Blind Source Separation of Single Channel Ship Radiated Noise Based on VMD-FastICA
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摘要: 针对在仅有单通道信号可用的极端条件下, 难以从混合信号中分离出不同目标舰船辐射噪声信号问题, 开展单通道盲源分离算法研究。提出一种基于变分模态分解(VMD)改进快速独立成分分析(FastICA)的舰船辐射噪声盲源分离算法。在单通道条件下, 首先通过VMD将单通道信号分解为频率成分相对独立的多阶模态, 初步实现独立频率成分的分离; 而后将各阶模态组合为虚拟多通道信号, 解决FastICA无法处理单通道信号的问题; 最后通过FastICA对虚拟多通道信号进行处理, 进一步分离独立信号成分, 从而实现单通道舰船辐射噪声盲源分离。仿真与试验数据分析结果显示, VMD-FastICA算法分离的目标信号与原目标信号的相似度, 较奇异谱分析-独立成分分析(SSA-ICA)算法均有提升, 表明其在单通道舰船辐射噪声信号盲源分离中效果良好, 可能够实现单通道条件下不同目标舰船辐射噪声信号的有效分离。Abstract: Addressing the challenge of separating different target ship radiated noise signal from mixed signal under extreme conditions where only single-channel signal is available, blind source separation algorithm under single-channel condition is researched. A ship radiated noise blind source separation algorithm based on the improved Fast Independent Component Analysis (Fast-ICA) using Variational Mode Decomposition (VMD) is proposed. Under single-channel condition, the single-channel signal is first decomposed into multiple relatively independent frequency components through VMD, initially achieving the separation of independent frequency0 components. Then, these modes are combined into virtual multi-channel signals to solve the issue that Fast-ICA cannot process single-channel signal. Finally, the combined virtual multi-channel signals are processed using Fast-ICA to further separate independent signal components, thereby achieving single-channel ship radiated noise blind source separation. Simulation and experimental data analysis results show that, both under the influence of environmental noise and without environmental noise, the similarity between the target signals separated by the proposed VMD-FastICA blind source separation algorithm and the original target signals is improved compared to the SSA-ICA algorithm. This demonstrates that VMD-FastICA blind source separation algorithm has good performance for single-channel ship radiated noise signal and can achieve blind source separation of different target ship radiated noise signals under single-channel condition.
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图 2 混合信号及目标一、二信号时域波形
Figure 2. Time domain waveform of mixed signal, target 1 signal and target 2 signal
图 3 SSA-ICA分离后目标一、二信号时域波形
Figure 3. Time domain waveform of target 1 signal and target 2 signal after SSA-ICA
图 4 VMD-FastICA分离后目标一、二信号时域波形
Figure 4. Time domain waveform of target 1 signal and target 2 signal after VMD-FastICA
图 5 混合信号及目标一、二信号频谱
Figure 5. Mixed signal, target 1 signal, and target 2 signal spectrum
图 6 SSA-ICA分离后目标一、目标二信号频谱
Figure 6. Target 1 signal and target 2 signal spectrum after SSA-ICA
图 7 VMD-FastICA分离后目标一、二信号频谱
Figure 7. Target 1 signal and target 2 signal spectrum after VMD-FastICA
图 10 混合信号及目标一、二信号时域波形
Figure 10. Time domain waveform of mixed signal, target 1 signal, and target 2 signal
图 11 SSA-ICA分离后目标一、二信号时域波形
Figure 11. Time domain waveform of target 1 signal and target 2 signal after SSA-ICA
图 12 VMD-FastICA分离后目标一、二信号时域波形
Figure 12. Time domain waveform of target 1 signal and target 2 signal after VMD-FastICA
图 13 混合信号及目标一、二信号频谱
Figure 13. Mixed signal, target 1 signal, and target 2 signal spectrum
图 14 SSA-ICA分离后目标一、二信号频谱
Figure 14. Target 1 signal and target 2 signal spectrum after SSA-ICA
图 15 VMD-FastICA分离后目标一、二信号频谱
Figure 15. Target 1 signal and target 2 signal spectrum after VMD-FastICA
图 16 混合信号及目标一、二信号时域波形
Figure 16. Time domain waveform of mixed signal, target 1 signal, and target 2 signal
图 17 SSA-ICA分离后目标一、二信号时域波形
Figure 17. Time domain waveform of target 1 signal and target 2 signal after SSA-ICA
图 18 VMD-FastICA分离后目标一、二信号时域波形
Figure 18. Time domain waveform of target 1 signal and target 2 signal after VMD-FastICA
图 19 混合信号及目标一、二信号频谱
Figure 19. Mixed signal, target 1 signal, and target 2 signal spectrum
图 20 SSA-ICA分离后目标一、二信号频谱
Figure 20. Target 1 signal and target 2 signal spectrum after SSA-ICA
图 21 VMD-FastICA分离后目标一、二信号频谱
