An ensemble weighted average conservative multi-fidelity surrogate modeling method for engineering optimization

Abstract

Multi-fidelity (MF) surrogate models have been widely used in engineering optimization problems to reduce the design cost by replacing computat ional expensive simulations. Ignoring the prediction uncertainty of the MF model that is caused by a limited number of samples may result in infeasible solutions. Conservative MF surrogate model, which can effectively improve the feasibility of the constraints, has been a promising way to address this issue. In this paper, an ensemble weighted average (EWA) conservative multi-fidelity modeling method that integrates the performance of different error metrics is proposed. In the proposed method, the bootstrap method and mean-square-error method are reasonably weighted to calculate the safety margin of the MF surrogate model. The weights for the two metrics are determined through an optimization problem, which considers the performance of the two metrics in different subsets of the sample points. The effectiveness of the proposed method is illustrated through several numerical examples and a pressure vessel design problem. Results show that the proposed method constructs a more accurate conservative MF surrogate model than other methods in different problems. Furthermore, applying the constructed conservative MF surrogate model into optimization problems obtains more accurate optimal solutions while ensuring the feasibility of it.