## 4 Intelligent Height Adjustment Model of Shearer Drum Based on AR-AIGA-FRRBFNN
### Parameter Optimization of FRRBFNN Based on Adaptive Immune Genetic Algorithm  
The parameters in FRRBFNN have the center \(\mu_{ij}\) and width \(\sigma_{ij}\) of the membership function corresponding to the hidden layer membership function, the connection weight \(\eta_{hc}\) between the hidden layer and the fuzzy rough membership layer, and the connection weight \(\omega_{c}\) between the fuzzy rough membership layer and the output layer. These parameters directly determine the accuracy of the entire network model, so the network determines the value of the most suitable parameters \(\mu_{ij}\),\(\sigma_{ij}\), \(\eta_{hc}\) and \(\omega_{c}\) through the appropriate algorithm, which is the key to the optimization of network parameters. The center \(\mu_{ij}\) and width \(\sigma_{ij}\) of the Gaussian membership function are usually calculated by unsupervised clustering algorithms, such as K-means method, etc. However, the number of categories of clustering methods must be preset, and the selection of the number of categories will directly affect the performance of clustering, thus affecting the network performance. The immune genetic algorithm is an improved genetic algorithm based on the organism's own immune regulation mechanism. The algorithm has significant advantages such as an immune memory function, an antibody diversity preservation function and a self-regulation function [34]. However, due to the preset crossover rate and mutation rate in the evolutionary iteration process, the local optimal solution will inevitably occur, which will affect the prediction accuracy of the shearer drum height. To solve this problem, adaptive crossover rate and mutation rate are designed, and adaptive immune genetic algorithm is constructed. The specific steps of FRRBFNN parameter optimization based on AIGA algorithm are as follows:  
Step 1: The variables \(\mu_{ij}\), \(\sigma_{ij}\), \(\eta_{hc}\) and \(\omega_{c}\) are optimized as antibodies, and encoded. Step 2: The operation parameters of AIGA are determined, including the population size \(Q\), the maximum number of iterations \(T\), the original number of iterations \(g=0\) and the fitness objective function \(F_{goal}\). Step 3: The fitness of each antibody is calculated. According to the actual situation of the height adjustment of the shearer drum, this study selects the FRRBFNN fitness function as the appropriate fitness function. \[F=\frac{1}{1+E},\;E=\frac{1}{n}{\sum\limits_{i=1}^{n}(\hat{y}-y)}^{2} \tag{20}\]  
where \(E\) is the prediction error of the FRRBFNN, \(n\) is the number of test samples, \(\hat{y}\) and \(y\) are the predictions of the \(i\) test sample point value and true value, respectively. When \(E\) is the minimum value, the parameter value of FRRBFNN is the best. Step 4: For the current population \(p_{t}\), according to the fitness of the antibodies, to prevent the optimal antibody of the current population from being lost in the next generation, the \"elite retention\" strategy is adopted [35]. The one with the highest fitness is selected and stored in a dedicated variable as the elite antibody. The specific operation is as follows: when the genetic algorithm evolves to the \(t\) generation, \(x_{1}(t)\) in the population is the optimal antibody. Let \(A(t+1)\) be a new generation group: if \(A(t+1)\) does not exist \(x_{1}(t)\), then add \(A(t+1)\) as an antibody of \(A(t+1)\), and \(A(t+1)\) eliminates an antibody with the lowest fitness. Step 5: Antibody selection operation: When the concentration is constant, the greater the fitness is, the greater the probability of the antibody being selected. When the fitness is constant, the higher the antibody concentration is, the smaller the probability of the antibody being selected. Antibody similarity and concentration are defined as follows: there is an antibody population of size \(m\), where each antibody can be represented as a one-dimensional vector with \(m\) elements.