一种与样本信息合理匹配的可靠性模型

针对随机变量具有一定的积累而又不足以确定概率分布的情况,提出了一种新的基于分段均匀描述的可靠性模型。该模型在积累数据构成的各个子区间上,采用区间不确定性情况下的非概率模型求得相应的非概率可靠性指标,并依据每个子区间内均匀分布假设下非概率可靠性指标与概率可靠度的关系,求得每个子区间内无频率信息情况下基于均匀分布描述变量不确定性时的概率可靠度。由于每个子区间在所积累的数据中出现的可能性相等,因此可将每个子区间内的概率可靠度进行平均来得到结构的可靠度。与非概率可靠性模型只利用了积累数据的最大值和最小值情况相比,此方法可以充分利用积累数据中包含的不确定性信息,避免了非概率模型描述时过于保守的结果。与概率模型相比,本文方法利用积累数据自然形成的子区间上的均匀分布描述,避免了关于分布的强假设以及分布参数估计在小样本情况下的较大误差。算例表明,所提模型是一种介于概率与非概率可靠性模型之间的合理方法,它可以与样本信息较好地匹配,从而合理地度量结构的安全程度。

A Novel Reliability Model Matching Information Involved in Sample Data

Based on stepwise uniform distribution, a novel reliability model is proposed to reasonably match information provided by sample data and that information is not enough to determine probability distributions of random variables. For the sub-intervals formed by the sample data, the corresponding non-probabilistic reliability indexes can be calculated by the non-probabilistic reliability model for interval uncertainty, then the non-probabilistic reliability indexes can be transformed to the probabilistic ones on the assumption of the variables uniformly distributed in the sub-intervals while no frequency information involved. Since each sub-interval holds the same probability emerging in the sample data, the proposed model employs the average of the probabilistic reliabilities of the sub-intervals as the reliability measure of the structure. Comparing with the non-probabilistic reliability model only using the maximum and minimum of the sample data, the proposed model avoids the conservative results by sufficiently using the information involved in sample data. In comparison with the probabilistic model, in which the distributions assumption of the random variables and the parameter estimations are required, the proposed model utilizing the stepwise uniform distribution of the variables avoids the great error of the probabilistic one. The examples show that the proposed model is a reasonable approach between the probabilistic one and the non-probabilistic one since it matches the information involved in the sample data sufficiently, thus it can rationally measure the safety of the structure.