Bayesian updating with two-step parallel Bayesian optimization and quadrature

This work proposes a Bayesian updating approach, called parallel Bayesian optimization and quadrature (PBOQ). It is rooted in Bayesian updating with structural reliability methods (BUS) and offers a coherent Bayesian approach for the BUS analysis by assuming Gaussian process priors. The first step of the method, i.e., parallel Bayesian optimization, effectively explores a constant c in BUS by a novel parallel infill sampling strategy. The second step (parallel Bayesian quadrature) then infers the posterior distribution by another parallel infill sampling strategy using subset simulation. The proposed approach enables to make the fullest use of prior knowledge and parallel computing, resulting in a substantial reduction of the computational burden of model updating. Four numerical examples with varying complexity are investigated for demonstrating the proposed method against several existing methods. The results show the potential benefits by advocating a coherent Bayesian fashion to the BUS analysis.