USING QUALITY CONTROL CHARTS TO SEGMENT ROAD SURFACE CONDITION DATA Amin El Gendy D Doctoral Candidate t l C did t Ahmed Shalaby Associate Professor Department of Civil Engineering Department of Civil Engineering University of Manitoba Wi Winnipeg, Manitoba, Canada i M it b C d
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 1. Cumulative Difference Approach (CDA) Cumulative Difference Approach (CDA) 2. Absolute Difference Approach (ADA) 3. 3 Classification and Regression Trees (CART) 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 Solutions are recursive and adaptable. Additional criteria i d d t bl Additi l it i are required to terminate the process.
The cumulative difference approach (CDA) (CDA) esponse, r i r r 2 Pavement Re r 1 r 3 X (a) Response X 1 X 2 X 3 ative Area, A x (a) A _ x A A Cumula x _ = − Z A A x x x (b) Cumulative Area X X 1 X X 2 X 3 Z x ve Difference, Z 1 2 3 (b) + Border (-) (c) Cumulative Differences (c) Cumulative Differences Cumulativ ( ) (+) X X X 1 (-) X 2 X 3 - Border (c)
The absolute difference approach (ADA) (ADA) Response range Average response Segment length = − Z r r r d i i d r i x i x d X The absolute difference approach ff
Classification and regression trees (CART) (CART) Each data set is divided into two homogeneous subsections by locating the position where the sum of the squared b l ti th iti h th f th d differences between the data in each segment and the corresponding mean of each segment is minimized. r Segmenting location X Exhaustive search for dividing the data set into two homogeneous subsections
Classification and regression trees (CART) (CART) The procedure is applied recursively to each segment until a maximum number of segments or a minimum til i b f t i i segment length is reached. Step 1 Step 2 r St Step 3 3 X Regression tree for eight delineated sections
Control chart approach (C-Chart) Response ibution Upper control limit, UCL +k σ = +3 σ Upper warning limit, UWL Upper warning limit UWL +2 σ 2 bability Distri Response 95.4% 9.73% µ 9 99 Normal Pro Lower warning limit, LWL -2 σ Lower control limit, LCL -k σ =- 3 σ 3 σ Observation number Typical control chart showing warning limits ( ± 2 σ ) and control limits ( ± 3 σ )
General model for control chart The centreline CL, the upper control limit UCL, and the lower control limit LCL are: lower control limit LCL are: = µ µ + σ k UCL = µ CL = µ − σ k k LCL LCL where k is the distance of the control limit from the centreline expressed in standard deviation unit. The outer limits are usually at 3 σ and the inner limits The outer limits are usually at 3 σ and the inner limits, usually at 2 σ
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 Must be recalculated with the addition of each data point to the segment Estimate of mean µ = ˆ r µ ˆ = estimate of mean for current segment r = average of responses in current segment Estimate of variance n ∑ − 2 2 r n r i σ = = = ˆ 2 2 1 1 i i − 1 n r i = response value σ = estimate of variance for current segment ˆ 2 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 Control limits can be assigned to not exceed a desired (practical) target range: = = µ µ + + ˆ UCL UCL c c = µ µ − ˆ LCL c σ ˆ in the segment and 0.5 r range c is the minimum of the 3
C-chart delineation algorithm 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 statistical parameters 2 2. On adding each new data sample, the estimated mean 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. σ ˆ 3. The lower of 3 and 0.5 r range are used to establish and update the control limits. 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 Segment border UCL 2 +c 2 r i Response, r UCL 1 µ 2 +c 1 -c 2 µ 1 LCL 2 Pavement -c 1 LCL 1 Segment 1 Segment 2 Km -post Identification of homogeneous segments using c-chart approach
Comparison of segmentation methods Comparison of segmentation methods Segmentation Characteristic Method Method Segmentation Minimum number Final number of Segment range Criterion of segments segments CDA CDA Diversion from Diversion from Two Two Unlimited Unlimited Not specified Not specified mean of entire profile ADA Target range g g One Unlimited Predetermined CART Minimum sum of Two Predetermined Unlimited squared error C-Chart Standard One Unlimited Optional p deviation
The AASHTO Example p 45 40 ) 0 (4 35 N F 30 km-post Segment borders 25 91.7 119 47.5 47.5 51.5 51.5 59.5 59.5 69.2 69.2 84.5 84.5 111.8 111.8 8 9 8.9 12.9 12 9 16.9 16 9 23 3 23.3 27 4 27.4 32.2 32 2 41.8 41 8 74.8 74 8 79.7 79 7 103 103 2 σ C-Chart 20 8.9 91.7 103 112.7 119 13.7 42.6 51.5 67.6 84.5 3 σ C-Chart 15 23.3 27.4 40.2 53.9 71.6 79.7 84.5 103 112.7 119 CDA CDA 10 8 40.2 53.9 84.5 92.5 104.6 CART 5 0 0 0 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 CDA 521 521 11 11 CART 431 7 2 σ C-Chart 264 19 3 σ 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. Minimum segment length r Similar statistical properties Original segmentation X r Joining adjacent segments X
Joining of adjacent segments g j g 45 Profile 40 FN(40) 35 30 km-post Segment borders g 25 91.7 111.8 119 84.5 8.9 12.9 16.9 23.3 27.4 32.2 41.8 47.5 51.5 59.5 69.2 74.8 79.7 103 2 σ C-Chart 20 12 15 18 23 23 Response Range % 29 10 35 5 41 47 53 53 0 0 R 59 70 -5 82 -10 0 20 40 60 80 100 120 Highway km-post Joining of adjacent segments generated by 2 σ c-chart method using various response ranges
Joining of adjacent segments g j g SSE Number of Segments 1200 22 1000 Segments 18 FN(40)] 800 14 600 600 SSE [F Number of 10 400 6 200 N 0 2 0 20 23 40 47 53 60 80 100 Response Range % Response Range % Relationship of sum of squared errors (SSE) and number of joined segments to 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 of the entire section is not affected by segmentation of 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 of a condition in a uniform subsection and the details provided by higher resolution data.
Recommend
More recommend
