piecewise multiple linear models for pavement marking...
TRANSCRIPT
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Piecewise Multiple Linear Models for PavementMarking Retroreflectivity Prediction under Effect of
Winter Weather Events
Chieh (Ross) Wang1, Dr. Zhaohua Wang2, andDr. Yichang (James) Tsai1
1School of Civil and Environmental Engineering2Center for GIS
Georgia Institute of Technology
95th TRB Annual MeetingJanuary, 2016
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Acknowledgment
Introduction Data Methodology Results Summary
Georgia TechDr. James TsaiDr. Zhaohua Wang
Georgia Department of TransportationRichard DoudsBinh Bui
National Transportation Product Evaluation ProgramDavid KuniegaKatheryn Malusky
State DOTsPennDOTFDOTMinnDOT
Wang, Wang, and Tsai #16-2425 2016 TRB 1 / 17
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Outline
Introduction Data Methodology Results Summary
1 Introduction
2 DataRaw DataWinter Weather Effects
3 MethodologyPiecewise Linear RegressionModel Formulation
4 ResultsFinal Models & Prediction ResultsDiscussions - Comparing PMLMs to MLMs
Wang, Wang, and Tsai #16-2425 2016 TRB 2 / 17
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Introduction
Introduction Data Methodology Results Summary
Pavement markings are important traffic control devices used toconvey messages to road users / autonomous vehicles
Maintaining the visibility (durability and retroreflectivity) ofmarkings under various weather and lighting conditions is crucialAccurate prediction of retroreflectivity and service life ofpavement marking materials (PMMs) help transportationagencies manage pavement markings in a timely andcost-effective mannerExtensive studies have been conducted to predict theretroreflectivity of different PMMs under various conditions inindividual statesChallenges (e.g. effect of winter weather events) andopportunities (e.g., performance of newer materials) presentresearch needs
Wang, Wang, and Tsai #16-2425 2016 TRB 3 / 17
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Introduction
Introduction Data Methodology Results Summary
Pavement markings are important traffic control devices used toconvey messages to road users / autonomous vehiclesMaintaining the visibility (durability and retroreflectivity) ofmarkings under various weather and lighting conditions is crucial
Accurate prediction of retroreflectivity and service life ofpavement marking materials (PMMs) help transportationagencies manage pavement markings in a timely andcost-effective mannerExtensive studies have been conducted to predict theretroreflectivity of different PMMs under various conditions inindividual statesChallenges (e.g. effect of winter weather events) andopportunities (e.g., performance of newer materials) presentresearch needs
Wang, Wang, and Tsai #16-2425 2016 TRB 3 / 17
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Introduction
Introduction Data Methodology Results Summary
Pavement markings are important traffic control devices used toconvey messages to road users / autonomous vehiclesMaintaining the visibility (durability and retroreflectivity) ofmarkings under various weather and lighting conditions is crucialAccurate prediction of retroreflectivity and service life ofpavement marking materials (PMMs) help transportationagencies manage pavement markings in a timely andcost-effective manner
Extensive studies have been conducted to predict theretroreflectivity of different PMMs under various conditions inindividual statesChallenges (e.g. effect of winter weather events) andopportunities (e.g., performance of newer materials) presentresearch needs
Wang, Wang, and Tsai #16-2425 2016 TRB 3 / 17
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Introduction
Introduction Data Methodology Results Summary
Pavement markings are important traffic control devices used toconvey messages to road users / autonomous vehiclesMaintaining the visibility (durability and retroreflectivity) ofmarkings under various weather and lighting conditions is crucialAccurate prediction of retroreflectivity and service life ofpavement marking materials (PMMs) help transportationagencies manage pavement markings in a timely andcost-effective mannerExtensive studies have been conducted to predict theretroreflectivity of different PMMs under various conditions inindividual states
Challenges (e.g. effect of winter weather events) andopportunities (e.g., performance of newer materials) presentresearch needs
Wang, Wang, and Tsai #16-2425 2016 TRB 3 / 17
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Introduction
Introduction Data Methodology Results Summary
Pavement markings are important traffic control devices used toconvey messages to road users / autonomous vehiclesMaintaining the visibility (durability and retroreflectivity) ofmarkings under various weather and lighting conditions is crucialAccurate prediction of retroreflectivity and service life ofpavement marking materials (PMMs) help transportationagencies manage pavement markings in a timely andcost-effective mannerExtensive studies have been conducted to predict theretroreflectivity of different PMMs under various conditions inindividual statesChallenges (e.g. effect of winter weather events) andopportunities (e.g., performance of newer materials) presentresearch needs
Wang, Wang, and Tsai #16-2425 2016 TRB 3 / 17
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Objectives
Introduction Data Methodology Results Summary
Observe the effect of winter weather events on retroreflectivityand incorporate winter weather effect into modeling;
Develop comprehensive retroreflectivity prediction modelsthat can be adopted by different states, whether or not winterweather is a primary concern;
Develop retroreflectivity prediction models for preformed tapeand methyl methacrylate MMA; and
Provide suggestions that enable state DOTs to incorporate theeffect of winter weather events into their pavement markingmanagement procedures.
