This paper presents a novel numerical method for the hybrid reliability analysis by using the uncertainty theory. Aleatory uncertainty and epistemic uncertainty are considered simultaneously in this method. Epistemic uncertainty is characterized by the uncertainty theory, and the effect of epistemic uncertainty is quantified by the sub-additive uncertain measure. Then, under the framework of the chance theory which can be interpreted as the combination of the probability theory and the uncertainty theory, a general uncertainty quantification model is established to deal with the hybrid reliability analysis problem, then the corresponding reliability metric is defined. After that, to improve the feasibility of the proposed model, by utilizing the polar coordinate transformation based dimension reduction method, a numerical analysis method for the hybrid reliability model are provided. At last, several application cases are presented to prove the effectiveness of the proposed method for the reliability analysis under hybrid uncertainty. The comparisons between the results of the proposed method and the Monte Carlo simulation also illustrate the merit of this method.

中文翻译：

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一种基于不确定性理论的混合不确定性结构混合可靠性分析数值方法

本文提出了一种利用不确定性理论进行混合可靠性分析的新数值方法。这种方法同时考虑了偶然的不确定性和认知的不确定性。认知不确定性的特征在于不确定性理论，认知不确定性的影响通过子可加性不确定性测度来量化。然后，在可解释为概率论和不确定性理论相结合的机会论的框架下，建立了通用的不确定性量化模型来处理混合可靠性分析问题，并定义了相应的可靠性度量。之后，为了提高模型的可行性，利用基于极坐标变换的降维方法，提供了混合可靠性模型的数值分析方法。最后，通过几个应用案例证明了所提出的方法在混合不确定性下的可靠性分析的有效性。所提出的方法的结果与蒙特卡罗模拟的结果之间的比较也说明了该方法的优点。