Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion

作者：Garcia Cabrejo Oscar^*; Valocchi Albert

来源：Reliability Engineering & System Safety, 2014, 126: 25-36.

DOI：10.1016/j.ress.2014.01.005

• Global Sensitivity Analysis
• Sobol indices
• Polynomial chaos
• Sparse polynomial chaos
• Regression

Many mathematical and computational models used in engineering produce multivariate output that shows some degree of correlation. However, conventional approaches to Global Sensitivity Analysis (GSA) assume that the output variable is scalar. These approaches are applied on each output variable leading to a large number of sensitivity indices that shows a high degree of redundancy making the interpretation of the results difficult. Two approaches have been proposed for GSA in the case of multivariate output: output decomposition approach [9] and covariance decomposition approach [14] but they are computationally intensive for most practical problems. In this paper, Polynomial Chaos Expansion (PCE) is used for an efficient GSA with multivariate output. The results indicate that PCE allows efficient estimation of the covariance matrix and GSA on the coefficients in the approach defined by Campbell et al. [9], and the development of analytical expressions for the multivariate sensitivity indices defined by Gamboa et al. [14].

• 出版日期2014-6