Wang, Wang, and Tsai #16-2425 2016 TRB 4 / 17
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Objectives
Introduction Data Methodology Results Summary
Observe the effect of winter weather events on retroreflectivityand incorporate winter weather effect into modeling;
Develop comprehensive retroreflectivity prediction modelsthat can be adopted by different states, whether or not winterweather is a primary concern;
Develop retroreflectivity prediction models for preformed tapeand methyl methacrylate MMA; and
Provide suggestions that enable state DOTs to incorporate theeffect of winter weather events into their pavement markingmanagement procedures.
Wang, Wang, and Tsai #16-2425 2016 TRB 4 / 17
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Objectives
Introduction Data Methodology Results Summary
Observe the effect of winter weather events on retroreflectivityand incorporate winter weather effect into modeling;
Develop comprehensive retroreflectivity prediction modelsthat can be adopted by different states, whether or not winterweather is a primary concern;
Develop retroreflectivity prediction models for preformed tapeand methyl methacrylate MMA;
and
Provide suggestions that enable state DOTs to incorporate theeffect of winter weather events into their pavement markingmanagement procedures.
Wang, Wang, and Tsai #16-2425 2016 TRB 4 / 17
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Objectives
Introduction Data Methodology Results Summary
Observe the effect of winter weather events on retroreflectivityand incorporate winter weather effect into modeling;
Develop comprehensive retroreflectivity prediction modelsthat can be adopted by different states, whether or not winterweather is a primary concern;
Develop retroreflectivity prediction models for preformed tapeand methyl methacrylate MMA; and
Provide suggestions that enable state DOTs to incorporate theeffect of winter weather events into their pavement markingmanagement procedures.
Wang, Wang, and Tsai #16-2425 2016 TRB 4 / 17
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Raw Data
Introduction Data Methodology Results Summary
AASHTO NTPEP DataMine 2.0(http://data.ntpep.org/)
Test DecksPennsylvania: 2008, 2011, 2014Florida: 2009, 2012Minnesota: 2010, 2013
Surface TypesAsphalt ConcretePortland Cement Concrete
Materials: Tape & MMAData: Installation / Field Inspection
Traffic Data from State DOTsAverage Daily Traffic (ADT)Average Daily Truck Traffic (ADTT)
NTPEP Test Decks
Wang, Wang, and Tsai #16-2425 2016 TRB 5 / 17
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Observing the Effect of Winter Weather Events
Introduction Data Methodology Results Summary
0
200
400
600
800
1000
1200
1400
1600
1800
0 3 6 9 12 15 18 21 24 27 30 33 36Interval (months)
Ret
rore
flect
ivity
( m
cd/m
2 /lux)
FL09
FL12
(a)
0
200
400
600
800
1000
1200
1400
1600
1800
0 3 6 9 12 15 18 21 24 27 30 33 36Interval (months)
Ret
rore
flect
ivity
( m
cd/m
2 /lux)
PA08
PA11
PA14
(b)MMA Retroreflectivity in (a) Florida; and (b) Pennsylvania
No Penn data in winters
Similar degradation trendsbefore 1st winter
Effect of 1st winter wassignificant
Relationship between numberof snowplows andretroreflectivity cannot beclosely evaluated
Wang, Wang, and Tsai #16-2425 2016 TRB 6 / 17
