PERFORMANCE MODELS - Articlebalkire/CE5403/Lec16.pdf8- 2 Approach: This module is taught through Slide presentations and discussion with the participants. The module provides an overview

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PERFORMANCE MODELS

Purpose:

This module introduces the use of pavement performance models topredict future pavement conditions for the highway network as part ofthe agency’s pavement management activities. The types of modelsnormally used at the network and project level are introduced andexamples of the principal approaches are provided. Guidelines ondetermining the reliability of the performance models and updaterequirements are also provided.

Objectives:

Upon completion of this module, the participant will be able toaccomplish the following:

■ Understand the use of performance models in pavement management.

■ Identify the common modeling approaches used to develop models forpavement management.

■ Understand methods for evaluating the reliability of the pavementperformance models.

■ Describe the requirements for updating the models over time.

Reference:

Module 8 of the Participant’s Notebook

Duration:

100 minutes

Equipment:

Laptop computer, multimedia projector, flipchart, overhead projector,blank transparencies, transparency pens

Teaching Aids:

43 Microsoft PowerPoint® Slides

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Approach:

This module is taught through Slide presentations and discussion withthe participants. The module provides an overview of the use ofmodels in pavement management and introduces the most commonmodeling techniques. Examples from Washington State and Illinoisare also provided.

Distance Learning:

There are no special instructions on Distance Learning for this module.All slides prepared can also be used for distance learning.

Encourage questions from andpromote discussion with theparticipants.

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Slide 8-1 Slide 8-1

Notes:

Describe the purpose of thismodule and the approach that willbe used.

Slide 8-2 Slide 8-2

Notes:

Describe the objectives for thismodule. This Slide lists theinformation the participants willlearn.

PERFO RM A N CE M O D ELS

• Understand use of performancemodels

• Identify common modelingapproaches

• Understand methods forevaluating reliability

• Describe requirements forupdating models

Instructio n a l O b jectiv e s

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Slide 8-3 Slide 8-3

Notes:

Introduce the early work of Carey-Irick to define pavementperformance in terms ofserviceability-performanceconcepts.

Today, it is common practiceamong practitioners and researchersto use terms such as deterioration torepresent the change in pavementperformance over time.

For this course, performancemodels represent the pavementdeterioration patterns that aremodeled.

Slide 8-4 Slide 8-4

Notes:

Pavement performance models arean important component of a multi-year analysis for these types ofactivities.

Pavement performance models areused differently at the network andproject levels. These are theprimary activities that performancemodels are used for at the networklevel.

Discuss typical network-levelmodeling approaches

§ Deterministic models

§ Probabilistic models

Have participants read from textPage 8-2.

O v e r v iew

• Serviceability-performance concepts

• Deterioration as a representation ofchange in performance

U ses of Perform a n ce Models inPa v e m e n t M a n a g e m ent

• Network Level

• Project Level

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Slide 8-5 Slide 8-5

Notes:

This is Table 8.1 on Page 8-3. Itshows the principal types of modelsused at different levels withintransportation agencies.

Point out that higher levels ofmanagement are more interested inmodels that predict compositeindexes of network condition. Atthe national level, models are usedfor policy and economic matters.At the district level, there is lessconcern about the performance ofindividual section and more of afocus on the overall condition ofthe pavement network for the entirestate or a subset of the network.

Point out that at the project level,the focus is on the performance ofindividual sections or designapproaches.

Slide 8-6 Slide 8-6

Notes:

This slide illustrates the importanceof accurate models to predict futureconditions. It is presented in thecourse materials as Figure 8.1. Itillustrates that a pavementcondition of 60 could be predictedin 10 years or 20 years, dependingon which model is used.

Types of Performance Models

Deterministic Probabilistic

PrimaryResponse

Structural Functional Damage SurvivorCurves

Transition ProcessModels

• Deflection• Stress• Strain

• Distress• Pavement

Condition

• PSI• Safety

• LoadEquiv.

