# NSGA-III-XGBoost-Based Stochastic Reliability Analysis of Deep Soft Rock Tunnel
## 1 Introduction
The reliability method in the framework of the Bayesian model update of the structural dynamic models using measured responses was implemented for high-dimensional model parameter spaces [22]. From the above analysis, we note that the reliability research in tunnel engineering of deep soft rock is still in its infancy, and most of the existing tunnel reliability calculation methods are proposed for circular tunnels. It is difficult to evaluate the large deformation risks of deep buried non-circular soft rock tunnels using these reliability methods. Using machine learning methods to establish the surrogate models of the nonlinear mapping relationship between geotechnical parameters and their responses can significantly reduce the time cost of numerical simulation calculations. However, there are still few application studies on machine learning algorithms in the reliability analyses of deep soft rock tunnels. Therefore, the reliability theories of deep soft rock tunnels urgently need to be further studied on the basis of machine learning algorithms such as the eXtreme Gradient Boosting (XGBoost) algorithm. XGBoost does not require high-performance hardware resources such as memory, and has strong robustness. Compared to deep learning models, XGBoost can achieve similar results without fine-tuning of parameters [23]. The surrogate modeling technology based on the XGBoost algorithm has recently been applied to the real-time design of tunnel alignment [24]. Hyper-parameter tuning is crucial for surrogate models based on machine learning algorithms. There are main methods for optimizing hyper-parameters in machine learning models such as Bayesian optimization, genetic algorithm, gradient-based optimization, grid search, Keras Tuner, population-based optimization, ParamILS, and random search. The third-generation non-dominated genetic algorithm (NSGA-III) can solve optimization problems with at least four or more objectives [25]. The XGBoost-based surrogate model hasat least nine hyper-parameters. Therefore, NSGA-III is very suitable for hyper-parameter tuning of XGBoost-based surrogate models. In this study, we propose a stochastic reliability method (SRM) based on XGBoost and NSGA-III. First, the Latin hypercube sampling (LHS) method is used to generate the sample dataset of geo-mechanical parameters of surrounding rock, and the corresponding finite difference numerical calculations based on this dataset are conducted. Second, the surrogate model is constructed using XGBoost, and the surrogate model hyper-parameters are optimized using NSGA-III. Finally, the tunnel reliability index is calculated using the Monte Carlo simulation reliability method (MCSRM) through the NSGA-III-XGBoost-based optimal surrogate model. The purpose of this paper is to provide a surrogate solution for numerical analysis to overcome the time-consuming reliability evaluation of initial support structures of soft rock tunnels under high stress. The main contribution of this paper is that it provides a novel calculation and analysis framework of system reliability to evaluate quickly the large deformation disaster risks of non-circular, deep-buried soft rock tunnels with low computational costs, high precision and high efficiency.