Research on slope reliability analysis using multi-kernel relevance vector machine and advanced first-order second-moment method

To increase the efficiency and accuracy in slope stability analysis, a reliability analysis method based on machine learning and the advanced first-order second-moment (AFOSM) method was proposed, and the partial derivative of the machine-learning algorithm was derived. First, a multi-kernel was introduced to establish the multi-kernel relevance vector machine (MKRVM). Then, the kernel parameters of the MKRVM were optimized by the harmony search (HS) method to use the high-precision MKRVM method instead of the traditional methods for determining the factor of safety. It was necessary to obtain the partial derivative of the performance function, which was explicitly expressed by the trained MKRVM in this paper. Finally, the AFOSM was adopted to calculate the reliability index of the slope, as the AFOSM was more reliable because the design point was located at the failure surface. With two samples, from a single-layer slope and a multilayer slope, the calculation results show that the MKRVM–AFOSM is easy to use, highly computationally efficient, and reliable.