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Implementation of Traffic Data Quality Verification for WIM Sites

1. 28 GVW for Test Sample Il re Obs LO 2 Estimated C9 rr io cco 100 110 120 130 140 150 Index in days CUSUM Based DI for Test Sample Il co cy ym n o ch o o 101 107 113 119 125 131 137 143 149 Time Figure 31 CUSUM Analysis indicating unstable truck population 29 CHAPTER 3 DEVELOPMENT AND IMPLEMENTATION A software implementation guideline and a Microsoft Windows based tool called WIM Data Analyst was developed using the Visual Studio package with R Net library version 1 5 13 based on the CUSUM methodology previously described The Graphical User Interface GUI of the WIM Data Analyst is displayed in Figure 32 For each station the monitoring process can begin with a training sample corresponding to a period when the system is known to be in calibration Then recursively new data sets say monthly data can be used as test samples and CUSUM analysis can be done as discussed in case studies in section 2 3 If no significant shift is found the testing sample may be appended to the training data set This process can be continued until a significant shift is observed in a testing sample Once the analysis signals a shift WIM operator can apply suitable adjustment factor to the WIM data 3 1 Software Implementation Guidelines An implementation guideline is proposed to distinguish cases where inconsistencies in average daily GVWs such as mentioned above are found As before we begin our analys
2. Minnesota Department of Transportation Implementation of Traffic Data Quality Verification RESEARCH for WIM Sites SERVICES amp LIBRARY Office of Transportation System Management Chen Fu Liao Principal Investigator Minnesota Traffic Observatory Department of Civil Environmental and Geo Engineering University of Minnesota May 2015 Research Project Final Report 2015 18 To request this document in an alternative format call 651 366 4718 or 1 800 657 3774 Greater Minnesota or email your request to ADArequest dotOstate mn us Please request at least one week in advance Technical Report Documentation Page 1 Report No 2 3 Recipients Accession No MN RC 2015 18 4 Title and Subtitle 5 Report Date Implementation of Traffic Data Quality Verification for WIM May 2015 7 Author s 8 Performing Organization Report No Chen Fu Liao Indrajit Chatterjee and Gary A Davis 9 Performing Organization Name and Address 10 Project Task Work Unit No Department of Civil Environmental and Geo Engineering CTS Project 2014027 University of Minnesota 500 Pillsbury Drive SE 11 Contract C or Grant G No Minneapolis MN 55455 c 99008 wo 133 12 Sponsoring Organization Name and Address 13 Type of Report and Period Covered Minnesota Department of Transportation Research Services amp Library 14 Sponsoring Agency Code 395 John Ireland Boulevard MS 330 St Paul MN 55155 15 Supple
3. S and Speigelhalter D 1999 Probabilistic Networks and Expert Systems Springer New York Dahlin C 1992 Proposed Method for Calibrating Weigh in Motion Systems and for Monitoring That Calibration Over Time Transportation Research Record 1364 161 168 Dempster A P Laird N M and Bubin D B 1997 Maximum Likelihood from Incomplete Data via EM Algorithm Journal of the Royal Statistical Society Series B Vol 39 1 38 Davis G A 1997 Estimation Theory Approach to Monitoring and Updating Average Daily Traffic Minnesota Dept of Transportation St Paul MN Davis G A and Yang S 1999 Bayesian Methods for Estimating Average Vehicle Classification Volumes Local Road Research Board St Paul MN Davis G A and Swenson T 2006 Collective Responsibility for Freeway Rear Ending Accidents An Application of Probabilistic Causal Models Accident Analysis and Prevention 38 4 728 736 Davis G A 2003 Bayesian Reconstruction of Traffic Accidents Law Probability and Risk 2 69 89 Elkins L and Higgins C 2008 Development of Truck Axle Spectra from Oregon Weigh in Motion Data for Use in Pavement Design and Analysis Research Unit Oregon Department of Transportation Salem OR Flinner M and Horsey H 2002 Traffic Data Editing Procedures Final report Transportation Pooled Fund Study SPR 2 182 FHWA U S Department of Transportation Washington DC http www fhwa d
4. to detect if there is any change in the mean level More detailed information about the CUSUM methodology and the decision interval selection can be found in Chapter 3 2 of the research report by Liao amp Davis 2012 CUSUM of standardized residuals E io tA 3 7 0 50 100 150 200 Index CUSUM Based Decision Interval for Residual Ew pan 30 e a Os Time Figure 2 CUSUM based decision interval for AR 1 residuals A new AR 1 process is as follows XxX 4 G0 X H 0wm vt lt 70 2 6 X 1 5 0 X 1 5 0m Wt gt 70 2 7 The above process suggests that there 1s change of 5 kips in mean level for time index greater than 70 We use the estimated model to predict the measurements for t gt 70 and record the residuals based on predicted values Figure 3 shows the residuals for the non stationary AR 1 process Residual of non staionary AR1 process res 0 20 40 60 80 100 Index Figure 3 Residuals after fitting a non stationary AR 1 process The next step is to perform CUSUM analysis on the residuals Figure 4 and 5 shows CUSUM plot and decision interval plots for the residuals Adjusted CUSUM plot for AR1 with change in mu cusum 20 40 30 50 index Figure 4 CUSUM plot for AR 1 residual CUSUM Based Decision Interval for AR1 with change in mu 10 Dipcusum 5 O 10 Time Figure 5 CUSUM based decision interval for AR 1 residual with change in mean As exp
5. 13 CUSUM based decision plots tor Case Terson reao nae ES O OAE OA 13 GVW for average daily fully loaded trucks station 29 Case I ooooooonnnnonnnnccnononnnnnnnnnnnononnnnnonnnnnnnnnnnnnnnnoss 14 Eine learnin sample Case Moues A AS 15 Comparison between estimated and observed testing sample Case H ocoooonoooooaconcncncnonononnnonnnonononons 15 CUSUM based decision plots Tor Case ler din lcciac 16 GVW for average daily fully loaded trucks station 37 Case IMI ooooonnnnnnnnnccnnnnnnnnnoncncnononononononnnnnnnnnnnnnnnos 17 Fittine learns sample Caso Ts a a sous dadeasaaatisetoctesansuasyeds 18 Comparison between estimated and observed testing sample Case IM oooooononnncncnnnnnnnnnonnnnnnnnnonos 18 CUSUM based decision plots tor Case M ceci il 19 Figure 19 GVW for average daily fully loaded trucks station 26 Case IV ooccccnnnnnnnnnnonononnnnnononnncnnncnnnnncninnnnnos 20 Pisure 20 Fitting learning sample Case LV da 21 Figure 21 Comparison between estimated and observed testing sample Case IV ooccccnnncncnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 21 Figure 22 CUSUM based decision plots for Case IM ac ii 22 Figure 23 Inconsistent GVWs for fully loaded trucks from Station 26 Lane 4 occcccccccccncnnnonononnnnnncnnnnnnnnnnnonnnnnnos 23 Figure 24 Inconsistent GVWs for fully loaded trucks from Station 37 ooooccncnncnnnnnonnnnnnnnnnnnnnnnnnnnnononnnnnnnnnnnnnnnnoss 24 Figure 25 Inconsi
6. 2010 End Data 6 8 201 1 check Use Calib Date and select Daily option from the CUSUM analysis window Click on Plot GVW9 or CUSUM Analysis button to display the results shown in Figure 54 Example 2 Select WIM 33 Lane 1 Start Date 1 20 2014 End Data 2 27 2015 uncheck Use Calib Date then set Learn Data to 5 1 2014 and select Daily option from the CUSUM analysis window Click on Plot GVW9 or CUSUM Analysis button to display the results MB CUSUM Analysis coe fm Set Code and Data Directory Data Aggregation a Daily Weekly E ChenftueMaAQOT 41m lmplementation A Code Latest 1 Select wlk 2 Select Date WIM Station Start Date 10 5 2010 WIM 29 Leam Date 315 207 4 Use Calib Date Lane 1 End Date 6 8 2011 El Plot GYW 9 Stationanty Test CUSUM Analysis CUSUM Analysis Logs Initializing and loading A routines G9 Processing WIM data class_id 49 station_id 29 lane_id 1 type GY Init_date 10 6 2010 Final date 67872011 Clear Log Close Figure 50 CUSUM analysis screen 46 Testing Period 64 92 50 End Date GVVV9 78 76 r N Start Date Learn or l Calibration Date tz 0 50 100 150 Figure 51 Illustration of selecting dates learning and testing periods 8 Gi Graph File Graph Help WIM 29 GVW9 Lane 1 10 0570 10290 112240 124640 01 0941 0202491 022641 03 2241 044941 0509 11 06 0271 Date Figure 52
7. Comma Separated Value Center for Transportation Studies Cumulative Sum Decision Interval Expectation Maximization Equivalent Single Axle Load Federal Highway Administration Feet Front Axle Spacing Front Axle Weight Geographic Information System Global Positioning System Graphical Users Interface Gross Vehicle Weight Hyper Text Markup Language Integrated Development Environment International Road Dynamics Inc Intelligent Transportation Systems kilo pound force a non SI unit of force 1 000 pounds force Kwiatkowski Phillips Schmidt Shin test for stationarity Long Term Pavement Performance Minnesota Depart of Transportation Minnesota Traffic Observatory Manual on Uniform Traffic Control Devices National Cooperative Highway Research Program Operating System Partial Auto Correlation Function Research amp Innovative Technology Administration SD SPC SXW TL TMAS TMG UMN USDOT VC VTRIS WIM Standard Deviation Statistical Process Control Steering Axle Weight Technical Liaison Travel Monitoring Analysis System Traffic Monitoring Guide University of Minnesota U S Department of Transportation Vehicle Class Vehicle Travel Information System Weigh In Motion EXECUTIVE SUMMARY Weigh In Motion WIM systems have been widely used by state agencies to collect the traffic data on major state roadways and bridges to support traffic load forecasting pavement design and analysis infrastructure in
8. Cumulative Sum CUSUM Analysis CUSUM Methodology Decision Interval DI 7 References 8 FHWA Vehicle Classification Chart 9 Known Issues 10 Contacting Us 11 Glossary 4 1 Getting Started 4 1 1 Systems Requirements l E o Operating System OS Windows 7 or later Microsoft NET framework 4 5 or later Please make sure your PC is connected to the Internet Minimum hardware requirements Intel Xeon CPU 2 0 GHz with 8 0 GB memory Additional software needed R Statistical software version 3 1 1 or later R 1s a free software environment for statistical computing and graphics This version of WIM Data Analysis was tested with a 64 bit Dell Precision T5600 computer which has dual Intel Xeon E5 2609 2 4 GHz CPUs running on the Microsoft Windows 7 OS with service pack 1 The R statistics software version 3 1 1 was also installed 4 1 2 Installation Guide Download and install R statistics software version 3 1 1 or later from http www r project org Unzip Installation zip file then run WIM Data Analyst installation package setup exe to install the software tool If the Publisher cannot be verified warning message 1s displayed click Install for software installation to continue Follow the instructions on the screen to complete the installation A shortcut icon will be added to your computer desktop when the installation 1s finished After the software is successfully installed run WIM Da
