一种新的基本随机变量重要性测度指标体系

 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。

A New Importance Measure Index System for Basic Random Variables

By combining the advantages of the existing variance-based importance measure and those of the moment independent importance measure,a new measure index system is established for importance analysis of basic random variables.This system analyzes the importance of the basic variables comprehensively in terms of the mean,variance and reliability index of the output responses.Therefore,it can measure the importance influences of the basic random variables on the whole range of uncertainty of the output responses of the system or model in accordance with different requirements.After the definitions of the importance measure index system are given,their relationships with the existing variance-based importance measure are studied.Several examples are used to illustrate the advantages of the new measure index system.The results show that the indices of the new importance measure index system can not only reflect the old indices,but can also be viewed as their modified version.They can overcome the disadvantage of the old ones,i.e.the effects of different realizations of the basic random variables on the output response may counteract each other.Hence,the new measure index system is more reasonable.Comparison with the existing moment independent importance measure index shows that the new measure index system can analyze the importance of random variables comprehensively from different aspects,while the advantage of the moment independent importance method is inherited in the new measure index system.Therefore,the new measure index system has a wider applicability scope.