# Coal–Rock Cutting Sound Denoising Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and an improved Fruit Fly Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Basic Theory

#### 2.1. CEEMDAN Denoising Algorithm

#### 2.2. Fruit Fly Optimization Algorithm

- (1)
- Several key parameters of the fruit FOA are determined: population size $P$, maximum iteration $N$, search range $LR$, flight distance $FR$, and the initialization of the population locations.$$\begin{array}{c}{X}_{axis}=LR\times rand(\xb7)\\ {Y}_{axis}=LR\times rand(\xb7)\end{array}$$
- (2)
- Using the sense of smell, the direction and distance of each fruit fly in the population are determined.$$\begin{array}{l}{X}_{i}={X}_{axis}+FR\times rand(\xb7)\\ {Y}_{i}={Y}_{axis}+FR\times rand(\xb7)\end{array}$$
- (3)
- After the location of each fruit fly in the population is determined, the distance $Dis{t}_{i}$ of each fruit fly to the origin is determined, and the reciprocal of $Dis{t}_{i}$ represents the judgment value of taste concentration at this location.$$\begin{array}{l}Dis{t}_{i}=\sqrt{{x}_{i}{}^{2}+{y}_{i}{}^{2}}\\ {S}_{i}=1/Dis{t}_{i}\end{array}$$
- (4)
- $Smel{l}_{i}$ is solved by ${S}_{i}$ and $Function$. The optimal odor concentration for each fruit fly in the population is determined.$$\begin{array}{l}Smel{l}_{i}=Funtion({S}_{i})\\ \left[bestsmell\right.\left.bestindex\right]=\mathrm{max}(smell)\end{array}$$
- (5)
- The location of the best flavor concentration causes the rest of the population to fly toward that point.$$\begin{array}{l}Smellbest=bestsmell\\ \left\{\begin{array}{c}{X}_{axis}={X}_{bestindex}\\ {Y}_{axis}={Y}_{bestindex}\end{array}\right.\end{array}$$
- (6)

## 3. The Proposed Method

#### 3.1. Improvement of FOA

#### 3.2. Flow of the Proposed Denoising Method

## 4. Simulation

#### 4.1. Experimental Data and Evaluation Indicators

_{in}) of 0 dB, 10 dB, 20 dB, and 30 dB was added to the pure sound signal, respectively. The original signal and the noisy signal were shown in Figure 5. It can be seen from the waveform of the original signal that the amplitude of the signal varied widely in the time domain, and there were two obvious ups and downs. The first amplitude rose and fell rapidly, while the second rose and fell relatively slowly. In addition, with the decrease in SNR

_{in}, the waveform of the original signal was gradually submerged. Taking SRN

_{in}= 10 dB as an example, the CEEMDAN decomposition of the noise-containing signal was then performed to obtain each order of IMF components and the residual signal as shown in Figure 6. The decomposed signal can be expressed as X = IMF1 + IMF2 + IMF3 + … + IMF14 + RES, which corresponds to Formula (1). It can be seen that each IMF component had no mode aliasing phenomenon and the noise was mainly distributed in the high-frequency inherent component.

_{out}) and mean square error (MSE) were introduced as evaluation indexes to compare the denoising effects of the five algorithms intuitively. The larger the SNR and the lower the MSE after denoising, the greater the denoising effect will be. The formulas of SNR

_{out}and MSE are as follows:

#### 4.2. Comparative Analysis

_{in}, SNR

_{out}, and MSE, they were shown in Table 1 after signal processing by five denoising algorithms. As can be seen from Table 1, with the decrease in the SNR

_{in}, SNR

_{out}gradually increases and MSE gradually decreases, indicating that the recovery degree of the denoising algorithm to the original signal was gradually enhanced. The improved CEEMDAN denoising algorithm showed that SNR

_{out}and MSE were better than the other four algorithms in the case of four different SNR

_{in}.

