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 n Y = a + bX Multiple Linear Regression n Y = a 0 + a 1 X 1 + a 2 X A n X n Non-Linear Regression n Y = a 0 + a 1 X 1 + a 2 X A n X n n Polynomial regression models may be constrained n 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 Curve For Individual Section Original Default Family Curve Actual/Specific Section Condition Age Condition Predicted Section Condition 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 (R 2 ) 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

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

transition probabilities matrix

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

Pavement Performance Example

NJDOT Performance Models

NJDOT Performance Models Original Models based on Expert Opinion SDI = SDI O - e(A−B*C ln(1/Age)) activitycoef_acoef_bcoef_ccoef_o 4" Overlay over AC " Overlay over AC Full Recon (BC) Micro Surf(NovaChip) Mill 2"+J Repr+Ov 4" Mill 2"+Overlay 2" Mill 2"+Overlay 4" Mill 2"+Overlay 6" Mill(3-4")Ovly(3-4") Mill2+Ovly4(Poly.) Overlay 2" over AC Partial Recon (BC) Patching

NJDOT Performance Models SDI 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 )) activitycoef_acoef_bcoef_ccoef_o Mill 2"+Overlay 2" Mill 2"+Overlay 4" Overlay 2" over AC Mill 2"+Overlay 6" Mill 2"+J Repr+Ov 4" Mill(2-4")+J Replace Micro Surf(NovaChip) Mill2+Ovly4(Poly.) Partial Recon (BC) Full Recon (BC) Patching " Overlay over AC " Overlay over AC Mill(3-4")Ovly(3-4")

NJDOT Performance Models IRI Predictive Model for the Mill 2”/ Overlay 2” activity Forced to Fail in 10 years

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

NJDOT Performance Models NJDOT Family Model Development Overall IRI Predictive Model

NJDOT Performance Models NJDOT Family Model Development Overall IRI Predictive Model Forced to fit 170 in/mile in 25 years

ANALYSES PERFORMACE PREDICTION MIN. ACCEPTABLE STRUCTURAL CAPACITY AGE (YEARS) DESIGN PERIOD MAX. ACCEPTABLE DISTRESS MIN. ACCEPTABLE SKID RESISTANCE RIDE QUALITY MIN. ACCEPTABLE

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