PERFORMANCE MODELS

• Understand use of performance models

• Identify common modeling approaches

• Understand methods for evaluating reliability

• Describe requirements for updating models

Instructional Objectives

Overview

• Serviceability-performance concepts

• Deterioration as a representation of change in performance

Performance Model Development Criteria

• Adequate database (Long-Term)• Inclusion of all significant variables that

affect performance

• Adequate functional form of the model

• Satisfaction of the statistical criteria concerning the precision of the model

• Understanding of the principles behind each modeling approach

Data Requirements

• Requirements vary depending on the type of model being developed

• Inventory Information

• Condition Monitoring Data

Lack of Historical Data

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

practitioners– update the models as additional data are

available

Data Requirements

• Sufficient amounts of data must be used

• Data must be measured accurately and without bias

• Data must be representative

• Data must be maintained over time

Model Limitations• Models must be used appropriately

• Limitations of models must be considered

• Boundary conditions should be identified and satisfied

Regression Analysis

• Statistical tool used to establish the relationship between two or more variables

• Often used in agencies with historical databases available

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

Deterministic Model Forms

Linear Polynomial Hyperbolic

Development of Deterministic Performance Models

• Very common modeling techniques in pavement management

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

• Can be empirical or mechanistic-empirical correlations calibrated using regression

• Condition is modeled as a function of other variables

Regression Model Forms

• Linear Regression Y = a + bX

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

• Non-Linear Regression Y = a0 + a1X1 + a2X2 + . . . AnXn

Polynomial regression models may be constrained

Least squares fit is used to improve the models

Family Models

• Reduces number of variables

• Group pavement sections by characteristics

• Assume similar deterioration patterns

• Reflects average deterioration for family

• Allows ranges of values to be used for developing families

Family Models

• Start simple (model for each pavement type)

• Increase sophistication (based on climatic zones, functional classes, specific materials, surface type, functional classification, traffic levels, and geographic location)

The assumption is that each pavement section within a family has a similar deterioration pattern.

The pavement performance model developed for the family represents the average deterioration pattern for all sections included in that family.

Shift of the Family Performance Model

Shift in CurveFor IndividualSection

Original Default Family Curve

Actual/Specific Section Condition

Age

Condition

Predicted SectionCondition

The condition of an individual section is determined by shifting the family curve to intersect the condition point for the section.

Advantages/Disadvantages to Family Models

Deterministic models using regression analysis are common in agencies seeking network-level models for a multi-year pavement management analysis such as multi-year prioritization.

These models are popular because: – easy to develop and interpret– can be developed with commonly available

statistical analysis packages– can be developed with any number of variables– a number of different model forms

Statistical Evaluation of Models

• Coefficient of determination (R2)

• Root mean square error (RMSE)

• Number of data points (n)

• Hypothesis tests on regression coefficients

Coefficient of Determination (R2)

• Provides an indication of how much of the total variation in the data is explained by the regression equation or performance curve

• Network Level normally < 0.9

RMSE

• Standard deviation of the predicted dependent variable value for a specific value of the independent variable

• Network Level: > 5

Limitation of Statistical Evaluations

• Statistical analyses only evaluate reliability of model for data used in its development

• A model can be statistically valid but not representative of actual deterioration patterns of network if poor quality data are used

Reliability of Performance Models

Regression Parameter Expectations

PMS Analysis

Level

R2 RMSE Sample Size

# of Independent

Variables Network Medium

to Low Medium to Low

Large Sample

>1

Project High Low Small Sample

1

Probabilistic Performance Models

• Predict a range of condition values rather than a single value of condition

• Survivor curves represent the percentage of pavements that remain in service as a function of time

• Markovian theory is founded on the assumption that the probability that a pavement will change from one condition state to another is only dependent on its current state

Probabilistic Performance Models transition probabilities matrix

Markov Transition Probability Matrix

100-90 90-80 80-70 70-60100-90 0.2 0.4 0.3 0.190-80 0.2 0.6 0.280-70 0.1 0.3 0.670-60 0.1 0.9

Current State

transition probabilities matrix

9 100-90

889-80

779-70

669-60

559-50

449-40

339-30

229-20

119-10

9 0.9 0.1

100-90

8 0.05 0.65 0.3

89-80

7 0.05 0.6 0.25 0.1

79-70

6 0.05 0.45 0.25 0.2 0.05

69-60

5 0.05 0.25 0.4 0.3

59-50

4 0.05 0.2 0.75

49-40

3 0.05 0.65 0.3

39-30

2 0.1 0.8 0.1

29-20

1 0.05 0.95

19-10

Update Requirements

• Performance models must be updated regularly to continue to reflect deterioration patterns

• Feedback loops should be established to link deterioration models with engineering practices.

