Active Learning Strategy for Surrogate-Based Quantile Estimation of Field Function

Uncertainty quantification is widely used in engineering domains to provide confidence measures on complex systems. It often requires to accurately estimate extreme statistics on computationally intensive black-box models. In case of spatially or temporally distributed model outputs, one valuable metric results in the estimation of extreme quantile of the output stochastic field. In this paper, a novel active learning surrogate-based method is proposed to determine the quantile of an unidimensional output stochastic process with a confidence measure. This allows to control the error on the estimation of a extreme quantile measure of a stochastic process. The proposed approach combines dimension reduction techniques, Gaussian process and an adaptive refinement strategy to enrich the surrogate model and control the accuracy of the quantile estimation. The proposed methodology is applied on an analytical test case and a realistic aerospace problem for which the estimation of a flight envelop is of prime importance for launch safety reasons in the space industry.