Adam Bayesian Gaussian Process Regression with Combined Kernel-Function-Based Monte Carlo Reliability Analysis of Non-Circular Deep Soft Rock Tunnel

Evaluating the reliability of deep soft rock tunnels is a very important issue to be solved. In this study, we propose a Monte Carlo simulation reliability analysis method (MCS–RAM) integrating the adaptive momentum stochastic optimization algorithm (Adam), Bayesian inference theory and Gaussian process regression (GPR) with combined kernel function, and we developed it in Python. The proposed method used the Latin hypercube sampling method to generate a dataset sample of geo-mechanical parameters, constructed combined kernel functions of GPR and used GPR to establish a surrogate model of the nonlinear mapping relationship between displacements and mechanical parameters of the surrounding rock. Adam was used to optimize the hyperparameters of the surrogate model. The Bayesian inference algorithm was used to obtain the probability distribution of geotechnical parameters and the optimal surrounding rock mechanical parameters. Finally, the failure probability was computed using MCS–RAM based on the optimized surrogate model. Through the application of an engineering case, the results indicate that the proposed method has fewer prediction errors and stronger prediction ability than Kriging or XGBoost, and it can significantly save computational time compared with the traditional polynomial response surface method. The proposed method can be used in the reliability analysis of all shapes of tunnels.