9. Fitting Open the EM fitting screen as shown in Figure 49 to process the gross vehicle weight GVW of class 9 vehicles e CUSUM Analysis Open the CUSUM analysis screen as illustrated in Figure 50 to perform CUSUM analysis for a selected WIM site 4 Help Display HTML online help document 4 2 3 EM Fitting When click on the GVW EM button from the main screen the EM fitting screen will be displayed as illustrated in Figure 49 1 Place the monthly WIM raw data file for example 201412 040 csv under the working directory Data Raw WIM Data directory 2 Select a WIM station from the station listbox Select a single lane or all lanes for the EM processing in the lane listbox 3 Choose a year and a month for GVW9 data analysis 4 Select Daily or Weekly data aggregation The Weekly aggregation option is for WIM stations with relatively low truck volumes in a day 5 Click Run EM Fitting button to begin the EM data processing 6 EM fitting results will be displayed in the bottom textbox 7 Use Clear Log button to remove results displayed in the textbox 44 g GVWO EM Fitting File WIM Data Directory Data Aggregation Code and Data Filepath Daily E Cherfu MnDOT WIM implementation R Code Latest Weekly Select WIM Lane Year Month WIM Station Lane s WIM 26 2 Initializing and loading R routines Loading 4 Preparing WIM 26 Daily data loaded Runnin
10. Sample GVW9 plot 47 Learning data is Dickey Fuller stationary Statistic 4 35 Lag order 4 p value 0 01 Alternative hypothesis stationary Figure 53 Sample stationarity test results File Graph Help Export Data WIM 29 GVW9 Lane 1 Page Setup pant sr CUSUM Lower CUSUM DI Threshold Close m 2 D a O 03 16 11 03 24 11 04 01 11 04 09 11 04 17 11 04 25 11 05 03 11 05 11 11 05 19 11 05 27 11 06 04 11 Date Figure 54 Sample results from a CUSUM analysis Figure 55 illustrates the weekly GVW plot of class 9 trucks from Jan 1 2014 to Feb 1 2015 The average GVW of class 9 vehicles increased abruptly around 2 5 2015 and stayed around 135 140 kips till 10 6 2014 48 A CUSUM Graph File Graph Help WIM 34 GVW9 Lane 1 Weekly Calibration Ho Adjustment Model e Predict ao 5 m m ds m de eee ee ed ee ee ee e e de e de e e e e de e ed a 01 0114 11 0154 Figure 55 Weekly GVW9 plot of WIM 34 49 CHAPTER 5 SUMMARY AND CONCLUSION A Weigh In Motion WIM system tends to go out of calibration from time to time and as a result generates biased and inaccurate measurements Several external factors such as vehicle speed weather pavement conditions etc can be attributed to such anomaly To overcome this problem a statistical quality control technique is warranted that would provide the WIM operator with some guidelines whenever the syst
11. behavior were included in Appendix A CHAPTER 2 WIM DATA MODELING AND ANALYSIS 2 1 Mixture Model In finite mixture modeling of normal densities the unknown density of a multivariate random vector g x can be expressed using the following equation McLachlan and Peel 2000 g x E 2419400 41 94 1 Ag Aggg x 2 1 Where g x is the i component density with normal distribution A is the i non negative component proportion 2 4 4 1 The GVW of class 9 vehicles GVW9 consists of unloaded partially loaded and fully loaded components A three component mixture model as described in equation 2 2 was formulated to estimate the parameters of the normal densities and corresponding mixture proportions using the Expectation Maximization EM algorithm Dempster et al 1997 The EM algorithm allows us to estimate the maximum likelihood of the model parameters R http www r project org scripts were developed to process GVW9 mixture modeling using EM fitting technique GVW x Ay gi x Aaga x Aggalx 2 2 Where GVW x is the Class 9 Gross Vehicle Weight GVW distribution 81 x is the empty class 9 truck normal GVW distribution g2 x is the partially loaded class 9 truck normal GVW distribution g3 x is the filly loaded class 9 truck normal GVW distribution A is the i non negative component proportion A 42 A 1 2 2 Simulation Based Analysis The CUSUM chart is a commonly used quali
12. determine traffic data editing procedures As a result of the study 120 traffic data quality rules were generated However the study was not able to develop software to assist in the evaluation of the rule base and to put revised software into production due to extensive data system integration and testing were needed Cumulative Sum CUSUM chart is a commonly used quality control method to detect deviations from benchmark values Hawkins amp Olwell 1998 used the CUSUM charts and charting as Statistical Process Control SPC tools for quality improvement Luce o 2004 used generalized CUSUM charts to detect level shifts in auto correlated noise Lin et al 2007 developed an adaptive CUSUM algorithm to robustly detect anomaly The cumulative sum of difference between each measurement and the benchmark value is calculated as the CUSUM value In addition to the regular CUSUM charts an adjusting CUSUM methodology will be used to for data quality assurance in this study Liao and Davis 2012 used adjusting CUSUM methodology to detect anomaly of the GVW of class 9 fully loaded trucks 1 4 Report Organization This report 1s organized as follows WIM data modeling and analysis are presented in Chapter 2 Software development and implementation are discussed in Chapter 3 User s manual of the WIM data analyst tool 1s discussed in Chapter 4 Finally Chapter 5 included project summary A few cases of WIM data analysis with non stationary
13. M station lane year and month the user can click the Run EM Fitting button to perform EM analysis Results of the EM analysis are stored in the working directory automatically 32 A Sid EM Fitting File WM Data Directory Code and Data Filepath E ChentueMnDOT WIM Implementation A CodeLatest Select WIM Lane Year Month a WM Station Lane wih 40 All Close Initializing and loading A routines Loading WIM 40 data loaded Running EM algorithm for TM 40 Lane AI 2010 11 Completed Results are placed in Data EM Processed folder Initializing and loading A routines Loading WIM 40 data loaded Running EM algorithm for IM 40 Lane All 2010 12 Cornpleted Results are placed in Data EM Processed folder Figure 35 User interface of EM analysis 8 CUSUM Analysis Set Code and Data Directory E ChentuceMnAQoT WIM Implementation A Code Latest 1 Select Wilh Data 2 Select Date WM Station Start Date We IM 29 107 542010 E Vehicle Class Data Type End Date 9 Gy Bf 8 2011 E Clear Log CUSUM Analysis CUSUM Analysis Log Processing IM data class id 9 lane_id 1 station_id 24 tupe yyy lrit_ date 10 5 2010 Final date 6 3 2071 Return Mag Are there missing obs TRUE WIM sensor shifted by 5 33 kips on 2011 05 09 Ao downward shift found in Wik sensor Figure 36 User interface of CUSUM analysis 33 Figure 36 illustrates the
14. SOTA Set Working Directory Code and Data Filepath E ChenfusMnDOT WIM Implementation A Code Latest Analysis Motes 1 Set working directory 2 Click GYW 9 EM button to load and process monthly WIM data GVW EM File 3 Click CUSUM Analysis to perform WIM data quality analysis EXIT CUSUM Analysis Figure 47 File menu bar Exit Exit the WIM Data Analyst tool Calibration Log Open WIM sensor calibration log file for editing This calibration log file is used for CUSUM analysis See Figure 48 displays an example of the calibration log table The Reload Save and Close options under the file menu bar in the calibration table screen allows users to reload the log table save the log file after editing or close the table The Edit menu contains Add Record and Delete Record options Use the Add Record to add a new log record to the end of the table To delete a record select a row and choose Delete Record to delete the selected calibration record Click on Help to get additional information 43 A Calibration Table File Edit Help wih Dat Initial Final Calib Station oe Weight Weight Percentage 1 26 671172011 HA HA 26 142422012 HA HA 26 4 30 2012 HA HA 26 172072011 HA HA 26 671172011 HA HA Zb 142422012 HA HA 26 of 14 2012 HA HA 26 142322013 HA HA 26 172072011 HA 1c C idd ndd LAES E Aa ABAE AMAA B mn Figure 48 Sample of WIM calibration log table 3 Options e GVW9 EM
15. Studio package based on the NET framework An open source software R NET https rdotnet codeplex com was integrated into the Microsoft NET framework to interface with the R software http www r project org another open source software package for statistical analysis The WIM data analyst tool consists of two key components 1 e EM Fitting and CUSUM analyses and a HTML online help document The EM analysis takes a monthly WIM raw data CSV file of each WIM station from MnDOT and estimates the mean and deviations of GVW of class 9 fully loaded trucks Results of the EM analyses are stored in a file directory for CUSUM analysis The CUSUM analysis takes inputs from the EM results and a calibration file based on MnDOT calibration logs to model a learning sample and estimates the residuals between the prediction and WIM observation Output from the CUSUM analysis will indicate whether there 1s any sensor drift during the analysis period 50 REFERENCES ASTM Standard E1318 94 1994 Standard Specification for Highway Weigh in Motion WIM Systems with User requirements and Test Method Philadelphia PA Chatterjee I Liao C F Davis G 2015 A Statistical Process Control Approach for Traffic Data Quality Verification and Sensor Calibration for Weigh In Motion Systems 15 1274 Transportation Research Board 94th annual meeting Compendium of Papers Washington D C January 11 15 2015 Cowell R Dawid P Lauritzen
16. USUM behavior is solely attributed to a plausible shift in WIM sensor However several case studies indicated that this might not be true always The proposed methodology first identified a learning period The learning sample was then analyzed to fit a time series model To identify if there is any shift in WIM sensor a CUSUM analysis on residuals which were obtained from predictions on testing sample was performed The underlying assumption of the methodology is if the data is generated from a stable process then the predictions based on the model estimated from the learning sample should consistently capture the variation in the testing sample Any introduction of instability or sensor shift in the testing sample should be reflected in the residuals Then CUSUM algorithm was implemented to detect such shift in WIM sensor This methodology could benefit state agencies such as MnDOT by identifying when calibration was lost and subsequently a proper modification factor could be applied to the out of calibration data to adjust for the bias Additional unknown factors besides WIM sensors such as varying truck population and other external factors are found to influence WIM measurements With only limited information available it 1s not possible to identify such factors and provide explanations for such an inconsistent pattern At this point the goal is to propose a methodology that would alert the WIM operator whenever such anomaly is detected To ide
