基于失效概率的矩独立重要性测度的高效算法
收稿日期: 2013-11-12
修回日期: 2013-12-02
网络出版日期: 2013-12-17
基金资助
国家自然科学基金（51175425）；高等学校博士学科点专项科研基金（20116102110003）
An Efficient Method for Failure Probability-based Moment-independent Importance Measure
Received date: 2013-11-12
Revised date: 2013-12-02
Online published: 2013-12-17
Supported by
National Natural Science Foundation of China (51175425); Research Fund for the Doctoral Program of Higher Education of China (20116102110003)
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。
张磊刚 , 吕震宙 , 陈军 . 基于失效概率的矩独立重要性测度的高效算法[J]. 航空学报, 2014 , 35(8) : 2199 -2206 . DOI: 10.7527/S1000-6893.2013.0483
The failure probability-based moment-independent importance measure can well analyze the effect of input uncertainties on the failure probability of a structure or system. However, compared with the variance-based importance measure, there are few accurate and efficient methods for the computation of the moment-independent importance measure at present. In this context, a highly efficient method to compute the failure probability-based moment-independent importance measure is proposed. The proposed method estimates efficiently the conditional probability density function of the model output using the fractional moments and high-dimensional model representation-based maximum entropy method, thus the conditional failure probability can be easily obtained by integration. Finally the three-point estimation method is applied to computing the variance, namely the failure probability-based moment-independent importance measure. Since the advantages of the maximum entropy method and the three-point estimation method are inherited directly, the proposed method can yield accurate results under a small number of function evaluations. Examples in the paper demonstrate the advantages of the proposed method as compared with existing methods, and indicate its good prospect for engineering application.
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