## 5 Experimental Test  
In order to validate the practical use of the efficient Wavelet analysis method, a gearbox practical model with fault is presented, as shown in Figure 4. This experimental model consists of a Dewetron 3000 multi-channel measuring device (Dewetron Services, Grambach, Austria), a one-stage helical gearbox (Hanoi, Vietnam) with two gear condition types: healthy (Figure 4a) and fault (Figure 4b), and an electromagnetic brake (Warner Electric, South Beloit, IL, USA) used to generate load. Two vertical axis acceleration sensors (Murata Manufacturing Co., Ltd., Kyoto, Japan) are mounted outside on the input shaft's rolling bearing sleeve. The gear is installed on the gearbox's input shaft for testing purposes. The signal is sampled at a frequency of 10,000 Hz. The rotational speed of shaft 1 is adjusted using a frequency Converter drive, with the frequency of rotation fluctuating between 8-25 Hz. The Meshing frequency is determined to fluctuate from 115 Hz to 355 Hz, as shown in Figure 5.  
Figure 4: An experimental model of a single-stage gearbox with healthy gear (**a**), fault gear (**b**), and fault gear position (red box). Figure 3: TFR of the signal using combined GFT and WSST. Spectrum analysis is a popular technique in modern industries, as per conventional signal analysis approaches [93]. Upon observing Figure 6, one can clearly see the signal waveform in the time domain (Figure 6a) and amplitudes in the frequency domain (Figure 6b). Due to non-stationary conditions, the frequency spectrum may become blurred, and the mechanical characteristics, such as gear meshing frequency and sidebands, may not be well defined. This instability could be caused by load variations, leading to rotational speed changes. Hence, the spectrum analysis method [94] is less effective when the gearbox is in a non-stationary condition. The signal is then given a continuous Wavelet transformation to obtain the healthy and fault gear results, as shown in Figure 7. Figure 7a shows that in the case of a healthy gear, there are slight increases in energy density corresponding to meshing frequency and its harmonics, without sidebands present. On the contrary, in Figure 7b, corresponding to the case of a fault gear, it can be observed that the energy density region around the meshing frequency increases. However, evaluating the energy level on TFR around the  
Figure 5: Meshing frequency of input shaft. Figure 6: Waveform and Spectrum of measured vibration signal. gear meshing frequency is not enough to make decisions about the gear fault condition. It is necessary to determine the sidebands around the meshing frequency. If there are any sidebands present, it is a symptom of faults, whereas the absence of sidebands indicates a healthy gear. Figure 8 depicts the TFR of gearbox case vibrations in a faulty gear tooth using these methods of WSST [95, 96, 97]. Compared to Figure 7, although the TFR of WSST has a higher signal concentration than that of CWT, the GMF is hard to detect, and the frequency curves are not smooth. The cause of the above problem is the high degree of complexity of the signal. In this experiment, the rotational shaft speed increases rapidly, which makes many closely spaced and overlapping vibration frequency components. So, the ability of WSST to distinguish and isolate the individual components is reduced. To solve the mentioned challenges, the proposal method is applied to extract the sidebands around the initial gear meshing frequency harmonic order. If the gear is healthy, there is no frequency sideband around the mesh frequency, as indicated in Figure 9a. In contrast, clear sidebands can be observed as symptoms in the TFR of the signal when having a gear fault, as shown in Figure 9b. From this, it can be concluded that updating knowledge about Wavelet transformation, specifically, and Wavelet analysis, in general, allows experts to easily identify fault symptoms in a gearbox operating in non-stationary conditions.