考虑参数空间变异性和基于高效代理模型的边坡可靠度分析

Slope reliability analysis considering spatial variability of parameters based on efficient surrogate model

在考虑参数空间变异性情况下评估小失效概率的边坡可靠度,传统可靠度分析方法往往存在耗时冗长或难以求解等问题。为此,提出了一种基于分段逆回归的主动学习多元自适应回归样条法与子集模拟结合的边坡可靠度分析方法,并探讨了分段逆回归方法对代理模型响应值的影响。首先,利用Karhunen-Loève展开法离散抗剪强度参数随机场,通过强度折减法计算得到一定数量的训练样本用于构建初始代理模型。接着,采用主动学习函数选取一定量最优样本点更新代理模型,使用最终的代理模型与子集模拟耦合进行边坡可靠度分析。最后,以两个典型的边坡算例,验证所提方法的有效性。结果表明:在考虑参数空间变异性情况下,所提方法可以采用更少的训练样本进行小失效概率边坡可靠度分析,不仅可得到比较精确的结果,而且避免出现内存溢出情况。

When evaluating the slope reliability with small failure probability considering the spatial variability of parameters,the traditional reliability analysis methods are often time-consuming or difficult to solve.Thus,it is aimed to propose an active learning multiple adaptive regression spline method based on the segmental inverse regression combined with the subset simulation for the slope reliability analysis,and the effects of the sliced inverse regression method on the response values of the surrogate model are explored.Firstly,the random field of shear strength parameters is discretized by the Karhunen-Loève expansion method,and a certain number of training samples are calculated by the strength reduction method to establish the initial surrogate model.Then,the active learning function is used to select a certain amount of optimal sample points to update the surrogate model,and the final surrogate model is coupled with the subset simulation for the slope reliability analysis.Finally,the effectiveness of the proposed method is verified by two typical spatial variation slope examples.It is shown that the proposed method can obtain more accurate results and avoid memory overflow by using fewer training samples for the slope reliability analysis with small failure probability.