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Piecewise Linear Regression
Introduction Data Methodology Results Summary
Order the entire dataset by the Ordering VariableDivide the dataset into segmentsFit each segment with a separate regression model
yi = αk + βkjxji
whereyi = the i th responsexji = the i th measurement of variable xjk = the k th segment
A Piecewise Simple Linear Regression Model with Two Segments
Wang, Wang, and Tsai #16-2425 2016 TRB 7 / 17
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Proposed Piecewise Multiple Linear Models
Introduction Data Methodology Results Summary
RLi =
{α1 + β11ADTi + β12Daysi + β13MaxRetroi , i = 1, ..., n1
α2 + β21ADTi + β22Days2i + β23MaxRetro2i , i = n1 + 1, ..., n
whereRL = Retroreflectivity (mcd/m2/lux)ADT = Average daily traffic (veh/day/ln)Days = Elapsed days from installationDays2 = Elapsed days after 1st winterMaxRetro = Maximum retroreflectivity from installationMaxRetro2 = Maximum retroreflectivity after 1st winter
Wang, Wang, and Tsai #16-2425 2016 TRB 8 / 17
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Model Coefficients and Goodness of Fit
Introduction Data Methodology Results Summary
RLi =
{α1 + β11ADTi + β12Daysi + β13MaxRetroi , i = 1, ..., n1
α2 + β21ADTi + β22Days2i + β23MaxRetro2i , i = n1 + 1, ..., n
Final PMLM Coefficients and R-Squared ValuesTape MMA
Asphalt Concrete Asphalt ConcreteWhite Yellow White Yellow White Yellow White Yellow
α1 96.720 77.289 171.705 86.402 137.060 39.100 126.905 74.688β11 -0.010 -0.003 -0.007 -0.003 -0.004 -0.003 -0.005 -0.006β12 -0.656 -0.374 -0.618 -0.319 -0.470 -0.124 -0.449 -0.138β13 0.917 0.828 0.821 0.824 0.771 0.883 0.796 0.887R2
1 0.878 0.868 0.752 0.793 0.804 0.941 0.784 0.919α2 124.032 60.985 22.129 28.050 153.497 114.484 87.460 75.205β21 -0.007 -0.001 0.004 0.002 -0.009 -0.007 -0.002 -0.003β22 -0.223 -0.145 -0.316 -0.194 -0.295 -0.168 -0.262 -0.155β23 0.643 0.554 0.716 0.666 0.693 0.643 0.713 0.718R2
2 0.768 0.701 0.831 0.828 0.640 0.747 0.744 0.800Note: all independent variables were significant variables in these models
Wang, Wang, and Tsai #16-2425 2016 TRB 9 / 17
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Model Coefficients and Goodness of Fit
Introduction Data Methodology Results Summary
RLi =
{α1 + β11ADTi + β12Daysi + β13MaxRetroi , i = 1, ..., n1
α2 + β21ADTi + β22Days2i + β23MaxRetro2i , i = n1 + 1, ..., n
Final PMLM Coefficients and R-Squared ValuesTape MMA
Asphalt Concrete Asphalt ConcreteWhite Yellow White Yellow White Yellow White Yellow
α1 96.720 77.289 171.705 86.402 137.060 39.100 126.905 74.688β11 -0.010 -0.003 -0.007 -0.003 -0.004 -0.003 -0.005 -0.006β12 -0.656 -0.374 -0.618 -0.319 -0.470 -0.124 -0.449 -0.138β13 0.917 0.828 0.821 0.824 0.771 0.883 0.796 0.887R2
1 0.878 0.868 0.752 0.793 0.804 0.941 0.784 0.919α2 124.032 60.985 22.129 28.050 153.497 114.484 87.460 75.205β21 -0.007 -0.001 0.004 0.002 -0.009 -0.007 -0.002 -0.003β22 -0.223 -0.145 -0.316 -0.194 -0.295 -0.168 -0.262 -0.155β23 0.643 0.554 0.716 0.666 0.693 0.643 0.713 0.718R2
2 0.768 0.701 0.831 0.828 0.640 0.747 0.744 0.800Note: all independent variables were significant variables in these models
Wang, Wang, and Tsai #16-2425 2016 TRB 9 / 17
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PMLM vs. MLM
Introduction Data Methodology Results Summary
