Abstract
Variance-based sensitivity indices have established themselves as a reference amongst practitioners of sensitivity analysis of model outputs. A variance-based sensitivity analysis typically produces the first-order sensitivity indices Sj and the so-called total-effect sensitivity indices Tj for the uncertain factors of the mathematical model under analysis. Computational cost is critical in sensitivity analysis. This cost depends upon the number of model evaluations needed to obtain stable and accurate values of the estimates. While efficient estimation procedures are available for Sj (Tarantola et al., 2006), this availability is less the case for Tj (Iooss and Lemaître, 2015). When estimating these indices, one can either use a sample-based approach whose computational cost depends on the number of factors or use approaches based on meta-modelling/emulators (e.g., Gaussian processes). The present work focuses on sample-based estimation procedures for Tj for independent inputs and tests different avenues to achieve an algorithmic improvement over the existing best practices. To improve the exploration of the space of the input factors (design) and the formula to compute the indices (estimator), we propose strategies based on the concepts of economy and explorativity. We then discuss how several existing estimators perform along these characteristics. Numerical results are presented for a set of seven test functions corresponding to different settings (few important factors with low cross-factor interactions, all factors equally important with low cross-factor interactions, and all factors equally important with high cross-factor interactions). We conclude the following from these experiments: a) sample-based approaches based on the use of multiple matrices to enhance the economy are outperformed by designs using fewer matrices but with better explorativity; b) amongst the latter, asymmetric designs perform the best and outperform symmetric designs having corrective terms for spurious correlations; c) improving on the existing best practices is fraught with difficulties; and d) ameliorating the results comes at the cost of introducing extra design parameters.
Original language | English |
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Article number | 107300 |
Number of pages | 13 |
Journal | Reliability Engineering and System Safety |
Volume | 206 |
Early online date | 5 Nov 2020 |
DOIs | |
Publication status | Published - Feb 2021 |
Bibliographical note
Funding Information:Elmar Plischke from Technische Universität Clausthal, Guillaume Damblin from CEA, Sergei Kucherenko from Imperial College of London, Stefano Tarantola and Thierry Mara from the Joint Research Centre of the European Commission, the guest editor and four anonymous reviewers, offered useful comments and suggestions. The remaining errors are uniquely due to the authors. This work was partially funded by a grant from the Peder Sather Centre for Advances Studies of the University of Berkeley “Mainstreaming Sensitivity Analysis and Uncertainty Auditing”, awarded in June 2017. Arnald Puy has worked on this paper on a Marie Sklodowska-Curie Global Fellowship, grant number 792178.
Publisher Copyright:
© 2020
ASJC Scopus subject areas
- Safety, Risk, Reliability and Quality
- Industrial and Manufacturing Engineering