IV. SURROGATE MODEL INITIALIZATION: VARIABLE SELECTION
IV.5 Results
The three variable selection processes must be compared both computationally and by accuracy, described by the R2Adj statistic. The R2Adj for each model as a function of ND is shown in FIGURE IV.1. All variable selection processes demonstrate an ability to select additional parameters in a positive order of significance, consistently improving R2Adj. The correlation matrix method chooses the most significant parameters for all MEPDG models in a manner that quickly achieves a large R2Adj value. The correlation matrix ranking procedure is based on a linear relationship between the input parameters and the MEPDG prediction outputs. The performance of this method indicates that the behavior of the trend of all of the prediction models is likely described well by a linear model.
FIGURE IV.1: Adjusted R-Squared Values for the Variable Selection Processes for each Prediction Model
0 10 20 30 40 50 60
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Number of Training Point Parameters
Adjusted R-squared
Terminal IRI
Anova Process Correlation Matrix GP Scale Length Factors
0 10 20 30 40 50 60
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Number of Training Point Parameters
Adjusted R-squared
Total Permanent Deformation
Anova Process Correlation Matrix GP Scale Length Factors
0 10 20 30 40 50 60
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Number of Training Point Parameters
Adjusted R-squared
AC Bottom Up Cracking
Anova Process Correlation Matrix GP Scale Length Factors
0 10 20 30 40 50 60
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Number of Training Point Parameters
Adjusted R-squared
AC Top Down Cracking
Anova Process Correlation Matrix GP Scale Length Factors
0 10 20 30 40 50 60
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
Number of Training Point Parameters
Adjusted R-squared
AC Permanent Deformation
Anova Process Correlation Matrix GP Scale Length Factors
IV.5.1 Sensitivity Analysis: Quantity of Training Point Parameters
In addition to the comparison between selection methods, FIGURE IV.1 can be used to investigate the sensitivity of the accuracy in predictions for each distress model to the quantity of training point parameters. Considering first the Correlation method, each of the five distress modes are shown to be highly sensitive to the quantity of parameters for approximately the first ten parameters. The R2Adj values for the models that include more than about ten parameters are nearly equal, demonstrating that the addition of parameters beyond this quantity provide a minimal amount of improved accuracy in predicted performance. The Anova and LSF methods do not perform in the same manner as the Correlation method and do not achieve the plateau, or convergence, in the R2Adj values.
The lack of convergence in the R2Adj value indicates that these processes achieve better accuracy with the addition of parameters and would require a larger number of parameters if a minimum R2Adj value was required. Further, this lack of convergence in the Anova and LSF methods indicates that the Correlation method is selecting the most significant parameters in a more efficient manner.
IV.5.2 Method for Selection of Training Point Parameters
Selection of the minimum quantity of training points for a surrogate can be performed with respect to a minimum R2Adj requirement. Considering a minimum requirement that the model achieve an R2Adj greater than or equal to 0.9, selection of the most significant parameters can be made for each distress model. TABLE IV.2 outlines the quantity and parameters required to achieve this standard, selected through the correlation matrix
method. This method is chosen because, as shown in FIGURE IV.1, this method consistently chooses the minimum quantity of training point parameters to quickly achieve large R2Adj values.
TABLE IV.2: Training Point Parameters Using Correlation Matrix
Terminal IRI Total Permanent Deformation
AC Bottom-Up Cracking
AC Top-Down Cracking
AC Permanent Deformation
Parameter Name
HMAThick HMAThick HMAThick HMAThick TrafficGrowth
TrafficGrowth TrafficGrowth AV AV HMAThick
%Pass#200 %Pass#200 %Pass#200 SubMod %Pass#200
AV SubMod TrafficGrowth TrafficGrowth %Ret#4
%Ret#4 %Ret#4 SubMod %Pass#200 AADTT
SubMod AADTT EBC AxleSpTand Wander
AADTT Wander GBMod EBC EBC
%Ret#4
The results in TABLE IV.2 provide insight into the sensitivity of these distress modes to the input parameters. Only twelve unique design parameters are necessary to adequately model all five pavement distress modes. Parameters describing the asphalt layer and material strength for all layers are shown to significantly impact pavement performance. The thickness of the HMA layer (HMAthick) is significant to all distress modes, which is not unexpected. Improved performance for the permanent deformation models relies heavily on the thickness of the HMA layer. The deformation is calculated as a sum of the product of strains and thicknesses for each layer in the structure, so modifications in the thickness of the HMA layer is significant, especially in the two layer pavement system evaluated here. Additional properties such as asphalt air voids (AV) and effective binder content (EBC) also are significant to most distress models. The fatigue
cracking models are evaluated as a function of strains and stresses in the asphalt layer, directly impacted by the asphalt thickness and these material properties. The sub-grade modulus is another parameter that is shown to be significant in the distress models.
Again, the strength of this layer impacts the stresses and strains utilized in all the distress functions. The impact of traffic growth is demonstrated to significantly impact all five distress modes. The likely cause of this significance is the impact of this projected growth on the accumulation of stresses and strains over time. Greater projected traffic growth would be expected to increase the rate of accumulation of strains in the pavement.