基于不确定性理论的混合不确定性结构混合可靠度分析方法
A numerical approach for hybrid reliability analysis of structures under mixed uncertainties using the uncertainty theory
摘要：
利用不确定性理论，提出了一种新的混合可靠性分析的数值方法。该方法同时考虑了情感的不确定性和认知的不确定性。认知不确定性由不确定性理论来刻画，认知不确定性的影响由次可加不确定性测度来量化。然后，在概率论和不确定性理论相结合的机会理论框架下，建立了处理混合可靠性分析问题的一般不确定性量化模型，并定义了相应的可靠性度量。然后，为提高模型的可行性，利用极坐标变换降维方法，给出了混合可靠性模型的数值分析方法。最后，通过算例验证了该方法在混合不确定性下可靠性分析中的有效性。通过与蒙特卡罗模拟结果的比较，说明了该方法的优越性。
英文摘要：
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.
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