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Data Quality Verification & Sensor Calibration for WIM Systems
Chen-Fu Liao & Gary DavisDepartment of Civil Engineering
University of Minnesota
TRB 2012 NATMEC ConferenceJune 4-7, Dallas, Texas
Acknowledgements
RITA, USDOT and UMN ITS Institute
MnDOT – Ben Timerson & Staff in Transportation Data & Analysis
Sushanth Kumar – Graduate Research Students
Minnesota Traffic Observatory, UMN
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Outline
Literature ReviewWIM Data MonitoringMixture Model – GVW9Cumulative Sum (CUSUM)
MethodologyAnalysis ResultsConcluding Remarks
Dahlin, 1992
Recommended 3 measures for WIM quality assurance
1. Class 9 steering axle weights1. Class 9 steering axle weights
< 32 kips 8.4 kips
32‐ 70 kips 9.3 kips
> 70 kips 10.4 kips
2. Class 9 GVW
2 peaks
unloaded 28 32 kipsunloaded: 28‐32 kips
fully loaded: 70‐80 kips
3. Flexible ESAL factor
compare with “properly calibrated system”
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Class-9, Speed Distribution N=2955 (Observed), 8/2/2010
Fre
qu
en
cy
02
00
50
0
Mean=65.2, Median=65.0, Sd= 4.2 (MPH)
40 50 60 70 80
Class-9, GVW Distribution N=2955 (Observed), 8/2/2010
enc
y
15
0
Peak1=30.0 (kips), Peak2=76.0 (kips)
Fre
qu
e
0 20 40 60 80 100 120
05
0
Han, Boyd, Marti, 1995
FHWA‐LTPP study
Formal use of statistical quality control methods to monitor WIM systems
Dahlin’s 3 classes: unloaded, partially loaded, fully loaded
Presented Shewhart charts for average and range of GVWPresented Shewhart charts for average and range of GVW for unloaded class
Discussed automatic re‐calibration
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WIM Station 37 (07/17/2010), Lane 1Shapiro-Wilk Normality Test – QQ Plot
910
1112
GVW < 32 kips, w=0.964
ple
Qua
ntile
s
2535
GVW 32 ~ 70 kips, w=0.503
ple
Qua
ntile
s
-2 -1 0 1 27
8
Theoretical Quantiles
Sam
p
-3 -2 -1 0 1 2 3
515
Theoretical Quantiles
Sam
p
30
GVW > 70 kips, w=0.406
ntile
s
-3 -2 -1 0 1 2 3
1020
3
Theoretical Quantiles
Sam
ple
Qua
n
Ott and Papagiannakis, 1996
Pilot study, connected with NCHRP study of WIM calibration
I i d i l 9 i l i h f i iInvestigated using class 9 steering axle weights for monitoring2 subgroups
< 50 kips and > 50 kips
2‐ components to variance “fleet” ‐ estimated from static weight data“dynamic”‐ estimated from VESYM simulation
Correction for air resistance effectsCorrection for air resistance effects
Displayed 2 plots of individual steering axle weightsmeasures falling with 99% CImeasures drifting in/out of 99% CI
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Traffic Monitoring Guide, 2001
“at this time an inexpensive WIM calibration system has not been developed”system has not been developed
Four “most common” statistics to monitor WIM health
class 9 front axle weight
class 9 GVW distribution class 9 GVW distribution
class 9 axle spacing
traffic volume by vehicle class
Traffic Data Editing Procedures, 2002Pooled Fund Study SPR‐2(182)
Described empirical procedure to locating peaks in GVW weight distributions for class 9 & 11
Four ‘Expected Peak’ rules (by lane) – 56, 57, 58, 59
#56 ‐ unloaded GVW9: 27 ‐ 30 kips
#58 ‐ loaded GVW9: 72 ‐ 80 kips
Six ‘Historical Peak’ rules – 111 112 114 115 116 118Six Historical Peak rules 111, 112, 114, 115, 116, 118
Current estimate of peak central tendency outside specified historical limits
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Nichols and Cetin, 2007
• Introduced multi‐component mixture models to characterize class 9 GVW distribution
O ll l 9 GVW l i i f l• Overall class 9 GVW population consists of several homogeneous, normally distributed, sub‐populations
• Used EM algorithm to estimate subpopulation parameters
Sub-pop mean std. dev. proportion
unloaded 30.9 3.4 0.12330.9 3.4 0.123
Partial load 53.3 13.6 0.556
Full load 76.4 3.1 0.321
Research Focus
• Detecting subtle calibration drifts and other sensor errorsother sensor errors
• Mixture modeling using EM technique to model GVW9 distribution
• Formal monitoring using statistical quality control
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3 Related Problems
WIMmonitoring:Requires data model characterizing normal operation
WIM diagnosis:Prior identification of operational modesData model characterizing each mode
WIM calibration:Diagnose mis‐calibrationCompute calibration factor(needed for data adjustment?)
