数据信息不完备下基于证据理论的可靠性分析

Reliability analysis method based on evidence theory under insufficient data information

针对具有一定数据信息而又不足以构造概率分布的认知不确定问题,提出了一种基于证据理论的可靠性分析方法。通过离散化不确定信息之间的一致、冲突以及忽略关系,建立了合理的信任分配函数,实现了不完备数据信息的有效表达,真实地反映了信息不确定的本质。在不确定测度计算中,基于无需精确求解极限状态函数极值的特性,提出了智能优化算法和不精确极值思想相结合的计算方法,以解决焦元数目和极限状态函数极值所导致的计算瓶颈。以塔架结构为例,考虑了风速和风向的不确定性,可靠性分析结果表明,本文所提方法充分利用了不完备的数据样本,形成了服从数据分布且不需任何假定的基本信任函数,且以区间测度度量结构的可靠性,避免了传统精确概率方法假设造成的误差,具有良好的鲁棒性。

A new reliability analysis technique based on evidence theory is developed to deal with the epistemic uncertainty with insufficient data information.The discretized rules of agreement,conflict and ignorance relationships in the data are used to construct a belief structure of evidence theory,consequently,an reliable uncertainty quantification consistent with available data is proceeded.Since it is not necessary to evaluate the precise extremes of the limit state function during uncertainty measurement,an improved method of evolutionary optimization design integrating with imprecise extremum idea is proposed to overcome the intensive computational cost.A tower structure under uncertainty wind load is investigated to demonstrate the effectiveness of the proposed method.The research indicates that the presented method makes full use of limited data information to construct the basic belief assignment function.Furthermore,the interval measurement based reliability analysis can avoid the error caused by conventional probability theory with the assumed parameters,and has a good robust result.