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Bayesian economic analyses of including reclaimed asphalt pavements in flexible pavement rehabilitation
Published in John Harvey, Imad L. Al-Qadi, Hasan Ozer, Gerardo Flintsch, Pavement, Roadway, and Bridge Life Cycle Assessment 2020, 2020
Hongren Gong, Miaomiao Zhang, Wei Hu, Baoshan Huang*
Equation (2) is the Bayesian equation, the denominator PD is the evidence that can be determined through marginalizing over the prior distribution of the parameters Pθ, the numerator of the equation is the likelihood. In a Bayesian regression model, instead of obtaining point estimates of the model as did in the ordinary least square regression, the posterior distribution of the parameters was obtained given the data (D). In estimating the posterior distribution, closed-form solutions are only available to a limited number of prior distributions, such as the Gaussian (normal) distribution, see Equation (3). In situations where no closed-form solution available, the Markov chain Monte Carlo (MCMC) simulation can be used (Gelman et al., 2014). This study used an implementation of the MCMC called Hamiltonian Monte Carlo sampling or hybrid Monte Carlo sampling (Gelman et al., 2014). The stan language was used to create the Bayesian models (Carpenter et al., 2017).
Investigating long-term performance of flexible pavement using Bayesian multilevel models
Published in Road Materials and Pavement Design, 2023
Haimei Liang, Hongren Gong, Yiren Sun, Jiachen Shi, Lin Cong, Wenyang Han, Peng Guo
This study investigated the effects of various rehabilitation strategies on the long-term performance of asphalt concrete overlay: RAP versus virgin HMA, milling versus no milling and thin (51 cm) versus thick overlay (127 cm). We approached the issues from a causal inference perspective. We first formulate the problems of interest using DAGs, and then statistically implement the models using Bayesian multilevel models to assess unobserved heterogeneity on the pavement performance model parameters. Hamiltonian Monte Carlo (HMC) is used to estimate the distributions of the individual parameters. We calibrated the models with data extracted from the SPS-5 of LTPP and make inferences considering site heterogeneity. Based on the analyses presented in the study, the following conclusions were reached: Using multilevel models benefitted both model inference and prediction. Across models for the three performance indicators, their WAIC and Bayesian R2 values are considerably higher than the regular regression models.All three controlled experiment factors are critical to alligator cracking. The RAP sections exhibited significantly more alligator cracking than the virgin HMA sections. Both milling before overlaying, thicker overlay mattress and coarse subgrade soil are beneficial for resisting alligator cracking. As expected, sections rehabilitated with mixtures of higher air voids are more prone to alligator cracking.Controlling for the climatic region and site dependence, the influence of mixture type on the rutting was insignificant, while the thicker overlay was beneficial for retarding rutting. On average, sections on top of the coarse soil subgrade showed less severe rutting conditions.The preoverlay preparation, overlay thickness and subgrade soil are critical to pavement roughness. However, the RAP sections presented a similar smoothness level to their virgin HMA counterparts.