随机变量概率信息不充分时的可靠性新模型

A NOVEL RELIABILITY MODEL FOR RANDOM VARIABLES LACKING SUFFICIENT PROBABILITY INFORMATION

针对随机变量具有一定的数据积累而又不足以确定概率分布的情况,提出了一种新的可靠性模型。对于具有m个试验样本数据的基本随机变量,给定一映射变量的(m+1)个样本数据以形成m个子区间,使得每个子区间只包含1个基本随机变量的样本数据,从而可以确定每个子区间的基本可信度分配BPA。用证据合成的Dempster法则对具有n个基本随机变量基本可信度分配BPA进行合成,而后求得结构失效F的信任测度函数Bel(F)和似真测度函数PI(F),进一步可用Bel(F)和PI(F)作为失效概率的上下边界来对失效概率进行近似估计。算例表明,所提模型可以充分地利用样本信息,从而可以合理地度量结构的安全程度。

In the case that sample data are insufficient to determine probability distributions of random variables,a novel reliability model is presented on the basis of evidence theory.For the original random variable with m sample data,a matching variable with（m＋1） sample data is constructed and the（m＋1） sample data form m sub-intervals that each sub-interval exactly only involves a sample datum of the original random variable,and then the basic probability assignment（BPA） for each sub-interval can be determined.For a failure mode of a structure with n-dimensional random variables,the BPAs of n-dimensional random variables can be synthesized by using the combination rule of Dempster,on which The belief measure of the structural failure F,Bel（F）,and the plausibility measure of F,PI（F）,can be uniquely determined.Further,the failure probability can be approximated by using Bel（F） and PI（F） as the upper and lower limits.The examples show that the presented model uses the information involved in the sample data sufficiently,thus it can rationally measure the safety of the structure.