Washington State DOT

• 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 as needed

• Capabilities exist for statistical analysis of performance trends

• Performance models for individual sections

Prediction Model

0

1

2

3

4

5

2000 2005 2010 2015 2020

Years

Dis

tres

s In

dex

Default Distress

Index Model

Trigger

Current Time

Site Specific

Distress Model

Predicted

Measured

Pavement Performance Example

NJDOT Performance Models

NJDOT Performance ModelsOriginal Models based on Expert Opinion

SDI = SDIO - e(A−B*C ln(1/Age))

activity coef_a coef_b coef_c coef_o

4" Overlay over AC 28.08 28.79 1.023 5

6" Overlay over AC 28.08 28.98 1.023 5

Full Recon (BC) 13.05 13.592 1.038 5

Micro Surf(NovaChip) 28.08 28.527 1.023 5

Mill 2"+J Repr+Ov 4" 13.05 13.35 1.038 5

Mill 2"+Overlay 2" 28.08 28.625 1.023 5

Mill 2"+Overlay 4" 28.08 28.79 1.023 5

Mill 2"+Overlay 6" 28.08 28.98 1.023 5

Mill(3-4")Ovly(3-4") 28.08 28.79 1.023 5

Mill2+Ovly4(Poly.) 28.08 28.923 1.023 5

Overlay 2" over AC 28.08 28.527 1.023 5

Partial Recon (BC) 13.05 13.509 1.038 5

Patching 13.05 13.408 1.038 5

NJDOT Performance ModelsSDI Predictive Model for the Mill 2”/ Overlay 2” activity

Forced to Fail in 10 years

NJDOT Performance Models Original Models based on Expert Opinion

IRI = IRIO + exp*(A−B*C ln(Age )) activity coef_a coef_b coef_c coef_o

Mill 2"+Overlay 2" 13.959 13.596 0.844 70

Mill 2"+Overlay 4" 25.886 25.463 0.928 70

Overlay 2" over AC 18.949 20.153 0.847 90

Mill 2"+Overlay 6" 25.886 26.057 0.928 70

Mill 2"+J Repr+Ov 4" 25.886 25.463 0.928 70

Mill(2-4")+J Replace 25.886 25.463 0.928 70

Micro Surf(NovaChip) 18.949 18.379 0.847 90

Mill2+Ovly4(Poly.) 25.886 25.781 0.928 70

Partial Recon (BC) 13.209 18.065 0.755 70

Full Recon (BC) 13.209 18.557 0.755 60

Patching 18.949 20.153 0.847 90

4" Overlay over AC 18.949 20.685 0.847 70

6" Overlay over AC 18.949 21.694 0.847 70

Mill(3-4")Ovly(3-4") 25.886 25.463 0.928 70

NJDOT Performance Models IRI Predictive Model for the Mill 2”/ Overlay 2” activity

Forced to Fail in 10 years

NJDOT Performance ModelsNJDOT Enhanced Model Development

based on measured data

• IRI and SDI data points from 1999 was used to analyze the current models and/or develop new curves. • The IRI and SDI condition data for 2001-2002, 2002-2003, 2004, 2005 and 2006 was used to develop actual performance histories of the construction projects completed in 1999 • The 1999 construction projects were divided into groups according to the treatment activities:

Mill 2"+Overlay 2" Mill 2"+Overlay 4"

NJDOT Performance ModelsNJDOT Enhance Model Development

based on measured data

Issues with model development:

• Over the long term, personnel, condition survey equipment, methods, materials, condition methods, and other variable change

• Performance of treatment is influenced by current pavement condition

NJDOT Performance Models

SDI Performance History for the Mill 2”/Overlay 2” Activity

NJDOT Family Model Development

NJDOT Performance ModelsNJDOT Family Model Development

IRI Predictive Model for the Mill 2”/ Overlay 2” activity

NJDOT Performance ModelsNJDOT Family Model Development

Overall IRI Predictive Model

Longterm IRI Prediction

0

50

100

150

200

250

0 5 10 15 20 25 30 35 40 45 50

Age

IRI

Average 502-559 Trigger IRI 30 yr Pred IRI

20 yr Pred IRI

40 yr Pred IRI

25 yr Pred IRI

NJDOT Performance ModelsNJDOT Family Model Development

Overall IRI Predictive Model

Forced to fit 170 in/mile in 25 years

ANALYSESPERFORMACE PREDICTION

MIN. ACCEPTABLE

STRUCTURAL CAPACITY

AGE (YEARS)

DESIGN PERIOD

MAX. ACCEPTABLE

DISTRESS

MIN. ACCEPTABLE

SKID RESISTANCE

RIDE QUALITY

MIN. ACCEPTABLE

Questions?