Actively learning deep Gaussian process models for failure contour and probability estimation.

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Queries of computer simulation experiments are computationally expensive, and failures are typically observed in the tails of probability distributions over the input variables, which renders typical Monte Carlo estimation prohibitively expensive. Instead, a statistical "surrogate" model can be leveraged to identify the failure contour from limited simulation data which then informs a biasing distribution for importance-sampling based estimation of failure probabilities. The goal of this work is to explore the viability of active learning for deep Gaussian process (DGP) surrogates towards failure contour and probability estimation problems with expensive simulation models. DGPs outperform traditional GPs in non-stationary settings. Contour locating sequential designs outperform space-filling counterparts. Combined, these result in more accurate failure probability estimates for fixed simulation effort. We demonstrate our method on synthetic test functions as well as two application problems, namely, the RAE-2822 airfoil aerodynamic performance and the thermal stress analysis of a gas turbine blade. We observe that, despite an additional cost for model inference, DGPs offer superior performance in predicting failure probabilities compared to GPs.