## 3 Theoretical Analysis and Model Construction
### Reconstruction Model of Hybrid Intelligent Optimization Algorithm  
#### 3.2.1 Reconstruction Objectives of Geo-Environmental Conditions  
With the rapid development of artificial intelligence and interdisciplinary collaboration, some advanced intelligent algorithms have been successfully applied in various industries [28; 29; 30; 31; 32]. Since 1985, these algorithms have been applied to geophysical inversion, especially in seismic inversion [33]. Subsequently, they were used in magnetotelluric inversion. However, there are not many studies and applications involving the use of intelligent algorithms in the electromagnetic wave tomographic inversion of working faces. The introduction of electromagnetic wave CT technology into the reconstruction and prediction of geological environments in working faces will overcome the conventional inversion algorithm's strong dependence on the single initial model and its theoretical local optimal solution problem.  
Intelligent algorithms are garnering increasing interest due to their capability for random nonlinear optimization [34], which reduces the dependence of their results on the initial model. This research converts the matrix problem in Formulas (1)-(4) into a functional extremum problem in order to incorporate intelligent algorithms into the electromagnetic wave CT reconstruction of the working face. The approximate solution of the matrix equation is then obtained when the objective function reaches the extreme value in the intelligent algorithm, which is then used as the initial solution of the conventional linear reconstruction model.  
The objective function is often defined as the gap between the observed data and the theoretical data. In the calculation of electromagnetic wave tomographic inversion, the measured field strength was first obtained from the receiving equipment, and then the measured loss of electromagnetic wave field strength during propagation could be derived according to Equation (4). In addition, the absorption coefficient value of the medium in the detection range within a certain range is randomly assigned, and then the theoretical loss value of the field strength of electromagnetic waves in the propagation process is calculated according to Equation (1). Finally, the theoretical values of the absorption coefficients of each grid are repeatedly updated by the intelligent algorithm until the difference between the measured and theoretical values of field strength loss reaches a minimum, i.e., when the stopping condition is satisfied, the value of absorption coefficient of each grid at the current moment can be output. The specific objective function is defined as shown in Equation (5) below:  
\[f(\mathbf{X})=\sqrt{\frac{1}{A}\sum_{i=1}^{A}{(H_{0}-H_{i}-\ln r_{i}-\sum_{j=1 }^{B}{d_{ij}x_{j}})^{2}}} \tag{5}\]  
where \(\mathbf{X}=(x_{1},x_{2},\cdots,x_{j},\cdots,x_{B})\) is the vector of absorption coefficients to be inverted.  
Therefore, the geological anomaly stratigraphic inversion model can be defined as follows: find \(\mathbf{X}^{\prime}\in C\) such that  
\[f(\mathbf{X}^{\prime})=\text{min}f(\mathbf{X}) \tag{6}\]  
where \(\mathbf{X}^{\prime}=(x^{\prime}_{1},x^{\prime}_{2},\cdots,x^{\prime}_{j}, \cdots,x^{\prime}_{B})\) is the value of the absorption coefficient obtained for each grid corresponding to the inversion when the objective function \(f(\mathbf{X})\) is minimized. _lb_ and _ub_ are the upper and lower limits of the variation of the variables, respectively.