子集模拟的混合采样算法

Subset simulation method with mixed sampler

子集模拟是当前可靠度计算领域常用的估计算法,相比于直接蒙特卡罗积分法,极大减少了函数调用的次数。子集模拟法一般使用单一采样器,然而不同采样器适用范围不同。如使用单一椭圆切片采样器,其遍历性较好但函数调用次数较多;而使用单一自适应条件采样时,其采样效率较高但样本容易陷入局部极值。单一采样器由于本身特性面对不同问题时失效概率的积分结果可能出现偏差,模拟效果不稳定。本文首次提出了一种混合采样子集模拟法,在子集模拟的前几层使用椭圆切片采样,此时失效区域收缩程度有限,函数调用次数在可接受的范围内,样本经过采样扩充后能充分探索参数空间,更有效地检测出所有失效区域。当失效区域收缩至一定限度后,使用自适应条件采样,此时种子样本继承了前几层样本较低的相关性,并在此基础上通过自适应条件采样更高效地增殖样本。本文通过四个模拟算例多种维度下的数值积分验证了该算法具有椭圆切片采样器较好的遍历性,同时采样效率位于椭圆切片采样与自适应条件采样之间,对于不同问题拥有良好的通用性。

Subset simulation method is a widely used Monte Carlo integration method in failure probability estimation.Compared with direct Monte Carlo integration method,it greatly reduces the number of function calls.Subset simulation method generally uses a single sampler,but different samplers have different application ranges.If a single elliptical slice sampler is used,its ergodicity is better,but the number of function calls is higher;When using single adaptive conditional sampling,its sampling efficiency is high,but it is easy for the samples to fall into a local extremum.When a single sampler faces different problems due to its own characteristics,the integration results of failure probability may deviate,and the simulation effect is unstable.In this paper,a mixed sampling set simulation method is proposed for the first time.Elliptic slice sampling is used in the first few layers of subset simulation.At this time,the shrinkage of failure area is limited,and the number of function calls is within an acceptable range.After sampling expansion,the sample can fully explore the parameter space and detect all failure areas more effectively.When the failure area shrinks to a certain limit,adaptive conditional sampling is used.At this time,the seed samples inherit the lower correlation of the previous layers of samples,and on this basis,the samples are multiplied more efficiently through adaptive conditional sampling.In this paper,the numerical integration of four simulation examples in multiple dimensions verifies that the algorithm has good ergodicity of elliptic slice sampler,and the sampling efficiency is between elliptic slice sampling and adaptive conditional sampling.It has good universality for different problems.