A new uncertainty propagation method considering multimodal probability density functions

In practical engineering applications, random variables may follow multimodal distributions with multiple modes in the probability density functions, such as the structural fatigue stress of a steel bridge carrying both highway and railway traffic and the vibratory load of a blade subject to stochas...

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Vydáno v:Structural and multidisciplinary optimization Ročník 60; číslo 5; s. 1983 - 1999
Hlavní autoři: Zhang, Z., Wang, J., Jiang, C., Huang, Z. L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019
Springer Nature B.V
Témata:
Computational Mathematics and Numerical Analysis
Engineering
Engineering Design
Maximum entropy method
Metal fatigue
Numerical methods
Probabilistic models
Probability density functions
Propagation
Random variables
Research Paper
Response functions
Steel bridges
Theoretical and Applied Mechanics
Uncertainty
Vibratory loads
Uncertainty propagation
Multimodal probability density function
Convergence mechanism
Sparse grid numerical integration
Maximum entropy method
ISSN:1615-147X, 1615-1488
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Popis
Shrnutí:In practical engineering applications, random variables may follow multimodal distributions with multiple modes in the probability density functions, such as the structural fatigue stress of a steel bridge carrying both highway and railway traffic and the vibratory load of a blade subject to stochastic dynamic excitations, etc. Traditional uncertainty propagation methods are mainly used to treat random variables with only unimodal probability density functions, which, therefore, tend to result in large computational errors when multimodal probability density functions are involved. In this paper, an uncertainty propagation method is developed for problems in which multimodal probability density functions are involved. Firstly, the multimodal probability density functions of input random variables are established using the Gaussian mixture model. Secondly, the uncertainties of the input random variables are propagated to the response function through an integration of the sparse grid numerical method and maximum entropy method. Finally, the convergence mechanism is developed to improve the uncertainty propagation accuracy step by step. Two numerical examples and one engineering application are studied to demonstrate the effectiveness of the proposed method.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-019-02301-y