Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol' indices and experimental design. (July 2019)

• Record Type: Journal Article
• Authors: Pronzato, Luc
• Is Part Of: Reliability engineering & system safety. Volume 187(2019)
• Page Start: 93
• Page End: 109
• Publication Date: 2019-07
• Subjects: Sensitivity analysis -- Sobol' Indices -- Random-field model -- Karhunen–Loève expansion -- Bayesian linear model -- Polynomial chaos -- Optimal design of experiments; Reliability (Engineering) -- Periodicals; System safety -- Periodicals; Industrial safety -- Periodicals; Fiabilité -- Périodiques; Sécurité des systèmes -- Périodiques; Sécurité du travail -- Périodiques; 620.00452
• DOI: 10.1016/j.ress.2018.01.010
• Languages: English
• ISSNs: 0951-8320

Abstract

Highlights: A method to estimate Sobol' indices for sensitivity analysis is proposed. It relies on a tensorised Bayesian linear model built from Kahrunen–Loève expansions. Posterior distributions of indices are derived and used to design adapted experiments. Abstract: We use the Karhunen–Loève expansion of a random-field model to construct a tensorised Bayesian linear model from which Sobol' sensitivity indices can be estimated straightforwardly. The method combines the advantages of models built from families of orthonormal functions, which facilitate computations, and Gaussian-process models, which offer a lot of flexibility. The posterior distribution of the indices can be derived, and its normal approximation can be used to design experiments especially adapted to their estimation. Implementation details are provided, and values of tuning parameters are indicated that yield precise estimation from a small number of function evaluations. Several illustrative examples are included that show the good performance of the method, in particular in comparison with estimation based on polynomial chaos expansion.