USING QUALITY CONTROL CHARTS TO SEGMENT ROAD SURFACE CONDITION DATA

Amin El GendyD t l C did tDoctoral Candidate

Ahmed ShalabyyAssociate Professor

Department of Civil EngineeringDepartment of Civil EngineeringUniversity of Manitoba

Wi i M it b C dWinnipeg, Manitoba, Canada

Outline

Segmentation as a classification tool

Current strategies for segmenting road surface condition pavement condition datapavement condition data

Limitations of the current segmentation methods

Fundamental concepts of quality control charts and application as a segmentation method

Compare results of c-chart segmentation with previous segmentation methods

Introduction

Many elements of road condition data are collected periodically at the network-level, for example IRI, friction, FWD, rut depth.

This data drives the selection of maintenance and rehabilitation strategies and the extent of each treatment

With the growth in stored data, there is a need to identify homogeneous and consistent condition-based subsections

A network could be segmented dynamically into homogeneous subsections which have statistically-uniformhomogeneous subsections which have statistically uniform properties using one or several condition data elements

Segmentation strategiesg g

Several approaches exist for classifying condition data.

Four methods will be discussed:1 Cumulative Difference Approach (CDA)1. Cumulative Difference Approach (CDA)2. Absolute Difference Approach (ADA)3 Classification and Regression Trees (CART)3. Classification and Regression Trees (CART)4. Quality Control Charts (C-Chart)

Important to note that there is no unique or final solution.

S l ti i d d t bl Additi l it iSolutions are recursive and adaptable. Additional criteria are required to terminate the process.

The cumulative difference approach (CDA)(CDA)

espo

nse,

r ir

Pav

emen

t Re

r1

r2

r3

X (a) Response

(a)X1 X3 X2

ativ

e A

rea,

Ax

_

AxA

Cum

ula

X1 X3X2Z x X

_

xxx AAZ −=

xA

X (b) Cumulative Area

(b)1 3 2

ve D

iffer

ence

, Z

( )(-)

+ Border

X (c) Cumulative Differences

(c)

Cum

ulat

iv X1

X3 X2(-)

(+)

-Border

X (c) Cumulative Differences

The absolute difference approach (ADA)(ADA)

Segment lengthAverage response

Response range

rd dii rrZ −=ri

Xxi xd

ffThe absolute difference approach

Classification and regression trees (CART)(CART)

Each data set is divided into two homogeneous subsections b l ti th iti h th f th dby locating the position where the sum of the squared differences between the data in each segment and the corresponding mean of each segment is minimized.

Segmenting locationr

Exhaustive search for dividing the data set into two homogeneous subsectionsX

Classification and regression trees (CART)(CART)

The procedure is applied recursively to each segment til i b f t i iuntil a maximum number of segments or a minimum

segment length is reached. Step 1

r Step 2

St 3Step 3

Regression tree for eight delineated sectionsX

Control chart approach (C-Chart)R

espo

nse

ibut

ion

2

+kσ = +3σUpper control limit, UCL

Upper warning limit UWL

µ

babi

lity

Dis

tri+2σUpper warning limit, UWL

9.73

%

95.4

%

Response

Nor

mal

Pro

-2σ

-kσ =-3σ

Lower control limit, LCL

Lower warning limit, LWL

999

Observation number

3σ

Typical control chart showing warning limits (±2σ) and control limits (±3σ)

General model for control chart

The centreline CL, the upper control limit UCL, and the lower control limit LCL are:

σµ k+=UCL

lower control limit LCL are:

µ

µ=CL

kLCL σµ k−=LCL

where k is the distance of the control limit from the centreline expressed in standard deviation unit.

The outer limits are usually at 3σ and the inner limitsThe outer limits are usually at 3σ and the inner limits, usually at 2σ

Estimating mean and standard deviation from segment datadeviation from segment dataMean and st. deviation are estimated from segment dataMust be recalculated with the addition of each data point to the segment

r=µ̂

Must be recalculated with the addition of each data point to the segment

Estimate of mean

= average of responses in current segmentµ̂r

= estimate of mean for current segment

ˆ 1

22

2−∑

=

rnrn

ii

Estimate of variance

112

−= =

niσ

ri = response value2σ̂ = estimate of variance for current segment

n = number of response points (i) in current segment

Modifying c-chart control limits using response rangeusing response range

St. deviation of a segment can be too large for practical applications

Control limits can be assigned to not exceed a desired

cUCL += µ̂

Control limits can be assigned to not exceed a desired (practical) target range:

cLCL

cUCL

−=

+=

µ

µ

µ̂

σ̂ in the segment and 0.5 rrangec is the minimum of the 3

C-chart delineation algorithm1. Proceed from the fifth data sample from the start of the

segment to allow for a reasonable initial estimate of the

C chart delineation algorithm

statistical parameters

2 On adding each new data sample the estimated mean2. On adding each new data sample, the estimated mean and variance of the segment are calculated based on data from start of segment up to the tested sample.

