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1. Lower CUSUM _ DI Threshold a ow o 081611 082441 04 0141 04 0991 04901791 042541 050341 094191 00451941 052211 06 04 11 Date Figure 39 CUSUM DI graph 3 3 Verification Using Simulated 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 40 shows the plot of the simulated data Our goal is to show how we can identify the inconsistency in the WIM sensor 31 Xe Het DA 1 He E 80 ift lt 95 u 4 75 if95 t lt 130 80 if t 130 les 0 45 er N0 0 2 3 1 Simulated AR1 with change in mu 84 Simulated Mean GVW Calibration Change Calibration No Change 82 80 78 76 74 72 Index Figure 40 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 Model yp Estimate 0 4118 80 105 Std error 0 116 0 258 1416 Then the next step 1s 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 t
2. 4 A shortcut icon will be added to your computer desktop when the installation 1s finished 5 After the software is successfully installed run WIM Data Analyst exe by clicking on the desktop shortcut icon to start the application 6 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 7 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 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 46 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 47 illustrates an example of the working directory The R files are used for EM and CUSUM analysis using R software package 37 The Data folder contains data needed to process both EM CUSUM analysis and store corresponding outputs for plotting the CUSUM results in Windows Set Working Directory Code and Data Filepath
3. C1304 Ph Ps Mm on Ph Bo Po D D mm Dd T wl 5 z a Figure 49 Sample of WIM calibration log table 39 3 Options e GVW9 EM Fitting Open the EM fitting screen as shown in Figure 50 to process the gross vehicle weight GVW of class 9 vehicles e CUSUM Analysis Open the CUSUM analysis screen as illustrated in Figure 51 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 50 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 Me GVW9 EM Fitting File WIM Data Directory Data Aggregation Code and Data Filepath a Daily E ChentusMnDOT YWIM Implementation R Code Latest Weekly Select WIM Lane
4. Year Month Check Data WIM Station Lane 3 Y A F bila Run EM Fitting Initializing and loading A routines Loading 4 Preparing WIM 26 Daily data loaded Running EM algorthm for WIM 26 Lane 2 2014 1 Completed Results are placed in DataEM_Processed Daily folder Logs in Data Logs folder Initializing and loading R routines Loading 4 Preparing WIM 26 Daily data loaded Running EM algorthm for WIM 26 Lane 2 2014 2 Completed Results are placed in DataEM_Processed Dailiy folder Logs in Data Logs folder Help Clear Log Close Figure 50 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 51 40 Select a WIM station from the station listbox Select a lane number from the lane listbox 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 1s a record of calibration date between the selected starting and ending dates as illustrated in Figure 52 When no calibration data is 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
5. Are there missing obs TRUE Wik sensor shifted by 5 33 kips on 2011 05 09 Ho dowrivwarnd shift found nw sensor Figure 37 User interface of CUSUM analysis Figure 37 illustrates the 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 38 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 39 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 37 as highlighted 30 A CUSUM Graph File Graph Help WIM 29 GVW9 Lane 1 Calibration No Adjustment s Model e Predict GVW KIPS 10 0440 11 0350 120350 01102711 0201411 03 0351 04 0241 1 DS024 4 06 0141 Date Figure 38 CUSUM graph CUSUM Graph File Graph Help WIM 29 GVWS9 Lane 1 e Upper CUSUM
6. a a LO 2 O 10 30 50 TO 30 110 130 150 170 Time Figure 22 CUSUM based decision plots for Case V 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 following 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 HI 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 knowledg
7. dates are considered as learning period as illustrated in Figure 52 GVW data between the learning and the ending dates are used for testing Select Daily or Weekly data analysis The Weekly option is for WIM stations with relatively low truck volumes in a day Click on Plot GVW9 button to plot the GVW9 of the fully loaded trucks A sample GVW9 plot is displayed in Figure 53 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 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 54 Click on CUSUM Analysis to start the CUSUM analysis A sample result from the CUSUM analysis is plotted in Figure 55 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 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
