GLOBAL SENSITIVITY ANALYSIS WITH SURROGATE MODELING

Abstract

Global sensitivity analysis studies how uncertainties in the input factors of a model affect the output. In this dissertation, we first introduce the widely used variance-based Sobol’ global sensitivity analysis, where ANOVA decomposition-based indices measuring the sole contribution of a parameter and its interaction with the other parameters are used. These indices are typically estimated directly by Monte Carlo simulations, which can be computationally intractable especially for computationally expensive models. We then introduce the classical Fourier Amplitude Sensitivity Test (FAST) for computing Sobol’ global sensitivity indices. We develop a novel surrogate model based on high dimensional model representation (HDMR) using FAST so that it can be used to not only estimate variance-based global sensitivity indices but also perform other tasks involved in uncertainty quantification. The accuracy of the resulting surrogate model, named FAST-HDMR, can be improved by various techniques. We show that sparse regression techniques, such as relevance vector machine and variational relevance vector machine, which retain only the significant terms in the FAST-HDMR expansion, as well as advanced Monte Carlo sampling methods, such as randomized quasi-Monte Carlo sampling and variance-reduction techniques, can be utilized for that purpose. In addition, we present multi-fidelity methods for surrogate modeling to estimate global sensitivity indices that leverage low-fidelity models to reduce computational cost while maintaining the accuracy of high-fidelity models. We perform global sensitivity indices based on Proper Orthogonal Decomposition Mapping Method (PODMM), and show that it outperforms a recent multi-fidelity Monte Carlo algorithm through a few examples. We also establish a framework that employs HDMR in the setting of multi-fidelity surrogate modeling for efficient global sensitivity analysis. Finally, we apply the proposed FAST-HDMR, PODMM and multi-fidelity HDMR approaches for global sensitivity analysis to two practical applications, where parameters’ global sensitivity information is needed.