考虑相关性的证据理论结构可靠性分析方法

The Structural Reliability Analysis Method of Evidence-theory Considering the Dependence

构建了一种考虑相关性的证据理论高效求解模型,讨论了该模型在结构可靠性中的应用。为了提高证据理论进行结构可靠性分析的准确性和效率,引入了非概率凸模型中的椭球模型和一种高效分析方法。通过把非概率凸模型中的椭球模型应用到证据理论中,考虑每对变量的相关系数,把变量的边缘基本可信度分配(BPA)转化为联合基本可信度分配。提出了一种高效计算方法,通过寻找最可能失效点(MPP)将不确定域划分可靠域和待确定域,结构可靠性的求解只需要在待确定域中进行。该方法减少了需要计算的焦元数,提高了证据理论模型求解结构可靠性的效率。

An efficient evidence-theory model considering the dependence among evidence variables is presented,and the application in the structural reliability analysis is discussed. The ellipsoidal model and an efficient analytical method to the structural reliability analysis is introduced based on the evidence-theory to improve the accuracy and efficiency of the analysis. Combining the ellipsoidal model with the marginal basic probability assignments（ BPA） of all the parameters,a joint BPA structure can be constructed. Then,an efficient calculation method is presented. In the present method,the uncertainty domain can be divided into two parts（ reliable domain and the domain to be determined） by finding the most probable point of failure（ MPP）. The present approach reduces the number of focal elements which need to calculate,and greatly improves the efficiency of structural reliability analysis based on the evidence-theory. A mathematic example is investigated to demonstrate the effectiveness of the present method.