Probabilistic Back Analysis Based on Nadam, Bayesian, and Matrix-Variate Deep Gaussian Process for Rock Tunnels

Efficiently determining the properties of the rock mass is essential for evaluating tunnel stability in tunneling projects. The back-analysis technique is commonly employed as an indirect approach for deriving rock mass parameters from field information. However, many back-analysis approaches are often time-consuming in numerical simulations and rely exclusively on monitoring data. This can lead to the identification of rock mass parameters that may not fully represent the characteristics of the surrounding rock. To improve the accuracy of prediction on the tunnel displacement during the tunnel excavation process, this study proposes a probabilistic back-analysis framework to update geo-mechanical parameters. A model based on the matrix-variate deep Gaussian process (MVDGP) and Nesterov-accelerated adaptive moment estimation algorithm (Nadam) is proposed to replace the finite element model to improve its computational efficiency. Initially, a training framework based on ABAQUS–MVDGP is used to conduct the training and evaluation. Subsequently, considering the uncertainty of the geo-mechanical parameters, a probabilistic back analysis is implemented by using the Bayesian theory. Finally, variational inference is used to solve the joint posterior distribution of the geo-mechanical parameters. A rock tunnel is chosen to illustrate the efficacy of the proposed framework. The findings indicate that utilizing the mixed types of monitoring data for vault settlement and convergence enhances the forecasting performance of MVDGP compared to models relying on a single type of monitoring data. The more stable the field monitoring data, the more conducive it is to conduct the back analysis of geo-mechanical parameters of rocks. Furthermore, the comparative results reveal that the presented method demonstrates superior prediction accuracy compared to existing back-analysis models. Highlights A novel probabilistic back-analysis framework based on matrix-variate deep Gaussian process (MVDGP), Nadam and Bayesian theory provides a significant method for identifying and determining rock mass parameters. Compared to single types of data, mixed types of data have better predictive performance in the MVDGP. The more stable the field monitoring data, the better is the performance of probabilistic back-analysis framework. MVDGP performs better than backpropagation neural network (BPNN), multiple output Gaussian process (MOGP), multi-output support vector regression, and proper or