Proximal-exploration multi-objective Bayesian optimization for inverse identification of cyclic constitutive law of structural steels

Abstract

Despite its importance in seismic response analysis, solving an inverse problem to identify the cyclic elastoplastic parameters for structural steels using conventional optimization algorithms still demands a substantial computational cost of repeatedly carrying out many nonlinear analyses. The parameters are commonly identified based on experimental measures from a single loading history, leading them to be biased and giving inaccurate predictions of structural behavior under other loading histories. To address these issues, we formulate a multi-objective inverse problem that simultaneously minimizes the error functions representing the differences between simulated responses and those measured experimentally from various cyclic tests of a steel specimen or a structural component. We then propose proximal-exploration multi-objective Bayesian optimization (MOBO) for solving the formulated inverse problem, resulting in an approximate Pareto front of parameters while limiting the number of costly simulations. MOBO sorts an initial Pareto front and constructs Gaussian process (GP) models for the error functions from a training dataset. It then relies on the hypervolume of the current solutions, the GP models, and a proximal exploration surrounding the current best compromise parameters to formulate an acquisition function that guides the improvement of the current solutions intelligently. Two identification examples show that the parameters obtained from the multi-objective inverse problem can reduce the bias induced using a single loading history for identification. The robustness of MOBO as well as a good prediction performance of the best compromise solution of identified parameters are demonstrated.