基于小子样试验的两种线性系统可靠度预测方法

TWO EVALUATION METHODS FOR THE RELIABILITY OF STRUCTURES BASED ON SMALL SAMPLES

本文提出了在小子样试验的前提下,结构系统关键失效模式可靠度预测的两种方法,其一是基于抽样分布分析的转换法。在这种方法中,严格推导了元件强度和外载为正态分布时,可靠度计算从正态分布概率积分到t分布概率积分的转换。它适用于试验样本数不小于2的情况;其二是基于模糊学原理的加权平均法。此方法要求根据专家经验和现场数据,给出强度和载荷分布参数的隶属函数,然后用加权平均法给出结构系统关键失效模式的可靠度,这种方法对试验样本数没有要求,但专家经验的丰富程度对这种方法预测的可靠度有较大影响。文中用算例说明了两种方法的差异,并且说明了在小子样试验情况下,直接用样本分布参数来进行可靠度计算的结果是偏危险的。

This paper presents two evaluation methods for the reliability of structures, i,e, the transformation method and the weighting average method, for the most significant failure mode, based on small number samples. In the first method, the transformation from normal distribution integration to t-distribution integration is strictly derived according to the sample distribution analysis, loads and component strength being assumed to be normal variables with unknown distribution parmeters in the derivation. The second method is established with the fuzzy theory, yet it requires a membership function of the distrbution parameters given by experts according to their experiences and the experimental data. The second method has no requirement about the number of the samples n, yet it relys strongly on the degree of accuracy of the experiences of experts (it requires n > 2) . An example is given to il-lustate differences of the two methods. And in the example it also shows that the reliability of the structure systems overestimated as the normal distribution method is used under the small samples.