Formulating a traditional multiple linear model (MLM) using samevariables for comparison:
RLi = α+ β1ADTi + β2Daysi + β3MaxRetroi
Coefficients, R-Squared Values, and Root Mean Square Errors of MLMTape MMA
Asphalt Concrete Asphalt ConcreteWhite Yellow White Yellow White Yellow White Yellow
α 155.830 96.357 103.345 134.178 234.968 123.548 188.004 215.013β1 0.013 0.013 0.009 0.007 0.003 0.000† 0.003 -0.007β2 -0.744 -0.500 -0.757 -0.516 -0.560 -0.340 -0.553 -0.369β3 0.523 0.450 0.631 0.526 0.496 0.585 0.538 0.570R2 0.676 0.640 0.660 0.600 0.566 0.599 0.625 0.570 Overall
RMSEFLmlm 175.1 94.8 264.6 191.4 119.2 107.2 158.0 144.8 170.6RMSEMNmlm 307.9 235.6 324.6 246.2 216.2 191.7 222.8 201.8 252.1RMSEPAmlm 207.8 130.8 248.1 156.3 178.5 152.8 170.4 141.0 182.4RMSEmlm 235.9 158.3 277.5 193.9 180.2 160.2 187.4 167.9 204.6
RMSEFLpmlm 150.0 85.8 243.2 132.3 119.0 77.6 147.5 87.7 144.7RMSEMNpmlm 108.3 90.0 114.4 62.9 118.9 52.3 127.5 62.3 95.9RMSEPApmlm 93.2 58.0 115.2 61.9 111.9 58.4 89.5 49.7 84.7RMSEpmlm 114.0 75.9 156.3 87.7 116.2 61.4 119.6 65.2 106.5
† Not statistically significant at 95% level
Wang, Wang, and Tsai #16-2425 2016 TRB 10 / 17
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PMLM vs. MLM
Introduction Data Methodology Results Summary
Formulating a traditional multiple linear model (MLM) using samevariables for comparison:
RLi = α+ β1ADTi + β2Daysi + β3MaxRetroi
Coefficients, R-Squared Values, and Root Mean Square Errors of MLMTape MMA
Asphalt Concrete Asphalt ConcreteWhite Yellow White Yellow White Yellow White Yellow
α 155.830 96.357 103.345 134.178 234.968 123.548 188.004 215.013β1 0.013 0.013 0.009 0.007 0.003 0.000† 0.003 -0.007β2 -0.744 -0.500 -0.757 -0.516 -0.560 -0.340 -0.553 -0.369β3 0.523 0.450 0.631 0.526 0.496 0.585 0.538 0.570R2 0.676 0.640 0.660 0.600 0.566 0.599 0.625 0.570 Overall
RMSEFLmlm 175.1 94.8 264.6 191.4 119.2 107.2 158.0 144.8 170.6RMSEMNmlm 307.9 235.6 324.6 246.2 216.2 191.7 222.8 201.8 252.1RMSEPAmlm 207.8 130.8 248.1 156.3 178.5 152.8 170.4 141.0 182.4RMSEmlm 235.9 158.3 277.5 193.9 180.2 160.2 187.4 167.9 204.6
RMSEFLpmlm 150.0 85.8 243.2 132.3 119.0 77.6 147.5 87.7 144.7RMSEMNpmlm 108.3 90.0 114.4 62.9 118.9 52.3 127.5 62.3 95.9RMSEPApmlm 93.2 58.0 115.2 61.9 111.9 58.4 89.5 49.7 84.7RMSEpmlm 114.0 75.9 156.3 87.7 116.2 61.4 119.6 65.2 106.5
† Not statistically significant at 95% level
Wang, Wang, and Tsai #16-2425 2016 TRB 10 / 17
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PMLM vs. MLM
Introduction Data Methodology Results Summary
Formulating a traditional multiple linear model (MLM) using samevariables for comparison:
RLi = α+ β1ADTi + β2Daysi + β3MaxRetroi
Coefficients, R-Squared Values, and Root Mean Square Errors of MLMTape MMA
Asphalt Concrete Asphalt ConcreteWhite Yellow White Yellow White Yellow White Yellow
α 155.830 96.357 103.345 134.178 234.968 123.548 188.004 215.013β1 0.013 0.013 0.009 0.007 0.003 0.000† 0.003 -0.007β2 -0.744 -0.500 -0.757 -0.516 -0.560 -0.340 -0.553 -0.369β3 0.523 0.450 0.631 0.526 0.496 0.585 0.538 0.570R2 0.676 0.640 0.660 0.600 0.566 0.599 0.625 0.570 Overall
RMSEFLmlm 175.1 94.8 264.6 191.4 119.2 107.2 158.0 144.8 170.6RMSEMNmlm 307.9 235.6 324.6 246.2 216.2 191.7 222.8 201.8 252.1RMSEPAmlm 207.8 130.8 248.1 156.3 178.5 152.8 170.4 141.0 182.4RMSEmlm 235.9 158.3 277.5 193.9 180.2 160.2 187.4 167.9 204.6