Markov Semi-Markov

NationalLevel

✔ ✔ ✔ ✔

State orDistrictLevel

✔ ✔ ✔ ✔ ✔ ✔

ProjectLevel

✔ ✔ ✔ ✔

I m p o r t a n ce o f A ccura teM o d e lin g

Condition

100

0

60

10 20

Age

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Slide 8-7 Slide 8-7

Notes:

In 1980, Darter introduced thebasic criteria that should befollowed to develop reliableperformance models. These criteriaare included.

In addition to these points, it isimportant that the limitations ofeach model be understood so thatthey are not used outside of therange of their intended use.

Slide 8-8 Slide 8-8

Notes:

Depending on the type of modelbeing developed, data requirementswill vary.

At the most basic level, inventoryand monitoring data re used todevelop the models.

Examples of inventory informationinclude geographic location orsection length.

Examples of monitoring datainclude pavement condition,cracking quantities, and AADT.

Data Requirements

§ Requirements vary depending onthe type of model being developed

§ Inventory information§ Monitoring data

Perform a nce M o d e lD e v e lopm e n t Cr ite r ia

• Adequate database

• Inclusion of all significant variablesthat affect performance

• Adequate functional form of the model• Satisfaction of the statistical criteria

concerning the precision of the model

• Understanding of the principles behindeach modeling approach

D a ta Requirem ents

• Requirements vary depending on thetype of model being developed

• Inventory Information

• Monitoring Data

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Slide 8-9 Slide 8-9

Notes:

This slide emphasizes that agenciesdo not have to wait until historicaldatabases are available in order todevelop performance models.Expert models have been usedsuccessfully in a number ofagencies. They can besupplemented as field data becomeavailable.

Slide 8-10 Slide 8-10

Notes:

This slide is Figure 8.2. It showsthat it is difficult to observedifferences in pavementperformance at the network leveldue to factors such as traffic,material variances, and climaticconditions because these factors areaccounted for in the design of thepavement structure through designprograms. As a result, if an agencysought to model the effect of trafficon pavement performance, this isdifficult to do without also lookingat pavement thickness because thethickness is a related factor that isaffected by the anticipated level oftraffic. Without consideringthickness data in the models,pavements with equal designperiods would show little variationin condition with traffic alone.

La ck o f H i sto r ica l Da ta

• If historical databases are not availabledue to changes in survey procedures,new rehabilitation techniques, or otherfactors, other techniques are available:– incorporate input from experienced

practitioners

– update the models as additional data areavailable

On- the-Dia g o n a l Issue

Traffic (ESALs)

Light Heavy

Thin

PavementThickness

Thick

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Notes:

Data Requirements

§ Sufficient amounts of datamust be used

§ Data must be measuredaccurately and without bias

§ Data must be representative

§ Data must be maintained overtime


Notes:

Model Limitations

§ Models must be usedappropriately

§ Limitations of models must beconsidered

§ Boundary conditions shouldbe identified and satisfied

D a ta Requirem ents

• Sufficient amounts of data must beused

• Data must be measured accurately andwithout bias

• Data must be representative

• Data must be maintained over time

M o d e l Lim ita tio n s

• Models must be used appropriately

• Limitations of models must beconsidered

• Boundary conditions should beidentified and satisfied

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Notes:

A number of different types ofdeterministic models can bedeveloped. This slide emphasizesthe primary approaches used todevelop deterministic models.

If deterministic models are notused, the agency probably usesprobabilistic models.

To date, no purely mechanisticmodels have been developedbecause they are only applicable tocalculating pavement response interms of mechanisms such as stress,strain, or deflection. These factorscould be used as the inputs for anempirical prediction model.


Notes:

Mechanistic Models

§ No purely mechanisticperformance models have beendeveloped

§ Calculated stress and strainattributes from mechanisticmodels can be used as theinput for an empiricalprediction model

Determ inistic v s. Prob a b ilistic

• Predicted Occurrence

• Techniques

M ech a n istic M o d e ls

• No purely mechanistic performancemodels have been developed

• Calculated stress and strain attributesfrom mechanistic models can be usedas the input for an empirical predictionmodel

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Notes:

Mechanistic-Empirical Models

§ Models developed usingpavement response as thedependent variable

§ Use elements of bothmechanistic models(fundamental principles ofpavement behavior) andempirical models (results fromexperience or experiments)

§ N=A * (1/e)B


Notes:

Regression used when historicaldata are available.

