z Cai ldquoIdenti-fication and optimization of energy consumption by shieldtunnel machines using a combined mechanical and regressionanalysisrdquoTunnelling andUnderground Space Technology vol 28no 1 pp 350ndash354 2012

[15] Q M Gong and J Zhao ldquoInfluence of rock brittleness onTBM penetration rate in Singapore graniterdquo Tunnelling andUnderground Space Technology vol 22 no 3 pp 317ndash324 2007

[16] J KHamidi K Shahriar B Rezai and J Rostami ldquoPerformanceprediction of hard rock TBM using Rock Mass Rating (RMR)systemrdquo Tunnelling and Underground Space Technology vol 25no 4 pp 333ndash345 2010

[17] A G Benardos and D C Kaliampakos ldquoModelling TBMperformance with artificial neural networksrdquo Tunnelling andUnderground Space Technology vol 19 no 6 pp 597ndash605 2004

[18] C Zhou L Y Ding and R He ldquoPSO-based Elman neuralnetwork model for predictive control of air chamber pressurein slurry shield tunneling under Yangtze Riverrdquo Automation inConstruction vol 36 pp 208ndash217 2013

[19] P Rothman ldquoForecasting asymmetric unemployment ratesrdquoReview of Economics and Statistics vol 80 no 1 pp 164ndash1681998

[20] G E P Box G M Jenkins and G C Reinsel Time SeriesAnalysis Forecasting and Control Holden-Day San FranciscoCalif USA 1970

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


The composition of the total thrust is very complex andusually includes dozens of components which are closelyrelated to the geological condition the equipment structureand operating statusHowever the influence laws between thethrust and those factors remain unclear Therefore analyzingthe effective information in mass tunneling data recorded bythe equipment airborne system and studying the correlationamong the major control parameters are important for thesetting and control of the tunneling thrust and for ensuringsafe and efficient construction

The classic Krause empirical formula is currently themain formula adopted to estimate the shield tunneling thrust[6] Krause a German engineer proposed an empiricalformula 119865 = 1205731198632 (119863 is the diameter and 120573 is the empiricalcoefficient) through the statistical analysis on engineeringdata from hundreds of shield machines [7] This empiricalformula describes the power relation between the thrust andthe equipment diameter However all the other factors suchas construction geological conditions andmachine operatingstatus are included in the wide-range empirical coefficient120573 as shown in Figure 1 In the early stage of thrust design600 kNm2 was used as the experience thrust value on unitarea of the tunneling interface [8] Besides Zhang et al [9]developed a linear regression model based on experimentaldata analysis which took the thrust the cutterhead rotatingspeed and the chamber pressure as independent variablesand the advance rate as the dependent variable Ates etal [10] discussed the statistical relationships between TBMdiameter and installed thrust capacity nominal cutterheadtorque capacity total weight maximum rotational speed ofcutterhead and number of disc cutters based on a databaseincluding 262 TBMsrsquo design parameters Hassanpour et al[11] proposed a performance prediction model which con-sidered two rock characteristic parameters as independentvariables through regression data analysis Yagiz et al [12]carried out a regression model of the advance rate consid-ering five geological parameters in which four independentvariables have a linear relationship with the advance rateexcept one Grima et al [13] presented a similar model ofthe advance rate using the neural-fuzzy method Zhang et al[14] proposed a regression model of the energy consumptioncombined with mechanical analysis Gong and Zhao [15]analyzed the on-site data from a project in Singapore todiscuss the relation between the rock brittleness and thetunneling performance Hamidi et al [16] discussed themapping relation between rock properties and the advancerate through Rock Mass Rating sorting technique Benardosand Kaliampakos [17] established a neural network model ofthe penetration considering rock property parameters thethrust force of single cutter the cutter dimension and therotating speed Zhou et al [18] proposed a prediction modelfor the air chamber pressure control in slurry shield tunnelingthrough the PSO-based Elman neural network method

Data mining technology has been gradually applied inthe analysis of mass measured data to extract the importantrelation among the parameters contained in shield engineer-ing However many problems remain in the actual use ofthis technology First most of the regression models built

180000

135000

90000

45000

0

Tota

l thr

ust (

kN)

F = 120573D2

120573 = 1200

120573 = 500

2 4 6 8 10 12

Diameter (m)

