Bayesian optimization-assisted approximate Bayesian computation and its application to identifying cyclic constitutive law of structural steels

Abstract

A costly finite element model discourages Bayesian inference of the underlying parameters from noise-corrupted experimental datasets. This arises because the likelihood of such a model is often computationally intractable, leading to the impossibility of performing a large number of costly simulations. This study presents Bayesian optimization-assisted approximate Bayesian computation (BO-assisted ABC) and showcases its application to identifying the approximate posteriors of parameters for known statistical models and of cyclic elastoplastic parameters for structural steels. ABC bypasses likelihood evaluations by generating prior samples that are assigned as samples constituting the posterior if discrepancies between the experimental dataset and the corresponding simulated datasets do not exceed a small, positive threshold. With a modest number of costly simulations, BO facilitates ABC by intelligently constructing a Gaussian process model that approximates the discrepancy mean function. Identification results from illustrative examples show that the approximate posteriors by the proposed approach not only reproduce a given posterior with acceptable accuracy but also capture the true nominal parameters of a statistical model. Moreover, the approximate posteriors of material parameters can simulate the cyclic elastoplastic behavior of a steel specimen under different loading conditions. The dependence of identification results on definitions of BO acquisition function is also investigated.