17. ail information WIM Data Analyst Help Doc Hide Print Options Contents Index Search Welcome are Welcome to the Weigh In Motion WIM Data Analyst Getting Started This tool is developed under the implementation project E G Tutorial Implementation of Traffic Data Quality Verification for WIM Sites Set Working Directory sponsored by the Minnesota Department of Transportation Menu Bar MnDOT The goal of this tool is to detect any abnormal change EM Fitting in the measurements from WIM sensors and provide an estimate CUSUM Analysis of the bias which can be then used to adjust the biased Broo Test measurements to retrieve accurate measurements al Plot CUSUM E Ly Expectation Maximization EM Project Team Gross Vehicle Weight GW P Misture Model PI Chen Fu Liao E E Cumulative Sum CUSUM CUSUM Methodology Co l Gary A Davis eel e Graduate Research Student Indrajit Chatterjee ils Hee Classification Chart e MnDOT TL Benjamin J Timerson nown Issues Contacting Us MnDOT AL Alan Rindels Glossary Figure 44 Welcome page of the WIM data analyst software help document 1 Welcome 2 Introduction 3 Getting Started System Requirements Installation Guide Technical Support 4 Tutorial Set Working Directory Menu Bar EM Fitting CUSUM Analysis Stationarity Test Plot GVW Plot CUSUM 5 Expectation Maximization EM 40 Gross Vehicle Weight GVW Mixture Model 6
18. analysis suggest that the proposed methodology is able to estimate a shift in the WIM sensor accurately and also indicate the time point when the WIM system went out of calibration A data analysis software tool WIM Data Analyst was developed using the Microsoft Visual Studio software development package based on the Microsoft Windows NET framework An open source software tool called R NET was integrated into the Microsoft NET framework to interface with the R software which is another open source software package for statistical computing and analysis 17 Document Analysis Descriptors 18 Availability Statement Weigh in motion scales Quality control Calibration No restrictions Document available from Cumulative Sum CUSUM Statistical quality control National Technical Information Services Alexandria Virginia 22312 19 Security Class this report 20 Security Class this page 21 No of Pages 22 Price Unclassified Unclassified 68 Implementation of Traffic Data Quality Verification for WIM Sites Final Report Prepared by Chen Fu Liao Indrajit Chatterjee Gary A Davis Department of Civil Environmental and Geo Engineering Minnesota Traffic Observatory Laboratory University of Minnesota May 2015 Published by Minnesota Department of Transportation Research Services amp Library 395 John Ireland Boulevard MS 330 St Paul MN 55155 This report documents the results of research conducted by the authors and does
19. ay Policy Information Federal Highway Administration http www fhwa dot gov policy ohpi travel qc index cfm accessed March 2015 52 USDOT 2001 Traffic Monitoring Guide U S Department of Transportation Federal Highway Administration Office of Highway Policy Information http www fhwa dot gov policyinformation tmguide accessed March 2015 Vehicle Travel Information System VTRIS Office of Highway Policy Information FHWA US Department of Transportation http www fhwa dot gov ohim ohimvtis cfm accessed March 2015 Wang R Y Ziad M and Lee Y W 2001 Data Quality Series Advances in Database Systems Vol 23 New York Springer 53 APPENDIX A WIM Data Analysis Non Stationary Scenarios A 1 Station 26 Lane 3 Period From 01 21 2011 to 06 31 2011 Time series of mu3 26_In2gvw_1 xlsx xx Tt 76 78 BO 82 Bd 14 0 20 40 60 80 Time Figure Al Linear trend in WIM measurements from no change period A 2 Station 32 Lane 4 Period From 10 19 2012 to 06 24 2013 Time series of mu3 32 In4gvw_1 xlsx XX Tt Tf fis 79 80 76 O 20 40 60 80 100 Time Figure A2 Linear trend in WIM measurements from no change period A 3 Station 26 Lane 4 Period From 01 21 2011 to 06 01 2011 xx It Time series of mu3 26 In4gvw_1 xlsx 82 80 fis 76 0 20 40 60 60 100 120 Time Figure A3 Linear trend in WIM measurements from no change period A 2
20. downward shift in WIM sensor for the first 30 days of the testing data 36 Prediction on Testing Sample1 61 to 90 Obs Predicted N 00 Lo TC 0 o Ml gt LL o 00 O 00 m 60 65 70 To 80 85 90 Index in days no weekend Figure 40 Predictions on testing sample t 61 to 90 Since no shift was found the estimated mean 1 parameter was kept unchanged and predictions were made for the next 30 days for the testing data Figure 41 shows the predictions results suggesting a change in the mean process Testing Sample 2 91 to 120 N 4 Predicted 00 o 00 Es w LO Oo o J3 0 gt E LL 5 oO Mm wT rt 90 95 100 105 110 115 120 Index in days no weekend Figure 41 Predictions on testing sample t 91 to 120 37 CUSUM analysis as shown in Figure 42 suggested sensor shifted by 3 79 units after t 93 which is consistent with the simulated sequence cusum2 CUSUM CUSUM of standardized residuals o gt o Y 90 95 100 105 110 115 120 Time index e Upper CUSUM Te Lower CUSUM Decision Interval o 9 O 90 95 100 105 110 115 120 Time index in days Figure 42 CUSUM analysis on testing sample t 91 to 120 After a nonzero shift in mean level was identified the final mean level was updated as u u 8 80 3 79 76 2 3 2 Using the updated mean level prediction was made for the remaining simulated data GVW Fully Loaded Tes
21. e above description is presented in the flowchart as shown in Figure 33 30 A WIM Data Analyst UNIVERSITY OF MINNESOTA Set Working Directory Code and Data Filepath E ChentuceMnQOT WIM Implementation A CodeLatest Analysis Notes 1 Set working directory 2 Click GWS EM button to load and process monthly Im data GVW9 EM File 3 Click CUSUM Analysis to perfor Wik data quality analysis CUSUM Analysis Figure 32 WIM data analyst main screen oo N 2 Compute EM estimates for 0 Begin with In daily mean fully loaded GVW calibration period 5 Compute EM estimates for 3 Estimate Time gt daily mean fully loaded GVW f fi Series Model for Testing Sample Parameters 7 Perform CUSUM on A iia estimated residuals Combine EM estimates from Testing Sample 6 Predictions on EM estimates from Testing Sample 8 Within a Yes DI 9 Estimate WIM sensor No shift E with Learning Sample Update WIM calibration Figure 33 Implementation guideline for CUSUM based algorithm for WIM calibration 3 2 WIM Data Analyst Tool A WIM data analysis software tool called WIM Data Analyst was developed using the Microsoft Visual Studio software development tool based on the Windows NET framework 4 An open source software R NET https rdotnet codeplex com was integrated to interface with R software http www r 31 project or
22. ected the lower CUSUM begins to deviate from 0 after time index 70 and exceeds the decision boundary h 4 at time index 74 The estimated shift in mean can be calculated as k 4 82 where k 0 5 u 2 0 which is consistent with the simulated sequence 74 70 The analysis based on simulation data demonstrates how we can identify any potential change in mean level for e g in this case 6 change and correctly estimate the bias 2 3 Analysis for WIM Measurements In this study we would primarily focus our analysis on fully loaded trucks as calibration tests are used with fully loaded trucks As mentioned in the previous section our usual line of attack would be to partition the data into two sets 1 Learning set 2 Testing set The learning set is defined by the period when the WIM system is supposedly in control The learning period is characterized by either of the two following conditions e Begin with a change in calibration to a time with no change in calibration e Begin with no change in calibration to a time with no change in calibration The testing set is the data from the period where the WIM system went out of calibration To identify those period WIM calibration files were referred and the data corresponding to those periods were extracted for selected stations In the following section we would demonstrate our analysis for selected stations The first step in the analysis 1s using the learning samp
23. el Information System VTRIS Traffic data quality control procedures were recommended to address general traffic data quality issues Nichols amp Bullock 2004 Turner 2007 However WIM sensor measurements drift over time due to its sensitivity on road surface smoothness temperature vehicle dynamics and many other factors The American Society for Testing and Materials ASTM has developed a standard specification for highway WIM systems The procedure for WIM acceptance and calibration involves using a combination of test trucks and statically weighed randomly selected vehicles from the traffic stream The standard specifies that each type of WIM system shall be capable of performing weight measurements within 15 for heavy duty vehicles gross weight and 30 for a single axle weight for 95 of all vehicles weight ASTM 1994 Although this is an improved method it is impractical to use in most cases due to the unavailability of static scales at most portable WIM sites Dahlin 1992 proposed a WIM performance monitoring methodology and calibration procedure for class 9 five axle tractor semitrailers He recommended three measures for WIM data quality analysis including bimodal Gross Vehicle Weight GVW front axle weight and flexible Equivalent Single Axle Load ESAL factor Han et al 1995 used statistical quality control methods to monitor WIM systems based on Dahlin s 3 classes of GVW However the proposed statistical quality con
24. em tends to go out of calibration Implementation guidelines for WIM calibration were developed to detect shifts in WIM sensor and suggest proper recommendation for WIM sensor adjustments A mixture modeling technique using Expectation Maximization EM algorithm was developed to divide the vehicle class 9 Gross Vehicle Weight GVW into three normally distributed components unloaded partially loaded and fully loaded trucks The well known Statistical Process Control SPC technique CUSUM was proposed to identify and estimate shifts in the WIM sensor However the presence of serial correlation in the data tends to make the CUSUM ineffective by producing uncomfortable levels of false alarms To overcome such limitations an auto regressive model was developed based on a training sample when the system was known to be in calibration Using the estimated model predictions were made for test samples and a CUSUM analysis was performed on the test residuals Any shift in WIM sensor would be reflected on CUSUM plots Here the underlying assumption is that any out of control CUSUM behavior is solely attributed to a plausible shift in WIM sensor However several case studies suggested this might not be true Additional unknown factors besides WIM sensors are found to influence WIM measurements A revised implementation plan is proposed to distinguish such scenarios A data analysis software tool WIM Data Analyst was developed using the Microsoft Visual