RMSEFLpmlm 150.0 85.8 243.2 132.3 119.0 77.6 147.5 87.7 144.7RMSEMNpmlm 108.3 90.0 114.4 62.9 118.9 52.3 127.5 62.3 95.9RMSEPApmlm 93.2 58.0 115.2 61.9 111.9 58.4 89.5 49.7 84.7RMSEpmlm 114.0 75.9 156.3 87.7 116.2 61.4 119.6 65.2 106.5
† Not statistically significant at 95% level
Wang, Wang, and Tsai #16-2425 2016 TRB 10 / 17
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PMLM vs. MLM (Prediction-Observation Plot)
Introduction Data Methodology Results Summary
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
A Typical Prediction-Observation (PO) Plot
AccuracyPO points align closely with the 45-degreedotted line
NormalityPO points distribute randomly on both sides ofthe dotted line
HomogeneityPO points deviate consistently from the dottedline, no matter how much the value of theobservation is
Wang, Wang, and Tsai #16-2425 2016 TRB 11 / 17
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PMLM vs. MLM (Prediction-Observation Plot)
Introduction Data Methodology Results Summary
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
A Typical Prediction-Observation (PO) Plot
AccuracyPO points align closely with the 45-degreedotted line
NormalityPO points distribute randomly on both sides ofthe dotted line
HomogeneityPO points deviate consistently from the dottedline, no matter how much the value of theobservation is
Wang, Wang, and Tsai #16-2425 2016 TRB 11 / 17
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PMLM vs. MLM (Prediction-Observation Plot)
Introduction Data Methodology Results Summary
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
Predicted versus Observed Retroreflectivity (White Tape on Asphalt)
Wang, Wang, and Tsai #16-2425 2016 TRB 12 / 17
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PMLM vs. MLM (Preformed Tape)
Introduction Data Methodology Results Summary
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
White Tape on Asphalt Yellow Tape on Asphalt
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
White Tape on Concrete Yellow Tape on Concrete
Wang, Wang, and Tsai #16-2425 2016 TRB 13 / 17
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PMLM vs. MLM (MMA)
Introduction Data Methodology Results Summary
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
White MMA on Asphalt Yellow MMA on Asphalt
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
MLM
0
500
1000
1500
2000
0 500 1000 1500 2000Observed ( mcd/m2/lux)
Pre
dict
ed (
mcd
/m2 /lu
x)
FL MN PA
PMLM
White MMA on Concrete Yellow MMA on Concrete
Wang, Wang, and Tsai #16-2425 2016 TRB 14 / 17
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Summary
Introduction Data Methodology Results Summary
A robust linear regression method (piecewise multiple linearregression) was proposed to predict pavement markingretroreflectivity under effect of winter weather events.
Significant improvement in prediction accuracy andprecision were achieved in all states (with or without severewinter).
In-depth discussions were made and useful insight on thecharacteristics of retroreflectivity degradation & modelselection were summarized.
Significant improvement in retroreflectivity prediction can beachieved by simply collecting retroreflectivty data right afterthe first winter.
