Probability-space Surrogate Modeling for Sensitivity Analysis and Optimization

Abstract

This paper presents probability-space surrogate modeling approaches for global sensitivity analysis (GSA) and optimization under uncertainty. A probability model is learned first based on the available data to capture the nonlinear probabilistic relationships between the quantity of interest and input variables as well as among different input variables. Based on the learned probability model, approaches are then developed for design optimization under uncertainty and fast computation of the first order and total-effect sensitivity indices. This framework is applicable to not only GSA with correlated random variables and for sets of input variables, but also coupled multidisciplinary systems design under uncertainty with multiple objectives. The implementation of the proposed framework is investigated through two probability models, namely Gaussian copula model and Gaussian mixture model. One numerical example and one aircraft wing design problem demonstrate the effectiveness of the proposed method for GSA and multidisciplinary design under uncertainty.