# Fault Diagnosis of Vehicle Gerboxes Based on Adaptive Wavelet Threshold and LT-PCA-NGO-SVM
## 4 Experimental Analysis
### Fault Category Identification  
Following LT-PCA dimensionality reduction, aggregated fault feature vectors are obtained. These feature vectors serve as inputs for a support vector machine (SVM) in the fault pattern recognition of gearboxes. For each fault type, 80 sets of samples are divided into two parts: 60 sets for training the SVM and 20 sets for testing its accuracy. In these  
Figure 16: Two-dimensional principal component analysis. (**a**) Two-dimensional principal component analysis of time–frequency mixed domain PCA. (**b**) Two-dimensional principal component analysis of wavelet domain PCA. (**c**) LT-PCA two-dimensional principal component analysis in the time–frequency mixed domain. (**d**) LT-PCA two-dimensional principal component analysis in the wavelet domain. samples, labels 1, 2, 3, and 4 denote normal state, mild fault, moderate fault, and severe fault, respectively. The following is the optimization process of the NGO-SVM. The optimization parameters 'c' and 'g' optimization process and fitness curve of the NGO algorithm are shown in Figure 17.  
According to Figure 17, optimizing the SVM using the NGO algorithm finds the parameter configurations that give the optimal cross-validation accuracy after only four iterations, specifically, \(c=147\) and \(g=0.02\). This indicates that the NGO algorithm converges rapidly, finding high-performance parameter configurations with minimal computations. Such fast convergence is highly beneficial for large-scale datasets and complex models, significantly reducing the optimization search time. The results show that the NGO algorithm has a significant advantage in optimizing SVM models. Figure 18 reveals multiple misclassified sample points in SVM classification without using the optimization algorithm directly. However, after optimization, the SVM classifies the points perfectly, demonstrating the excellent performance of the optimization algorithm. Figure 17: Optimization process and iteration curve of parameters ‘c’ and ‘g’. (**a**) Optimization process of parameter ‘c’. (**b**) Optimization process of parameter ‘g’. (**c**) Iteration curve. The confusion matrix (CM) is a valuable tool in machine learning and statistics for evaluating the performance of a classification model, offering a detailed perspective on how the model performs across different categories. Its primary purpose is to compare the model's classification results with the actual categories, enabling the calculation of various performance metrics. When testing experimental data, fault diagnosis results are visually represented using the confusion matrix, as depicted in Figure 19. The horizontal and vertical coordinates of the figure, labeled 1, 2, 3, and 4, represent the four data categories, allowing for joint diagnosis of no fault, as well as mild, moderate, and severe faults. The rows of the graph represent true category cases, and the columns represent the predicted cases. For example, in column 2 of Figure 19, where the horizontal coordinate is 2 (representing mild faults), 14 samples are correctly classified, and 6 samples are considered to be in the no-fault state, with an accuracy of 70%. Similarly, for the NGO-SVM, see column 2 of Figure 19, where the classification accuracy is 100%. The classification prediction of the NGO optimization algorithm surpasses that of the original SVM algorithm. Similarly, the processed feature dataset is analyzed using MFO-SVM and PSO-SVM algorithms to compare the classification accuracy of each state under the same operating conditions. The classification accuracies of the various algorithms are presented in Table 9, and the results are averaged over 10 tests. Figure 19: Confusion matrix for classification of original and NGO optimization algorithms. (**a**) Original classification test set confusion matrix. (**b**) NGO optimization algorithm test set confusion matrix.