Multifidelity Gaussian processes for failure boundary andprobability estimation

Abstract

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation (FPE) involves resolving tails of probability distribution and Monte Carlo (MC) sampling methods are intractable when expensive high-fidelity simulations have to be queried. We propose a method to use models of multiple fidelities, which trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity. Furthermore, we propose a novel acquisition function within a Bayesian optimization framework, which can sequentially select samples (or batches of samples for parallel evaluation) from appropriate fidelity models to make predictions about quantities of interest in the highest fidelity. We use our proposed approach within a multifidelity importance sampling (MFIS) setting, and demonstrate our method on the failure level set estimation on synthetic test functions as well as the transonic flow past an airfoil wing section.