25. fitting results for the learning sample Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample Figure 13 shows the comparison of the estimated and extracted testing sample The figure also indicates the calibration factor was decreased by 8 2 after the testing period 14 Fitting Learning Sample 84 Observed Predicted 78 80 82 GVW 76 I 1 I I I I I I 1 1 74 l 70 Q 20 40 60 B0 100 120 Index in days no weekend Figure 12 Fitting learning sample Case II Testing Sample 29 lane 1 2011 04 06 to 2011 06 17 Obs Estimated Calibration factor changed by 8 2 a z Index Figure 13 Comparison between estimated and observed testing sample Case I 15 The next step 1s to perform CUSUM analysis on the standardized residuals Figure 14 shows the CUSUM plot along with CUSUM based decision plot for the residuals CUSUM of standardized residuals cusum 30 50 10 0 10 20 30 40 50 60 Time index CUSUM Based Decision Interval for Residual Dipcusum 0 0 10 20 30 40 50 60 Time Figure 14 CUSUM based decision plots for Case II The CUSUM analysis also indicates that the system went out of calibration after time index 40 of the testing period 2 3 3 Case III Station 37 Lane 2 Period 11 29 2011 to 05 21 2012 In Figure 15 red dotted lines indicate the time when WIM calibration was changed and green dot
26. for fully loaded trucks from Station 37 Time series of mu3 out32_In4_1 xlsx r Obs Saa 4 Alib No change a Cha lipbechange 11m O F T O cu 00 3 i uu 1 E ea LO F 0 20 40 60 60 100 Time index in days no weekends Figure 25 Inconsistent GV Ws for fully loaded trucks from Station 32 24 Time series of mu3 out26_In1_2 xlsx B Obs r Calib No a 82 t Calib Cha i GVW fully loaded v4 76 76 80 72 70 0 100 200 300 Time index in days no weekends Figure 26 Inconsistent GVWs for fully loaded trucks from Station 26 Lane 1 2 5 Impact of External Factors on GVW Estimates Simulation Study Now we define an AR 1 process as follows X 80 0 40 X 80 m we lt 80 X 88 0 40 X1 88 w we gt 80 lt t 120 X 70 0 40 1 70 a vwt gt 120 2 13 The above process indicates that the process began with mean 80 units After time index 80 the mean level shifted to 88 until time index 120 followed by another negative shift in mean level 70 to the end of the process The first 80 outcomes of the above process can be treated as observations from WIM system when calibration is in control condition The next set of observations from t 80 to t 120 corresponds to the period when WIM sensor went out of calibration with a positive shift of 10 units And the final period from t 121 to t 150 represents the period where mean level shifted t
27. from Weigh in Motion Data Transportation Research Record No 1993 1 148 154 Ott W C and Papagiannakis A T 1996 Weigh in Motion Data Quality Assurance Based on 3 S2 Steering Axle Load Analysis Transportation Research Record 1536 12 18 Qu T Lee C E and Huang L 1997 Traffic Load Forecasting Using Weigh in Motion Data Center for Transportation Research University of Texas Austin TX Ramachandran A N 2009 Weight in Motion data Analysis MS Thesis North Carolina State University Raleigh NC R project for statistical computing http www r project org accessed March 2015 R NET https rdotnet codeplex com accessed March 2015 Seegmiller L W 2006 Utah Commercial Motor Vehicle Weight In Motion data Analysis and Calibration Methodology MS Thesis Brigham Young University Provo UT Southgate H F 2001 Quality assurance of weigh in motion data Washington D C Federal Highway Administration http www thwa dot gov ohim tvtw wim pdf accessed March 2015 Taroni F Aitken C Garbolino P and Biedermann A 2006 Bayesian Networks and Probabilistic Inference in Forensic Science New York Wiley Turner S 2002 Defining and Measuring Traffic Data Quality http ntl bts gov lib jpodocs repts_te 13767 html accessed March 2015 Turner S 2007 Quality Control Procedures for Archived Operations Traffic Data Synthesis of Practice and Recommendations Office of Highw
28. g another open source software package for statistical analysis The WIM data analysis tool consists of two key components 1 e EM fitting and CUSUM analyses as illustrated in Figure 34 The EM analysis takes MnDOT s monthly WIM raw data for example 201501 040 CSV file for each WIM station and estimates the mean and deviations of gross vehicle weight GVW of class 9 fully loaded trucks Results of the EM analysis are stored in a file directory for CUSUM analysis The CUSUM analysis takes inputs from the EM results and a calibration file based on MnDOT calibration to model a learning sample and estimates the residuals between the prediction and WIM observation Output from the CUSUM analysis will indicate whether there is any sensor drift during the analysis period EM Analysis EM ee SelectStation MM LoadGvwo MM Process Output EM Analysis Lane Year Month BELE Data to File Calibration Files il CUSUM Analysis CUSUM Set Path Select Station Load Calibration Load Processed Analysis Lane Date Period Log File EM Data Model Testing Model Learning Estimate Ln UM Analvsi CUSUM Analysis Sample Sample Sensor Drift Result Output Figure 34 Flowchart of the WIM data analysis software Figure 35 shows the user interface of the EM analysis A user needs to first set a working directory where the R code WIM data input and output files will be stored After select a WI
29. g EM algorithm for WIM 26 Lane 2 2014 1 Completed Results are placed in Data EM_Processed Daily folder Logs in Data Logs folder Initializing and loading R routines Loading amp Preparing WIM 26 Daily data loaded Running EM algorithm for WIM 26 Lane 2 2014 2 Completed Results are placed in Data EM_Processed Daily folder Logs in Data Logs folder Figure 49 EM fitting screen 4 2 4 CUSUM Analysis When click on the CUSUM Analysis button from the main screen the CUSUM analysis screen will be displayed as illustrated in Figure 50 1 Select a WIM station from the station listbox Select a lane number from the lane listbox 2 Select a starting and an ending When the Use Calibration Date checkbox is checked The CUSUM analysis will use the calibration date from the calibration log file assuming there is a record of calibration date between the selected starting and ending dates as illustrated in Figure 51 3 When no calibration data 1s available between the starting and ending dates uncheck the Use Calibration Date checkbox to enable the learning date selection option and manually choose a learning date for CUSUM analysis Stationary GVW data between the starting and the learning dates are considered as learning period as illustrated in Figure 51 GVW data between the learning and the ending dates are used for testing 4 Select Daily or Weekly data anal
30. g Learning Sample 79 Observed OE Predicied GVW 76 77 75 0 20 40 60 80 Index in days no weekend Figure 20 Fitting learning sample Case IV Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample Figure 21 shows the comparison of the estimated and extracted testing sample The figure also indicates the calibration factor was decreased by 7 after the testing period Testing Sample 26 lane 2012 05 14 to 2013 01 28 Obs Estimated Calibration factor changed by 7 GVW 0 50 100 150 Index Figure 21 Comparison between estimated and observed testing sample Case IV 21 The next step 1s to perform CUSUM analysis on the standardized residuals Figure 22 shows the CUSUM plot along with CUSUM based decision plot for the residuals CUSUM of standardized residuals co Liy ce E F ur _ g co io co O 10 30 50 TO 390 110 130 150 170 Time index CUSUM Based Decision Interval for Residual co E io 3 or i a Aa ag a O 10 30 50 TO og 110 130 150 170 Time Figure 22 CUSUM based decision plots for Case IV The CUSUM decision plots suggests that WIM system had initially an upward drift and then followed by a downward drift at the end of testing period which is contrast to the calibration test run where a negative change in calibration factor was made 2 3 5 Case Analysis Summary Our analysis of WIM data suggests fo
31. g sample I Figure 30 shows the CUSUM plot along with CUSUM based decision plot for the residuals The CUSUM decision plots suggests that WIM system had an upward drift that exceed the threshold limit around 83 data point GVW for Test Sample 1 7 Obs Estimated ao oo oO oO hy GVW 84 A iy RS yw J 7 os Ioni oo O 00 oo F m 60 70 80 90 100 Index in days Figure 29 Predictions on testing sample I 21 CUSUM Based DI for Test Sample O b E Ta E 5 2 o 3 2 o LO I O i 61 65 69 73 M 1 8 69 93 OF Time Figure 30 CUSUM based decision interval for testing sample I Using equation 2 12 estimated shift was calculated as 6 8 28 units Hence the mean level is updated to 80 8 28 88 28 units Using the updated mean level and keeping the other AR 1 parameters same predictions are made for testing sample II If the truck weights are generated from a stable population then given the true shift in WIM sensor our predicted outcomes should able to capture the variability in testing sample I Failure to predict the Testing sample observations correctly would suggest unstable truck weights which might be caused by some unknown factors external to the WIM system CUSUM analysis is used again to identify such anomaly Figure 31 indicates that updated mean level after accounting for estimated shift in WIM sensor could not able to capture the GVW estimates from the testing sample II
32. ge Calib Change 82 80 y loaded 78 GVW full 76 74 0 50 100 150 200 250 Time index in days no weekends Figure 6 GVW for average daily fully loaded trucks station 26 Case I 10 Auto correlation for learning sample Partial auto correlation for learning sample 1 0 0 3 0 8 N O Ce o O Loy o O lt _ lt oO a o N o o 3 gt N N Q Q 0 5 10 15 5 10 15 Lag Lag Figure 7 CF and PACF plots for Case I Table 2 Estimated AR 1 parameters for learning sample Case I AR 1 model is deemed suitable as it was able to knock out all the auto correlation present in the learning sample Figure 8 below shows the fitting results for the learning sample 11 Fitting Learning Sample Observed Predicted T oo a oo 5 e co rH rH 0 20 40 60 50 Index in days no weekend Figure 8 Fitting learning sample Case I Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample And then the residual is calculated as the difference of the estimated from the observed Figure 9 shows the comparison of the estimated and extracted testing sample The figure also indicates the calibration factor was increased by 6 after the testing period 12 Testing Sample 26 lane 6 1 11 to 1 23 12 Obs Predictpd I oo 00 r Lo Eb T r 0 20 100 150 Index Figure 9 Comparison between estima
