## 4 Results and Discussion
On balance, for a realistic experimental signal without adding noise, the best decomposition level should be 6 in the denoising process. In Table 1, the EMD-changed thresholding wavelet algorithm had better performance than the traditional EMD-wavelet denoising method, which illustrates that the changed thresholding was efficient at signal denoising. Moreover, comparing other algorithms, such as the EMD-wavelet method, the EMD-DWT algorithm, and the EMD-DFA method, the changed thresholding VMD-DWT algorithm showed the highest SNR and cross-correlation with the smallest MAE in four algorithms when the decomposed number and balance parameter were chosen optimally. The quantitative denoising analysis results indicate that the proposed algorithm had the best denoising effect, and among all four methods mentioned, was the most robust. Additionally, the changed thresholding VMD-DWT algorithm effectively removed noise from experimental signals, laying the foundation for further experiments in FBG signal denoising operations. **Case 2:** The Experimental FBG Signal  
In Case 1, the best decomposition number level \(K\), equaling 6, and the balance parameter \(\alpha\), equaling 200, were obtained to process the realistic experimental signals collected from the damage monitoring experiment mentioned above. The EMD-wavelet algorithm, EMD-DFA denoising method, and the EMD-DWT method were selected for comparison to evaluate the denoising ability of the proposed algorithm. The intuitive denoising analysis results of the initial experimental signals can be seen in Figure 7a, and the noise that eliminated the realistic experiment signal is clearly shown in Figure 7b. It can be seen that the VMD-changed thresholding wavelet could remove the noise more completely than the other three algorithms. To evaluate the proposed algorithm and other algorithms, the RMSE was proposed as a quantitative evaluation index based on the literature [13]. The RMSE results of different denoising algorithms can be seen in Figure 8. The figure shows the results of the RMSE indicator being used to quantity the denoising ability of the proposed algorithm. For a quantitative index, the standard deviation \(\sigma\) between the initial realistic experimental signal and the denoising signal was calculated, and is mathematically expressed as in Equation (2). The RMSE results presented at different crack lengths during the damage monitoring experience are shown in Figure 8. The changed thresholding VMD-DWT denoising algorithm has the lowest RMSE compared with the other methods. Thus, the effectiveness of this proposed algorithm in denoising experimental FBG signals was verified. This technique has thus been successfully validated in experimental conditions. These results may be used in crack growth monitoring. In order to denoise the FBG signals obtained from the fatigue crack detection experiment, we proposed a VMD combined with the changed thresholding wavelet denoising method. The thresholding definition in the algorithm considers the energy distribution in each basic mode. Furthermore, in order to deal with the best balance parameters \(\alpha\), which was obtained by comparing the central frequency of the original and mixed signals with well overlapped at different parameter numbers. Different to other definition methods, the central frequency corresponds to the physical parameter central wavelength of the spectrum. Additionally, the denoising performance under different SNRinput mixed signals are used to acquire the best decomposition number \(K\). It is obvious that the proposed algorithm showed the best denoising ability for mixed signals for the highest SNRinput and cross correlation, compared with the traditional signal denoising methods, such as the EMD-wavelet (soft), EMD-DFA, and the EMD-DWT algorithm. Furthermore, in the fatigue crack detection experiment, we proposed a VMD-based thresholding algorithm for the first time. The proposed algorithm is based on the proposed algorithm. The proposed algorithm is based on the proposed algorithm.