# Fault Diagnosis of Vehicle Gerboxes Based on Adaptive Wavelet Threshold and LT-PCA-NGO-SVM
## 4 Experimental Analysis
### Signal Feature Vector Dimensionality Reduction  
To demonstrate the accurate reflection of gearbox fault characteristics by the LT-PCA extracted in this article, PCA and LT-PCA dimensionality reduction analyses are carried out on the hybrid domain features and wavelet domain features of the obtained signal, respectively. In this process, the contribution rate and cumulative contribution rate of each principal component are shown in Table 8. Notably, the first four cumulative contribution rates contain over 99% of the information, surpassing the theoretical value of 85% [35]. Consequently, the decision is made to downsize the data to a four-dimensional feature vector, facilitating improved visualization and result comparison.  
The features of the two principal components meeting the conditions after dimensionality reduction are projected into two-dimensional space, as shown in Figure 16.  
Figure 16: _Cont._  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature** & **Contribution Rate (\%)** & **Cumulative Contribution Rate (\%)** \\ \hline M1 & 85.55 & 85.55 \\ M2 & 9.59 & 95.14 \\ M3 & 2.65 & 97.79 \\ M4 & 1.53 & 99.32 \\ M5\(\sim\)M27 & 0.68 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Contribution rate and cumulative contribution rate for each principal component.  
Figure 16 is used to illustrate the distribution of data points for four different categories. Each point represents a data sample, with colors distinguishing the four categories (states 1, 2, 3, and 4 indicating normal state, mild, moderate, and severe faults, respectively), and the axes indicating different feature dimensions.  
Figure 16, it is evident that different domains perform differently in PCA dimensionality reduction concerning classification effects under various faults. In Figure 16a, for the time-frequency hybrid domain, the clustering effect is obviously the worst after normal PCA dimensionality reduction. Except for the moderate fault and normal state, which exhibit some aggregation effects, the classification effects of other faults show overlapping categories, indicating a serious misdiagnosis phenomenon in PCA downsizing classification relying on the time-frequency hybrid domain. Conversely, under LT-PCA dimensionality reduction, as shown in Figure 16c, the aggregation effect is evident, and different faults are clearly demarcated, achieving the best classification effect.  
For wavelet domain features, as shown in Figure 16b, under normal PCA dimensionality reduction, the aggregation effect of data points is obvious for normal state and moderate fault cases, and the accuracy of analysis and diagnosis is high. However, for mild and severe fault categories, the proximity of data points makes it challenging to separate them, and the wide gap between data points of a single category increases the likelihood of misjudgment when determining the fault type. In the wavelet domain features under LT-PCA dimensionality reduction, as shown in Figure 16d, the aggregation of different fault datasets is more effective than ordinary PCA aggregation. However, light and moderate faults appear mixed, and fault categories cannot be effectively distinguished.  
Overall, the effect of dimensionality reduction in the time-frequency hybrid domain is more pronounced than in a single time-frequency domain. After LT-PCA dimensionality reduction, both time-frequency hybrid and wavelet domains exhibit excellent aggregation effects compared with ordinary PCA dimensionality reduction of the principal components. The results demonstrate that the proposed dimensionality reduction method in this part is superior to the traditional method of dimensionality reduction.