基于主动学习径向基函数的边坡系统可靠度分析

相较于极限平衡法，强度折减法在计算边坡稳定性系数上有许多优势，但更大的计算量在一定程度上限制了其在边坡可靠度分析中的应用。为了有效地减少可靠度分析中数值模型的计算次数，以减轻使用强度折减法所带来的计算压力，引入了基于主动学习径向基函数（ARBF）代理模型的高效分析方法：利用主动学习函数在极限状态面附近搜索训练样本更新代理模型，加快模型训练的收敛速度；采用线性核径向基插值函数简化模型参数优化过程，建立简洁、稳定的代理模型。此外，为了充分发挥主动学习代理模型的优势，提出针对土质边坡特性的初始采样策略。当得到稳定的代理模型后，结合蒙特卡罗模拟计算边坡的系统失稳概率。作为对比，基于两个典型边坡算例，测试了两种经典的可靠度方法：主动学习克里金模型（AK）和二次响应面法（QRSM），论证了引入的主动学习径向基函数代理模型在计算效率上的高效性和计算模型上的稳定性。

System reliability analyses of slopes based on active-learning radial basis function

The strength reduction method (SRM) has many advantages compared with the limit equilibrium method (LEM) in computing the safety factor of slopes, but the high computational cost, to some extent, limits the application of SRM in system reliability analyses of slopes. To effectively reduce the number of numerical analyses required for reliability analyses to alleviate the computation work when employing SRM, an efficient analysis method based on active-learning radial basis function (ARBF) surrogate model is introduced. This model uses the active-learning function to select trained samples near the limit state surface to update the surrogate model, which accelerates the convergence speed of the training process. With the linear kernel-based radial basis function, the optimization procedure of model parameters is simplified, by which a concise and stable surrogate model can be established. Moreover, an initial sampling strategy considering the characteristics of soil slopes is proposed to fully take advantage of active-learning process. Once a stable surrogate model is established, Monte Carlo simulation (MCS) is used to calculate the probability of system failure. As a comparison, two conventional reliability methods: active-learning Kriging (AK) model and the quadratic response surface method (QRMS), together with two typical soil slope cases, are tested to illustrate the computational efficiency and model stability of the introduced ARBF.