8. l l l 1 l l 1 l l l l l l l l l l l l l l l l l l l l l l l l l l l l 0 50 100 150 200 250 Time index in days no weekends Figure 23 Inconsistent GVWs for fully loaded trucks from Station 26 21 y loaded GW full 65 80 15 70 65 Time series of mu3 out37_In2_test1_week xlsx Calib Change Calib No change 20 40 60 60 Time index in days no weekends Figure 24 Inconsistent GVWs for fully loaded trucks from Station 37 y loaded GVW full 80 79 78 PI 76 y Time series of mu3 out32_In4 _1 xlsx Ob S a Alib No change da lbihange 20 40 60 60 100 Time index in days no weekends Figure 25 Inconsistent GVWs for fully loaded trucks from Station 32 22 Time series of mu3 out26_In1_2 xlsx T Obs po can cong B2 t Calib Cha ij 80 y loaded fis 76 GWW full 74 72 7O 0 100 200 300 Time index in days no weekends Figure 26 Inconsistent GVWs for fully loaded trucks from Station 32 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 w wes 80 X 88 0 40 X 388 m wte gt 80 lt t lt 120 X 70 0 40 X1 70 a Yt 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 negati
9. o 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 18 Fitting Learning Sample Observed pana Predicied GVW 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 Calibration factor changed by 7 GVW 0 50 100 150 Index Figure 21 Comparison between estimated and observed testing sample Case IV 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 19 CUSUM of standardized residuals Li cd E D i 3 C3 co io co O 10 30 50 TO 30 110 130 150 170 Time index CUSUM Based Decision Interval for Residual a Wo 5 EE
10. 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 dot 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 TRB National Research Council Washington D C pp 72 80 Hawkins D M and Olwell D H 1998 Cumulative Sum Charts and Charting for Quality Improvement Springer Verlag New York 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 Final Report Center for Transportation Studies CTS 12 26 University of Minnes
11. 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 positive shift found in the WIM sensor Without any further knowledge it is not possible to provide any explanation for such 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 7 Obs Calib No change Calib Change 76 78 80 y loaded GVVV_full 74 72 70 l 4 l Ll l
12. ccc cece eee e ee eeneeeeeeees 5 Table 2 Estimated AR 1 parameters for learning sample Case I 0 cece ccc c cece ec neee eee 1 Table 3 Estimated AR 1 parameters for learning sample Case H ccc cece cece eee e eee ee ees 13 Table 4 Estimated AR 1 parameters for learning sample Case MI 0 0 cece ccc cece eee 16 Table 5 Estimated AR 1 parameters for learning sample Case IV ccc cece cece ee eee eee ees 18 Table 6 Estimated AR 1 Parameters for learning sample cc cece ccc cece cece ence eeneees 23 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 investment decision making and transportation planning The significant amount of data being collected on a daily basis by WIM system requires 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 which is 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
13. control Then the statistical model based on GV Ws under normal condition is used to predict the GVWs 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 Travel 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 s
14. data analysis software Figure 36 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 WIM 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 A AO EM Fitting File WM Data Directory Code and Data Filepath E ChentulmMnDOT Wih Implementation A Codes Latest A Load WIM Data Select WIM Lane Year Month Pee WIM Station Lane z Close Initializing and loading A routines Loading WIM 40 data loaded Running ER algorithm for Wik 40 Lane All 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 wih 40 Lane All 2070 12 Completed Results are placed in Data EM Processed folder Figure 36 User interface of EM analysis 29 A CUSUM Analysis Set Code and Data Directory E ChentueMnQOT WIM mplementation A Code Latest 1 Select WIM Data 2 Select Date WIM Station Start Date Wilh 29 1 10 542010 Vehicle Class Data Type End Date g Lt bf 8201 Er Clear Log CUSUM Analysis LUSUM Analysis Log Processing IM data clazs_ 1d 9 lane_ 1d 1 station_id 29 pe Gw lrit_ date 10 5 2010 Final date 68 011 Return Mg