33. is with observations learning sample from period where system is known to be in control We perform an additional check to verify the stationarity of the data Stationarity is defined as a time series process whose parameters such as the mean and variance do not change over time and do not follow any trends For example white noise is stationary Currently a popular statistical test Kwiatkowski Phillips Schmidt Shin KPSS is used to test for stationary of the learning sample Once the stationarity of the learning sample is confirmed time series model parameter is estimated The next step is to divide the test sample into two parts test sample I and test sample II The idea is to first perform CUSUM analysis on Test Sample I using the estimated model parameters from the learning sample If the CUSUM analysis indicates the system has gone out of calibration the estimated shift in WIM sensor is calculated Then the estimated shift is used to update the mean level in the time series model If the estimated shift correctly reflects the WIM sensor status then the predictions based on updated time series parameter would successfully capture the variation in the testing sample II Failure to do so would indicate the influence on external factors other than WIM sensor on GV Ws At this point the WIM operator would be alerted On the other hand if correct predictions are made the estimated shift can be used to update the WIM calibration Th
34. ive shift found in the WIM sensor Without any further knowledge it is not possible to provide any explanation for such an inconsistent behavior Several factors such as varying truck populations or miscellaneous conditions external to WIM system may have caused such phenomenon More importantly if such driving forces are not detected or identified our proposed methodology may provide incorrect conclusions about the status of WIM sensor With only limited information available at this point the focus of our research is to propose a methodology to alert the WIM operators whenever such anomaly is detected It would be up to the state agencies to take necessary actions or conduct further investigations to identify the factors driving such phenomenon Figure 24 25 and 26 shows more evidence of such anomalies in the estimates of GVWs for fully loaded trucks from other stations Time series of mu3 out26_In4_test1 xlsx 82 Obs Calib No change Calib Change 80 00 Rh TD w pe Lie O WO m i wz Rh 72 70 0 50 100 150 200 250 Time index in days no weekends Figure 23 Inconsistent GVWs for fully loaded trucks from Station 26 Lane 4 23 Time series of mu3 out37 In2 testl week xlsx Lia I an Tr Obs Calib No change CalibChange o iii i 5 i m I O l cu a LO 5 FP 3 de co F La co o 20 40 60 60 Time index in days no weekends Figure 24 Inconsistent GVWs
35. le fit a time series model Auto Correlation Function ACF and Partial Auto Correlation Function PACF suggested AR 1 process as a good candidate to explain the serial correlation Formally AR 1 process 1s given by A p P X 4 u rae lp lt 1 2 8 Where X represents f observation H represents mean of the process qa is the lag 1 autocorrelation coefficient N 0 0 are independent and identically distributed normal random variables with mean 0 and standard deviation o representing the inherent variability of the process The residuals e are given by following equation Ay A 4 2 9 If the AR 1 model explains the serial correlation in the observations correctly then residuals e can be treated as independent and identically distributed normal random variables with mean 0 and standard deviation o Suppose the true mean value u shifts to u at time f Assuming ji and are unbiased estimates of the true parameters expected standardized residuals are given by Ele 0 if t lt t E if t t E if t gt t 2 10 ao Now suppose the segment of the CUSUM began to shift from general horizontal pattern to a non horizontal linear drift after time point m for which CUSUM value S 0 and then crossed the decision interval h at time point n where CUSUM value is given by S Then from equation 2 12 the upward CUSUM on standardized residuals is given by E AA T 2 11 Substituting re
36. llowing First we found presence of auto correlation in most of the WIM data And hence it is essential to develop a model that could capture the auto correlation The preliminary analysis suggests AR 1 auto correlation structure should be sufficient to capture such auto correlation and able to produce consistent results in terms of identifying any systematic calibration system see Case I II II in previous section However there are scenarios such as Case IV where the current methodology fails The implicit assumption of our approach is the mean of the learning sample defined as the period of no calibration changes should be stationary in nature That is there should be no systematic trend or drift in the measurements when the WIM system is in control However measurements from WIM system from various stations see Appendix A for more cases exhibit such kind of unexpected non stationary behavior Since these periods are marked by no change in calibration some exogenous factor might be driving such pattern and without any knowledge of such factor our usual quality control approach for change detection would provide inaccurate results From implementation point of view the first step is to detect and isolate those cases with unexpected trends and alert the WIM operator of their existence For other cases without such trend our usual change detection approach based on CUSUM can be performed Once a change in mean level is identified the WIM ope
37. m Protocol for Calibrating Traffic Data Collection Equipment April 1998 http www fhwa dot gov ohim tvtw natmec 00009 pdf accessed March 2015 LTPP Traffic QC Software Volume 1 Users Guide Software Version 1 61 updated Nov 1 2001 http www fhwa dot gov publications research infrastructure pavements Itpp reports traftqc trfqc pdf accessed March 2015 Luce o A 2004 CUSCORE Charts to Detect Level Shifts in Autocorrelated Noise International Journal Quality Technology amp Quantitative Management 1 1 27 45 McLachlan G and Peel D 2000 Finite Mixture Models Hoboken N J John Wiley amp Sons MnDOT WIM monthly reports http www dot state mn us traffic data reports monthly wim html accessed March 2015 Montgomery D C and Mastrangelo C M 1991 Some Statistical Process Control Methods for Autocorrelated Data Journal of Quality Technology 23 3 179 204 National Cooperative Highway Research Program NCHRP 2004 2002 Design Guide Design of New and Rehabilitated Pavement Structures NCHRP Washington DC Nichols N and Bullock D 2004 Quality Control Procedures for Weigh in Motion Data FHWA IN JTRP 2004 12 Indiana Department of Transportation and FHWA US Department of Transportation http docs lib purdue edu cgi viewcontent cgi article 1647 amp context jtrp accessed March 2015 Nichols A and Cetin M 2007 Numerical Characterization of Gross Vehicle Weight Distributions
38. mentary Notes http www Irrb org pdf 201518 pdf 16 Abstract Limit 250 words Weigh In Motion WIM system tends to go out of calibration from time to time as a result generate biased and inaccurate measurements Several external factors such as vehicle speed weather pavement conditions etc can be attributed to such anomaly To overcome this problem a statistical quality control technique is warranted that would provide the WIM operator with some guidelines whenever the system tends to go out of calibration A mixture modeling technique using Expectation Maximization EM algorithm was implemented to divide the Gross Vehicle Weight GVW measurements of vehicle class 9 into three components unloaded partially loaded and fully loaded Cumulative Sum CUSUM statistical process technique was used to identify any abrupt change in mean level of GVW measurements Special attention was given to the presence of auto correlation in the data by fitting an auto regressive time series model and then performing CUSUM analysis on the fitted residuals A data analysis software tool was developed to perform EM Fitting and CUSUM analyses The EM analysis takes monthly WIM raw data and estimates the mean and deviations of GVW of class 9 fully loaded trucks Results of the EM analyses are stored in a file directory for CUSUM analysis Output from the CUSUM analysis will indicate whether there is any sensor drift during the analysis period Results from the
39. nnnnnnononononononnncnnnnnnnnnnononononnnnos 11 Table 3 Estimated AR 1 parameters for learning sample Case H ooooooonnnnnnncnnnnnnnnnnnnnnnnnonononnnnnncnnnnnnnnnnononnnnnnnnos 14 Table 4 Estimated AR 1 parameters for learning sample Case llT ooooonnnnnnnnncnncnnnnnnnnonnnnnonononnnnnnnnnnnnnnnnnnnonnnnnnos 17 Table 5 Estimated AR 1 parameters for learning sample Case IW oooooooonnnnnnnocnnnnnnnnnnnnononononononnnnnnnnnnnnnnnonnnononnnnos 20 Table 6 Estimated AR 1 parameters for learning sample occccccncccccnnnnonononnnnnnnnnnnnnonononononononnnnnnnnnnnnnnnnnnnononnnnnnos 26 Table 7 Estimated parameters from the learning sample ooooonnnncnnnnnnnccccnnnononnnonncnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnonnnnnnos 36 AADT AADTT AASHTO ACF AL AR ARL ASTM ATR CDF CEGE CI CPU CSV CTS CUSUM DI EM ESAL FHWA ft FXS FXW GIS GPS GUI GVW HTML IDE IRD ITS kips KPSS LTPP MnDOT MTO MUTCD NCHRP OS PACF RITA LIST OF ACRONYMS AND ABBREVIATIONS Annual Average Daily Traffic Annual Average Daily Truck Traffic American Association of State Highway and Transportation Officials Auto Correlation Function Administration Liaison Auto Regression Average Run Length American Society for Testing and Materials Automatic Traffic Recorder Cumulative Distribution Function Department of Civil Enviornmental and Geo Engineering Confidence Interval Central Processing Unit
40. not necessarily represent the views or policies of the Minnesota Department of Transportation or the University of Minnesota This report does not contain a standard or specified technique The authors the Minnesota Department of Transportation and the University of Minnesota do not endorse products or manufacturers Trade or manufacturers names appear herein solely because they are considered essential to this report ACKNOWLEDGMENTS This project is sponsored by the Minnesota Department of Transportation MnDOT We would like to acknowledge MnDOT staff and engineers for their invaluable support and providing Weigh In Motion WIM data We also thank members of the technical advisory panel TAP and the following individuals and organizations for their invaluable feedback and assistance in making this study possible e Benjamin Timerson technical liaison MnDOT e Joshua Kuhn MnDOT e Gregory Wentz MnDOT e Susan Anderson MnDOT e Alan Rindels administration liaison MnDOT e Nelson Cruz administration liaison MnDOT e Minnesota Traffic Observatory Department of Civil Environmental and Geo Engineering CEGE University of Minnesota e Center for Transportation Studies CTS University of Minnesota TABLE OF CONTENTS Chapter LINTRODUCTION ssaa acaso Sc OSO cascessecectesascaureuseeeseeusecaseewseeens 1 Vel Backoround essien iaa ieee l RO A l AA RENTEN ea l FA Report Orsaniz a ON nononono a e Aa a ooie 3 Chapte
