USING QUALITY CONTROL CHARTS TO SEGMENT ROAD SURFACE CONDITION DATA - - PowerPoint PPT Presentation

USING QUALITY CONTROL CHARTS TO SEGMENT ROAD SURFACE CONDITION DATA

Amin El Gendy D t l C did t Doctoral Candidate Ahmed Shalaby Associate Professor Department of Civil Engineering Department of Civil Engineering University of Manitoba Wi i M it b C d Winnipeg, Manitoba, Canada

Outline

Segmentation as a classification tool Current strategies for segmenting road surface condition

pavement condition data pavement 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-uniform homogeneous subsections which have statistically uniform properties using one or several condition data elements

Segmentation strategies g 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 i Solutions are recursive and adaptable. Additional criteria are required to terminate the process.

The cumulative difference approach (CDA) (CDA)

esponse, ri r Pavement Re r1 r2 r3 X

(a) Response

(a) X1 X3 X2 ative Area, Ax

_

A

x

A Cumula X1 X3 X2 Zx X

_ x x x

A A Z − =

x

A X

(b) Cumulative Area

(b)

1 3 2

ve Difference, Z ( ) (-) + Border X

(c) Cumulative Differences

(c) Cumulativ X1 X3 X2 (-) (+)

• Border

X

(c) Cumulative Differences

The absolute difference approach (ADA) (ADA)

Segment length Average response Response range rd

d i i

r r Z − =

ri X xi xd

ff The 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 d by 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 location r

Exhaustive search for dividing the data set into two homogeneous subsections

X

Classification and regression trees (CART) (CART)

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

Step 1

r

Step 2 St 3 Step 3 Regression tree for eight delineated sections

X

Control chart approach (C-Chart)

Response ibution 2 +kσ = +3σ Upper control limit, UCL Upper warning limit UWL µ bability Distri +2σ Upper warning limit, UWL 9.73% 95.4% Response Normal Pro

• 2σ
• kσ

=- 3σ Lower control limit, LCL Lower warning limit, LWL 99 9 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: σ µ k + = UCL lower control limit LCL are: µ µ = CL k LCL σ µ 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 limits The outer limits are usually at 3σ and the inner limits, usually at 2σ

Estimating mean and standard deviation from segment data deviation from segment data

Mean and st. deviation are estimated from segment data Must be recalculated with the addition of each data point to the segment

r = µ ˆ

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

Estimate of mean

= average of responses in current segment

µ ˆ r

= estimate of mean for current segment

ˆ

1 2 2 2

−

∑

=

r n r

n i i

Estimate of variance 1

1 2

− =

=

n

i

σ

ri = response value

2

ˆ σ = estimate of variance for current segment

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

Modifying c-chart control limits using response range using response range

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

applications Control limits can be assigned to not exceed a desired c UCL + = µ ˆ Control limits can be assigned to not exceed a desired (practical) target range: c LCL c UCL − = + = µ µ ˆ µ σ ˆ in the segment and 0.5 rrange c is the minimum of the 3

C-chart delineation algorithm

• 1. 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 mean

• 2. 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. σ ˆ

• 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 approach Segmentation using c-chart approach

ri Segment border +c2 UCL2 Response, r µ1 +c1 UCL1 µ2

• c2

LCL2 Pavement

• c1

LCL1 Segment 1 Segment 2 Km -post

Identification of homogeneous segments using c-chart approach

Comparison of segmentation methods Comparison of segmentation methods

Segmentation Method Characteristic Method Segmentation Criterion Minimum number

• f segments

Final number of segments Segment range CDA Diversion from Two Unlimited Not specified CDA Diversion from mean of entire profile Two Unlimited Not specified ADA Target range One Unlimited Predetermined g g CART Minimum sum of Two Predetermined Unlimited squared error C-Chart Standard One Unlimited Optional deviation p

The AASHTO Example

45

p

35 40

F N (4 )

25 30

Segment borders

23 3 16 9 12 9 8 9 103 84.5 79 7 74 8 69.2 59.5 51.5 47.5 41 8 32 2 27 4 119 111.8 91.7

km-post

15 20

2σ C-Chart CDA 3σ C-Chart

23.3 16.9 12.9 8.9 103 84.5 79.7 74.8 69.2 59.5 51.5 47.5 41.8 32.2 27.4 111.8 13.7 8.9 103 84.5 67.6 51.5 42.6 119 112.7 91.7 23.3 103 84.5 71.6 53.9 40.2 27.4 119 112.7 79.7 5 10

CART CDA

8 92.5 53.9 40.2 104.6 84.5 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 11 CDA 521 11 CART 431 7 2σ C-Chart 264 19 3σ C-Chart 331 11

Joining of adjacent segments Joining 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 uniform considered uniform.

r Similar statistical properties Minimum segment length

Original segmentation

r X

Joining adjacent segments

X

Joining of adjacent segments

40 45

Profile

g j g

30 35

FN(40) Segment borders km-post

15 20 25

12 23 18 g

23.3 16.9 12.9 8.9 103 79.7 74.8 69.2 59.5 51.5 41.8 32.2 27.4 119 111.8 91.7 84.5 47.5

2σ C-Chart

5 10

53 47 41 35 29 23 Response Range %

• 10
• 5

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 segments g j g

1200 22 SSE Number of Segments 600 800 1000 FN(40)] 14 18 Segments 200 400 600 SSE [F 6 10 Number of 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 of should 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

• f the entire section is not affected by segmentation
• f 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 approximation It is important to strike a balance between approximation

• f 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 ti homogeneous sections.

Several available methods for segmenting road condition Several available methods for segmenting road condition

data are presented. C h t b l d t ti t l d

C-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 pp autonomous process that does not require prior knowledge

• f 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 segmentation segmentation

Segmentation tools and criteria should be tuned to achieve

g the desired solution

Th k Y Thank You