15. for fully loaded trucks from Station 26 oooooocccccnnnccccccnnncnos 21 Figure 24 Inconsistent GV Ws for fully loaded trucks from Station 37 oooooocccoccccocononcnnnnn 22 Figure 25 Inconsistent GVWs for fully loaded trucks from Station 32 oooooooccccccnnncccnnncno 22 Figure 26 Inconsistent GVWs for fully loaded trucks from Station 32 c cccceeee ee cononononornnnns 23 Figure 28 Simulated GVWs with WIM shift followed by an unstable GVW pattern 24 Fioure 29 Pitted learning Sample a do 24 Figure 30 Predictions on testing sample l ooooooccccccccccccccccnnnnnnnnnnnnonnnno ron cnn nc Eai 25 Figure 31 CUSUM based decision interval for testing sample ooooocooccccccocooccnnonocos 25 Figure 32 CUSUM analysis indicating unstable truck population ooooooccccccccccccccconannnncos 26 Figure 33 WIM data analyst Main Screen sr a 27 Figure 34 Implementation guideline for CUSUM based algorithm for WIM calibration 28 Figure 35 Flowchart of the WIM data analysis software cccc cece cece eee e eee eeeeeeeeeeeeaaaeees 29 Fig re 360 User interface OL EM analysis sreci ia T a ic 29 Figure 37 User interface of CUSUM analysis a eds 30 Figure 9 CUSUM Drap Moreno eea E aE EENE A AEAT T 31 Firre 39 C USUM DESTA Martes T RRETA E E T OR 31 Figure 40 Simulated AR 1 process with change in mean level ooooooooccccccccccccnonccoos 32 Figure 41 Predictions on
16. indicate the influence on external factors other than WIM sensor on GVWs 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 The above description is presented in the flowchart as shown in Figure 34 A WIM Data Analyst pe CD fmt UNIVERSITY OF MINNESOTA Set Working Directory Code and Data Filepath E ChentuyMnDOT WIM lmplemnentation A Code Latest Browse nave Analysis Notes 1 Set working directory 2 Click GVW9 EM button to load and process monthly WIM data GYW EM File 3 Click CUSUM Analysis to perform WIM data quality analysis CUSUM Analysis EXIT Figure 33 WIM data analyst main screen 21 UN y 2 Compute EM estimates for 0 Begin with In daily mean fully loaded GVW calibration period 5 Compute EM estimates for 3 Estimate Time daily mean fully loaded GVW Fi Je Series Model for Testing Sample Parameters 6 Predictions on EM estimates from Testing i estimated residuals Go to Step 3 Sample Withi r Combine EM estimates ni from Testing Sample DI 9 Estimate WIM sensor shift 15 with Learning Sample Update WIM calibration Figure 34 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 dev
17. interval c Help Display help document Click on Clear Log button to remove results displayed in the textbox Example 1 Select WIM 29 Lane 1 Start Date 10 5 2010 End Data 6 8 2011 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 55 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 41 GVW9 A CUSUM Analysis so Jime Set Code and Data Directory Data Aggregation a Daily Weekly E ChenfueMaQOT WIM lmplementation A Code Latest 1 Select wlk 2 Select Date Wilh Station Start Date 10 82010 fr Wi 29 Learn Date 2 75 0074 Use Calib Date Lane 1 End Date B 822011 El Plot GYW 9 Stationanty Test CUSUM Analysis CUSUM Analysis Logs Initializing and loading A routines av Processing WIM data class 1d 3 station_id 29 lane_id 1 type Gy Init_date 10 5 2010 Final_date 67872011 Clear Log Close Figure 51 CUSUM analysis screen Testing Period 84 82 50 End Date 78 q Learning Period 76 74 N Start Date Learn or Calibration Date T2 0 50 100 Figure 52 Illustration of selecting dates learnin
18. 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 16 37_In2 2012 01 10 to 2012 05 21 Obs A factor changed by 4 GVW Index Figure 17 Comparison between estimated and observed testing sample Case III The next step 1s to perform CUSUM analysis on the standardized residuals Figure 18 shows the CUSUM plot along with CUSUM based decision plot for the residuals CUSUM of standardized residuals 0 10 20 30 40 50 60 70 80 90 Time index 10 0 cusum 30 CUSUM Based Decision Interval for Residual Dipcusum Time Figure 18 CUSUM based decision plots for Case II The CUSUM analysis also indicates that the system went out of calibration at the end of the testing period 17 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 Time series of mu3 26 n4_test1l_week xIsx EC oo i i Tm Obs Calib No change Calib Change I 00 om re O a E 3 2 p ca zz Ss Testing Sample Learning Sample
19. testing sample t 61 to 90 oooooccccccccccccccccccccccnnnnncccn nn nn 33 Figure 42 Predictions on testing sample t 91 to 120 ooooooccccccccccccnconcnnnnnonccccccnnnnnnoo 33 Figure 43 CUSUM analysis on testing sample t 91 to 120 oooooocccccccccccccccconnccnononncnnoo 34 Figure 44 Predictions on testing sample t 93 to 150 ooooooccccccccccccnncnccnnnnnnnnnnccnnnnnnnos 34 Figure 45 Welcome page of the WIM data analyst software help document 00008 36 Figure 46 Main screen of the WIM data analyst tool ccc ccc cccc cece eee e enna eeeene eens ee eneneaes 38 Figure 47 Illustration of a selected working directory 0 cc ccc cece eee eeene eee eeeeeeennnees 38 Heuras Pile mentalidad diana tdi 39 Figure 49 Sample of WIM calibration log table oooococococcccccconcncnnnnncccconccc cra nonnnnnnos 39 Etsure 0 ENERO recorra RI den aaa 40 Pistire si CUS UN Ema SIS CTE us doi 42 Figure 52 Illustration of selecting dates learning and testing periods 0 c cece eee eeeee ees 42 Freire SoS ale 6 VW Diao 43 Pisure 54 Sample stanonarity test Tesults sli io lia 43 Figure 55 Sample results from a CUSUM analysis 0 ccc ccc cece cence eee eee eee nnn ee ene e nena aes 44 Figure 56 Weekly GVW9 plot of WIM 34 0 0 ccc cece cece ee nnn eee eee n nee e en EEE Ee eens 44 LIST OF TABLES Table 1 Estimated AR 1 parameters for simulated data ccc
