基于证据理论的结构失效概率计算方法

Method for Calculating the Failure Probability of Engineering Structure Using Evidence Theory

提出了一种基于证据理论的失效概率P_f计算方法.对于具有n个随机影响因素的工程结构,定义结构失效的命题为F.把每个随机变量的样本空间等分成有限个子区间,确定每个子区间的基本可信度分配(BPA).用Dempster法则对n个随机因素的BPA进行合成,然后求得F的信度Bel(F)和似真度Pl(F).用Bel(F)和Pl(F)的平均值作为失效概率P_f的近似估计.数值验证表明,用该方法计算P_f可达到满意的精度.用所提出的方法计算四方形混凝土基础的失效概率,计算结果验证了该方法的正确性和有效性.

A method for calculating the failure probability of engineering structure was proposed based on evidence theory. For a failure mode of a structure with n random variables, F was defined as an event of failure. The sample space of each random variable was discretized into finite intervals. The basic probability assignment （BPA） for each interval was determined according to probability density function, and then the BPAs of n random variables were fused by using the Dempster＇s rule of combining. The belief measure of F, Bel （F）, and the plausibility measure of F, P1 （ F）, were uniquely determined by using the Dempster-Shafer theory. The failure probability was bracketed by Bel（F） and PI（F）. The average of Bel（F） and Pl（F） was regarded as an approximation to the failure probability. A mathematical example shows that satisfactory calculation accuracy of failure probability could be achieved by using the proposed method. This method was used to calculate the failure probability of a shallow concrete base, and its result demonstrated the validity of the proposed method.