## 4 Experiment and Result  
### Numerical Example Simulation Experiments  
To verify the denoising effect of the algorithm, 5%, 10%, 15%, 20%, 25%, 30% and 35% white noise were added to the acceleration signal, respectively. The observed acceleration was denoised using the denoising algorithm of the symmetric Gaussian distribution curve spectral morphology fitting(GD), the denoising algorithm of the asymmetric Gaussian distribution curve spectral morphology fitting (AGGD) and the denoising algorithm proposed in this paper (AGMD). The observed acceleration after denoising is integrated in the frequency domain to investigate the denoising effect of different denoising algorithms and the influence on the signal accuracy after integration. The relative error of integration peak (Erp), the relative error of integration difference (Erd) and the relative error of integration average (Era) are introduced as evaluation metrics. The expressions are as follows:  
\[\delta_{Erp}=\frac{1}{2}\times\left[\left|\frac{\max(v(t))-\max(v_{real}(t))}{ \max(v_{real}(t))}\right|+\left|\frac{\min(v(t))-\min(v_{real}(t))}{\min(v_{real }(t))}\right|\right]\right. \tag{19}\]  
\[\delta_{Erd}=\frac{1}{2}\times\left[\left|\frac{\max(v(t)-v_{real}(t))}{\max(v _{real}(t))}\right|+\left|\frac{\min(v(t)-v_{real}(t))}{\min(v_{real}(t))} \right|\right] \tag{20}\]  
\[\delta_{Era}=\frac{\sum_{i=1}^{N}(v_{real}(t_{i})-v(t_{i}))^{2}}{\sum_{i=1}^{ N}(v(t_{i}))^{2}} \tag{21}\]  
where \(\delta_{Erp}\) is the relative error of integration peak, \(\delta_{Erd}\) is the relative error of integration difference, \(\delta_{Era}\) is the relative error of integration average, \(v_{real}\) is the true value of vibration velocity at the measuring point position and \(v\) is the reconstructed vibration velocity calculated by denoising algorithm and frequency domain integration. Figure 10 shows the integration accuracy comparison between the denoising algorithm of spectral morphology fitting based on variational mode decomposition and the denoising algorithm of the symmetric Gaussian curve spectral morphology fitting. Figure 10a shows that the relative error of integration peak of the denoising algorithm proposed in this paper is significantly lower than the denoising algorithm of the symmetric Gaussian curve spectral morphology fitting. The relative error of integration peak of the former is always less than 2.6%. The results show that compared with the other two denoising algorithms, the denoising algorithm proposed in this paper is more accurate in the reduction of signal peak. Figure 10b shows that the trend in the relative error of the integration difference is essentially the same for both algorithms. When the relative noise energy is relatively low, the relative error of the integral difference of the proposed algorithm is slightly lower than the other two denoising algorithms. The results show that the difference between the denoised signal and the real signal by the two algorithms is relatively stable. The denoising stability of the algorithm is good. Figure 10c shows that the denoising algorithm proposed in this paper has lower relative error of integration average and higher integration accuracy when integrating the  
Figure 9: Flow chart of denoising algorithm. acceleration under different noise relative energy. Compared with the other two denoising algorithms, the average relative error of the proposed algorithm is basically below 2%, which has better integration accuracy. Figure 10 shows the error between the integral result and the real value. In order to further analyze the denoising effect of the three algorithms, the acceleration spectrum after denoising by the three algorithms and the velocity time history curve after integration can be selected for comparative analysis when the noise relative energy ratio is 30%. Figure 11 shows the comparison results of acceleration spectra. Figure 12 shows the comparison results of velocity time history curves. Figure 11: Comparison of acceleration spectrum after denoising 30% noise energy by algorithm.