20. 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 te Assuming and Y are unbiased estimates of the true parameters expected standardized residuals are given by Ele 0 Fiat faj up Up FT if t gt t 2 10 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 Sa Sm t Aimy lE 10 2 11 Substituting residuals with its expected value and after some algebra we get an estimator of E pt m a k 45n7Smy 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
21. 1 correlation is defined as follows Simulated AR 1 process 0 7 Where Mean u 80 and w N 0 o 2 Figure 1 shows the time series measurements from the simulated sequence 86 84 82 80 78 76 74 0 50 100 150 200 index Figure 1 Simulated AR 1 process with mean 80 kips The mean 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 r X A Xy 10 2 4 Cusum 2 2 2 5 CUSUM and Decision Interval Hawkins and Olwell 1998 were plotted Figure 1 amp 2 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 i ti gt Q 0 50 100 150 200 Index CUSUM Based Decision Interval for Residual Ew J 5o de a O o Time Figure 2 CUSUM based decision interval for AR 1 residuals A new AR 1 process is as follows X b o _ pw tw vt lt 70 06 XxX u 5 p X_ pt 5 m Yt gt 70 2 7 The above process suggests that there is change of 5 kips in mean level for time index greater than 70 We use the estimated mo
22. 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 Highway Policy Information Federal Highway Administration http www fhwa dot gov policy ohpi travel qc index cfm accessed March 2015 47 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 Springer New York NY 48 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 fis 78 80 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 24 201
23. 3 Time series of mu3 32 In4gvw_1 xlsx XX Tt TT 78 79 80 76 0 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 Tt 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
24. 7A 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 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 pp 12 18 Qu T Lee C E and Huang L 1997 Traffic Load Forecasting Using Weigh in Motion Data Research Report 987 6 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 fhwa dot gov ohim tvtw wim pdf accessed March
25. Analysis Stationarity Test Plot GVW Plot CUSUM 5 Expectation Maximization EM Gross Vehicle Weight GVW Mixture Model 36 6 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 1 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 is a free software environment for statistical computing and graphics 6 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 Microsoft Windows 7 OS with service pack 1 The R statistics software version 3 1 1 was also installed va i 4 1 2 Installation Guide 1 Download and install R statistics software version 3 1 1 or later from http www r project org 2 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 3 Follow the instructions on the screen to complete the installation
26. E Chenfu MnDOT WIM Implementation R Code Latest Analysis GVW9 EM File CUSUM Analysis Organize v Include in library Y En Documents a Music Pictures E Videos jE Computer E 05 c do ALK Technologies de apps Lo data log Le dell de Drivers de Intel Lo MSOCache de PerfLogs Z 12 items Notes 1 Set working directory a Ron Ex UNIVERSITY OF MINNESOTA 2 Click GWw 9 EM button to load and process monthly WIM data 3 Click CUSUM Analysis to perform WIM data quality analysis Figure 46 Main screen of the WIM data analyst tool Share with Burn A Name de Data 7 confid R CUSUM_ANALYSIS R _ EM_ANALYSIS R 1 get_data_daily R _ get_data_weekly R Important Notes _ ipak R _ modifiedWim R _ pupdate R _ STATIONARITY R zupdate R Tr EXIT 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 47 Illustration of a selected working directory Important Note Type File folder R File R File R File R File R File Text Document R File R File R File R File R File 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 Th
27. Implementation of Traffic Data Quality Verification for WIM Sites DRAFT FINAL REPORT Prepared by Chen Fu Liao Minnesota Traffic Observatory Laboratory MTO Department of Civil Environmental and Geo Engineering CEGE University of Minnesota Indrajit Chatterjee Department of Civil Environmental and Geo Engineering CEGE University of Minnesota Gary A Davis Department of Civil Environmental and Geo Engineering CEGE University of Minnesota March 2015 Published by Minnesota Department of Transportation Research Services 395 John Ireland Boulevard MS 330 St Paul MN 55155 This report documents the results of research conducted by the authors and does 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 invaluab