Wang, Wang, and Tsai #16-2425 2016 TRB 15 / 17
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Summary
Introduction Data Methodology Results Summary
A robust linear regression method (piecewise multiple linearregression) was proposed to predict pavement markingretroreflectivity under effect of winter weather events.
Significant improvement in prediction accuracy andprecision were achieved in all states (with or without severewinter).
In-depth discussions were made and useful insight on thecharacteristics of retroreflectivity degradation & modelselection were summarized.
Significant improvement in retroreflectivity prediction can beachieved by simply collecting retroreflectivty data right afterthe first winter.
Wang, Wang, and Tsai #16-2425 2016 TRB 15 / 17
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Summary
Introduction Data Methodology Results Summary
A robust linear regression method (piecewise multiple linearregression) was proposed to predict pavement markingretroreflectivity under effect of winter weather events.
Significant improvement in prediction accuracy andprecision were achieved in all states (with or without severewinter).
In-depth discussions were made and useful insight on thecharacteristics of retroreflectivity degradation & modelselection were summarized.
Significant improvement in retroreflectivity prediction can beachieved by simply collecting retroreflectivty data right afterthe first winter.
Wang, Wang, and Tsai #16-2425 2016 TRB 15 / 17
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Summary
Introduction Data Methodology Results Summary
A robust linear regression method (piecewise multiple linearregression) was proposed to predict pavement markingretroreflectivity under effect of winter weather events.
Significant improvement in prediction accuracy andprecision were achieved in all states (with or without severewinter).
In-depth discussions were made and useful insight on thecharacteristics of retroreflectivity degradation & modelselection were summarized.
Significant improvement in retroreflectivity prediction can beachieved by simply collecting retroreflectivty data right afterthe first winter.
Wang, Wang, and Tsai #16-2425 2016 TRB 15 / 17
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Moving Forward
Introduction Data Methodology Results Summary
Include additional variables into material-specific modelingInstallation methods (e.g. sprayed, extruded, or patterned)Installation environment (e.g. road temperature)Bead properties (e.g. types of beads & mix)
Acquire more comprehensive datasets (training/testing)Longer analysis period (effect of the 2nd/3rd winter)More diverse traffic conditions & roadway characteristics
Apply proposed models to predict the service life of variousPMMs for informed decisions on the selection and managementof pavement markings
Wang, Wang, and Tsai #16-2425 2016 TRB 16 / 17
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Moving Forward
Introduction Data Methodology Results Summary
Include additional variables into material-specific modelingInstallation methods (e.g. sprayed, extruded, or patterned)Installation environment (e.g. road temperature)Bead properties (e.g. types of beads & mix)
Acquire more comprehensive datasets (training/testing)Longer analysis period (effect of the 2nd/3rd winter)More diverse traffic conditions & roadway characteristics
Apply proposed models to predict the service life of variousPMMs for informed decisions on the selection and managementof pavement markings
Wang, Wang, and Tsai #16-2425 2016 TRB 16 / 17
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Moving Forward
Introduction Data Methodology Results Summary
Include additional variables into material-specific modelingInstallation methods (e.g. sprayed, extruded, or patterned)Installation environment (e.g. road temperature)Bead properties (e.g. types of beads & mix)
Acquire more comprehensive datasets (training/testing)Longer analysis period (effect of the 2nd/3rd winter)More diverse traffic conditions & roadway characteristics
Apply proposed models to predict the service life of variousPMMs for informed decisions on the selection and managementof pavement markings
Wang, Wang, and Tsai #16-2425 2016 TRB 16 / 17
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Q&A
Introduction Data Methodology Results Summary
Chieh (Ross) WangPhD Student
Georgia Institute of [email protected]
Wang, Wang, and Tsai #16-2425 2016 TRB 17 / 17
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Review of Retroreflectivity Degradation Models
Introduction Data Methodology Results Summary
Summary of Pavement Marking Degradation Models in the LiteratureYear Author(s) Model(s) Variable(s) Material(s) R2 Location(s)1997 Andrady Logarithmic Time, Initial Retro Multiple 0.85+ Across the US1999 Lee et al. Simple Linear Regression Time Polyester, Thermo, WB