Regressio n A n a ly sis

• A technique used to determine therelationship between variables

• Often used in agencies with historicaldatabases available

M ech a n istic-Em p irica l M o d e ls

• Models developed using pavementresponse as the dependent variable

• Use elements of both mechanisticmodels (fundamental principles ofpavement behavior) and empiricalmodels (results from experience orexperiments)

• N = A * (1/e)B

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Notes:

Subjective models are used whenno historical data are available.


Notes:

Deterministic models are the mostcommon types of models forpavement management.

With these models, some type ofcondition (such as an overallcondition index or distressquantity) is modeled as a functionof variables such as pavement age,traffic, environment, pavementconstruction characteristics, andmaintenance and rehabilitationactions.

Subjectiv e A p p r o a ches

• Used in agencies that do not havehistorical data available

• Can be used to develop eitherdeterministic or probabilistic models

D e v e lopm e n t of Determ inisticPerform a nce Mode ls

• Very common modeling techniques inpavement management

• Predict a single number based on itsrelationship with one or more variables

• Can be empirical or mechanistic-empirical correlations calibrated usingregression

• Condition is modeled as a function ofother variables

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Notes:

Regression Analysis

§ Statistical tool used toestablish the relationshipbetween two or morevariables.

§ Models can be linear or non-linear, depending on therelationship between variables.


Notes:

This slide shows the equations forvarious regression model forms.

In polynomial regression, thenumber of curves in the regressionline is equal to one less than thedegree of the polynomial. Thesecurves may be constrained so thatthe curve can not increase overtime.

The term least squares fit comesfrom the minimization of thesquared differences between theactual data points and theircorresponding points on the fittedline (or curve). Polynomial leastsquares models are popular forpredicting the change in thedependent variable as a function ofthe independent variable(s).

Regressio n A n a ly sis

• Statistical tool used to establish therelationship between two or morevariables

• Models can be linear or non-linear,depending on the relationship betweenvariables

Regressio n M o d e l Form s

• Linear Regression■ Y = a + bX

• Multiple Linear Regression■ Y = a0 + a1X1 + a2X2 + . . . AnXn

• Non-Linear Regression■ Y = a0 + a1X

1 + a2X2 + . . . AnX

n

■ Polynomial regression models may beconstrained

■ Least squares fit is used to improve themodels

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Notes:

The functional form of aperformance model, or the way inwhich the variables are arranged,can only be determined throughconsideration of the actualrelationships between the variablesand the trends from the data on theplots.

These figures are shown in thenotebook as Figure 8.3. Itillustrates several types ofdeterministic model forms.

The individual developing themodel must understand therelationships between the variablesbeing considered in order to selectthe appropriate form.


Notes:

Family Models

§ Reduces number of variables

§ Group pavement sections becharacteristics

§ Assume similar deteriorationpatterns

§ Reflects average deteriorationfor family

Allows ranges of values to be usedfor developing families

Determ inistic M o d e l Form s

Linear Polynomial Hyperbolic

Fa m ily M o d e ls

• Reduces number of variables

• Group pavement sections bycharacteristics

• Assume similar deterioration patterns• Reflects average deterioration for family

• Allows ranges of values to be used fordeveloping families

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Notes:

Figure 8.4 discuss diagram.

The performance of each section isfound by shifting the family curveto intersect the condition point forthe section. The shift is alwaysparallel to the family predictioncurve.

