# Fault Diagnosis of Vehicle Gerboxes Based on Adaptive Wavelet Threshold and LT-PCA-NGO-SVM
## 4 Experimental Analysis
### Signal Denoising  
Because of the influence of the experimental environment and other factors, the vibration data contain significant noise, making the calculation of the SNR challenging. The fault form can be analyzed according to the time domain and energy spectrum of the signal. The theoretical fault characteristic frequency of the planetary gear single tooth is 30.6 Hz, and its frequency is obtained through the calculation of gearbox parameters. As the motor speed is not stable, accurately determining the theoretical frequency and its similar frequencies is crucial for subsequent data processing and analysis.  
The signal with CEEMDAN decomposition is denoised by wavelet threshold. The IMF component with a correlation coefficient greater than 0.1 was decomposed by sym8 wavelet and five-layer wavelet, and the IMF component after noise reduction was reconstructed. Figure 13 displays the time-domain diagram of the IMF component obtained by the CEEMDAN decomposition of the gear fault signal, and Table 7 presents the calculated correlation coefficients. Figure 14 displays the original gear fault signal and the signal with or without CEEMDAN decomposition.  
Figure 14 reveals numerous burr impact signals generated by gear meshing in the signal, and the fault form cannot be identified by time-domain analysis at this stage. Because the measured signal lacks an original pure signal, indicators such as SNR cannot be used to determine noise reduction results. The energy spectrum of the signal is selected as the analysis method, and the energy spectrum transformation analysis of the signal is performed [33], as displayed in Figure 15.  
The Teager-Kaiser energy operator, a nonlinear operator, efficiently extracts signal energy by enhancing transient characteristics to highlight shock components. The continuous-time signal \(x(t)\) us defined as follows [34]:  
\[\psi[x(t)]=\ [\dot{x}(t)]^{2}-x(t)\ddot{x}(t) \tag{30}\]  
where \(\dot{x}(t)\) and \(\ddot{x}(t)\) are the first and second order derivatives, respectively, of \(x(t)\). For discrete signals, it is defined as:  
\[\psi[x(n)]=x^{2}(n)-x(n+1)x(n-1) \tag{31}\]  
Figure 14: Gear failure signal comparison. (**a**) Noisy signal. (**b**) Denoising signal using CEEM-DAN and improved thresholds. (**c**) Denoising signal with an improved threshold is used without CEEMDAN.  
Figure 15: Gear failure signal energy spectrum. (**a**) The energy spectrum of noisy signals. (**b**) The energy spectrum after noise reduction is decomposed without using CEEMDAN. (**c**) The energy spectrum after noise reduction is decomposed using CEEMDAN.  
According to Equation (31), the signal energy is calculated using three consecutive sampling points, which has a small computational effort. It exhibits better adaptability to the non-stationary and transient characteristics of the signal.  
The energy spectrum of the signal with noise in Figure 15a,b reveals that the fault frequency is hidden in the noise, and the fault information cannot be accurately identified. However, direct wavelet denoising fails to clearly identify the characteristic frequency, leaving the actual fault frequency obscured and resulting in a less-than-ideal denoising effect. In Figure 15c, the proposed method's decomposition and noise reduction unveil the characteristic fault rotation frequency and the frequency doubling of the planetary wheel, which can be extracted as follows: 32.0, 63.5, and 95.5 Hz. The characteristic frequency is obvious, and the energy value corresponding to it is prominent, nearing the theoretical calculation frequency. Thus, the noise reduction method is effective.