Author Affiliations
1School of Electronic Information Engineering, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China2College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130012, China3College of Physics & Information Engineering, Fuzhou University, Fuzhou 350108, Chinashow less
Fig. 1. Experimental device diagram of distributed optical vibration sensing system
Fig. 2. Vibration simulation signal and the composition of the time-domain waveform
Fig. 3. EMD decomposition results of simulation signal
Fig. 4. CEEMD decomposition results of simulation signal
Fig. 5. MEEMD decomposition results of simulation signal
Fig. 6. Reconstruction error of three decomposition methods
Fig. 7. Phase-time change curves of vibration signals of different frequencies demodulated by the system
Fig. 8. Hilbert spectrum after three kinds of empirical mode decomposition and Hilbert transforn of vibration signal whose frequency is 100 Hz
Fig. 9. Hilbert spectrum after three kinds of empirical mode decomposition and Hilbert transforn of vibration signal whose frequency is 200 Hz
Fig. 10. Hilbert spectrum after three kinds of empirical mode decomposition and Hilbert transforn of vibration signal whose frequency is 50 Hz,200 Hz,350 Hz
Fig. 11. Hilbert spectrum after three kinds of empirical mode decomposition and Hilbert transforn of vibration signal whose frequency is 150 Hz,250 Hz,450 Hz
Fig. 12. Marginal spectra of three decomposition methods on different frequencies
| ${x_1}\left( t \right)$![]() ![]() | ${x_2}\left( t \right)$![]() ![]() | ${x_3}\left( t \right)$![]() ![]() | ${x_4}\left( t \right)$![]() ![]() | ${x_5}\left( t \right)$![]() ![]() | ${x_6}\left( t \right)$![]() ![]() | ${x_7}\left( t \right)$![]() ![]() | ${x_8}\left( t \right)$![]() ![]() | ${H_p}$ | 0.4610 | 0.1753 | 0.2002 | 0.1427 | 0.0060 | 0.2273 | 0.6163 | 0.9689 |
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Table 1. Permutation entropy of eight signals
Method | Added noise’ amplitude:
${a_i}$![]() ![]() | Added noise’ number:
${N_e}$![]() ![]() | Computing time/s | Completeness | Index of orthogonality | IMF’s number | EMD | None | None | 0.1819 | 0.2664 | 0.4171 | 7 | CEEMD | 0.3 | 50 | 6.5873 | 0.1897 | 0.2053 | 7 | MEEMD | 0.3 | 50 | 1.2732 | 0.0152 | 0.0027 | 4 |
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Table 2. Each method index
Test frequency/Hz | 10 | 50 | 100 | 150 | 200 | 300 | 400 | 500 | Average accuracy | The average time/s | Sample number/Group | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | EMD’s accuracy | 78% | 80% | 84% | 86% | 88% | 86% | 83% | 80% | 83.1% | 0.1635 | CEEMD’s accuracy | 90% | 86% | 94% | 94% | 92% | 96% | 91% | 90% | 91.6% | 3.2534 | MEEMD’s accuracy | 98% | 98% | 100% | 100% | 100% | 100% | 100% | 98% | 99.2% | 1.0387 |
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Table 3. Frequency extraction accuracy test
Feature extraction method | Average accuracy | Average number of eigenvectors | Average time/s | EMD-HHT | 82.5% | 9.2 | 3.8634 | CEEMD-HHT | 91.1% | 7.1 | 7.1857 | MEEMD-HHT | 98.1% | 4.2 | 3.8259 |
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Table 4. Three methods of experimental results