A high-precision probabilistic uncertainty propagation method for problems involving multimodal distributions

• Published in: Mechanical systems and signal processing Vol. 126; pp. 21 - 41
• Main Authors: Zhang, Z., Jiang, C., Han, X., Ruan, X.X.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.07.2019; Elsevier BV
• Subjects: High-order moment; Maximum entropy method; Metal fatigue; Multimodal distribution; Probabilistic methods; Probabilistic models; Probabilistic uncertainty propagation; Probability density functions; Probability theory; Propagation; Random variables; Response functions; Statistical analysis; Steel bridges; Uncertainty; Vibratory loads; Probabilistic uncertainty propagation; Multimodal distribution; High-order moment
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.01.031

•High-precision uncertainty propagation is achieved for multimodal distributions.•A convergence mechanism is formulated to ensure the propagation accuracy.•The maximum entropy method is revised to obtain multimodal distributions precisely.•The proposed method is of satisfied computational efficiency. 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 probabilistic uncertainty propagation methods are mainly used to treat random variables with only unimodal distributions, which, therefore, tend to result in large computational errors when multimodal distributions are involved. In this paper, a high-precision probabilistic uncertainty propagation method is proposed for problems involving multimodal distributions. Firstly, the multimodal probability density functions of input random variables are constructed based on the Gaussian mixture model. Secondly, the high-order moments of the response function are calculated using the univariate dimension reduction method, based on which the input uncertainty is effectively propagated. Thirdly, the probability density function of the response is estimated using the maximum entropy method. Finally, a convergence mechanism is formulated to help ensure the uncertainty propagation accuracy. Two mathematical problems and two truss structures are investigated to demonstrate the effectiveness of the proposed method.