Slide 8-24

Slide 8-24

Notes:

Advantages/Disadvantages toFamily Models

§ Advantages- Fairly easy to develop and

interpret- Reduces the number of

variables in the model- Allows ranges of values to be

used rather than exactmeasurements

§ Disadvantages- Does not explicitly deal with

errors in data or model form- Difficult to measure the effect

of independent variables

Shift of the Fa m ily Per form a nceM o d e l

Shift inCurveForIndividualSection

Original Family Curve

Actual SectionCondition

Age

Condition

Predicted SectionCondition

A d v a n ta g es/ Disa d v a n ta g es toFa m ily M o d e ls

• Advantages

• Disadvantages

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Notes:

These are some of the statisticaltools that are available forevaluating the fit of theperformance models to the datafrom which they were developed.

Before performing a statisticalevaluation, the agency must ensurethat the form of its models adheresto the boundary conditions or otherphysical principles that influencethe predicted value of thedependent variable.


Notes:

This test provides an indication ofhow much of the total variation inthe data is explained by theregression equation or performancecurve.

Sta tistica l Ev a lua tion o f M o d e ls

• Coefficient of determination (R2)

• Root mean square error (RMSE)

• Number of data points (n)

• Hypothesis tests on regressioncoefficients

Coefficient of Determ ina tio n(R2 )

• Provides an indication of how much ofthe total variation in the data isexplained by the regression equation orperformance curve

• Network Level normally < 0.9

• Project Level normally > 0.9

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Notes:

The RMSE is the standarddeviation of the predicteddependent variable value for aspecific value of the independentvariable.

Root – Mean – Square – Error

This might be drawn graphically ona flipchart.


Notes:

. Other Tests

§ Number of Data Points shouldbe at least 30 to test validity ofregression equation.

Statistician should be involvedin this process.

§ Hypothesis Test of RegressionConstants

RM SE

• Standard deviation of the predicteddependent variable value for a specificvalue of the independent variable

• Project Level: <=5• Network Level: > 5

O ther Tests

• Number of Data Points

• Hypothesis Test of RegressionConstants

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Notes:

Limitation of Statistical Evaluations

§ Statistical analysis onlyevaluate reliability of modelfor data used in itsdevelopment.

§ A model can be statisticallyvalid but not representative ofactual deterioration patterns ofnetwork if poor quality dataare used.


Notes:

Reliability of Performance Models

§ Network level- Transformations may be

required- Correlations between

independent variables mayinfluence reliability

- Significance of coefficientsmust be considered

§ Project level- Expect higher coefficients

of determination andlower RMSE

Relia b ility o f Per form a nceM o d e ls

• Network Level

• Project Level

Limitation of StatisticalEvaluations

• Statistical analyses only evaluatereliability of model for data used in itsdevelopment

• A model can be statistically valid butnot representative of actualdeterioration patterns of network ifpoor quality data are used

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Notes:

This is Table 8.3. It summarizesthe expectations of regressionparameters as a function of the useof the model at the network and

project levels.


Notes:

Update Requirements

§ Performance models must beupdated regularly to continueto reflect deterioration patterns

§ Feedback loops should beestablished to linkdeterioration models withengineering practices

Update Requirements

• Performance models must be updatedregularly to continue to reflectdeterioration patterns

• Feedback loops should be establishedto link deterioration models withengineering practices.

Relia b ility o f Per form a nceM o d e ls

Regression Parameter Expectations

PMSAnalysis

Level

R2 RMSE SampleSize

# ofIndependent

VariablesNetwork Medium

to LowMediumto Low

LargeSample

>1

Project High Low SmallSample

1

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Notes:

Examples

§ Washington Department ofTransportation- Deterministic models

§ Illinois Department ofTransportation- Deterministic models


Notes:

This slide provides and overview ofthe modeling activities in WSDOT.

W a shington Sta te DO T

• Priority programming process

• Developed in-house• Prediction models developed for

combined ratings• Raw distress severity and extent data

are stored so models can be modified asneeded

• Capabilities exist for statistical analysisof performance trends

• Performance models for individualsections

Ex a m p les

• Washington DOT– Deterministic models

• Illinois DOT– Deterministic models

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Notes:

This is Figure 8.8. It shows thegeneral shape of WSPMSperformance curves. Definevariables for students.

