A sequential sampling-based Bayesian numerical method for reliability-based design optimization

For efficiently solving the Reliability-Based Design Optimization (RBDO) problem with multi-modal, highly nonlinear and expensive-to-evaluate limit state functions (LSFs), a sequential sampling-based Bayesian active learning method is developed in this work. The penalty function method is embedded to transform the constrained optimization problem into a non-constrained one to reduce the model complexity. The proposed method for solving RBDO problems starts by training a Gaussian process (GP) model, in the augmented space of random and design variables. It is then based on an efficient sampling scheme for simulating the GP model, the adaptive Bayesian optimization (BO) and Bayesian reliability analysis (BRA) procedures are combined in a collaborative way for sequentially producing the joint training points. BO driven by expected improvement (EI) function is used for inferring the global optimum in the design space with global convergence, and the BRA equipped with U function is implemented for inferring the failure probabilities at the identified design points with the desired accuracy. The superiority of the proposed method is demonstrated with two numerical and two real-world engineering examples.