基于已有信息的转移区域抽样可靠度数值模拟方法

Structural Reliability Analysis by Transfer Region Method based on the Information Obtained

对结构可靠度计算中的数值模拟方法进行了讨论,推导出模拟值方差的理论公式和影响因素。提出了一种可以降低模拟值方差、增加抽样效率的重要抽样方法——基于已有信息的转移抽样区域法。应用这种方法时,可只在包括失效区的且概率已知的某局部区域内抽样。在相同的抽样数量下,由于利用该区域的已知抽样概率作为已有信息,其模拟方差与直接抽样的比值小于1,且该比值随着抽样区的减小而减小,近似呈线性变化。该局部区域可取以原点为中心以结构可靠指标为半径的圆形区域外部空间。理论分析和模拟结果都表明,转移抽样区域法得到的模拟值方差与直接抽样法的比值,随结构可靠指标的增大而呈非线性降低。当可靠指标大于3时,这个比值可以降低到1/100以下。

In the paper, simulation for structural reliability is discussed thoroughly. The formula of simu- lation variance is deduced and analysis of influencing factors on the variance is given. A new sampling method transfer sampling region method is given which can reduce the simulation variance and praise the sampling efficiency. In the method, sampling points only come from some region with known probability and where, the failure area is included entirely. The certain region is choose because the probability of sampling points come from here is obtained easily for simple geometry, and by the known information, the simulation can be approached efficiently. The ratio of the variance of simulation from the method to that of direct method is less than 1, and the value will decrease with the size of sampling region linearly. The outer space of the circle with the origin as center and the reliability index as radius can be choose as the certain sampling region. Analysis and simulation results show that the ratio of the variance of simulation from transfer sampling region method to that from direct method will decrease with the increasing of reliability index nonlinearly and it can be reduced to be less than 1/100 when the reliability is greaterr than 3.