Paint, Tape0.14 to 0.18 MI
2001 Migletz et al. Simple Linear Regression,Quadratic, and ExponentialModels
CTP Multiple N/A 19 States in theUS
2002 Abboud and Bow-man
Logarithmic Time, ADT Paint and Thermo 0.32 and 0.58 AB
2003 Thamizharasan etal.
Multiple Linear Regression Time, CTP Thermo and Epoxy 0.21 to 0.78 SC
2006 Bahar et al. Inverse Polynomial Model Time Multiple N/A AB, CA, MN, MS,PA, TX, UT, WI
2006 Zhang and Wu Smoothing Spline and TimeSeries Model
Time Multiple N/A MS
2007 Fitch Logarithmic Time Thermo, Epoxy, andPolyurea
0.53 to 0.87 VT
2009 Sasidharan et al. Multiple Linear Regression Time, ADT, Line Type, Pavement Type Epoxy and WB Paint N/A PA2009 Sitzabee et al. Multiple Linear Regression Time, Initial Retro, AADT, Line Loca-
tion, Line ColorThermo and Paint 0.60 and 0.75 NC
2011 Hummer et al. Linear Mixed-Effects Model Time Paint N/A NC2012 Sitzabee et al. Multiple Linear Regression Time, AADT, Bead Type, Initial Retro,
Line LocationPolyurea 0.64 NC
2012 Mull and Sitzabee Multiple Linear Regression Time, Initial Retro, AADT, and PlowEvents
Paint 0.76 NC
2012 Robertson et al. Multiple Linear Regression Time, AADT, CTP, Lane Width, andShoulder Width
WB Paint and HB Paint 0.24 to 0.34 SC
2012 Fu and Wilmot Multiple Linear Regression Time, AADT, CTP Thermo, Tape, and InvertedProfile Thermo
0.18 to 0.89 LA
2014 Ozelim and Tur-ochy
Multiple Linear Regression Time, AADT, Initial Retro Thermo 0.45 to 0.49 AB
Wang, Wang, and Tsai #16-2425 2016 TRB 17 / 17
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Model Application - Service Life Prediction
Introduction Data Methodology Results Summary
Li =
100−α1−β11ADTi−β13MaxRetroi
β12, i = 1, ..., n1
100−α2−β21ADTi−β23MaxRetro2iβ22
, i = n1 + 1, ..., n
Pavement Marking Service Life till 100 mcd/m2 /lux (in years) and Prediction Precision (in ± mcd/m2 /lux)Tape MMA
Life ADT Asphalt Concrete Asphalt Concrete(veh/day/ln) White Yellow White Yellow White Yellow White Yellow
5,000 3.8 (53)‡ 3.7 (33) 4.6 (84) 5.3 (59) 3.6 (63) 7.8 (69) 4.0 (71) 8.2 (77)No Snow 10,000 3.5 (43) 3.6 (28) 4.4 (74) 5.2 (53) 3.4 (53) 7.4 (62) 3.8 (61) 7.6 (67)
20,000 3.1 (29) 3.4 (21) 4.1 (60) 4.9 (43) 3.2 (39) 6.7 (50) 3.5 (47) 6.4 (50)5,000 2.5 (22) 1.4 (11) 2.0 (20) 1.3 (8) 3.1 (37) 2.2 (14) 2.7 (32) 1.9 (14)
After Snow 10,000 2.0 (14) 1.3 (7) 2.2 (17) 1.5 (5) 2.7 (30) 1.6 (9) 2.6 (25) 1.6 (9)20,000 1.1 (42) 1.1 (28) 2.6 (20) 1.8 (8) 1.9 (42) 0.6 (17) 2.4 (24) 1.0 (9)
MaxRetro (mcd/m2/lux) 1039 655 1212 784 773 483 883 532MaxRetro2 (mcd/m2/lux) 331 209 407 229 473 237 392 211
‡ All values in this table are presented in format a(b), where a denotes the expected service life (in years), and b denotes the precision of retroreflectivity