Figure 21. Target 1 signal and target 2 signal spectrum after VMD-FastICA
表 1 混合信号、分离后目标信号与原目标信号相关系数绝对值
Table 1. Absolute correlation coefficients between mixed signal, separated target signal and original target signal
处理方法 目标一信号 目标二信号 混合信号 0.7852 0.7263 SSA-ICA 0.8416 0.3881 VMD-FastICA 0.9607 0.9488 
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表 2 混合信号、分离后目标信号与原目标信号相关系数绝对值
Table 2. Absolute correlation coefficients between mixed signal, separated target signal and original target signal
处理方法 目标一信号 目标二信号 混合信号 0.7110 0.7110 SSA-ICA 0.7806 0.5706 VMD-FastICA 0.8860 0.8863
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表 3 混合信号、分离后信号与原信号相关系数绝对值
Table 3. Absolute correlation coefficients between mixed signal, separated signal and original signal
处理方法 目标一信号 目标二信号 混合信号 0.7160 0.7160 SSA-ICA 0.7533 0.4590 VMD-FastICA 0.7593 0.7538
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表 4 加入噪声后混合信号及SSA-ICA/VMD-FastICA分离信号与原目标的相关系数绝对值
Table 4. Absolute correlation coefficients of original target signals with noise-added mixed signals and SSA-ICA/VMD-FastICA separated signals
处理方法 目标一信号 目标二信号 混合信号 0.5871 0.5776 SSA-ICA 0.6385 0.5362 VMD-FastICA 0.7906 0.6760
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表 5 加入噪声后混合信号、分离后信号与原信号相关系数绝对值
Table 5. Absolute correlation coefficients of original signals with noise-added mixed signals and separated signals
处理方法 目标一信号 目标二信号 混合信号 0.6047 0.5488 SSA-ICA 0.4238 0.5892 VMD-FastICA 0.6654 0.6249
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表 6 VMD-FastICA分离后信号与原信号相关系数绝对值(试验一)
Table 6. Absolute correlation coefficients between VMD-FastICA separated signal and original signal (Experiment 1)
(a)α= 1450 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.8805 0.8896 0.8898 0.8858 0.8659 目标二 0.8854 0.8850 0.8863 0.8867 0.7982 (b)α= 1500 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.8800 0.8896 0.8900 0.8860 0.8658 目标二 0.8849 0.8846 0.8859 0.8863 0.7978 (c)α= 1550 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.8805 0.8896 0.8898 0.8858 0.8659 目标二 0.8854 0.8850 0.8863 0.8867 0.7982
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表 7 VMD-FastICA分离后信号与原信号相关系数绝对值(试验二)
Table 7. Absolute correlation coefficients between VMD-FastICA separated signal and original signal (Experiment 2)
(a)α= 1450 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6519 0.7516 0.7599 0.7599 0.7451 目标二 0.7679 0.7540 0.7533 0.7540 0.7269 (b)α= 1500 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6510 0.7508 0.7592 0.7593 0.7442 目标二 0.7671 0.7537 0.7530 0.7538 0.7266 (c)α= 1550 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6503 0.7499 0.7586 0.7588 0.7432 目标二 0.7663 0.7534 0.7528 0.7536 0.7264
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表 8 加入环境噪声, VMD-FastICA分离后信号与原信号相关系数绝对值(试验一)
Table 8. Added environmental noise, absolute correlation coefficients between VMD-FastICA separated signal and original signal (Experiment 1)
(a)α= 1450 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.7760 0.7756 0.7994 0.7903 0.7900 目标二 0.6722 0.6751 0.6763 0.6754 0.6553 (b)α= 1500 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.7753 0.7751 0.7904 0.7906 0.7904 目标二 0.6721 0.6750 0.6557 0.6760 0.6557 (c)α= 1550 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.7747 0.7745 0.8002 0.7909 0.7908 目标二 0.6720 0.6749 0.6773 0.6765 0.6561
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表 9 加入环境噪声, VMD-FastICA分离后信号与原信号相关系数绝对值(试验二)
Table 9. Added environmental noise, absolute correlation coefficients between VMD-FastICA separated signal and original signal (Experiment 2)
(a)α= 1450 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6078 0.5956 0.6234 0.6656 0.6289 目标二 0.5238 0.4773 0.6657 0.6252 0.6444 (b)α= 1500 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6069 0.5920 0.6230 0.6654 0.6288 目标二 0.5234 0.4701 0.6655 0.6249 0.6441 (c)α= 1550 信号类别 K=5 K=6 K=7 K=8 K=9 目标一 0.6060 0.5881 0.6228 0.6652 0.6286 目标二 0.5230 0.4626 0.6653 0.6246 0.6438
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