28. ack 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 is using the learning sample 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 is given by X E Pm tses lel E 1 2 8 Where X represents 1 observation H represents mean of the process 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 Ap l 2 9 If the AR 1 model explains the serial correlation in
29. 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 is 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 is discussed in Chapter 4 Finally Chapter 5 included project summary A few cases of WIM data analysis with non stationary behavior were included in Appendix A 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 2141900 agi x A2gala Agga ad 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 GV W9 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 paramet
30. ctors external to the WIM system CUSUM analysis 1s used again to identify such anomaly Figure 32 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 GVW for Test Sample Il oD Obs LO S A Estimated rm i LO 100 110 120 130 140 150 Index in days CUSUM Based DI for Test Sample Il O cy E 3 o a3 aL a o 101 107 113 119 125 4131 137 143 149 Time Figure 32 CUSUM Analysis indicating unstable truck population 26 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 33 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 adjust
31. del 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 o 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 10 cusum 40 30 20 10 50 index Figure 4 CUSUM plot for AR 1 residual CUSUM Based Decision Interval for AR1 with change in mu 10 Dipcusum O 5 10 0 20 40 60 60 100 Time Figure 5 CUSUM based decision interval for AR 1 residual with change in mean As expected 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 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 att
32. e file menu bar illustrated in Figure 48 is implemented for additional features in the future At current release only limited functions are implemented 38 Hel UNIVERSITY OF MINNESOTA Set Working Directory Code and Data Filepath E Chenfu MnDOT WIM Implementation R Code Latest Analysis Notes 1 Set working directory 2 Click GWw9 EM button to load and process monthly WIM data GVW3 EM File 3 Click CUSUM Analysis to perform WIM data quality analysis y EXIT CUSUM Analysis Figure 48 File menu bar 1 File e Exit Exit the WIM Data Analyst tool 2 Edit e Calibration Log Open WIM sensor calibration log file for editing This calibration log file is used for CUSUM analysis See Figure 49 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 File Edit Help Wik Dat Initial El Station he wf eight Weight Percentage 6 11 2011 1 i Dd T Pan i i ee ae ee ee E Aa oO El OO mM Oo os A am mm am h uam h
33. e 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 operator can be notified 2 4 External Impacts on Truck Weights The underlying assumption of the proposed 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 Then a fixed shift in WIM sensor should be captured by CUSUM 20 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 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
34. ed 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 Implementation guidelines for WIM calibration was developed to detecting 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 Then 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 unk
35. ed 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 detail information E WIM Data Analyst Help Doc He S E Hide Print Options Contents Index Search Welcome a arame Welcome to the Weigh In Motion WIM Data Analyst Getting Started This tool is developed under the implementation project E iy Tutorial Implementation of Traffic Data lity 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 ie Test measurements to retrieve accurate measurements a Plot CUSUM E t Expectation Wlasimizatior EM Project Team Gross Vehicle Weight GW Mixture Model PI Chen Fu Liao E 4 Cumulative Sum CUSUM CUSUM Methodology e Co 1 Gary A Davis es Graduate Research Student Indrajit Chatterjee ils bees Classification Chart MnDOT TL Benjamin J Timerson nown Issues Contacting Us MnDOT AL Alan Rindels Glossary Figure 45 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
