## 4 Experiment and Result
### Comparative Experiment of Denoising Effect  
In order to verify whether the algorithm can effectively solve the problem that the micro-vibration signal is disturbed by noise, the linear sinusoidal excitation system is used to sinusoidally excite the sensor to output the standard sinusoidal signal. In order to verify whether the algorithm can effectively solve the problem of noise interference in micro-vibration signals, in this paper, we used a linear sinusoidal excitation system to excite the transducer so that it can output a standard sinusoidal signal. The measurement signal is compared and analyzed with that of the laser Doppler vibrometer. Figure 13 shows the schematic diagram of the comparative experimental scheme.  
In this paper, the original acceleration signal is denoised by using the denoising algorithm of the symmetric Gaussian curve spectral morphology fitting and the denoising algorithm proposed in this paper. The denoised signal is compared with the output signal of the laser Doppler vibrometer. Because the sampling frequency of the output signal of the laser Doppler vibrometer is different from the sampling frequency of the measurement system set up in this paper, the average error of peak-to-peak vibration velocity is used as the evaluation criterion for the denoising effect. Signal comparison results before and after denoising are shown in Table 1.  
Figure 14 shows the acceleration spectrum of the vibration signal before denoising. In addition to the main frequency signal, it is also mixed with broadband noise randomly distributed in the whole spectrum range. Figure 15 shows the comparison results of acceleration time curves after algorithm denoising. As shown in Table 1, the original  
Figure 12: Comparison of velocity time history curves after the algorithm denoised 30% noise energy.  
Figure 13: Schematic diagram of the comparative experimental scheme.  
signal acceleration time-domain waveform is obviously disturbed by complex noises which are aliased by various frequency noises. The relative error of peak-to-peak acceleration is 27.51%. Using the denoising algorithm of the symmetric Gaussian curve, spectral morphology fitting can complete the separation of the main frequency signal from the noise signal. The fitting curve is symmetric and can only be fitted to the frequency band with a single peak. Therefore, it is inevitable that the radius of the fitted Gaussian curve is different from the spectrum curve of the real signal when the asymmetric main frequency signal is fitted. As a result, the effective frequency band information is lost or redundant noise information is introduced. The peak-to-peak error of acceleration is 5.30%. The proposed denoising algorithm in this paper uses an asymmetric Gaussian mixture model to fit the curve when fitting to an asymmetric main frequency signal. According to the shape of the main frequency signal, the left and right radius of the fitting curve are automatically adjusted, which is more flexible in the curve fitting of the spectrum peak region, so as to achieve better denoising effect. Comparing the acceleration signals obtained before and after denoising with the standard acceleration signals obtained by the laser Doppler vibriometer, it is obvious that the proposed algorithm has a better denoising effect than other denoising algorithms. The peak-to-peak error of acceleration decreased from 27.51% to 1.52% after denoising. The algorithm is applied to the micro-vibration measurement system, which can effectively solve the problem of micro-vibration signal interference by noise.  
Figure 14: Effect comparison before and after denoising.