Fig. 1. Structural diagram of the Φ-OTDR system

Fig. 2. Flow chart of the I/Q orthogonal demodulation algorithm

Fig. 3. Flow chart of the CEEMD algorithm

Fig. 4. Flow chart of the calculated multiscale permutation entropy

Fig. 5. Flow chart of the MVO algorithm

Fig. 6. Flowchart of the MVO-CEEMD algorithm for improved wavelet thresholds

Fig. 7. Simulated positioning experiment diagram, superimposed with white noise with a standard deviation of 0.2. (a) Vibration positioning curve; (b) Vibration positioning curve after noise removal

Fig. 8. The experimental platform

Fig. 9. (a) Acquisition electrical signal; (b) Amplitude curve; (c) Amplitude curve near the vibration position; (d) Vibration positioning curve

Fig. 10. Number of optimized iterations of the MVO algorithm. (a) Iterations 0-500 algorithm optimization diagram; (b) 0-50 iterations local magnification diagram

Fig. 11. CEEMD decomposes the IMF component signals

Fig. 12. Location curve of the 600 Hz vibration signal after denoising

Fig. 13. Denoising result of positioning when the vibration frequency is 10 Hz. (a) EMD-PCC; (b)VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm

Fig. 14. Denoising result of positioning when the vibration frequency is 200 Hz. (a) EMD-PCC; (b)VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm

Fig. 15. Denoising result of positioning when the vibration frequency is 1.2 kHz. (a) EMD-PCC; (b) VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm

Fig. 16. Location map of the denoised vibration signal with a vibration frequency of 200 Hz. (a) EMD-PCC; (b) VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm

Fig. 17. Phase frequency domain of vibration signal after denoising with vibration frequency of 200 Hz. (a) EMD-PCC; (b) VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm

Fig. 18. Phase time domain of vibration signal after denoising with vibration frequency of 200 Hz. (a) EMD-PCC; (b) VMD-NWT; (c) CEEMDAN; (d) Proposed algorithm