Model distance-based approach for global sensitivity analysis in engineering systems with multivariate outputs

Abstract

In engineering systems, uncertainties in input parameters can significantly influence the output responses. This paper proposes a model distance-based approach to perform global sensitivity analysis for quantifying the influence of input uncertainties on multiple responses in an engineering system. The sensitivity indices are determined by comparing a reference model that incorporates all system uncertainties, with an altered model, where specific uncertainties are constrained. The proposed framework employs probability distance measures such as Hellinger distance, Kullback–Leibler divergence, and l₂ norm which are based on joint probability density functions. The study also demonstrates the equivalence between the l₂ norm-based approach and Sobol’s analysis in multivariate sensitivity context. The proposed methodology effectively manages correlated random variables, accommodates both Gaussian and non-Gaussian distributions, and allows for the grouping of input variables. Illustrative examples consist of static analysis of a truss system and dynamic analysis of a frame subjected to seismic excitation. The sensitivity indices are estimated using brute-force Monte Carlo simulations. The relative ranking of these sensitivity indices can be utilized to identify the most and least significant variables contributing to the response uncertainty. The numerical results show a consistent ranking of input variables across different probability measures, indicating the robustness of proposed framework.

Graphical abstract

Keywords

multivariate outputs / moment-independent sensitivity analysis / probability distance measures / multivariate Sobol’s analysis / Monte Carlo simulation / uncertainty quantification

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