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利用鞍点逼近法可以直接逼近单个线性响应功能函数概率分布的特点,提出了基于鞍点逼近的基本随机变量重要性测度分析方法。在所提方法中,首先将非线性响应功能函数进行线性化,再利用鞍点逼近方法近似得到响应功能函数的概率密度函数及其在变量某个实现值下响应功能函数的条件概率密度函数,进而根据基本随机变量重要性测度的定义计算出相应变量对响应功能函数分布影响的重要程度。最后给出了该方法的实现步骤和原理,并通过算例验证了该方法的合理性和可行性。
The saddlepoint approximation method can be used to directly approximate the characteristics of the probability distribution of a single linear response function. Based on the saddle point approximation, the method of importance measure of basic random variables is proposed. In the proposed method, the nonlinear response function is first linearized, then the saddlepoint approximation method is used to approximate the probability density function of the response function and its conditional probability density function in response to the function at an implementation value of the variable According to the definition of importance measure of basic random variables, the importance of the corresponding variables on the distribution of response function is calculated. At last, the realization steps and principles of this method are given. Finally, an example is given to verify the rationality and feasibility of this method.