## 4 Results and Discussion
Hence, under different \(\alpha\) values that increase from 1 to 5000 with a step width equal to 100, the center frequency of Mode 1 was calculated sequentially, and the result can be seen in Figure 6. It was found that with a larger SNRinput, the center frequency of noisy signals approached the center frequency of original signals more closely, which means a better anti-noise performance. It is worth noting that the central frequency of Mode 1 in different SNR noise signals most closely approaches the central frequency of the original signal with good anti-noise performance when \(\alpha\) is approximately 200. In this research, the value of \(\alpha\) was set to 200 to guarantee the value accuracy of the center frequency when the experiment signal was processed later. Taking the mixed FBG noisy signals shown in Figure 4a as an example, the proposed denoising algorithm was applied to the samplings, and the results are given in Table 1. The EMD-wavelet, EMD-DFA, and EMD-changed thresholding wavelet (named EMD-DWT) algorithms are used for comparison due to their well-developed characteristics in terms of removing WSN from signals. The parameters of VMD were also chosen as follows: \(\alpha=200\), \(\tau=0\), and \(\varepsilon=1\ \times 10^{-7}\). EMD with the traditional wavelet thresholding method was chosen as the basic denoising algorithm to evaluate the effectiveness of other three methods. Moreover, the EMD-DWT algorithm was used to assess the denoising performance under the VMD and EMD domains. Moreover, the traditional denoising method of EMD-DFA was proposed as a reference algorithm. The mixed FBG noise signal with SNRs from 5 to 35 dB were processed, and the quantity evaluation results can be seen in the following table. Table 1(a) presents the SNRout of the above four denoising algorithms, Table 1(b) presents the cross correlation, and Table 1(c) presents the MSE of the above-mentioned denoising methods. The bold numbers in the figure below presents the best SNRout of the three traditional algorithms and the proposed algorithm under different decomposition numbers. Figure 6: \(\alpha\) of Mode 1 with mixed and original signals under various SNRs. For the VMD-changed thresholding wavelet algorithm, the decomposition number \(K\) determines the proposed algorithm denoising performance. According to previous research, the results of three parameters, the SNR\({}_{\text{out}}\), the MAE, and the correlation coefficient, to quantitatively evaluate the  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & & & \\ \hline
**SNR (dB)** & **5** & **7** & **10** & **15** & **20** & **25** & **30** & **35** \\ \hline EMD-wavelet (soft) & **28.27289** & **29.03794** & **29.94879** & **34.62247** & 36.03779 & 38.70505 & 40.36963 & 40.66328 \\ EMD-DFA & 21.45639 & 20.79891 & 27.80233 & 20.84781 & 37.91600 & 43.04961 & 48.30413 & 53.24952 \\ EMD-DWT & 22.98264 & 24.93801 & 27.80229 & 33.08285 & **37.91601** & **43.04964** & **48.30413** & **53.24952** \\ VMD-DWT & & & & & & & \\ \(K=1\) & 18.79288 & 18.65518 & 18.38846 & 18.80969 & 26.82166 & 27.21651 & 32.46437 & 32.66283 \\ \(K=2\) & 23.01841 & 23.64160 & 19.52073  
denoising performance, were used to analyze the best VMD decomposition number under different SNR\({}_{\text{input}}\) values. It is clear that when the decomposition number \(K\) was set too high, too many basic modes were obtained (overbinning); when the decomposition number was set too low, there may be too few basic modes (underbinning). The three quantitative evaluating parameters show that the denoising effect apparently does not reach the best expectations. Additionally, \(K\) is related to the SNR of the input signal. A higher SNR\({}_{\text{input}}\) of mixed signals corresponds to a higher decomposition level. The best decomposition level number is 4 with a mixed signal with a low SNR\({}_{\text{input}}\); however, with a mixed signal with a high SNR\({}_{\text{input}}\), the best basic mode number increases and maintains stability at 6.