Figure 1 Predicted thrust range by Krause empirical formula

for the above mentioned work are linear or quasilinearregression models which exhibit difficulty in recognizingthe nonlinear structure as a explicit model Recognizingand building a explicit function expression with a definitephysical connotation and control law from the seeminglyldquoblack boxrdquo mass data are the difficult points Second exist-ing research lacks the internal-mechanism-analysis-basedtheoretical direction in the selection and representation ofengineering parameters and cannot effectively describe theinternal relation among core factors Lastly no instructivemodeling standard exists for the equal treatment and directadding of independent variables in different classes anddimensions during the modeling of multivariable problemsThese problems are difficult to be solved only relying onthe development of mining technologies The nature andcharacteristics of specific project objects for research mustbe combined With the development of data inverse analysisresearch problem-based internal mechanism analysis anddata mining technology need to be combined to facilitatethe application of the measured data analyses in complexengineering system modeling

This paper aims to conduct a systematical analysis ofmass on-site data from the airborne recording system ofshield machines in order to identify and build an explicitfunction expression for tunneling thrust Dimensional anal-ysis method is integrated with the regression and residualanalysis technologies used in modeling A systematic masson-site data inverse analysis method is then establishedThe influencing factors of the thrust are detailed analyzedA mechanical model of tunneling thrust is built and theeffectiveness of the model is discussed with on-site data fromseveral project cases

2 Mechanical Characteristic Analysis andModeling of Tunneling Thrust

A shield machine which is usually composed of severalparts can perform integrated-underground constructionincluding excavation deslagging and lining Figure 2 gives



Chamber






119865 = 119865119900+ 119865119890 (1)

119865119900= 119891 (119882 V 120596) (2)

119865119890= 119892 (119882119863119867119867

1015840) (3)





120575 =V

120596 (4)


Geologicalcondition

Equipmentfeature

Rotatingspeed

Advancerate

Adjust of o

peratin

g

paramete

rs

Change of geology

Over-burden


Operatingstatus

Effect of shield

diameter


Ground

Cutterhead



119865119900= 119891 (119882 120575) (5)


119865119890= 119892 (119882119863 119875) (6)


119865119900prop 119882119886120575119887

119865119890prop 119875119888119863119890+119882119889119863119890

(7)



119865 = 119865119900+ 119865119904= 1205731119882119886120575119887+ (1205732119875119888+ 1205733119882119889)119863119890 (8)

where12057311205732 and120573







[119872] [119871] [119879]minus2= [119872]

119886[119871]minus119886[119879]minus2119886[119871]119887

[119872] [119871] [119879]minus2= [119872]

119888[119871]minus119888[119879]minus2119888[119871]119890

+ [119872]119889[119871]minus119889[119879]minus2119889[119871]119890

(9)


1 1205732 and 120573

3are

then obtained as

119865 = 12057311198821205752+ (1205732119882+ 120573

3119875)1198632 (10)














119865 = 18 times 1041198821205752+ (12119882 + 079119875)119863

2 (11)







(b) 119865-test

Model 119865-test 1198772

119865 Prob0994 17310787 0000

(c) 119905-test


18383878 9800 00001205732

1179 7877 00001205733

0792 13268 0000








Penetration (mmrev)

Tunn

elin

g th

rust

(kN

)

30000

25000

20000

15000

1000030 40 50 60 70 80 90 100









30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings


(a)

200

150

100

50

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)



Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000








20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Chamber






119865 = 119865119900+ 119865119890 (1)

119865119900= 119891 (119882 V 120596) (2)

119865119890= 119892 (119882119863119867119867

1015840) (3)





120575 =V

120596 (4)


Geologicalcondition

Equipmentfeature

Rotatingspeed

Advancerate

Adjust of o

peratin

g

paramete

rs

Change of geology

Over-burden


Operatingstatus

Effect of shield

diameter


Ground

Cutterhead



119865119900= 119891 (119882 120575) (5)


119865119890= 119892 (119882119863 119875) (6)


119865119900prop 119882119886120575119887

119865119890prop 119875119888119863119890+119882119889119863119890

(7)



119865 = 119865119900+ 119865119904= 1205731119882119886120575119887+ (1205732119875119888+ 1205733119882119889)119863119890 (8)

where12057311205732 and120573







[119872] [119871] [119879]minus2= [119872]

119886[119871]minus119886[119879]minus2119886[119871]119887

[119872] [119871] [119879]minus2= [119872]

119888[119871]minus119888[119879]minus2119888[119871]119890

+ [119872]119889[119871]minus119889[119879]minus2119889[119871]119890

(9)


