## 2 Methods
### Prediction Parameters of PIM Solution Based on Robust Genetic Algorithm  
Robust estimation is a parameter estimation method used in statistics. The stability of the method's estimation results is maintained when there are outliers in the data or slight deviations in the model assumptions. This study adopts the robust estimation method--the selection-weighted iteration method--and combines it with a genetic algorithm to invert the parameters. The process is as follows: firstly, the weights of all measured subsidence values are equal, parameter inversion is performed using the genetic algorithm, and the predicted subsidence values of all points are calculated; secondly, the absolute residual value of each point is compared; finally, the selection-weighted iteration method is used to assign corresponding updated weights to each observation value, thereby adding the influence of the updated weights to the original square sum of residuals. Equation (7) is used for the minimum residual sum of squares after adding weights:  
\[V_{min}=\sum_{i=1}^{j}P_{i}\gamma_{i}^{2} \tag{7}\]  
In Equation (7), \(V_{min}\) is the minimum residual sum of squares after adding weights; \(P_{i}\) represents the weight corresponding to the observation value with the observation number \(i\); \(j\) represents the number of points; and \(v_{i}\) represents the absolute residual value between the i-th estimated subsidence and the actual subsidence. This study adopts the IGG selection weighting iteration method [30; 31; 32], and the method for determining the weighting function using the IGG selection weighting iteration method is Equation (8):  
\[P_{i}=\left\{ \begin{array}{ll}1&|v_{i}|\leq 1.5\sigma\\ \frac{1}{|v_{i}|+k}&1.5\sigma<|v_{i}|\leq 2.5\sigma\\ 0&|v_{i}|>2.5\sigma\end{array} \right. \tag{8}\]  
In Equation (8), \(k\) is a constant coefficient; \(\sigma\) is the mean square error of the observation value; and \(v_{i}\) is the residual value of the i-th observation value fitting. According to Equation (8), when \(\mid v_{i}\mid\) is less than \(1.5\sigma\), the error contained in the corresponding observation value should be accidental. When \(\mid v_{i}\mid\) is greater than \(2.5\sigma\), the corresponding observation value should contain a gross error (observational errors or data errors that deviate from normal values). When \(\mid v_{i}\mid\) is greater than \(1.5\sigma\) and less than or equal to \(2.5\sigma\), the corresponding observation value should contain a certain proportion of gross errors, and appropriate weights can be assigned to avoid being affected by gross errors. This section describes a method for solving parameters based on a selection-weighted iterative robust GA. The method is carried out using the following six steps:  
(1) When applying this method to solve the parameters based on the selection-weighted iterative robust genetic algorithm, the mining working face condition parameters G and the measured subsidence data are inputted. The interval position of parameter B is determined based on the mining working face condition parameters of adjacent working faces, and the parameters of the genetic algorithm are set (in this experiment, the number of iterations was maxGEN = 500, population size was NIND = 100, mutation rate was PM = 0.02, crossover rate was GGAP = 0.95, and binary encoding length was PRECI = 10). (2) Population encoding and generation are carried out. According to the known parameters of the mine working face, the predicted subsidence parameter B in this mining area is within the known range; the binary encoding of each parameter is randomly generated using binary encoding rules to establish an initial population. (3) The population binary code is decoded into parameter B, and the F of each individual in the population is solved by substituting parameter B for the probability integral model. The fitness calculation equation is as follows:  
\[F=C-V_{min} \tag{9}\]  
In the equation, \(C\) is a constant that makes F greater than zero.