International Journal of Fuzzy Systems

, Volume 21, Issue 2, pp 454–467

# Global Sensitivity Analysis of the Failure Probability Upper Bound to Random and Fuzzy Inputs

• Yan Shi
• Zhenzhou Lu
• Lufeng Zhao
Article

## Abstract

For structure with both random and fuzzy input variables, a global sensitivity analysis (GSA) model is established to quantitatively evaluate the effects of these two kinds of input uncertainties on the upper bound of the fuzzy failure probability. The relationship between failure possibility and fuzzy failure probability upper bound is firstly derived in this paper. Based on this relationship, the single-loop nested sampling method can be applied to estimate the GSA index of the random inputs to the upper bound of the fuzzy failure probability. A solution framework is also established to estimate the GSA indices of the fuzzy inputs based on the relationship between the upper bound of the fuzzy failure probability and the failure possibility. Several examples are introduced to show that the established global sensitivity analysis model can reflect the effects of these two kinds of inputs on the safety of the structural system. Furthermore, the proposed method can improve computational efficiency which is significant in the engineering application.

## Keywords

Global sensitivity analysis Failure probability upper bound Failure possibility Mixed input variables

## Notes

### Acknowledgements

This work was supported by the Natural Science Foundation of China (Grants 51475370 and 51775439).

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