Use of Bayesian Model Averaging to Estimate Model Uncertainty for Predicting Strain in a Four-Layered Flexible Pavement

Abstract

Because most of the numerical approaches are intensive in terms of computational effort and time, researchers have resorted to the use of surrogate models. For example, surrogate models for predicting the response of flexible pavement under given traffic and environmental conditions rely on the conventional approach of relating covariates with the response through simplified models. Usually, these covariates are chosen based on experience and data availability. Further, the form of the model is finalized based on statistical indicators and goodness-of-fit values. Thus, the concept of uncertainty in selecting the model is completely ignored, often leading to overconfident results and an increased risk in the prediction. Under these circumstances, Bayesian model averaging (BMA) could be a potential model building tool. The current study presents a BMA-based approach to choose influencing variables and quantify the uncertainty associated with linear regression models used to predict strain in a four-layered pavement structure. Initially, modulus and thickness of individual layers were used as input into a surrogate model building exercise. Out of 128 possible models, the best 100 models were used in conjunction with the BMA technique to rank various models and variables. Further, model uncertainty was represented by plotting the marginal density function of the coefficients, coefficient of variation, and normalized uncertainty range. BMA indicated that modulus (asphaltic layer and binder layer) and thickness of the asphaltic layer accounted for the majority of variability (up to 88%) associated with tensile strain in the asphaltic layer. Similarly, the thickness of the asphaltic layer and modulus of subgrade affected vertical compressive strain prediction models up to 38%. These variables also had lower uncertainty indicators when compared to other variables. Also, ranking based on the posterior inclusion probability can be used as an alternative for traditional sensitivity analysis.