Harmonic Detection Method Based on Parameter Optimization VMD-IWT Combined Noise Reduction
Abstract
:1. Introduction
2. VMD Parameter Optimization and Wavelet Noise Reduction
2.1. Variational Mode Decomposition
2.2. Optimize VMD Based on RIME
2.2.1. Initial Population
2.2.2. Soft Rime Search
2.2.3. Hard Rime Piercing
2.2.4. Greedy Choice
2.3. IMF Component Screening
2.4. Improved Wavelet Thresholding Denoising
3. Harmonic Detection Process Based on RIME-VMD-IWT
- Step 1:
- Read the harmonic signal data and preprocess it with noise.
- Step 2:
- RIME was employed in the search for the optimal parameters K and α in VMD, utilizing sample entropy as the fitness function during the iterative process. Through RIME, the individual with the minimum sample entropy was identified, and the corresponding parameter combination [K,α] of this individual was designated as the optimal parameter set for VMD.
- Step 3:
- After the noisy signal is decomposed by VMD, K modal components are obtained. Based on the correlation coefficient of each IMF, the components are categorized into effective IMFs and ineffective IMFs.
- Step 4:
- The invalid IMFs are eliminated, and the effective IMFs undergo de-noising treatment using IWT, resulting in the reconstruction of the signal and obtaining the final de-noised harmonic signal.
- Step 5:
- Utilize the Hilbert transform to extract amplitude, frequency, and other information for detecting harmonic signal parameters.
4. Simulation Signal Verification
4.1. Noise Reduction Effect Analysis
4.2. Detection Accuracy Analysis
5. Test Signal Verification
5.1. Noise Reduction Effect Analysis
5.2. Detection Accuracy Analysis
6. Conclusions
- By utilizing the RIME optimization algorithm to optimize the VMD parameters (K,α), the issue of manually setting the K and α values in the traditional VMD algorithm is effectively addressed. This approach achieves optimal signal decomposition, reduces the VMD decomposition error, demonstrates stronger adaptability, and has a faster optimization speed compared to PSO and WOA algorithms.
- By introducing the Pearson correlation coefficient and improving wavelet threshold denoising, the effective signal and noise signal can be effectively separated from the mixed signal, while retaining the original characteristics of the signal. This improves the overall noise robustness of the algorithm, making it suitable for harmonic signal denoising.
- In comparison with EMD, WT, and VMD methods, the proposed approach exhibits a remarkable noise reduction effect and demonstrates accurate detection of harmonic amplitude and frequency even in high-noise environments. Its detection performance surpasses that of traditional methods, showcasing significant advantages in accuracy.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Correlation Coefficient | Degree of Correlation |
---|---|
0.8 < |ρ| ≤ 1.0 | extremely relevant |
0.6 < |ρ| ≤ 0.8 | highly relevant |
0.4 < |ρ| ≤ 0.6 | moderately relevant |
0.2 < |ρ| ≤ 0.4 | weakly relevant |
0.0 < |ρ| ≤ 0.2 | almost irrelevant |
Denoising Method | SNR/dB | RMSE |
---|---|---|