Mixture Model
Combined Density Function
1
1 1 2 2 3 3
Component Density Function
Combined Density Function
Nichols and Cetin, 2007
Mixing Property
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Mixture Model
Nichols and Cetin, 2007
Mixture Model Expectation Maximization (EM)
0.1
0.12Sample GVW9 N=2374
Empirical
EM Model
Tue, 8/3/2010
0.02
0.04
0.06
0.08
Den
sity
20 30 40 50 60 70 80 90 100 110 1200
GVW9 (kips)
ComponentLower Bound
(kips)Mean (kips)
Upper Bound (kips)
SD (kips) Proportion
1 – Unloaded 32.6 33.0 33.5 4.1 0.252 – Partially loaded 54.9 55.8 58.7 13.5 0.4753 – Fully loaded 75.6 76.0 76.4 3.8 0.275
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70
75Station 37 Class 9 Lane 2 EM Mean for calibration date 37101210
Expectation Maximization (EM)GVW9 Mean with 95% CI
35
40
45
50
55
60
65
GV
W M
ean
(kip
s)
Mean1
Mean2Mean3
confidence interval
25
30
35
3710
1208
3710
1209
3710
1210
3710
1213
3710
1214
WIM 37 Lane 1 GVW9 Group 3 Estimation (95% CI)
GVW9 MonitoringFully Loaded
65
75
85
95
105
115
125
GVW (kips)
p ( )
Mu3_L Mu3 Mu3_U
55
37091019
37091029
37091110
37091120
37091202
37091214
37091224
37100105
37100115
37100127
37100208
37100218
37100302
37100312
37100324
37100405
37100415
37100427
37100507
37100519
37100531
37100610
37100622
37100702
37100714
37100726
37100805
37100817
37100827
37100908
37100920
37100930
37101012
37101109
37101119
37101201
37101213
37101223
37110104
37110114
37110126
37110207
37110218
37110302
37110314
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Class 9 Daily Steering Axle Weight
< 32 kips 32 ~ 70 kips > 70 kips
WIM Station 37 (10/19/2009 ~ 08/10/2010)
9
10
11
12
13
14
kips
8
9
91019
91029
91108
91118
91128
91208
91218
91228
100107
100117
100127
100206
100216
100226
100308
100318
100328
100407
100417
100427
100507
100517
100527
100606
100616
100626
100706
100716
100726
100805
WIM DiagnosisLoadometer Scale
10 #1 10 #1
2.8
2.9
3
3.1
3.2
3.3
10(FXW/FXS)
log10(FXW/FXS) Reference Equation Max FXW Linear (log10(FXW/FXS))
y = ‐0.7002x + 3.7179R² = 0.5347
2.5
2.6
2.7
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
log 1
log10(FXS) N=2,893
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Cumulative Sum(CUSUM)
• A commonly used quality control method to detect deviations from benchmark values
• Detect small but persistent deviations• Monitor change detection• A statistical process control (SPC) tool for quality
improvement• Detect level shifts in auto-correlated noise
WIM DiagnosisCUSUM
A
B
C
D
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Adjusting CUSUM
WIM DiagnosisAdjusting CUSUM
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WIM DiagnosisDecision Interval
CU
SU
M
Upper CUSUM, S+
k = 0.5, h = 4, = 1.0
Out of control allowance
Number (n)
C
Lower CUSUM, S-
WIM GVW9 AnalysisFully Loaded (Lane #1)
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WIM GVW9 AnalysisUnloaded (Lane #2)
CUSUM Deviation vs. Calibration Adjustment
15%
Calibration Adjustment vs. CUSUM Deviation
y = 0.0046x + 0.0213R² = 0.0113
‐5%
0%
5%
10%
‐4 ‐2 0 2 4
Calibration Adjustment (%)
Linear (Calibration Adjustment (%))
‐15%
‐10%
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Summary
• A mixture modeling technique using Expectation Maximization (EM) algorithm ( ) g
• GVW9, SXW or FXW and FXS were analyzed for 4 WIM stations
• Use adjusting CUSUM methodology for WIM data diagnosis and drift detection together with DI (h) and reference value (k)
• Adjusting CUSUM methodology was able to detect the fsensor drifts prior to the actual calibration
• Did not find any relationship between CUSUM deviation and historical calibration adjustment
Ongoing and Future Work
• Better understand current calibration process & proceduresp
• Validate adjusting CUSUM methodology by select a test site for implementation and compare drift detection with current calibration process
• Quantify the impact of vehicle speed, weather, and pavement condition to the WIM sensors
• Estimate calibration factors
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Thank You !
Chen-Fu LiaoMinnesota Traffic Observatory
Department of Civil EngineeringUniversity of Minnesota
(612) [email protected]