41. ntify such scenarios a revised implementation plan is proposed and tested for a simulated set of observations Although the proposed plan looks promising further investigation and analysis on historical data will be performed for validation and final implementation A data analysis software tool WIM Data Analyst was developed using the Microsoft Visual Studio software development package based on the Microsoft Windows NET framework An open source software tool called R NET https rdotnet codeplex com was integrated into the Microsoft NET framework to interface with the R software http www r project org which 1s another open source software package for statistical computing and analysis The developed WIM data analyst tool consists of two key components 1 e EM Fitting and CUSUM analyses In addition a HTML online help document was also created and embedded into the software tool to provide comprehensive online help information The EM analysis takes a monthly WIM raw data CSV file of each WIM station from MnDOT and estimates the mean and deviations of GVW of class 9 fully loaded trucks Results of the EM analyses are stored in a file directory for CUSUM analysis The CUSUM analysis takes inputs from the EM results and a calibration file based on MnDOT calibration logs to model a learning sample and estimates the residuals between the prediction and WIM observation Output from the CUSUM analysis will indicate whether there is any
42. o 70 as a consequence of possible change in truck population or other factors which are external to WIM system Further suppose the first 60 observations represents the period when the system is known to be in contro state 1 e the learning sample The rest of the observations are partitioned into two testing samples testing sample I and testing sample II as shown in Figure 27 Testing sample I includes data from index 61 to 100 And testing sample II includes data from index 101 to 150 The learned period is bracketed by green vertical strips The red vertical strips represent two testing samples As mentioned previously the first step is to check for stationarity of the learning sample In this case we know the learning set is stationary Next an AR 1 model is fitted to the learning sample Figure 28 Table 6 shows the estimated parameters for AR 1 process 25 Table 6 Estimated AR 1 parameters for learning sample 30 85 Testing Sam ple Il GVN 80 5 TO Testing Sample I 65 0 50 100 150 Time index in days Figure 27 Simulated GVWs with WIM shift followed by an unstable GVW pattern 26 Fitting Learning Sample GVN 78 80 B2 76 Td 0 10 20 30 40 50 60 Index in days Figure 28 Fitted learning sample Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample Figure 29 shows the comparison of the estimated and extracted testin
43. on CUSUM type analysis causing dramatic increase in the frequency of false alarms Montgomery and Mastrangelo 1991 This research proposes methods where first time series models are used to adjust for any auto correlation and then CUSUM is used to detect and estimate any change in the mean levels 1 2 Objectives The objective of this study is to characterize the WIM measurements and develop a statistical quality control methodology to effectively detect any sensor drifts and estimate the measure of the drift To achieve the goal first we need to understand the characteristics of GVW weight measurements obtained from a period when the WIM system is supposedly in control Then the statistical model based on GVWs under normal condition is used to predict the GV Ws for the period where the system drifted and then CUSUM analysis is performed on the deviation of predicted from the GVW measurements obtained from EM algorithm 1 3 Literature Review Weigh In Motion WIM systems have been widely used to collect the traffic loading data to support traffic load forecasting Qu et al 1997 Lee amp Nabil 1998 Seegmiller 2006 and Ramachandran 2009 pavement design and analysis NCHRP 2004 Elkins 2008 infrastructure investment decision making and transportation planning MnDOT and other state DOTs collect WIM data every year to meet federal traffic reporting requirements as part of the Long Term Pavement Performance Program LTPP and Vehicle Trav
44. onnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 37 Figure 41 Predictions on testing sample 9 1 to TO is 37 Figure 42 CUSUM analysis on testing sample t 91 to 120 ooocccnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 38 Figure 43 Predictions on testing sample t 93 to 150 ccccccecccccsseeeessseseeeeeeeeeeecccccssccecesasseeseeeeeeseccecesseeeeessees 38 Figure 44 Welcome page of the WIM data analyst software help document ooocccccnnnnnnnnnnnnnnnnnononnnnnnnnnnnnnnnnnnnos 40 Figure 45 Main screen of the WIM data analyst tool suscitan ii idas 42 Figure 46 Illustration of a selected Working directory oooooooononncccnnnnnnnnnnnnnnnnnnnonnnnncnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 42 Fiege Ar Pale Tey Dal a AA n 43 Figure 48 Samipleor WIM calibration los 1a Ble ia dos 44 Fase AI EIT ESCHER ii 45 Prsure 50 CUSUM Analysis Sr oidos 46 Figure 51 Illustration of selecting dates learning and testing perlOdS ooooooonnnnnnnnnnnnnnnnnnnnnnnnnononanonnncnnnnnnnnnnnnnnnnnnnnnos 4 Hones oamp e GV WO Dlls iia 47 Figure 53 Samplesstationarity testresulls arta tala aaa 48 Figure 54 sample results trom a CUSUM analysis eiroet A SA E A E 48 Pigsure 55 Weekly GVW Plot Ob WIMA adas 49 LIST OF TABLES Tablet Estimated AR L parameters tor Simulated data ida lito li tii 5 Table 2 Estimated AR 1 parameters for learning sample Case l ooooooonnnnnnnnnnnnnnnnn
45. ot gov policy ohpi tdep htm accessed March 2015 FHWA 2004 Traffic Data Quality Measurement Final Report http isddc dot gov OLPFiles FHW A 013402 pdf accessed March 2015 FHWA 1998 WIM Scale Calibration A Vital Activity for LTPP Sites TechBrief FHWA RD 98 104 http www fhwa dot gov publications research infrastructure pavements Itpp 98 104 98 104 pdf accessed March 2015 Han C Boyd W T and Marti M M 1995 Quality Control of Weigh in Motion Systems Using Statistical Process Control Transportation Research Record 1501 72 80 Hawkins D M and Olwell D H 1998 Cumulative Sum Charts and Charting for Quality Improvement New York Springer Verlag Lee C E and Nabil S S 1998 Final Research Findings on Traffic Load Forecasting Using Weigh In Motion Data Research Report 987 7 Center for Transportation Research University of Texas Austin TX Liao C F and Davis G 2012 Traffic Data Quality Verification and Sensor Calibration for Weigh In Motion WIM Systems Center for Transportation Studies CTS 12 26 University of Minnesota Minneapolis MN 51 Lin S Y Liu J C and Zhao W 2007 Adaptive CUSUM for Anomaly Detection and Its Application to Detect Shared Congestion Technical Report 2007 1 2 Department of Computer Science Texas A amp M University http engineering tamu edu media 697 122 tamu cs tr 2007 1 2 pdf accessed March 2015 Long Term Pavement Performance LTPP Progra
46. r 2 WIM DATA MODELING AND ANALYSIS eeeeeeesssssssssscccccccccccccsssssssscccccccececccosssssssssescseee 4 ZN Mire ModE A AE EEE E AAEE 4 2a Smilin Based ASS A A ia 4 DIAM YSIS AOL WIM Measure menis nrun a a 8 2 3 1 Case I Station 26 Lane 3 Period From 01 21 2011 to 01 23 2012 eessen 10 2 3 2 Case II Station 29 Lane 1 Period 10 06 2010 to 06 17 2011 ooooocccccnccnnccnccnccnccnonnnonns 14 2 3 3 Case III Station 37 Lane 2 Period 11 29 2011 to 05 21 2012 ooonnnnnccccouonoconanononccnnnnos 16 2 3 4 Case IV Station 26 Lane 4 Period From 01 25 2012 to 01 28 2013 0 eee eeeee 19 23 5 Case Analysis SUMMA ii ii 22 ZA External Impactson Truck Welt iaa ii A a a eati 23 2 5 Impact of External Factors on GVW Estimates Simulation StUAY ooooooooooncccncnnnnnnnnnnonononnnnannononnnos 25 Chapter 3 DEVELOPMENT AND IMPLEMENTATION cccccccccssccccsssssssssssccsccccccccccscccccssssssees 30 3 1 Soltware Implementation CUASI a a E 30 Size WANE Data Analyst Told a a a 31 3 3 Verification Using Simulated ScenarlOS ooooccnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn rn rra 35 Chapter 4 WIM Data ANALYST User s Mannuial csssssssssssssssccccccsscccccssssssssccssssssscccccssssscssssssssees 40 Ae WIT Sarlo desta il coco cc 41 A NLS ystems Require ment pte letal clas 41 A Is talla to nude eaea A E E E 41 Alo Technical ON 41 A A O te nncaty A abe nctuienaosg tae nacesschanks shad anat iennosetldenaamiicnan
47. rator can be notified 22 2 4 External Impacts on Truck Weights The underlying assumption of the proposed methodology is 1f the data is generated from a stable process then the predictions based on the model estimated from the learning sample should consistently capture the variation in the testing sample Then a fixed shift in WIM sensor should be captured by CUSUM analysis on estimated residuals An out of control CUSUM behavior is solely attributed to a plausible shift in WIM sensor However several case studies indicated that this might not be true always Figure 23 1s a typical evidence of such an inconsistent pattern Figure 23 shows the average daily EM estimates of GVWs for fully loaded trucks for station 26 lane 4 from 01 25 2012 to 01 28 2013 As usual the vertical red columns denote the days when the MnDOT s test runs found the WIM system to be out of calibration whereas green vertical strip calibration date 05 14 12 indicate the time point when the system was found to be in control condition Figure 23 suggests after 05 14 12 the WIM sensor seems to have a positive shift however at the later part of the observation a clear downward shift can be observed MnDOT s test run on 01 29 2013 which is a day before the last observation in Figure 23 suggested a positive shift in the WIM sensor and consequently calibration factor was adjusted by 7 However the downward shift in the later part of the Figure 23 contradicts the posit
