# Back Analysis of Geotechnical Engineering Based on Data-Driven Model and Grey Wolf Optimization
## 1 Introduction  
The geomaterial property is critical to guiding construction and assuring safety during the feedback analysis and dynamic design for geotechnical engineering [1, 2, 3]. The back analysis based on field monitoring data has been widely used in geotechnical engineering. The back analysis aims to obtain the geomaterial properties by minimizing the objective function, which represents the response difference of geotechnical structure between the monitored field and the predicted by the physical model, based on the optimization technology. The core of the back analysis technique is the optimization technique and physical model. Generally, the numerical method is widely used to calculate the structure response field in practical geotechnical engineering [4, 5]. However, a numerical method is time-consuming due to the repetitive computing in back analysis, especially for the practical large-scale geotechnical structure. Meanwhile, optimal techniques often have problems in back analysis, such as high dimensionality, complexity, and local minima. In order to solve the above two problems, various surrogate models and optimal technology have been proposed in the back analysis [2, 3, 6]. In this study, the reduced order model (ROM) and the grey wolf algorithm (GWO) were combined to improve the practicability of back analysis. Last century, displacement back analysis was proposed by [PERSON] and [PERSON] to identify the rock mechanical parameters based on the monitoring information of the tunnel [7]. However, the numerical method is time-consuming and limits the engineering application of back analysis. In order to overcome the limitations of the numerical method,various machine learning-based surrogate models were a focus of attention to approximate the response of the geotechnical structure in the past decades [8; 9; 10; 11]. The neural network method was utilized to construct the intelligent displacement back analysis model for identifying the mechanical property of the surrounding rock mass [12; 13; 14; 15]. The support vector machine and the relevance vector machine were selected to build a displacement back analysis model to recognize the geomaterials parameters [16; 17; 18]. Machine learning provides an excellent tool for predicting the structural response and is selected as the surrogate model in the geotechnical back analysis. However, some limits of artificial intelligence, such as overfitting, trapping local minimum, etc., hinder the practical application in back analysis for geotechnical engineering. Meanwhile, the traditional surrogate model does not reflect the physical mechanism of geological engineering and only obtains information about the discrete response at some monitoring points. Therefore, obtaining the total response fields using this classical approach is challenging due to the learning efficiency. The ROM was developed that contains some knowledge about the engineering structure under consideration and can overcome the limits of machine learning and the traditional surrogate model. So, this study adopted the ROM to establish the surrogate model for back analysis. In order to acquire the appropriate geomaterial property, various intelligent optimization methods, such as genetic algorithm [16; 19; 20], artificial bee colony [18], particle swarm optimization [21; 22], etc., have been widely utilized to seek the geomechanical property in the back analysis. Due to the complexity of geomaterials, trapping the local minimum solution is the main drawback of the back analysis method, which hinders its application in practical engineering. Grey wolf optimization (GWO) is an efficient metaheuristic method developed recently [23]. The GWO algorithm is suitable for solving nonlinear and complex problems due to its simple concept, small number of adjustable parameters, fast convergence, and strong global optimization capacity. It only considers the function evaluation and does not need the derivative information, which is suitable for black box global optimization problems.