36. eloped using 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 project org 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 35 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 if the there is any sensor drift during the analysis period 28 EM Analysis Select Station Load GVW9 Process Output EM Lane Year Month BEJE EM Data to File Calibration l Files CUSUM Set Path Select Station zx Load Calibration Load Processed Analysis Lane Date Period Log File EM Data EM Analysis Set Path CUSUM Analysis Estimate Model Testing Model Learning Sensor Drift Sample Sample Result Output Figure 35 Flowchart of the WIM
37. ers 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 GVWs xx 449400 Arga x A393 x 2 2 Where GVW x is the Class 9 Gross Vehicle Weight GVW distribution g x is the empty class 9 truck normal GVW distribution 2 X is the partially loaded class 9 truck normal GVW distribution g x is the filly loaded class 9 truck normal GVW distribution A is the i non negative component proportion A A A 1 2 2 Simulation Based Analysis The CUSUM chart is a commonly used quality 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
38. esting sample Figure 41 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 downward shift in WIM sensor for the first 30 days of the testing data 32 Prediction on Testing Sample1 61 to 90 Obs Predicted ON 00 UD Dm pej 0 o gt 3 TE o 00 oO 00 Rh 60 65 70 75 80 85 90 Index in days no weekend Figure 41 Predictions on testing sample t 61 to 90 Since no shift was found the estimated mean H parameter was kept unchanged and predictions were made for the next 30 days for the testing data Figure 42 shows the predictions results suggesting a change in the mean process Testing Sample 2 91 to 120 4 Predicted GVW Fully Loaded 90 95 100 105 110 115 120 Index in days no weekend Figure 42 Predictions on testing sample t 91 to 120 33 CUSUM analysis as shown in Figure 43 suggested sensor shifted by 3 79 units after t 93 which is consistent with the simulated sequence cusum2 CUSUM CUSUM of standardized residuals 20 40 90 95 100 105 110 115 120 Time index Upper CUSUM 1D Lower CUSUM Decision Interval 5 10 90 95 100 105 110 115 120 Time index in days Figure 43 CUSUM analysis on testing sample t 91 to 120 After a nonzero shift in mean level was identified the final mean leve
39. evelopment 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 Standard Deviation SPC SXW TL TMAS TMG UMN USDOT VC VTRIS WIM 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 LIST OF FIGURES Figure 1 Simulated AR 1 process with mean 80 kips oooccooccocccccccccccccccccc cnc eee eee eeeeaaneeees 5 Figure 2 CUSUM based decision interval for AR 1 residuals ooooooococcccoooccoccccccnnnnnnoo 6 Figure 3 Residuals after fitting a non stationary AR 1 process 0 cc cee eeee eee e eee eee e ee enees 7 Figure 4 CUSUM plot for AR 1 residual Ber PE PON Figure 5 CUSUM based decision interval A AR 1 ee al wih dawei in mean oo Figure 6 GVW for average daily fully loaded trucks station 26 Case I 0 cece cece ee eeees 10 Figure 7 ACE and PAGE p
40. g and testing periods 42 150 AE OW Graph File Graph Help WIM 29 GVW9 Lane 1 100510 102950 112240 124640 0409 11 02102917 022611 082241 044941 09 0941 06 0279 1 Date Figure 53 Sample GVW9 plot stationarity Test Es Learning data is Dickey Fuller stationary statistic 4 359 Lag order 4 p value 0 01 Alternative hypothesis stationary Figure 54 Sample stationarity test results 43 8 CUSUM Graph oc te fat File Graph Help Export Data WIM 29 GVWS9 Lane 1 Page Setup Print er CUSUM Lower CUSUM DI Threshold CUSUM DI 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 55 Sample results from a CUSUM analysis Figure 56 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 CUSUM Graph File Graph Help WIM 34 GVW9 Lane 1 Weekly Calibration e No Adjustment s Model Predict oO o D m m h ee h a de m See el e de e de e e le de e e eee e e ed a 01 0114 11 0154 Figure 56 Weekly GVW9 plot of WIM 34 44 5 SUMMARY AND CONCLUSION 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 spe
41. g 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 is not possible to identify such factors and provide explanations for such inconsistent pattern At this point the goal is to propose a methodology that would alert the WIM operator whenever such anomaly is detected To identify 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 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 Microsift NET framework to interface with the R software http www r project org which is another open source
42. hall 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 control 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 compo
43. l was updated as 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 Testing 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 44 Predictions on testing sample t 93 to 150 34 Figure 44 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 35 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 Microsoft Compiled HTML online help format which consists of a collection of HTML pages an index and other navigation tools As illustrated in Figure 45 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 discuss
