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An uncertainty propagation method for multimodal distributions through unimodal decomposition strategy

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Abstract

In practical engineering problems, random variables may follow a multimodal distribution. Traditional uncertainty propagation methods may yield poor effectiveness for multimodal distribution problems. In this paper, an uncertainty propagation method is proposed for multimodal distributions via a unimodal decomposition strategy. First, a Gaussian mixture model is used to build the probability density function of multimodal random variables. Second, a set of unimodal elements is constructed based on the decomposed multimodal random variables. In this way, it avoids computing higher-order statistical moments and the first 4th-order statistical moments can satisfy the accuracy requirements. Third, the probability density function of the response function in each element is computed using an arbitrary polynomial chaos expansion and the maximum entropy method. Finally, the probability density function of the response function in the complete probability space can be obtained by accumulating the probability density functions of the response functions in the elements. Three examples are investigated to validate the effectiveness of the proposed method.

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Acknowledgements

The research presented in this paper was conducted with the support of The National Natural Science Foundation of China (Grant No. 52235005), Fundamental Research Program of China (JCKY2020110C105), The National Science Fund for Distinguished Young Scholars (Grant No. 51725502), and The National Natural Science Foundation of China (Grant No. 52105253).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, China

    Boqun Xie, Chao Jiang, Zhe Zhang, Jing Zheng & Jinwu Li

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  1. Boqun Xie
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  2. Chao Jiang
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  3. Zhe Zhang
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  4. Jing Zheng
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  5. Jinwu Li
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Correspondence to Chao Jiang.

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The results reported in this research were performed in MATLAB. The authors will help interested researchers reproduce the results given in the article. Interested readers can contact the corresponding author for basic codes of this research with reasonable requests.

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Xie, B., Jiang, C., Zhang, Z. et al. An uncertainty propagation method for multimodal distributions through unimodal decomposition strategy. Struct Multidisc Optim 66, 141 (2023). https://doi.org/10.1007/s00158-023-03591-z

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