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在同时包含随机不确定性和模糊不确定性结构系统中,为了分别度量随机输入变量和模糊输入变量对输出响应的统计特征的影响,提出了随机输入变量和模糊输入变量的全局灵敏度新指标。在模糊变量可能性矩定义的基础上,分析了混合不确定性下输出响应的特征。从输出响应可能性矩的角度出发,以输出响应的可能性期望为例,通过比较输出响应有条件和无条件可能性期望的概率密度函数(PDF)的平均差异,分别建立了随机输入变量和模糊输入变量关于输出响应的可能性期望的灵敏度指标。讨论了所提指标的性质,并采用Kriging代理模型来提高混合不确定性全局灵敏度指标的计算效率。最后通过算例验证了本文所提方法的准确性和高效性。
In order to separately measure the influence of random input variables and fuzzy input variables on the statistical characteristics of output responses, a new global sensitivity index for both random input variables and fuzzy input variables is proposed in a structural system that includes both random and fuzzy uncertainties. Based on the definition of the probabilities of fuzzy variables, the characteristics of output responses under mixed uncertainties are analyzed. Taking the expectation of the output response as an example, we compare the average difference of probability density function (PDF) of the expected and expected output response to the output in terms of the probability of output response to establish random input variables and fuzzy Enter the desired sensitivity indicator for the likelihood of outputting a response. The properties of the proposed index are discussed and the Kriging agent model is used to improve the computational efficiency of the global sensitivity index of mixed uncertainties. Finally, an example is given to verify the accuracy and efficiency of the proposed method.