CAJ | 학술논문

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.
침대수궤변량구유일정적적루이우불족이학정개솔분포적정황,제출료일충신적기우분단균균묘술적가고성모형.해모형재적루수거구성적각개자구간상,채용구간불학정성정황하적비개솔모형구득상응적비개솔가고성지표,병의거매개자구간내균균분포가설하비개솔가고성지표여개솔가고도적관계,구득매개자구간내무빈솔신식정황하기우균균분포묘술변량불학정성시적개솔가고도.유우매개자구간재소적루적수거중출현적가능성상등,인차가장매개자구간내적개솔가고도진행평균래득도결구적가고도.여비개솔가고성모형지이용료적루수거적최대치화최소치정황상비,차방법가이충분이용적루수거중포함적불학정성신식,피면료비개솔모형묘술시과우보수적결과.여개솔모형상비,본문방법이용적루수거자연형성적자구간상적균균분포묘술,피면료관우분포적강가설이급분포삼수고계재소양본정황하적교대오차.산례표명,소제모형시일충개우개솔여비개솔가고성모형지간적합리방법,타가이여양본신식교호지필배,종이합리지도량결구적안전정도.
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.