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

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