48. sensor drift during the analysis period CHAPTER 1 INTRODUCTION 1 1 Background WIM system tends to go out of calibration from time to time as a result generate biased and inaccurate measurements Several external factors such as vehicle speed weather pavement conditions etc can be attributed to such anomaly In order to overcome this problem a statistical quality control technique is warranted that would provide the WIM operator with some guidelines whenever the system tends to go out of calibration This study focuses on developing such models that would detect any abnormal change in the measurements from WIM system and provide an estimate of the bias which can be then used to adjust the biased measurements to retrieve accurate measurements Following the methodology developed in the first phase of this research Liao amp Davis 2012 where a mixture modeling technique using Expectation Maximization EM algorithm was used to divide the Gross Vehicle Weight GVW measurements of vehicle class 9 into three components 1 e unloaded partially loaded and fully loaded trucks Once the average daily GVW estimates of fully loaded trucks are obtained statistical process control techniques such as CUSUM technique was used to identify any abrupt change in mean level of GVW measurements However the previous analysis doesn t account for any presence of correlation in the measurements Presence of such auto correlation can have a serious impact
49. siduals with its expected value and after some algebra we get an estimator of 6 Seren is pt m A a k 45n75m Sm y m 2 12 Where 6 u u denotes the true shift in mean level The underlying assumption of the methodology is if the data is generated from a stable process then the predictions based on the model estimated from the learning sample should consistently capture the variation in the testing sample Any introduction of instability or sensor shift in the testing sample should be reflected in the residuals Then CUSUM algorithm can be implemented to detect such shift in WIM sensor This methodology could benefit state agencies such as MnDOT by identifying when calibration was lost and subsequently a proper modification factor could be applied to the out of calibration data to adjust for the bias 2 3 1 Case I Station 26 Lane 3 Period From 01 21 2011 to 01 23 2012 In Figure 6 red dotted lines indicates the time when WIM calibration was changed and green dotted line represents the time point when no change in calibration was made The first step is to characterize the learning sample and then use the learning sample to fit a time series model Figure 7 confirms presence of auto correlation in the time sequence of GV Ws The next step is to estimate the time series model Estimation results after fitting an AR 1 process are shown in Table 2 Time series of mu3 26_In3_test1_week xisx Obs Calib No chan
50. stent GVWs for fully loaded trucks from Station 32 ooooocccncnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnonnnnnnnnnnninonos 24 Figure 26 Inconsistent GVWs for fully loaded trucks from Station 26 Lane l ccccccccnnooooooooocccncnonnnnnnnonononnnnnnos 25 Figure 27 Simulated GVWs with WIM shift followed by an unstable GVW pattern cooooococoononncccnncnnnnnnncnnnnnnnnnnos 26 Fisu 28 Fittedicamn sample AA E cuallemdains 21 Ersure 29 Predictions On 1estino Sample di id A A DAI 2d Figure 30 CUSUM based decision interval for testing sample l oooooooooooncncncnonnnnnnnnnnnnnnnnnnnonononnnnnnnnnnnnnnnnnnnnnnnnnos 28 Figure 31 CUSUM Analysis indicating unstable truck population oooooonnnnnnnnnnnnnnnnnnnnnnnonononononnnncnnnnnnnnnonnnononnnnos 29 Peine WIM datd anialy st iodo alitas 31 Figure 33 Implementation guideline for CUSUM based algorithm for WIM calibration ooocccccccnnnnnnnnnnnnnnnnnnnss 31 Figure 34 Flowchart of the WIM data analysis SO TWAre oococcccconnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnoss 32 SAO AAA A A Sa untss 33 Fiette S0sUseriateriacs of CUSUM analy do 33 igure 3 1 CUSUM crap tad iii is 34 Preune 36 CUSUMID ESTA e ios 35 Figure 39 Simulated AR 1 process with change in mean level oooooooonnnnccnnnnnnnnnnnnononononononnncnnnnnnnnnnonnnonnnnnnos 36 Figure 40 Predictions on testing sample t 61 to 90 oooooooonnnnncnononononnnnnnnnononon
51. t ed anae 42 Az Set WOKING DICC ClO 5 ces otnanccs gael dur banes dad gatncemonen a 42 A Doe WY MMA B Ale tartar yer ester ate ese EE E tasted EA 43 AyD EM Te WUCM co 5 asdinsi cs areatietst cata aa a a O taestains 44 A 2 AGUSU MEA ALY SIS ia a tl 45 Chapter 5 SUMMARY AND CONCLUSION eeeeeosssssssssccccccccccccccsscscssscccecceceececcssssssssseccecececeeceossssssssse 50 REFERENCES tai 51 Appendix A LIST OF FIGURES Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Simulated AR I Process With mean S0 KIDS Sie 5 CUSUM based decision interval for AR 1 residuals occoocccnncccnnocncnnnccnnnoccnnnccnnaconnnocononcnnnoccnnnccnnancnns 6 Residuals after fitting a non stationary AR 1 process coooooocoonoonnnncncnnnnnnnnnnnnnnonononnnnnnnnnnnnnnnnnnnnnnnnnnanannnnnnnos 7 CUS UM plot for Fe Ci Tes Qala oie cal 7 CUSUM based decision interval for AR 1 residual with change in MeAN cccccceeeeeeeeeeeeeeeeeeeeeeeeees 8 GVW for average daily fully loaded trucks station 26 Case l ooooooonnnnnnnncnnnnnnnnncnonononononnnnnnnnccnnnnnnnonononnnnnos 10 NO A O E TA 11 Fitting learnin samples Case iscisnonicsaine tail aO OEA OE O NATO 12 Comparison between estimated and observed testing sample Case l occcccccnnnnnnnnnnnnooncnnnnnnnnnnnnnnnnononnnnos
52. ta Analyst exe by clicking on the desktop shortcut icon to start the application Unzip the R_Src_Data zip to a working directory for example C R_Src_Data on your PC The zip file contains several R script files R and a data folder for WIM data analysis Please go to the tutorial section section 4 2 or click Help from the file menu on the main screen of the WIM data analyst tool to learn more about the analyst tool 4 1 3 Technical Support Please contact Chen Fu Liao at cliao umn edu for any technical problems with the WIM Data Analyst software Please also report any errors or bugs to Chen Fu at cliao umn edu 41 4 2 Tutorial 4 2 1 Set Working Directory After executing the application WIM Data Analyst exe the main screen of the software tool will be displayed as shown in Figure 45 Click on the Browse button in the Set Working Directory group box to choose the working directory where the data analysis R scripts reside Figure 46 illustrates an example of the working directory The R files are used for EM and CUSUM analysis using R software package The Data folder contains data needed to process both EM amp CUSUM analysis and store corresponding outputs for plotting the CUSUM results in Windows UNIVERSITY OF MINNESOTA Set Working Directory Code and Data Filepath E ChenfusMnDOT WwiIM lmplementation A Code Latest Analysis GVW9 EM File CUSUM Analysis Organize Include in library E
53. ted and observed testing sample Case I The next step is to perform CUSUM analysis on the standardized residuals Figure 10 shows the CUSUM plot along with CUSUM based decision plot for the residuals The CUSUM analysis also indicates that the system went out of calibration at the end of the testing period CUSUM of standardized residuals 20 a 9 o O a o gt 0 10 20 30 40 50 60 70 80 90 100 120 140 160 Time index CUSUM Based Decision Interval for Residual LO g y w a o a O 10 0 10 20 30 40 50 60 70 80 90 100 120 140 160 Time Figure 10 CUSUM based decision plots for Case I 2 3 2 Case Il Station 29 Lane 1 Period 10 06 2010 to 06 17 2011 In Figure 11 red dotted lines indicates the time when WIM calibration was changed and green dotted line represents the time point when no change in calibration was made The first step 1s to characterize the learning sample and then use the learning sample to fit a time series model Time series of mu3 29 In1_test1l_week xlsx Obs 322 CalibiNo change Calib Change 85 N y loaded 80 GYW full an Testing Sample 75 Learning Sample 70 0 50 100 150 Time index in days no weekends Figure 11 GVW for average daily fully loaded trucks station 29 Case II Estimation results from AR 1 process for learning sample is shown in Table 3 Table 3 Estimated AR 1 parameters for learning sample Case II Figure 12 below shows the
54. ted line represents the time point when no change in calibration was made The first step is to characterize the learning sample 16 Time series of mu3 37_In2_test2_week xlsx Obs i 7 7 7 Calib No change 00 Calib Change r 0 r O e O co q 5 Hp 3 TE i l o Testing Sample Learning Sample 0 20 40 60 80 100 120 Time index in days no weekends Figure 15 GVW for average daily fully loaded trucks station 37 Case III Estimation results from AR 1 process for learning sample is shown in Table 4 Figure 16 shows the fitting results for the learning sample Table 4 Estimated AR 1 parameters for learning sample Case III 17 Fitting Learning Sample Observ ed 2222 Predicte H GVW 13 14 PO 16 1 o O 10 15 20 25 30 Index in days no weekend Figure 16 Fitting learning sample Case III Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample Figure 17 shows the comparison of the estimated and extracted testing sample The figure also indicates the calibration factor was decreased by 4 after the testing period 37_In2 2012 01 10 to 2012 05 21 Obs Estimated Calibration factor changed by 4 78 GVW 72 74 76 70 Index Figure 17 Comparison between estimated and observed testing sample Case III The next step 1s to perform CUSUM analysis on the standardized residuals Fig
55. ting Sample 3 93 to 150 Obs Predicted 82 80 78 76 74 72 100 110 120 130 140 150 Index in days no weekend Figure 43 Predictions on testing sample t 93 to 150 38 Figure 43 shows predictions based on the updated mean level was consistent with the simulated outcome till time index t 130 Since the true mean level shifted back to 80 kips the predictions based on the updated mean level fail to capture the variation in the simulated data after time index t 130 As expected CUSUM analysis on the residuals identified the previously estimated sensor shift of 3 79 units as inconsistent Through this simulated example we have shown how splitting the testing data in to chunks of 30 day period we can verify consistency of WIM sensor shift 39 CHAPTER 4 WIM DATA ANALYST USER S MANUAL A compiled HTML help document was created for the WIM Data Analyst software The help document WIM_Help chm is based on the Microsoft Compiled HTML online help format which consists of a collection of HTML pages an index and other navigation tools As illustrated in Figure 44 the outline of the HTML help document is listed as follows Structure of the help document is presented as follows Documentation on the Getting Started and Tutorial sections are discussed in section 4 1 and 4 2 Please refer to the WIM_Help chm file or click on the Help file menu option form the WIM Data Analyst software tool for det
