一种用于蠕变损伤失效概率计算的分层抽样方法

A New Stratification Sampling Method for Creep Damage Failure Probability

根据蠕变损伤试验和相关的研究资料,确定出影响材料蠕变损伤的随机参数;建立了蠕变损伤失效的概率模型。其次根据分层抽样法的基本思想,建立了一种考虑对蠕变损伤失效概率区间分情况抽样的蒙特卡洛分层抽样方法。并且在蠕变损伤模型中选择等效应力作为一个分层抽样变量。随后根据工程实际情况,提出了一种在统计意义下确定抽样变量的安全区域和失效区域的分层抽样的策略,以减少抽样次数。并推导出确定分层抽样区间的计算方法。然后对选择区间大小进行了讨论,可知如果所选择的分层抽样区间太小,会漏掉许多导致蠕变损伤失效的等效应力抽样值,从而使计算结果误差增大;但是如果分层抽样区间选择太大,会增加无效抽样次数,因而降低抽样效率。最后的算例表明了该方法在同样的计算精度下,其计算效率比直接抽样法的效率要高。

Based on the creep experiments and research imformation, the random parameters of the creep damage were determined and the creep damage failure probability model was presented. According to the stratification monte carlo simulation, a new stratification monte carlo sampling method of creep damage failure probability was presented. In this model, the equivalent stress was considered as a stratification sampling paramenter. For reducing the sampling numbers, a new strategy to determined a safety area and a failure area is presented. And the equation of the stratification sampling areas was deduced. With the discussion of sampling area, if the area is too small, a lot of equivalent stress sampling are lose, the error of calculate result is large. But if the area is too large, the large invalid sample will be used in the sam- pling, the sampling efficent is low. Finally, the examples show the effect and efficiency.