A Novel Denoising Method for an Acoustic-Based System through Empirical Mode Decomposition and an Improved Fruit Fly Optimization Algorithm
Abstract
:1. Introduction
2. Basic Theory
2.1. Empirical Mode Decomposition-Based Denoising
2.2. Fruit Fly Optimization Algorithm
3. The Proposed Method
3.1. Improvement on FOA
3.2. Flow of the Proposed Denoising Method
4. Simulation and Analysis
4.1. Signal Preprocessing
4.2. Signal Decomposition and Denoising
- (1)
- Wavelet threshold denoising. The noisy signal was first decomposed by db2 wavelet at five levels [32], and the decomposition result was presented in Figure 5. Then, the soft threshold function was adopted to shrink the wavelet coefficients. Inverse wavelet transform was conducted consequently to reconstruct the signal.
- (2)
- EMD denoising. The noisy signal was first decomposed by EMD adaptively, which could be shown in Figure 6. The noisy signal could be decomposed as x = imf1 + imf2 + imf3 + … + imf12 + res. Then, the shrinkage threshold of each IMF was determined according to Equations (5) and (6). Soft threshold function was applied and the denoised signal was reconstructed as Equation (9). Some parameters in Equations (5), (6) and (9) were set as follows [10]: C = 0.7, α = 0.719, β = 2.01, M1 = 2 and M2 = 4.
- (3)
- EMD-PSO denoising. The noisy signal was first decomposed by EMD adaptively. Then, the threshold of each IMF was determined according to PSO intelligently. Soft threshold function was applied and the denoised signal was reconstructed as Equation (9). Some parameters during the EMD-PSO were set as recommended in [23]: M1 = 2, M2 = 4, the dimensionality of each particle was M2 − M1 + 1 = 3, the learning factor c1 and c2 were set as 2, the iteration number was 100 and the particle number of the population was 10.
- (4)
- EMD-FOA denoising. The noisy signal was first decomposed by EMD adaptively. Then, the threshold of each IMF was determined according to FOA automatically. Soft threshold function was applied and the denoised signal was reconstructed as Equation (9). Some parameters during the EMD-FOA were set as follows: M1 = 2, M2 = 4, the number of fruit fly population was M2 − M1 + 1 = 3, the iteration number was 100, the fly number in each population was 10, the fruit fly location range and the random fly distance range was 1.
- (5)
- EMD-IFOA denoising. The noisy signal was first decomposed by EMD adaptively. Then, the threshold of each IMF was determined according to IFOA automatically. Soft threshold function was applied and the denoised signal was reconstructed as Equation (9). Some parameters during the EMD-IFOA were set as follows: M1 = 2, M2 = 4, the number of fruit fly population was M2 − M1 + 1 = 3, the iteration number was 100, the fly number in each population was 10, the fruit fly location range and the random fly distance range was 1, the variation coefficient Cv = 0.2 and disturbance coefficient Cd = 5. The denoised signal of the five noise elimination schemes are presented in Figure 7.
4.3. Application
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Index | Wavelet | EMD | EMD-PSO | EMD-FOA | EMD-IFOA |
---|---|---|---|---|---|
MSE | 0.1154 | 0.1062 | 0.0728 | 0.0722 | 0.0686 |
SNRimp (dB) | −5.0651 | −4.7038 | −3.0634 | −3.0298 | −2.8053 |
PRD | 100.46% | 96.36% | 79.78% | 79.47% | 77.44% |
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Xu, J.; Wang, Z.; Tan, C.; Si, L.; Liu, X. A Novel Denoising Method for an Acoustic-Based System through Empirical Mode Decomposition and an Improved Fruit Fly Optimization Algorithm. Appl. Sci. 2017, 7, 215. https://doi.org/10.3390/app7030215
Xu J, Wang Z, Tan C, Si L, Liu X. A Novel Denoising Method for an Acoustic-Based System through Empirical Mode Decomposition and an Improved Fruit Fly Optimization Algorithm. Applied Sciences. 2017; 7(3):215. https://doi.org/10.3390/app7030215
Chicago/Turabian StyleXu, Jing, Zhongbin Wang, Chao Tan, Lei Si, and Xinhua Liu. 2017. "A Novel Denoising Method for an Acoustic-Based System through Empirical Mode Decomposition and an Improved Fruit Fly Optimization Algorithm" Applied Sciences 7, no. 3: 215. https://doi.org/10.3390/app7030215
APA StyleXu, J., Wang, Z., Tan, C., Si, L., & Liu, X. (2017). A Novel Denoising Method for an Acoustic-Based System through Empirical Mode Decomposition and an Improved Fruit Fly Optimization Algorithm. Applied Sciences, 7(3), 215. https://doi.org/10.3390/app7030215