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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

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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

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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

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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 Technologycwang325@gatech.edu

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