边坡失效概率估计的高斯过程动态响应面法

针对传统响应面法在求解具有高度非线性隐式功能函数边坡可靠性问题上的局限性，采用适用于处理高维度、小样本、非线性回归问题的高斯过程回归模型构建隐式功能函数的响应面，将高斯过程响应面与蒙特卡罗模拟法相结合，通过构造合理的迭代方式，在利用高斯过程回归模型的不确定性评价功能获取最优采样点的基础上，实现了高斯过程响应面动态更新，由此提出了边坡失效概率快速估计的高斯过程动态响应面法。利用数值算例验证了该方法的有效性，在此基础上对3个边坡算例进行了可靠性分析。结果表明，与传统响应面法相比较，该方法计算精度与计算效率明显较高，易于与既有的边坡分析软件相结合，且实现容易，适用于边坡可靠性的快速分析。

Gaussian process-based dynamic response surface method for estimating slope failure probability

In light of the limitation of the traditional response surface method for slope reliability analysis with high nonlinear implicit performance function, Gaussian process regression (GPR) model，which is a capable of solving the highly nonlinear regression problem with small samples and high dimensions, is applied to rebuild response surface of implicit performance function. Basing on the optimum sample selected by the function of uncertainty evaluation of GPR model, an iterative algorithm is presented to update GPR response surface self-adaptively. Thus, a new method combing GPR based dynamic response surface with Monte Carlo Simulation (MCS) method for slope reliability is proposed. The accuracy and feasibility of the presented method are demonstrated by numerical examples. The reliability of three slopes are analyzed using the presented method. The results show that the proposed method has higher efficiency and higher accuracy compared to traditional response surface method. It could be achieved easily and can directly take advantages of existing slope analysis codes without any modification. Thus, the proposed method provides a powerful tool for fast analysis of slope reliability.