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28 July 2023 The application of adaptive divided-difference perturbation method for stochastic problems with multimodal distribution
Dongwei Huang, Feng Wu, Changzhe Li, Hongwu Zhang
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Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275617 (2023) https://doi.org/10.1117/12.2685895
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China
Abstract
The focus of this paper is efficiently and accurately solving the stochastic problems with multimodal distribution. Based on the stochastic perturbation method, the divided-difference method is adopted to approximate the partial derivative term in the perturbation method, and regard the divided-difference nodes as the collocation points to construct a nonintrusive statistical method. In addition, we also propose an adaptive method to select perturbation expansion terms, which can improve the calculation efficiency of statistical moments by ignoring the insignificance items. Because the Gaussian mixture model is often used to deal with the random problem of multimodal distribution, combined with the proposed method in this paper, the calculation processes of the statistical moments and probability density function are given. Finally, the accuracy and efficiency of the method proposed in this paper and the quasi-Monte Carlo method are compared by two numerical examples. The results show that the proposed method can efficiently and accurately obtain the statistical moments and probability density function of random response.
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Dongwei Huang, Feng Wu, Changzhe Li, and Hongwu Zhang "The application of adaptive divided-difference perturbation method for stochastic problems with multimodal distribution", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275617 (28 July 2023); https://doi.org/10.1117/12.2685895
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KEYWORDS
Statistical analysis
Uncertainty analysis
Quasi Monte Carlo methods
Statistical modeling
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