Adam - Bayesian - Gaussian process regression based Monte Carlo simulation reliability analysis of deep soft rock tunnel

Abstract

To evaluate the reliability of deep soft rock tunnels is a very important issue to be solved. In this paper, we proposed a novel Monte Carlo simulation reliability analysis method (MCS-RAM) integrating adaptive momentum stochastic optimization algorithm (Adam), Bayesian inference theory and Gaussian process regression (GPR) ——ABGPR-MCS-RAM, and implemented it by Python. The proposed method used the Latin hypercube sampling method to generate the dataset sample of geo-mechanical parameters, constructed combined kernel functions of GPR and adopted GPR to establish the surrogate model of the nonlinear mapping relationship between displacements and mechanical parameters of the surrounding rock. Adam was used to optimize the hyper-parameters of the surrogate model. 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 by the MCS-RAM based on the optimized surrogate model. Through the application of engineering case, the results indicate that the proposed method has less prediction error and stronger prediction ability than Kriging or XGBoost, and it can significantly save computational time compared with the traditional polynomial response surface method (PRSM). The proposed method can be used in the reliability analysis of all shapes of tunnels.