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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。
Aiming at the fact that the random variables have some data accumulation but not enough to determine the probability distribution, a new reliability model is proposed. For a base random variable with m test sample data, given (m + 1) sample data for a mapped variable to form m subintervals such that each subinterval contains only sample data for a base random variable, one can determine The basic credibility of each subinterval is assigned BPA. Dempster’s law of evidence synthesis is used to synthesize BPA with the basic credibility of n basic random variables, then the trust measure function Bel (F) and the plausibility measure PI (F) of structural failure F can be obtained, F) and PI (F) as the upper and lower bounds of failure probability. The example shows that the proposed model can make full use of the sample information so that the structural safety can be reasonably measured.