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综合当前基于方差的重要性测度与矩独立重要性测度的优点,建立了一个新的随机变量重要性测度指标体系。该体系从输出响应量的均值、方差以及可靠度指标方面对随机变量的重要性进行了分析,进而根据不同的要求衡量基本随机变量对系统或模型输出的影响程度。给出了各个重要性测度指标的定义,并探讨了他们与现有的基于方差的重要性测度指标的关系。通过算例说明了所提新的重要性测度指标体系的优越性。结果表明:新指标体系中的指标不但可以反映旧的指标,而且还对其进行了修正,克服了基于方差的重要性分析中随机变量取不同实现值时对输出响应量的影响相互抵消的问题,从而更加合理地衡量随机变量的重要性;与当前矩独立的重要性分析方法相比,新的指标体系在继承其优点的基础上能够从不同侧面更加全面地对随机变量的重要性进行分析,因而具有更广泛的应用范围。
Based on the current variance-based measure of importance and the merit of moment independent importance measure, a new measure index system for the importance of random variables is established. The system analyzes the importance of stochastic variables in terms of mean, variance and reliability of output responses, and then measures the influence of stochastic variables on the output of the system or model according to different requirements. The definitions of each measure of importance are given and the relationship between them and the existing measure of importance based on variance is discussed. An example is given to illustrate the superiority of the proposed index system of importance measures. The results show that the indicators in the new index system can not only reflect the old indicators but also correct them and overcome the problem that the influence of output variables when the random variables take different realization values offset each other in the variance-based importance analysis So as to measure the importance of stochastic variables more reasonably. Compared with the method of analyzing the importance of independent moments, the new index system can analyze the importance of stochastic variables more comprehensively from different aspects on the basis of inheriting its advantages , Which has a wider range of applications.