WT (Hard) | 16.36 | 0.3364 |
WT (Soft) | 17.53 | 0.3182 |
EMD-WT (Soft) | 21.94 | 0.2904 |
VMD-WT (Soft) | 22.59 | 0.2512 |
RIME-VMD-IWT | 27.64 | 0.2137 |
Method | Frequency True Value/Hz | Frequency Detection Value/Hz | Frequency Error | Amplitude True Value/A | Amplitude Detection Value/A | Amplitude Error |
---|---|---|---|---|---|---|
RIME-VMD-IWT | 50 | 50.0026 | 5.1 × 10−4 | 5 | 4.9984 | 3.2 × 10−4 |
150 | 150.4950 | 3.3 × 10−3 | 10 | 9.9975 | 2.5 × 10−4 | |
180 | 180.0504 | 2.8 × 10−4 | 15 | 14.9972 | 1.9 × 10−4 | |
284 | 284.0224 | 7.9 × 10−5 | 30 | 29.9760 | 1.1 × 10−3 | |
EMD | 50 | 57.1034 | 14.2 × 10−2 | 5 | 4.0812 | 18.4 × 10−2 |
150 | 166.5371 | 11.0 × 10−2 | 10 | 8.2933 | 17.1 × 10−2 | |
180 | 198.5419 | 10.3 × 10−2 | 15 | 17.4750 | 16.5 × 10−2 | |
284 | 239.6962 | 15.6 × 10−2 | 30 | 35.0717 | 16.9 × 10−2 | |
CEEMD | 50 | 53.1033 | 6.2 × 10−2 | 5 | 5.2352 | 4.7 × 10−2 |
150 | 136.9581 | 8.7 × 10−2 | 10 | 9.3846 | 6.2 × 10−2 | |
180 | 165.7834 | 7.9 × 10−2 | 15 | 14.3250 | 4.5 × 10−2 | |
284 | 260.1447 | 8.4 × 10−2 | 30 | 31.6207 | 5.4 × 10−2 | |
VMD | 50 | 48.3981 | 3.2 × 10−2 | 5 | 5.3651 | 7.3 × 10−2 |
150 | 156.1574 | 4.1 × 10−2 | 10 | 10.6204 | 6.2 × 10−2 | |
180 | 173.1641 | 3.8 × 10−2 | 15 | 15.8762 | 5.8 × 10−2 | |
284 | 295.9287 | 4.2 × 10−2 | 30 | 28.4790 | 5.1 × 10−2 |
Denoising Method | SNR/dB | RMSE |
---|---|---|
WT (Hard) | 36.14 | 0.0971 |
WT (Soft) | 37.02 | 0.0962 |
EMD-WT (Soft) | 41.47 | 0.0918 |
VMD-WT (Soft) | 43.71 | 0.0875 |
RIME-VMD-IWT | 49.39 | 0.0794 |
Method | Frequency True Value/Hz | Frequency Detection Value/Hz | Frequency Error | Amplitude True Value/A | Amplitude Detection Value/A | Amplitude Error |
---|---|---|---|---|---|---|
RIME-VMD-IWT | 50 | 50.1208 | 2.4 × 10−3 | 100 | 99.9542 | 4.6 × 10−4 |
125 | 125.4715 | 3.8 × 10−3 | 74.813 | 75.2469 | 5.8 × 10−3 | |
25 | 25.0342 | 1.4 × 10−3 | 64.933 | 65.7142 | 1.2 × 10−2 | |
EMD | 50 | 45.7328 | 8.6 × 10−2 | 100 | 89.7300 | 1.0 × 10−1 |
125 | 114.8753 | 8.1 × 10−2 | 74.813 | 66.2843 | 1.1 × 10−1 | |
25 | 26.9254 | 7.7 × 10−2 | 64.933 | 71.8808 | 1.1 × 10−1 | |
CEEMD | 50 | 52.2517 | 4.5 × 10−2 | 100 | 91.1271 | 8.9 × 10−2 |
125 | 117.1252 | 6.3 × 10−2 | 74.813 | 81.6958 | 9.2 × 10−2 | |
25 | 26.8513 | 7.4 × 10−2 | 64.933 | 69.8679 | 7.6 × 10−2 | |
VMD | 50 | 51.9520 | 3.9 × 10−2 | 100 | 94.3417 | 5.7 × 10−2 |
125 | 130.7500 | 4.6 × 10−2 | 74.813 | 79.4506 | 6.2 × 10−2 | |
25 | 26.0542 | 4.2 × 10−2 | 64.933 | 68.2438 | 5.1 × 10−2 |
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Xu, J.; Ma, H.; He, W. Harmonic Detection Method Based on Parameter Optimization VMD-IWT Combined Noise Reduction. Appl. Sci. 2024, 14, 5076. https://doi.org/10.3390/app14125076
Xu J, Ma H, He W. Harmonic Detection Method Based on Parameter Optimization VMD-IWT Combined Noise Reduction. Applied Sciences. 2024; 14(12):5076. https://doi.org/10.3390/app14125076
Chicago/Turabian StyleXu, Jiechuan, Hongyan Ma, and Wei He. 2024. "Harmonic Detection Method Based on Parameter Optimization VMD-IWT Combined Noise Reduction" Applied Sciences 14, no. 12: 5076. https://doi.org/10.3390/app14125076