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 引用本文: 宋述芳 吕震宙. 基于鞍点估计及其改进法的可靠性灵敏度分析[J]. 力学学报, 2011, 43(1): 162-168.
Song Shufang Lv Zhenzhou. The reliability sensitivity analysis based on saddlepoint approximation and its improved method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 162-168.
 Citation: Song Shufang Lv Zhenzhou. The reliability sensitivity analysis based on saddlepoint approximation and its improved method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 162-168.

## The reliability sensitivity analysis based on saddlepoint approximation and its improved method

• 摘要: 鞍点估计可以直接逼近非正态变量空间中线性功能函数概率分布, 进而得出功能函数的失效概率. 在此基础上进行了基于鞍点估计的可靠性灵敏度分析. 对于非线性功能函数, 尤其是强非线性功能函数, 基于鞍点估计进行可靠性及灵敏度分析时存在较大的误差, 为此建立了基于鞍点估计的改进方法------鞍点线抽样方法的可靠性灵敏度分析. 在标准化的变量空间中利用线抽样方法的样本点将系统失效概率转化为一系列线性响应功能函数失效概率的平均值, 从而可靠性灵敏度转化为一系列线性响应功能函数的失效概率对随机变量分布参数偏导数的平均值, 再采用鞍点概率估计方法直接估计非正态变量标准化空间中这一系列线性响应功能函数的失效概率及可靠性灵敏度. 通过比较两种方法的基本思想、实现过程和算例结果可以发现: (1) 第1种方法只适用于线性程度较好的功能函数的情况, 其误差主要来源于非线性极限状态函数的线性化; (2) 改进方法给出的是失效概率及失效概率对随机变量分布参数偏导数的估计值, 这些估计值随样本点数的增加而趋于真值, 并且该方法可以考虑功能函数的非线性对失效概率的影响, 因此具有广泛的适用范围.

Abstract: The saddlepoint approximation (SA) can directly estimateprobability distribution of linear performance function in non-normalvariables space and then calculate the failure probability of structure.Based on the property of SA, SA based reliability sensitivity analysismethod is developed. For the nonlinear performance function, SA method needsthe linearization of performance function firstly, but they neglect theinfluence of nonlinearity of performance function on the failureprobability. So the reliability sensitivity analysis method based itsimproved method, named as SA based line sampling (LS), is presented. Thereliability sensitivity can be estimated by the average of these partialderivatives of failure probabilities with respect to the distributionparameter of random variables, and the probabilities and sensitivities ofthe linear performance functions can be estimated by the SA in thenon-normal variables space. By comparing basic concepts, implementations andresults of illustrations, the following conclusions can be drawn, (1) SAbased reliability sensitivity method is only acceptable for the linearperformance function. The error mostly results from the linearization of theperformance functions. (2) The SA based LS method can obtain the estimatorsof failure probability and reliability sensitivity, which converge to theactual value along with the increase of sample size. The SA based LS methodconsiders the influence of nonlinearity of performance function on thefailure probability and reliability sensitivity; therefore it has the wideapplicability.

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