The purpose of this article is to develop an effective method to evaluate the reliability of structures with epistemic uncertainty so as to improve the applicability of evidence theory in practical engineering problems. The main contribution of this article is to establish an approximate semianalytic algorithm, which replaces the process of solving the extreme value of performance function and greatly improve the efficiency of solving the belief measure and the plausibility measure. First, the performance function is decomposed as a combination of a series of univariate functions. Second, each univariate function is approximated as a unary quadratic function by the second‐order Taylor expansion. Finally, based on the property of the unary quadratic function, the maximum and minimum values of each univariate function are solved, and then the maximum and minimum values of performance function are obtained according to the monotonic relationship between each univariate function and their combination. As long as the first‐ and second‐order partial derivatives of the performance function with respect to each input variable are obtained, the belief measure and plausibility measure of the structure can be estimated effectively without any additional computational cost. Two numerical examples and one engineering application are investigated to demonstrate the accuracy and efficiency of the proposed method.

中文翻译：

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基于有效证据论的不确定性结构可靠性分析算法

本文的目的是开发一种有效的方法来评估具有认知不确定性的结构的可靠性，以提高证据理论在实际工程问题中的适用性。本文的主要贡献是建立了一种近似半解析算法，该算法取代了求解性能函数极值的过程，大大提高了求解置信度和似然度的效率。首先，将性能函数分解为一系列单变量函数的组合。其次，每个二元函数通过二阶泰勒展开式近似为一元二次函数。最后，根据一元二次函数的性质，求解每个单变量函数的最大值和最小值，然后根据每个单变量函数及其组合之间的单调关系获得性能函数的最大值和最小值。只要获得相对于每个输入变量的性能函数的一阶和二阶偏导数，就可以有效地估计结构的置信度和合理度，而无需任何额外的计算成本。研究了两个数值示例和一个工程应用，以证明该方法的准确性和效率。只要获得相对于每个输入变量的性能函数的一阶和二阶偏导数，就可以有效地估计结构的置信度和合理度，而无需任何额外的计算成本。研究了两个数值示例和一个工程应用，以证明该方法的准确性和效率。只要获得相对于每个输入变量的性能函数的一阶和二阶偏导数，就可以有效地估计结构的置信度和合理度，而无需任何额外的计算成本。研究了两个数值示例和一个工程应用，以证明该方法的准确性和效率。