**Uncertainty propagation analysis using sparse grid technique and saddlepoint approximation based on** parameterized **p-box representation**

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## Abstract

Uncertainty propagation analysis, which assesses the impact of the uncertainty of input variables on responses, is an important component in risk assessment or reliability analysis of structures. This paper proposes an uncertainty propagation analysis method for structures with parameterized probability-box (p-box) representation, which could efficiently compute both the bounds on statistical moments and also the complete probability bounds of the response function. Firstly, based on the sparse grid numerical integration (SGNI) method, an optimized SGNI (OSGNI) is presented to calculate the bounds on the statistical moments of the response function and the cumulants of the cumulant generating function (CGF), respectively. Then, using the bounds on the first four cumulants, an optimization procedure based on the saddlepoint approximation is proposed to obtain the whole range of probability bounds of the response function. Through using the saddlepoint approximation, the present approach can achieve a good accuracy in estimating the tail probability bounds of a response function. Finally, two numerical examples and an engineering application are investigated to demonstrate the effectiveness of the proposed method.

## Keywords

Uncertainty propagation Parameterized p-box Probability bounds Sparse grid numerical integration Saddlepoint approximation## Notes

### Acknowledgements

This work is supported by the National Science Fund for Distinguished Young Scholars (51725502), the Major Projects of the National Natural Science Foundation of China (51490662), the National Key Research and Development Plan (2016YFD0701105) and the Open Funds for State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, China (Grant No.31515010).

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