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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) 626-1697cliao@umn.edu