56. trol methodology was unusable due to calibration drift Later Ott and Papagiannakis 1996 investigated using class 9 steering axle weights for monitoring 2 subgroups less and greater than 50 kips Static and dynamic GVW variations were estimated to generate anticipated Confidence Interval CI plots for a WIM station Nichols and Cetin 2007 introduced multi component mixture models to characterize class 9 GVW distributions which is consist of several homogeneous normally distributed subpopulations Expectation Maximization EM algorithm was then used to estimate subpopulation parameters They illustrated several patterns suggesting calibration drift and component failure FHWA has developed a framework that provides guidelines and methodologies for calculating data quality measures for various applications FHWA 2004 Turner 2002 The data quality measurement framework suggested 6 fundamental measures accuracy completeness validity timeliness coverage and accessibility for traffic data quality These quality parameters are often user specific or application specific They are typically derived from either the underlying quality indicators or other quality parameters Wang et al 2001 Traditionally traffic data quality control is performed manually However due to the increasing data volume and complexity a logical structure for evaluating traffic data is needed A pooled fund study Flinner 2002 led by MnDOT was conducted in 2002 to
57. ty control method to detect deviations from benchmark values Hawkins amp Olwell 1998 used CUSUM charts and charting as Statistical Process Control SPC tools for quality improvement Luce o 2004 used generalized CUSUM charts to detect level shifts in auto correlated noise Lin et al 2007 developed an adaptive CUSUM algorithm to robustly detect anomaly To demonstrate our proposed methodology we would first analyze simulated GVW weight measurements with serial correlation and show how an abrupt change in mean level can be detected and estimated First a simulated sequence of time series measurements with first order autoregressive AR model was created The AR 1 correlation is defined as follows Simulated AR 1 process 0 7 Where Mean u 80 and wm N 0 o 2 Figure 1 shows the time series measurements from the simulated sequence 86 84 82 xt 80 78 76 74 0 50 100 150 200 index Figure 1 Simulated AR 1 process with mean 80 kips The mean 11 and correlation coefficient can be estimated using statistical estimation technique available in standard R software Estimation Results are listed as follows Table 1 Estimated AR 1 parameters for simulated data The residuals for the fitted model can be obtained as follows Residuals n x B id 1 a i 2 4 F Cusum 2 2 5 CUSUM and Decision Interval Hawkins and Olwell 1998 were plotted Figure 1 amp 2
58. ulated Scenarios Consider the following simulated AR 1 process with T 150 observations The mean of process went down by 5 units after time point t 75 which is the initial shift in the WIM sensor After time point t 130 the mean process again went up by 5 units Figure 39 shows the plot of the simulated data Our goal is to show how we can identify the inconsistency in the WIM sensor X pet OCX _1 Ue E 80 ift lt 95 475 if95 t lt 130 80 if t gt 130 0 45 N 0 0 2 3 1 35 Simulated AR1 with change in mu 84 Simulated Mean GVW Calibration Change Calibration No Change 82 80 78 76 74 72 Index Figure 39 Simulated AR 1 process with change in mean level Consider the first 60 observations as the learning sample The using the traditional Maximum likelihood technique AR 1 model is estimated form the learning sample and the estimated parameters are shown in Table 7 Table 7 Estimated parameters from the learning sample Moda o u 0 4118 80 105 0 116 0 258 AN ims Then the next step is to split the testing samples into 30 days Based on the estimated model from the learning sample predictions were made for the first 30 days of the testing sample Figure 40 shows the predictions on the testing sample from t 61 to t 90 As expected the prediction results are consistent with the simulated outcomes Further CUSUM analysis verifies neither upward nor
59. ure 18 shows the CUSUM plot along with CUSUM based decision plot for the residuals 18 CUSUM of standardized residuals EA O 5 3 O e 0 10 20 30 40 50 60 70 80 90 Time index CUSUM Based Decision Interval for Residual a 5 Dipcusum 0 10 5 0 10 20 30 40 50 60 70 80 90 Time Figure 18 CUSUM based decision plots for Case HI The CUSUM analysis also indicates that the system went out of calibration at the end of the testing period 2 3 4 Case IV Station 26 Lane 4 Period From 01 25 2012 to 01 28 2013 In Figure 19 red dotted lines indicates the time when WIM calibration was changed and green dotted line represents the time point when no change in calibration was made The first step is to characterize the learning sample 19 Time series of mu3 261n4_test1_week xlsx cl oo 2522 CalibiNo change Calib Change I 00 oO FP O LD pS I ad 3 q q 2 ____ a Testing Sample Learning Sample 0 50 100 150 200 250 Time index in days no weekends Figure 19 GVW for average daily fully loaded trucks station 26 Case IV Estimation results from AR 1 process for learning sample is shown in Table 5 as follows Table 5 Estimated AR 1 parameters for learning sample Case IV Figure 20 below shows the fitting results for the learning sample Results suggest that the model may not able to capture the variability present in the learning sample 20 Fittin
60. user interface for CUSUM analysis CUSUM analysis can only be performed when EM analysis results are available in the working directory After selecting WIM station lane starting and ending date the user can click on the CUSUM Analysis button to perform CUSUM analysis A GVW9 graph will pop up when the analysis is completed as shown in Figure 37 The blue line represents the average GVW of class 9 vehicles from WIM observations The Magenta line represents the modeled learning data from a period when WIM is in calibration The red line represents the predicted mean of GVW9 when sensor is in normal condition Figure 38 displays the results from the CUSUM decision interval analysis AS indicated the CUSUM curve drifts upward exceeding the decision interval around 5 23 2011 The CUSUM analysis result indicates the WIM sensor shifted by 5 33 kips starting on 5 9 2011 as displayed in the textbox in Figure 36 as highlighted A CUSUM Graph File Graph Help WIM 29 GANS Lane 1 Calibration Ho Adjustment Model e Predict wo D 10 0440 11 03 10 120350 01102511 0201411 03 0351 04102411 oazi 4 06 0141 Date Figure 37 CUSUM graph 34 A CUSUM Graph File Graph Help WIM 29 GYW9 Lane 1 UpoerCuSUM e Lower CUSUM Ol Threshold CUSUM DI 031611 032441 0401 11 04 0941 04901791 042541 050341 094141 05 19 11 05 27 11 06 04 1 Date Figure 38 CUSUM DI graph 3 3 Verification Using Sim
61. vestment decision making and transportation planning The significant amount of data being collected on a daily basis by WIM system requires a substantial amount of effort to verify data accuracy and ensure data quality However the WIM system itself presents difficulty in obtaining accurate data due to sensor characteristics that are sensitive to vehicle speed weather condition and changes in surrounding pavement conditions This research focuses on developing a systematic methodology to detect WIM sensor bias and support WIM calibration in a more efficient manner An implementation guideline for WIM sensor calibration was developed A mixture modeling technique using Expectation Maximization EM algorithm was developed to divide the vehicle class 9 Gross Vehicle Weight GVW into three normally distributed components unloaded partially loaded and fully loaded trucks A popular statistical process control technique Cumulative Sum CUSUM was performed on daily mean GVW estimates for fully loaded class 9 vehicles to identify and estimate any shift in the WIM sensor Special attention was given when presence of auto correlation in the data was detected by fitting time series model and then performing CUSUM analysis on the fitted residuals Results from the analysis suggested that the proposed methodology was able to estimate shift in the WIM sensor accurately and also indicated the time point when the system went out of calibration An out of control C
62. x Documents a Music E Pictures F Videos jE Computer E os C Ly ALK Technologies Le apps de data log Lo dell de Drivers Lo Intel Ly MSOCache Le PerfLogs j 12 items Motes 1 Set working directory Browse Save 2 Click GYW 9 EM button to load and process monthly WIM data 3 Click CUSUM Analysis to perform WIM data quality analysis Share with Burn New folder Name uid Data _ confid R _ CUSUM_ANALYSIS R EM_ANALYSIS R _ get_data_daily R _ get_data_weekly R E Important Notes _ Ipak R _ modifiedWim R pupdate R _ STATIONARITY R _ zupdate R Date modified 3 2 2015 2 33 PM 12 20 2014 9 48 PM 12 30 2014 5 34 PM 12 30 2014 6 20 PM 12 30 2014 5 27 PM 12 30 2014 9 31 PM 3 2 2015 2 30 PM 9 30 2014 3 01 PM 12 30 2014 8 49 PM 8 25 2014 1 38 PM 12 30 2014 5 34 PM 8 27 2014 12 08 PM Figure 46 Illustration of a selected working directory 42 File folder R File R File R File R File R File Text Document R File R File R File R File R File Important Note Removing any files or modify the Data folder in the working directory will fail the WIM Data Analyst application or generate incorrect results 4 2 2 Menu Bar The file menu bar illustrated in Figure 47 is implemented for additional features in the future At current release only limited functions are implemented 1 File 2 Edit MB WIM Data Analyst UNIVERSITY OF MINNE
63. ysis The Weekly option is for WIM stations with relatively low truck volumes in a day 5 Click on Plot GVW9 button to plot the GVW9 of the fully loaded trucks A sample GVW9 plot 1s displayed in Figure 52 Right click inside the graph plotting area to display more options including copy save image as page setup print show point values zoom and set scale 6 Click on Stationarity Test button to test the stationarity of the average GVW9 of fully loaded trucks in the learning period The output of a sample stationarity test is shown in Figure 53 7 Click on CUSUM Analysis to start the CUSUM analysis A sample result from the CUSUM analysis is plotted in Figure 54 Right click inside the graph plotting area to display more options 45 including copy save image as page setup print show point values zoom and set scale In addition the CUSUM graph file menu has the following features to export the data print the graph or plot different graph a File Export Data Export the data of the display graph to a csv file Page Setup Setup page for printing Print Print current graph Close Close the CUSUM graph window b Graph GVW Display GVW plot CUSUM Display CUSUM plot DICUSUM Display adjusting CUSUM with decision interval c Help Display help document 8 Click on Clear Log button to remove results displayed in the textbox Example 1 Select WIM 29 Lane 1 Start Date 10 5

Implementation of Traffic Data Quality Verification for WIM Sites

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