44. le 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 University of Minnesota e Center for Transportation Studies CTS University of Minnesota TABLE OF CONTENTS Amro UNO IA rr oO l IIS Li A O l ROD ECN E AA dea l LS aerate EW da ista l 14 Report Of ean ZallOn soria diet osos 3 2 WINE Data Models and Anal did aia 4 ON Mode bearna an O E aeuseb nasrsuae 4 22 mo lato Based A SS ranna a E toi wade buda 4 2 3 Analysis for WIM Measurements 0ooooooocccccccccccnnnnnnnnnnnononnnnnn nn rr nana n anna a eaeeees 8 2 3 1 Case I Station 26 Lane 3 iS EA it ai Isi 10 2 3 2 Case II Station 29 Lane 1 daa rr it 13 2 5 0 Case ME Staton 37 Lane F sia 15 2 3 4 Case IV Station 26 Lane 4 ooocccccccccccnccnccncnrnn rc cee cnceecencueenceees 18 232 ase Anansi SUMA a 20 2 4 External Impacts on Truck Weights 0 0 0 ccc c cece cece ence cece cece cece eee nese nneeeeas 20 2 5 Impact of External Factors on GVW Estimates Simulation Study ooooom 23 3 Development and Implementar E ia ences 27 3 1 Software Implementation Guidelines cusissiacren rresia is 27 5 2 W IM Data Analyst TOO ein 28 3 3 Verification Using Si
45. lotsor Cased stes adds ie oes 10 Figure S Pittine learmine sample Case Loans ool asia E EE 11 Figure 9 Comparison between estimated and observed testing sample Case l ooooooommm 12 Figure 10 CUSUM based decision plots for Case I cece cece eee c cece cece nee e eee e eens ene tenes 12 Figure 11 GVW for average daily fully loaded trucks station 29 Case II 0 cece cece eee 13 Figure 1 Fitting leaming sample Case Mostra 14 Figure 13 Comparison between estimated and observed testing sample Case I 14 Figure 14 CUSUM based decision plots for Case H cece cece cece cece cence eee e en eeeeeeneneas 15 Figure 15 GVW for average daily fully loaded trucks station 37 Case III 0 0 eee eceeeeee LS Figure 16 Fitne learmne sample Case Mbs te sii seatberiadat 16 Figure 17 Comparison between estimated and observed testing sample Case III 17 Figure 18 CUSUM based decision plots for Case IM oooooooocccccccccccccccccccconcnnnnnccnnos 17 Figure 19 GVW for average daily fully loaded trucks station 26 Case IV 0 0 00 cece eee eee e ees 18 Figure 20 Fittine learning sample Case IV aa A AA 19 Figure 21 Comparison between estimated and observed testing sample Case IV 19 Figure 22 CUSUM based decision plots for Case IV oooocccccccccccccccncnnnnnnn no ncnnn no eeeennneees 20 Figure 23 Inconsistent GVWs
46. ment 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 analysis 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
47. 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 CUSUM 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 testin
48. mple GVN 78 80 82 76 74 0 10 20 30 40 50 60 Index in days Figure 29 Fitted learning sample Based on the estimated parameters from the learning sample we estimate the measurements for the testing sample Figure 30 shows the comparison of the estimated and extracted testing sample I Figure 31 shows 24 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 Obs Estimated oO 00 0 oo h GVW 84 A y ius ye wv 82 50 78 76 60 FO 60 90 100 Index in days Figure 30 Predictions on testing sample I CUSUM Based DI for Test Sample 10 Dipecusum 0 10 61 65 69 B ff 61 8 B 93 OF Time Figure 31 CUSUM based decision interval for testing sample I Using equation 2 12 estimated shift was calculated as 0 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 25 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 II Failure to predict the Testing sample observations correctly would suggest unstable truck weights which might be caused by some unknown fa
49. mulated Scenari0s 0 ccc eee eee e eee e ee ee eee e eae 31 4 WIM Data Analyst User s Mana ia 36 Al ACUI OS LALLCO A o EGO a EEE 37 A T E N a aN 37 A Set ea A EARE EE 37 Ad Ment Dilo 38 AS EM PIN 2 cara a O 40 A DA OU SUE ANALY SIS a AA 40 Un ar and CONCIUSION lr a a aa i 45 RETENC PP a a a a E E E AER 46 Appendix A WIM Data Analysis Non Stationary Scenarios 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 SD 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 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 D
50. nent 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 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
51. nown 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 Microsoft Visual Studio package based on the NET framework An open source software R NET https rdotnet codeplex com was integrated into the Microsift 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 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 if the there is any sensor drift during the analysis period 45 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 Quali
