## 3 The Proposed Method
### Flow of the Proposed Denoising Method  
In order to eliminate noise component from the acoustic signal adaptively, an EMD-based denoising solution optimized by an improved FOA is proposed in this paper. As some key denoising parameters in Equations (5) and (6), such as \(C\), \(\alpha\) and \(\beta\), are estimated according to statistic and experiment analysis, the determination of denoising threshold is always tough work and consumes much time. Moreover, an appropriate threshold gives significant efficiency of the EMD-based noise elimination process. In order to solve the above problems, the denoising thresholds in Equation (7) or (8) are determined automatically through the improved FOA instead of Equations (5) and (6). The flow of the proposed EMD-IFOA can be summarized as follows:  
Step 4.1: Parameter initialization. The parameters in EMD-IFOA such as the lower-order coefficient \(M_{1}\) and high-order coefficient \(M_{2}\) are given firstly, so the number of fruit fly group is \(M_{2}-M_{1}+1\). The maximal iteration number is \(N\), the number of fruit flies in each swarm is \(P\), the terminal fitness \(\eta\), the fruit fly location range \(LR\), the random fly distance range is \(FR\), the variation coefficient \(C_{v}\) and disturbance coefficient \(C_{d}\). The initial locations of the fruit fly groups are obtained by Equation (10).  
Step 4.2: Signal decomposition. The original noise-added signal \(x(t)\) is decomposed by EMD, which can be presented as \(x(t)=imf_{1}+imf_{2}+\ldots+imf_{k}+res\).  
Step 4.3: Threshold optimization. The location and smell concentration judgement of each fly individual can be obtained by the improved FOA subsequently. It should be pointed out that any \(M_{2}-M_{1}+1\) smell concentration from different fruit fly swarm can be treated as a potential optimal combination of threshold set. For example, \(S_{ij}\) donates \(i\)-th smell concentration judgement in \(j\)-th swarm, where \(i=1\), \(2\), \(3\), \(\ldots\), \(P\), \(j=1\), \(2\), \(3\), \(\ldots\), \(M_{2}-M_{1}+1\). Then, the useful and noise signal are separated by hard threshold function in Equation (7) or soft function in Equation (8). The estimated signal is reconstructed as the final series according to Equation (9). In order to evaluate the denoising performance of different thresholds, a fitness function or smell concentration function in IFOA based on the independent measurement principle is established as follows:  
\[f=\frac{1}{1+g} \tag{17}\]  
\[g=\frac{\left[r_{22}\times hr_{21}\right]^{2}}{{r_{11}}^{2}} \tag{18}\]  
where \(r_{11}\) and \(r_{22}\) are second-order correlation coefficient of useful signal and noise signal, respectively, and \(hr_{21}\) is high-order correlation coefficient between the two series. An increasing value of \(r_{11}\) implies that the useful component is more than the component of noise. If \(r_{22}\) and \(hr_{21}\) are decreasing, then it means that the two signals become more independent to each other. Thus, the original signal and noise are separated gradually. In general, the noise elimination process performances are better with larger \(r_{11}\) and smaller \(r_{22}\) and \(hr_{21}\).  
Step 4.4: Iteration termination. If the iteration number reaches \(N\) or the fitness reaches the preset value \(\eta\), the iteration process is terminated; otherwise, the optimization is continued. The flow of the proposed denoising method based on EMD-IFOA can be presented as Figure 3.