## 1 Introduction
### Support Vector Machine Algorithm  
SVM is a commonly used machine learning method that has been widely used in the prediction, classification, and solution of pattern recognition problems. In the specific application process, how to choose the key parameters is a key issue. The choice of parameters determines the learning ability and generalization ability. At present, the methods of support vector machine parameter optimization are the grid method, gradient descent method, genetic algorithm, and particle swarm algorithm. Among them, PSO is a new artificial intelligence computing technology that has the advantages of fast convergence \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Detection Method** & **Strengths** & **Drawbacks** \\ \hline Impedance method & 1. Low requirements on equipment insulation & 1. Affected by the system operation mode 2. Low measurement accuracy \\ \hline STFT & 1. Reliable, 2. Small calculation; & 1. Time–frequency resolution is limited \\ \hline WT & 1. High time–frequency resolution & 1. High complexity \\ \hline S-transform & 1. High precision 2. Fast response speed & 1. The robustness is low \\ \hline Traveling wave method & 1. Not affected by the system running mode & 1. Difficulty in capturing the initial traveling Bob 2. Low sensitivity \\ \hline Injection method & 1. Strong recognition ability & 1. Requires a large number of training samples 2. Engineering application limitation \\ \hline Artificial neural network & 1. Good fault tolerance & 1. A lot of training data are required 2. The model structure and parameter selection are complex \\ \hline Zero-sequence over current protection & 1. Effective grounding short-circuit protection & 1. Difficulty to detect high-impedance faults 2. Accuracy is susceptible to noise interference \\ \hline Threshold method & 1. Small computation 2. High reliability & 1. The requirements for setting the threshold are high 2. Poor adaptability \\ \hline Artificial intelligence method & 1. Strong ability to deal with complex nonlinear relationships & 1. A lot of training data are required \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Compares the advantages and disadvantages of different fault detection methods. and only requires a small number of parameters to be adjusted, so PSO can be used to optimize the SVM parameters. For the traditional linearly differentiable case, SVM maximizes the classification interval by using an optimization algorithm; for the nonlinearly differentiable case, SVM transforms the data from the input space to a higher dimensional space by means of a suitable kernel function to make them linearly differentiable in this space so as to achieve the classification of the samples. An improvement in the efficiency of model detection and a reduction in the running memory of the computer can be realized by reducing the dimension of the original data, that is, by feature extraction. Feature extraction is a way to reflect the effect of the whole original data by selecting several more representative feature data. By using the Fourier transform method to extract different features from the original time window data table, the extracted data set is divided into a training set, verification set, and test set according to the ratio of 7:1:2. Specifically, the test selected 208,890 data sets as the training set, 146,223 data sets as the validation set, and the remaining 41,778 data sets as the test set. The basic idea of the SVM algorithm is to classify the samples by transforming the training data at the very beginning into higher dimensional data. A linearly differentiable optimal hyperplane is found in the higher dimensions, through which the data can be classified. Let \((x_{i},y_{i})\) denote that there are m sample sets \(1\leq i\leq m\) in a set, \(x_{i}\) denotes the input vector, i.e., the vector of the feature space, and \(y_{i}\) denotes the real vector of outputs corresponding to \(x_{i}\), which is a class label.