52. ota Minneapolis MN 46 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 697122 tamu cs tr 2007 1 2 pdf accessed March 2015 Long Term Pavement Performance LTPP Program 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 ltpp reports traffqc 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 Vol 1 No 1 pp 27 45 McLachlan G and Peel D 2000 Finite Mixture Models John Wiley amp Sons Hoboken N J 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 Vol 23 No 3 July National Cooperative Highway Research Program NCHRP 2004 2002 Design Guide Design of New and Rehabilitated Pavement Structures Draft Final Report NCHRP Study 1 3
53. rm CUSUM analysis on the standardized residuals Figure 14 shows the CUSUM plot along with CUSUM based decision plot for the residuals 14 CUSUM of standardized residuals LO wm O 0 10 20 30 40 50 60 Time index CUSUM Based Decision Interval for Residual oa LO un o a ao 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 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 Time series of mu3 37 In2 test2 week xlsx Obs 2222 Calib iNo change 2222 Calib Change 5 0 i im 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 15 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 Fitting Learning Sample GYW 13 14 15 16 1 o gt 10 15 20 25 30 Index in days no weekend Figure 16 Fitting learning sample Case III Based
54. s 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 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
55. 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 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 if the there is any sensor drift during the analysis period 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 bia
56. 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 1s 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 GVWs 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 change Calib Change 82 o 00 oa D Le oO 2 ac E ES u 0 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 Auto correlation for learning sample Partial auto correlation for learning sample 1 0 o 0 2 o N o O o S LL o o x S oO o o N o o E N N F Q 0 5 10 15 a 10 15 Lag Lag Figure 7 ACF and PACF plots for Case I 10 Table 2 Estimated AR 1 parameters for learning sample Case I AR 1 model is deemed suitable as 1t was able to knock out all the auto correlation present in the learning sample Figure 8 below shows the fitting resul
57. ts for the learning sample Fitting Learning Sample Observed Predicted TCH 00 co 00 5 e co Pb Pb 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 11 Testing Sample 26 lane 6 1 11 to 1 23 12 Predicted GVW 70 80 76 14 a on 100 150 Index Figure 9 Comparison between estimated 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 cusum 60 40 20 80 0 10 20 30 40 50 60 70 80 90 100 120 140 160 Time index CUSUM Based Decision Interval for Residual Dipcusum 0 Time Figure 10 CUSUM based decision plots for Case I 12 2 3 2 Case II 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 do
58. tted 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_testl1_week xlsx Obs CalibiNo change Calib Change 85 N y loaded 80 GVW full PO sn Testing Sample 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 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 13 Fitting Learning Sample 84 Observed Predicted 78 80 82 GVW 74 76 l 70 0 20 40 60 50 100 120 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 GVW 0 10 20 30 40 30 60 FO Index Figure 13 Comparison between estimated and observed testing sample Case II The next step is to perfo
59. ty 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 S and Speigelhalter D 1999 Probabilistic Networks and Expert Systems Springer New York NY Dahlin C 1992 Proposed Method for Calibrating Weigh in Motion Systems and for Monitoring That Calibration Over Time Transportation Research Record 1364 TRB National Research Council Washington D C pp 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 pp 1 38 Davis G A 1997 Estimation Theory Approach to Monitoring and Updating Average Daily Traffic Report MN RC 97 05 to 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
60. ve 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 to 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 control 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 28 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 29 Table 6 shows the estimated parameters for AR 1 process Table 6 Estimated AR ree en for learning sample 23 Simulated GVW for Fully Loaded Trucks GYW 80 85 90 fis 70 65 0 50 100 150 Time index in days Figure 28 Simulated GVWs with WIM shift followed by an unstable GVW pattern Fitting Learning Sa

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