Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction

Abstract

This paper examines the efficient variance-based global sensitivity analysis (GSA), quantified by estimating first-/higher-order and total-effect Sobol’ indices, for applications involving complex numerical models and high-dimensional outputs. Two different, recently developed, techniques are combined to address the associated challenges. Principal component analysis (PCA) is first considered as a dimensionality reduction technique. The GSA for the original output vector is then formulated by calculating variance and covariance statistics for the low-dimensional latent output space identified by PCA. These statistics are efficiently approximated by extending recent work on data-driven, probability model-based GSA (PM-GSA). The extension, constituting the main novel contribution of this work, pertains to the estimation of covariance statistics beyond the variance statistics examined in the original PM-GSA formulation. Specifically, a Gaussian mixture model (GMM) is developed to approximate the joint probability density function between some subset of the input vector, and each latent output, or each pair of latent outputs. The GMM is then utilized to estimate the aforementioned statistics. Results across two natural hazards engineering examples show that the dimensionality reduction and transformation of output space established through PCA do not impact the overall accuracy of the PM-GSA, and that the proposed implementation accommodates highly-efficient GSA estimates.