Gaussian process regression-based response surface method and reliability analysis of slopes
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摘要: 提出了一种新型高斯过程响应面法(GPRSM),通过高斯过程回归算法构建随机变量与功能函数响应值之间的关系。该方法相较多项式响应面法对于功能函数为高维和高度非线性的可靠度问题,具有更高的精度和计算效率。此方法可以通过新增加训练点以动态更新响应面函数。与此同时,为了模拟岩土参数的空间变异性,通过KL展开构建随机场,并与极限平衡法结合进行边坡稳定性分析。使用提出的GPRSM构建替代模型并用于蒙特卡洛模拟求解边坡失稳概率,在保障计算精度的同时减少了对边坡稳定性分析程序的调用。最后将所提出的方法分别应用于功能函数为显式和隐式两个案例,并与其他论文中的方法对比,证明了该方法的有效性和适用性。Abstract: A novel Gaussian process response surface method (GPRSM) is proposed, in which the Gaussian process regression algorithm is used to construct the relationship between the random variables and the response value of the performance function. Compared with the polynomial-based response surface method, the proposed method has high accuracy and efficiency for the reliability analysis with high-dimensional and highly nonlinear performance functions. This method can update the response surface dynamically by adding new training points. Meanwhile, to consider the spatial variability of soil properties, the random field is constructed by KL expansion and combined with the limit equilibrium method to evaluate the stability of slopes. The proposed GPRSM is used to build the surrogate model and used in Monte Carlo simulation for the failure probability of slopes, which reduces the calls to the slope stability analysis program while ensuring the calculation accuracy. Finally, the proposed method is applied to two case studies with explicit and implicit performance functions, respectively. Compared with those of other methods in the published papers, the validity and capability of the proposed method are proved.
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