## 4 Simulation and Analysis
### Signal Decomposition and Denoising
The results were shown in Table 1.  
It can be seen from the Figure 7 and Table 1 that adaptive noise cancellation methods based on intelligent searching technology performed better than wavelet and traditional EMD threshold denoising. The selection of wavelet basis and decomposition level might be inappropriate. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Index** & **Wavelet** & **EMD** & **EMD-PSO** & **EMD-FOA** & **EMD-IFOA** \\ \hline MSE & 0.1154 & 0.1062 & 0.0728 & 0.0722 & 0.0686 \\ SNR\({}_{\text{imp}}\) (dB) & \(-5.0651\) & \(-4.7038\) & \(-3.0634\) & \(-3.0298\) & \(-2.8053\) \\ PRD & 100.46\% & 96.36\% & 79.78\% & 79.47\% & 77.44\% \\ \hline \end{tabular}
\end{table} 
Table 1: The denoising performance of the five methods (with SNR = 5 dB). SNR: signal-to-noise ratio; MSE: mean squared error; PRD: percent root mean square difference; SNR\({}_{\text{imp}}\): signal-to-noise ratio improvement; EMD: empirical mode decomposition; PSO: particle swarm optimization algorithm; FOA: fruit fly optimization algorithm; IFOA: improved fruit fly optimization algorithm. Figure 7: The denoised signal of the five noise elimination schemes. PSO: particle swarm optimization algorithm; WT: wavelet transform; FOA: fruit fly optimization algorithm. The recommended threshold for wavelet and EMD denoising shrank the decomposed coefficients excessively, which resulted in an amplitude of denoised signal that was much smaller compared with the original signal. The EMD-FOA exhibited slightly better than the EMD-PSO. Moreover, the EMD-IFOA had obvious preponderance of the MSE, signal-to-noise ratio improvement (SNR\({}_{\text{imr}}\)) and PRD compared with the previous four schemes, which indicated that basic FOA and PSO fell into the local extreme during searching optimal threshold and the population diversity of the EMD-IFOA was enhanced to produce more threshold candidates. The MSE of EMD-IFOA decreased 5.77% and 4.99% compared with EMD-PSO and EMD-FOA. The PRD reduced 2.34% and 2.03% respectively. The SNR\({}_{\text{imr}}\) of the proposed method improved 8.43% and 7.41% compared to the other two intelligent denoising approaches. In order to research the denoising performance at different SNRs, a further comparison was made and the average value of ten simulation results was discussed. The performance of the proposed and other four denoising methods in 0 dB, 5 dB, 10 dB, 15 dB, 20 dB noisy conditions in terms of MSE is shown in Figure 8. It can be seen from the figure that the MSE did not have an obvious difference when the SNR was greater than 10 dB for wavelet and EMD threshold denoising. The other three denoising approaches based on intelligent optimization solutions outperformed both in higher and lower noise component. As expected, the proposed EMD-IFOA showed the best performance in all noisy conditions and decreased 8.24% and 6.73% compared with EMD-PSO and EMD-FOA even in the worst case scenario, which proved the proposed method had stronger global searching ability. Another comparison illustrated the performance in term of SNR\({}_{\text{imr}}\) at different SNR value and was presented in Figure 9. It can be seen from the figure that the SNR\({}_{\text{imr}}\) decreased almost linearly with the SNR. The proposed method obtained the biggest value in all SNRs than other approaches. Moreover, the PRD of the five methods was presented in Figure 10 and exhibited similar changing tendency with MSE. The PRD of the EMD-IFOA deceased 6.77%, 5.17%, 4.18%, and 3.39% respectively, compared with wavelet, EMD, EMD-PSO and EMD-FOA denoising schemes. In summary, the proposed method exhibited obvious superiority in the denoising effect, which revealed its terrific searching ability.