Probability models for data-Driven global sensitivity analysis

Abstract

This paper presents a probability model-based global sensitivity analysis (PM-GSA) framework, to compute various Sobol’ indices when only input-output data are available. The PM-GSA framework consists of two main elements, namely data extraction and probability model training. The data extraction step extracts data of the variables of interest (VoI) and quantity of interest (QoI) from an input-output data matrix. Following that, a probability model is built to approximate the joint probability density function between the VoI and QoI. The learned probability model is then used to compute various Sobol’ indices. The implementation of the PM-GSA framework is investigated through three probability models including Gaussian copula model, Gaussian mixture model, and a new Gaussian mixture copula model. The number of dimensions of the probability model in the PM-GSA framework, is independent of the number of input variables and is always N+1 (e.g. 2 for the first-order index), where N is the order of the Sobol’ index. In addition, the PM-GSA framework is applicable to global sensitivity analysis with not only independent input variables, but also with dependent input variables and for sets of variables. Four numerical examples are used to demonstrate the effectiveness of the proposed method and analyze the advantages and disadvantages of the different probability models.