The deceleration rate ofdeterioration is attributed to theapplication of temporary fixes tohold the pavement together until amajor remedy can be applied.These temporary fixes tend to causeshort duration, random fluctuationsin the pavement rating – probablybest represented by a curve thatpasses through the mean value inthis phase.

WSDOT Limitations to RegressionAnalysis

§ New surfaces without historical datapoints

- Default models used- When three points are

available, regressionis used.

§ Random fluctuation in data (poor data fit).


Notes:

The degree of curvature in themodel is influenced by the constantselected for P, as shown in Figure8.10.

The P that provides the highest R2 isselected as the best fit model.

W SDO T M o d e l Form

Condition

Age

Random Fluctuationin Ratings

PCR = C-mAP

Fluctua tio n s in Degree o fCurva ture in W SDO T M o d e ls

Age (Years)

PCR

10 15

100

0

PCR = 100-10(Age)0.5

PCR = 100-0.1(Age)2.5

PCR = 100-10.0(Age)1.0

PCR = 100-1.0(Age)2.0

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Notes:

This is Figure 8.11. Because theWSDOT performance curvesoverestimate remaining life in earlystates, a process was established toadd the default curve to the lastdata point. The default curves areused to establish two artificialpoints that are added to the existingdata point, then a regressionequation is developed that best fitsboth actual and artificial datapoints. This process provides amore realistic estimate of specificproject performance by recognizingthe past performance trends uniqueto each project and alsoincorporating knowledge of themost likely rate of futuredeterioration from typical pavementperformance experience.


Notes:

In order to understand theperformance model development inIllinois, it is important to provide alittle background on the CRS andthe changes that occurred to theprocess when they automated thedata collection activities.

IDOT Model Objectives

§ Describe the expectedconditions at any point in thefuture

§ Develop alternativerehabilitation strategies

§ Prioritize need pavementimprovements

Illin o is D O T Determ inisticM o d e ls

• Condition Rating Survey (CRS)– 1.0 to 9.0

– Type, severity, and extent of 5predominant distress

• Automated the CRS Process– Safety of expert panel

– Reduction in staff

– PaveTech vans purchased

– Calculation of CRS value

O v e r Estim a tion o fPer form a nce

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Notes:

These are the family groupsthat were established formodel development


Notes:

This is Figure 8.12. This is the firstattempt at developing the models.Note the flat spot in thedeterioration curves, usuallyoccurring between a conditionrating (CRS) of 7.5 to 6.0, the timewhen IDOT typically schedulespavement sections forrehabilitation. This was notacceptable for programmingpurposes, so a new approach wasdeveloped.

IDO T Fa m ily M o d e lsSystem Surface District TotalInterstate Composite (2) 1-4

5-94

Concrete (2) 1-45-9

4

Non-Interstate

Flexible (3) 1-45-9(1-9)ST

3

Overlays (5) 1-45-9(1-9)CRC

9

Concrete (4) 1-45-9

8

SMART Flexible & OL(4)

All 4

IDO T Po ly n o m ia l Approa ch

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30 35 40 45 50

Age (Years)

CRS

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Notes:

This is Figure 8.13. It shows thetrajectories of CRS for eachpavement section in a family. Theaverage deterioration rate of eachsection is calculated to determinethe average deterioration rateassociated with the family type.The deterioration rates were thentranslated into deduct points.


Notes:

Adjustments were made if thepavements are susceptible to D-cracking, as shown here.

IDO T Tr a jector ies

D-Cr a ck A d justm e n ts

• Asphalt concrete overlays: deductsincreased by 20%

• Jointed reinforced concrete: deductsincreased by 20%

• CRCP: deducts increased by 50%

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Notes:

Review the objectives for thismodule.

• Understand use of performancemodels

• Identify common modelingapproaches

• Understand methods forevaluating reliability

• Describe requirements forupdating models

Instructio n a l O b jectiv e s

Documents

PERFORMANCE MODELS - Articlebalkire/CE5403/Lec16.pdf8- 2 Approach: This module is taught through Slide presentations and discussion with the participants. The module provides an overview