Upload
terence-glenn
View
217
Download
0
Tags:
Embed Size (px)
Citation preview
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?