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Belief reliability-based design optimization method with quantile index under epistemic uncertainty

Chen Yubing, Wen Meilin, Zhang Qingyuan, Kang Rui

Eksploatacja i Niezawodność

2023

Vol. 25, no. 2

art. no. 163545

Product reliability design optimization is affected by epistemic uncertainty greatly, which leaves significant risks in product use. In this paper, a new belief reliability-based design optimization (BRBDO) method under epistemic uncertainty is established to handle this problem. First, the belief reliability theory is introduced into the design optimization problem, and a quantile index is proposed to quantify belief reliability level based on uncertainty theory, through which a rapid analysis method called first order belief reliability analysis (FOBRA) method is developed. Then, according to the different trade-off strategies, two types of design optimization models are established, and corresponding FOBRA-based computation methods are also demonstrated. Finally, several case applications are studied to verify the effectiveness of the analysis and design optimization methods proposed in this paper. The results indicate that the BRODO method with the quantile index can save a lot of computational time with acceptable accuracy and can rationally cope with epistemic uncertainty.

Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

Zhou Shuang, Zhang Jianguo, You Lingfei, Zhang Qingyuan

Eksploatacja i Niezawodność

2021

Vol. 23, no. 2

231--241

Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.