3. The lower of 3 and 0.5 rrange are used to establish and update the control limits.

σ̂

4. A new segment is started when the tested data sample falls outside the control limits.falls outside the control limits.

5. The process continues until all profile data is segmented

Segmentation using c-chart approachSegmentation using c-chart approachr i

Segment border

+c2

UCL2

Res

pons

e, r

µ1

+c1

UCL1 µ2

-c2LCL2

Pav

emen

t

-c1LCL1

Segment 1 Segment 2

Km -postIdentification of homogeneous segments using c-chart approach

Comparison of segmentation methodsComparison of segmentation methods

Segmentation Method

Characteristic Method

Segmentation Criterion

Minimum number of segments

Final number ofsegments

Segment range

CDA Diversion from Two Unlimited Not specifiedCDA Diversion from mean of entire profile

Two Unlimited Not specified

ADA Target range One Unlimited Predeterminedg g

CART Minimum sum of Two Predetermined Unlimitedsquared error

C-Chart Standard One Unlimited Optionaldeviation

p

The AASHTO Example

45

p

35

40

FN(4

0)

25

30

Segment borders

23 316 912 98 9 10384.579 774 869.259.551.547.541 832 227 4 119111.891.7

km-post

15

202σ C-Chart

CDA

3σ C-Chart

23.316.912.98.9 10384.579.774.869.259.551.547.541.832.227.4 111.8

13.78.9 10384.567.651.542.6 119112.791.7

23.3 10384.571.653.940.227.4 119112.779.7

0

5

10

CART

CDA

8 92.553.940.2 104.684.5

00 20 40 60 80 100 120

Highway km-post

Delineating a Friction Number profile using various methods

The sum of squared errors (SSE)The sum of squared errors (SSE)Comparison of sum of squared errors (SSE) using three segmentation methods

Segmentation Method SSE [FN(40)] Number of subsections

CDA 521 11CDA 521 11

CART 431 7

2σ C-Chart 264 19

3σ C-Chart 331 11

Joining of adjacent segmentsJoining of adjacent segments

If two adjacent segments have similar statistical properties, joining should be examined.joining should be examined.

Joining is performed if the resulting (joined) segment is considered uniformconsidered uniform.

r Similar statistical propertiesMinimum segment length

Original segmentation

rX

Joining adjacent segmentsX

Joining of adjacent segments

40

45

Profile

g j g

30

35

FN(4

0)

Segment borderskm-post

15

20

25

12

23

18

g

23.316.912.98.9 10379.774.869.259.551.541.832.227.4 119111.891.784.547.52σ C-Chart

0

5

10

53

4741

35

29 23

Res

pons

e R

ange

%

-10

-5

0

0 20 40 60 80 100 120

70

59

53

82

R

Highway km-post

Joining of adjacent segments generated by 2σ c-chart method using various response ranges

Joining of adjacent segmentsg j g

1200 22

SSE Number of Segments

600

800

1000

FN(4

0)]

14

18

Seg

men

ts

200

400

600

SSE

[F

6

10

Num

ber

of

00 20 40 60 80 100

Response Range %

2

N

23 47 53

Relationship of sum of squared errors (SSE) and number of joined segments to response range

Response Range %

Limitations

No clear winner. Selection of a segmentation method should be based on the type of data and the quality ofshould be based on the type of data and the quality of information to be extracted.

No unique or perfect answer. The lowest SEE is when each segment contains exactly one sample and the mean of the entire section is not affected by segmentationof the entire section is not affected by segmentation.

Process can be “nearsighted” if it cannot recognize brief disturbances

It is important to strike a balance between approximationIt is important to strike a balance between approximation of a condition in a uniform subsection and the details provided by higher resolution data.

Conclusions and recommendations

Segmentation allows for the extraction of uniform h tihomogeneous sections.

Several available methods for segmenting road conditionSeveral available methods for segmenting road condition data are presented.

C h t b l d t ti t l dC-chart can be employed as a segmentation tool and selecting a practical target range provides additional control over the solution.

The AASHTO example was used to demonstrate the various methods.various methods.

Conclusions and recommendations

The main advantage of the c-chart approach is that it is an g ppautonomous process that does not require prior knowledge of the statistical characteristics of the data.

If the characteristics of data are known, additional criteria such as target range can be incorporated to improve the segmentationsegmentation

Segmentation tools and criteria should be tuned to achieve gthe desired solution

Th k YThank You