1 1205732 and 120573

3are

then obtained as

119865 = 12057311198821205752+ (1205732119882+ 120573

3119875)1198632 (10)














119865 = 18 times 1041198821205752+ (12119882 + 079119875)119863

2 (11)







(b) 119865-test

Model 119865-test 1198772

119865 Prob0994 17310787 0000

(c) 119905-test


18383878 9800 00001205732

1179 7877 00001205733

0792 13268 0000








Penetration (mmrev)

Tunn

elin

g th

rust

(kN

)

30000

25000

20000

15000

1000030 40 50 60 70 80 90 100









30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings


(a)

200

150

100

50

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)



Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000








20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119865 = 119865119900+ 119865119904= 1205731119882119886120575119887+ (1205732119875119888+ 1205733119882119889)119863119890 (8)

where12057311205732 and120573







[119872] [119871] [119879]minus2= [119872]

119886[119871]minus119886[119879]minus2119886[119871]119887

[119872] [119871] [119879]minus2= [119872]

119888[119871]minus119888[119879]minus2119888[119871]119890

+ [119872]119889[119871]minus119889[119879]minus2119889[119871]119890

(9)


1 1205732 and 120573

3are

then obtained as

119865 = 12057311198821205752+ (1205732119882+ 120573

3119875)1198632 (10)














119865 = 18 times 1041198821205752+ (12119882 + 079119875)119863

2 (11)







(b) 119865-test

Model 119865-test 1198772

119865 Prob0994 17310787 0000

(c) 119905-test


18383878 9800 00001205732

1179 7877 00001205733

0792 13268 0000








Penetration (mmrev)

Tunn

elin

g th

rust

(kN

)

30000

25000

20000

15000

1000030 40 50 60 70 80 90 100









30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings


(a)

200

150

100

50

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)



Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000








20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














(b) 119865-test

Model 119865-test 1198772

119865 Prob0994 17310787 0000

(c) 119905-test


18383878 9800 00001205732

1179 7877 00001205733

0792 13268 0000








Penetration (mmrev)

Tunn

elin

g th

rust

(kN

)

30000

25000

20000

15000

1000030 40 50 60 70 80 90 100









30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings


(a)

200

150

100

50

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)



Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000








20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










30000

24000

18000

12000

6000

0

Tunn

elin

g th

rust

(kN

)

0 50 100 150 200 250 300 350

Number of rings


(a)

200

150

100

50

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)



Step 119876-stat Prob1 52737 00002 88529 00003 13690 00004 16048 00005 18260 00006 18986 00007 19665 00008 20411 00009 20690 000010 21077 0000








20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20000

16000

12000

80002000016000120008000

Mod

el p

redi

cted

thru

st (k

N)


Testing data

Y = X

Y = 0953X

(a)

120

100

20

40

60

80

0

Freq

uenc

y


Discrepancy ()

150

100

50

0

Accu

mul

ativ

e (

)


(b)


Residualrequirement




Comparison

Yes

No

Improve


Dimensionalanalysis

Mechanical modeling


Multipleregression

Residual analysis


Thrust model


Chamber



Geologicalcondition

Equipmentfeature

CutterheadRotating

speedAdvance

rate

Adjust of o

peratin

g

paramete

rs

Change of geology

Ove

r-bu

rden

Geo

logi

cal

cate

gorie

s

Controlstatus

Effect of shield

diameter

Gro

und-

wat

er

adad


Mod

el p

redi

cted

thru

st (k

N)


Y = X

Y = 0953X

20000

16000

12000

8000

2000016000120008000



Discrepancy ()

200

150

100

50

0

Freq

uenc

y

150

100

50

0

Accu

mul

ativ

e (

)

Tunn

elin

g th

rust

(kN

)Tu

nnel

ing

thru

st (k

N)

25000

20000

15000

10000

350 400 450 500 550 600 650 700

Number of ring

Number of ring


Residual

Predicted value

300020001000


0 50 100 150 200 250 300 350






eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










eque

ncy

Discrepancy ()

Accu

mul

ativ

e (

)

350

280

210

140

70


140

120

100

80

60

40

20

0


(a)

Freq

uenc

y

Discrepancy ()

Accu

mul

ativ

e (

)


140

120

100

80

60

40

20

0

140

120

100

80

60

40

20

0


(b)




11198821205752+ (1205732119882+ 120573

3119875)1198632


31198821205752+ (061119882 + 039119875)119863

2


31198821205752+ (059119882 + 039119875)119863

2

6 Conclusions





Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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