# Research on a Coal Seam Gas Content Prediction Method Based on an Improved Extreme Learning Machine
## 2 Development of Prediction Models for Coal Seam Gas Content
### Establishment of a Gas Content Prediction Model Based on the GASA-SVM Algorithm  
The theory of SVM encompasses optimal classification hyperplanes, kernel functions, and margin theory. The SVM offers several advantages, such as suitability for handling small sample sizes, robust generalization ability, and simple structure. In a wide range of domains, including medicine, electricity, and economics, SVMs have found practical applications for pattern recognition and regression problems [29; 30]. The fundamental tenet of SVM is to identify the optimal classification hyperplane in the sample space that can segregate various classes of samples while minimizing the empirical and structural risks associated with the classifier. To illustrate the principle of SVM for linear classification in two dimensions, consider the example shown in Figure 9. The orange circles denote one class of samples, while the blue circles correspond to another class. The classification line for these samples is represented by H, whereas H\({}_{1}\) and H\({}_{2}\) are two parallel lines that pass through the points of the two classes that are closest to the classification line. The distance between H\({}_{1}\) and H\({}_{2}\) is known as the classification margin. To enhance the model's generalization ability, it is crucial to maximize the classification margin, indicating that the greater the margin, the more robust the model's generalization ability to unobserved examples and the higher the accuracy of the model's prediction. Sample \(D=\{(\mathbf{x}_{1},y_{1}),(\mathbf{x}_{2},y_{2}),\ldots,(\mathbf{x}_{m},y_{m} )\},y_{i}\in\mathbb{R}\), conventional regression models evaluate prediction error by directly computing the difference between the predicted value of the model and the actual value \(y\). A fitting error of zero is achieved only when the predicted value matches \(y\) precisely. However, support vector regression uses a different method to calculate errors. SVR permits a maximum error of \(\epsilon\) between the predicted value and the measured value, assuming that the deviation between the predicted value and the measured value is zero. Figure 10 illustrates this concept, with the red line representing the true value and the black circle representing the predicted value. A sample is accurately predicted if the predicted values of the training set fall within the interval band created by the central line of \(f(x)\) with a width of \(2\epsilon\), resulting in a prediction error of zero. The selection of the kernel width parameter and regularization factor has a profound impact on the predictive performance of SVM. However, traditional grid search algorithms have limitations, such as undefined value ranges and large computational costs. To overcome these challenges, a GASA algorithm is proposed to initialize the core parameters of SVM. The optimized parameters are then assigned to SVM, and the GASA-SVM gas content prediction model is established by training the SVR machine with the original data. Since the process of initializing SVM and ELM parameters using the GASA algorithm is similar to the process of initializing BPNN parameters, in the following text, only the key steps of the initialization process for SVM and KELM are retained. Figure 9: Schematic diagram of the optimal classification surface. The process of constructing the GASA-SVM prediction model is depicted in Figure 11. The steps involved in building the model are as follows:  
1. The 10-fold cross-validation method is used to split the data into test and training sets;
2. GA initialization: The parameters \(\sigma\) and \(c\) of the kernel function are encoded using the floating-point number encoding rule. A population of 50 individuals is randomly initialized, and the population size and GA parameters such as maximum generation and crossover probability are set;
3. Fitness evaluation function: The MSE between the predicted gas content and the actual output is minimized as the fitness evaluation function. The randomly initialized individuals from step (2) are evaluated.