An efficient modularized sample-based method to estimate the first-order Sobol׳ index. (September 2016)

• Record Type: Journal Article
• Authors: Li, Chenzhao; Mahadevan, Sankaran
• Is Part Of: Reliability engineering & system safety. Volume 153(2016:Sep.)
• Page Start: 110
• Page End: 121
• Publication Date: 2016-09
• Subjects: Global sensitivity analysis -- Sobol׳ index -- Sample-based -- Correlated variables; 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.2016.04.012
• Languages: English
• ISSNs: 0951-8320

Abstract

Abstract: Sobol׳ index is a prominent methodology in global sensitivity analysis. This paper aims to directly estimate the Sobol׳ index based only on available input–output samples, even if the underlying model is unavailable. For this purpose, a new method to calculate the first-order Sobol׳ index is proposed. The innovation is that the conditional variance and mean in the formula of the first-order index are calculated at an unknown but existing location of model inputs, instead of an explicit user-defined location. The proposed method is modularized in two aspects: 1) index calculations for different model inputs are separate and use the same set of samples; and 2) model input sampling, model evaluation, and index calculation are separate. Due to this modularization, the proposed method is capable to compute the first-order index if only input–output samples are available but the underlying model is unavailable, and its computational cost is not proportional to the dimension of the model inputs. In addition, the proposed method can also estimate the first-order index with correlated model inputs. Considering that the first-order index is a desired metric to rank model inputs but current methods can only handle independent model inputs, the proposed method contributes to fill this gap. Highlights: An efficient method to estimate the first-order Sobol׳ index. Estimate the index from input–output samples directly. Computational cost is not proportional to the number of model inputs. Handle both uncorrelated and correlated model inputs.