prediction (in ± mcd/m2 /lux) at 95% confidence level
Wang, Wang, and Tsai #16-2425 2016 TRB 17 / 17
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Model Application - Service Life Prediction
Introduction Data Methodology Results Summary
Li =
100−α1−β11ADTi−β13MaxRetroi
β12, i = 1, ..., n1
100−α2−β21ADTi−β23MaxRetro2iβ22
, i = n1 + 1, ..., n
Pavement Marking Service Life till 100 mcd/m2 /lux (in years) and Prediction Precision (in ± mcd/m2 /lux)Tape MMA
Life ADT Asphalt Concrete Asphalt Concrete(veh/day/ln) White Yellow White Yellow White Yellow White Yellow
5,000 3.8 (53)‡ 3.7 (33) 4.6 (84) 5.3 (59) 3.6 (63) 7.8 (69) 4.0 (71) 8.2 (77)No Snow 10,000 3.5 (43) 3.6 (28) 4.4 (74) 5.2 (53) 3.4 (53) 7.4 (62) 3.8 (61) 7.6 (67)
20,000 3.1 (29) 3.4 (21) 4.1 (60) 4.9 (43) 3.2 (39) 6.7 (50) 3.5 (47) 6.4 (50)5,000 2.5 (22) 1.4 (11) 2.0 (20) 1.3 (8) 3.1 (37) 2.2 (14) 2.7 (32) 1.9 (14)
After Snow 10,000 2.0 (14) 1.3 (7) 2.2 (17) 1.5 (5) 2.7 (30) 1.6 (9) 2.6 (25) 1.6 (9)20,000 1.1 (42) 1.1 (28) 2.6 (20) 1.8 (8) 1.9 (42) 0.6 (17) 2.4 (24) 1.0 (9)
MaxRetro (mcd/m2/lux) 1039 655 1212 784 773 483 883 532MaxRetro2 (mcd/m2/lux) 331 209 407 229 473 237 392 211
‡ All values in this table are presented in format a(b), where a denotes the expected service life (in years), and b denotes the precision of retroreflectivity
prediction (in ± mcd/m2 /lux) at 95% confidence level
Wang, Wang, and Tsai #16-2425 2016 TRB 17 / 17
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Model Application - Service Life Prediction
Introduction Data Methodology Results Summary
Li =
100−α1−β11ADTi−β13MaxRetroi
β12, i = 1, ..., n1
100−α2−β21ADTi−β23MaxRetro2iβ22
, i = n1 + 1, ..., n
Pavement Marking Service Life till 100 mcd/m2 /lux (in years) and Prediction Precision (in ± mcd/m2 /lux)Tape MMA
Life ADT Asphalt Concrete Asphalt Concrete(veh/day/ln) White Yellow White Yellow White Yellow White Yellow
5,000 3.8 (53)‡ 3.7 (33) 4.6 (84) 5.3 (59) 3.6 (63) 7.8 (69) 4.0 (71) 8.2 (77)No Snow 10,000 3.5 (43) 3.6 (28) 4.4 (74) 5.2 (53) 3.4 (53) 7.4 (62) 3.8 (61) 7.6 (67)
20,000 3.1 (29) 3.4 (21) 4.1 (60) 4.9 (43) 3.2 (39) 6.7 (50) 3.5 (47) 6.4 (50)5,000 2.5 (22) 1.4 (11) 2.0 (20) 1.3 (8) 3.1 (37) 2.2 (14) 2.7 (32) 1.9 (14)
After Snow 10,000 2.0 (14) 1.3 (7) 2.2 (17) 1.5 (5) 2.7 (30) 1.6 (9) 2.6 (25) 1.6 (9)20,000 1.1 (42) 1.1 (28) 2.6 (20) 1.8 (8) 1.9 (42) 0.6 (17) 2.4 (24) 1.0 (9)
MaxRetro (mcd/m2/lux) 1039 655 1212 784 773 483 883 532MaxRetro2 (mcd/m2/lux) 331 209 407 229 473 237 392 211
‡ All values in this table are presented in format a(b), where a denotes the expected service life (in years), and b denotes the precision of retroreflectivity
prediction (in ± mcd/m2 /lux) at 95% confidence level
Wang, Wang, and Tsai #16-2425 2016 TRB 17 / 17