_{in}, compared with EMD denoising, CEEMDAN denoising, CEEMDAN-PSO denoising, and CEEMDAN-FOA denoising, the SNR

_{out}of the proposed algorithm improved by 8.92%, 5.05%, 3.11%, and 1.29% on average, respectively, and the maximum increase was 9.60% (SNR

_{in}= 10 dB), 5.42% (SNR

_{in}= 0 dB), 3.67% (SNR

_{in}= 20 dB), and 1.36% (SNR

_{in}= 0 dB). The MSE and SNR

_{out}had similar variation patterns. Compared with the four algorithms, MSE improved by 39.55%, 32.60%, 20.99%, and 12.19% on average, respectively, and the maximum improved by 42.71% (SNR

_{in}= 10 dB), 38.82% (SNR

_{in}= 0 dB), 37% (SNR

_{in}= 0 dB), and 21.68% (SNR

_{in}= 10 dB). This indicates that under different noise input conditions, the proposed algorithm can achieve better denoising effects compared with EMD denoising, CEEMDAN denoising, CEEMDAN-PSO denoising, and CEEMDAN-FOA denoising.

## 5. Industrial Application

## 6. Conclusions and Future Work

_{out}and MSE of the proposed algorithm were improved in different input noise environments. It showed that the algorithm has obvious advantages in denoising under different input noise environments. In the denoising experiment of the shearer coal–rock cutting sound signal, it was found that the noise component of the signal in the time domain diagram and the noise frequency in the frequency spectrum diagram were significantly reduced. In addition, the frequency domain diagram shows a wave peak that determines the working state. The method’s effectiveness in practical applications was proved.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Original sound signal; (

**b**) SNR

_{in}= 0 dB noisy sound signal; (

**c**) SNR

_{in}= 10 dB noisy sound signal; (

**d**) SNR

_{in}= 20 dB noisy sound signal; (

**e**) SNR

_{in}= 30 dB noisy sound signal.

**Figure 7.**Five algorithms for denoising output waveform. (SNR

_{in}= 10 dB). (

**a**) EMD denoised output signal; (

**b**) CEEMDAN denoised output signal; (

**c**) CEEMDAN-PSO denoised output signal; (

**d**) CEEMDAN-FOA denoised output signal; (

**e**) Improved CEEMDAN denoised output signal.

**Figure 8.**(

**a**) Experimental site equipment arrangement; (

**b**) Experimental process of coal-rock cutting.

**Figure 11.**(

**a**) Middle-frequency spectrogram of the original signal (6.2016-8.9578 kHz); (

**b**) Middle-frequency spectrum of the denoised signal (6.2016-8.9578 kHz); (

**c**) High-frequency spectrogram of the original signal (11.7141-17.2266 kHz); (

**d**) High-frequency spectrum of the denoised signal (11.7141-17.2266 kHz).

SNR_{in}/dB | Evaluation Indicators | EMD Denoising | CEEMDAN Denoising | CEEMDAN-PSO Denoising | CEEMDAN-FOA Denoising | Improved CEEMDAN Denoising |
---|---|---|---|---|---|---|

0 | SNR_{out} | −48.0023 | −46.5517 | −45.1962 | −44.6335 | −44.0268 |

MSE | 0.7263 | 0.6965 | 0.6720 | 0.5076 | 0.4261 | |

10 | SNR_{out} | −46.5269 | −44.3750 | −43.2623 | −42.5764 | −42.0625 |

MSE | 0.6674 | 0.5823 | 0.5010 | 0.4881 | 0.3823 | |

20 | SNR_{out} | −45.1762 | −43.2473 | −42.6886 | −41.3492 | −41.1201 |

MSE | 0.5543 | 0.4892 | 0.3942 | 0.3118 | 0.3072 | |

30 | SNR_{out} | −45.0268 | −43.0642 | −42.5108 | −41.1682 | −41.0623 |

MSE | 0.5261 | 0.4631 | 0.3752 | 0.3479 | 0.3326 |

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**MDPI and ACS Style**

Ren, C.; Xu, J.; Xu, J.; Liu, Y.; Sun, N.
Coal–Rock Cutting Sound Denoising Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and an improved Fruit Fly Optimization Algorithm. *Machines* **2022**, *10*, 412.
https://doi.org/10.3390/machines10060412

**AMA Style**

Ren C, Xu J, Xu J, Liu Y, Sun N.
Coal–Rock Cutting Sound Denoising Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and an improved Fruit Fly Optimization Algorithm. *Machines*. 2022; 10(6):412.
https://doi.org/10.3390/machines10060412

**Chicago/Turabian Style**

Ren, Chaofan, Jing Xu, Jie Xu, Yanxin Liu, and Ning Sun.
2022. "Coal–Rock Cutting Sound Denoising Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and an improved Fruit Fly Optimization Algorithm" *Machines* 10, no. 6: 412.
https://doi.org/10.3390/machines10060412