Multifidelity Gaussian processes for failure boundary and probability estimation

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 and thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework, which can automatically 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 importance sampling setting, and demonstrate our method on the failure level set estimation and FPE on synthetic test functions as well as the reliability analysis of a gas turbine engine blade. We demonstrate that our method predicts the failure boundary and probability more accurately and computationally efficiently while using varying fidelity models compared to using just a single fidelity expensive model.