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基于失效概率的矩独立重要性测度能够有效地分析输入变量不确定性对结构系统失效概率的影响程度。然而,相比于基于方差的重要性测度,目前很少有足够准确、高效的方法计算该重要性测度。基于此,提出了一种高效求解基于失效概率的矩独立重要性测度新算法。所提算法采用基于分数矩和高维模型替代的极大熵法来高效估计条件概率密度函数,进而求得条件失效概率,再采用三点估计法求得相应条件失效概率的方差,即基于失效概率的矩独立重要性测度。由于所提算法中极大熵法和三点估计法的优点直接被继承,因此所提方法能够在较少的模型计算量的前提下给出足够准确的计算结果。算例表明了本文所提方法相对已有计算方法的优势,体现了更好的工程适用性。
The independent moment importance measure based on failure probability can effectively analyze the degree of influence of the uncertainty of input variables on the failure probability of structural system. However, compared with the variance-based importance measure, there are seldom enough accurate and efficient methods to calculate the importance measure. Based on this, a new algorithm for efficiently calculating the moment independent importance measure based on failure probability is proposed. The proposed algorithm uses the maximum entropy method based on fractional moments and high-dimensional models to efficiently estimate the conditional probability density function, and then obtains the conditional failure probability, and then uses the three-point estimation method to obtain the variance of the corresponding conditional failure probability, that is, Moment independent moment importance measure. Because the advantages of the maximum entropy method and the three-point estimation method in the proposed algorithm are directly inherited, the proposed method can give sufficiently accurate calculation results with a small amount of model computation. The example shows the advantages of the method proposed in this paper over the existing calculation methods and shows better engineering applicability.