Cable Defect Location Based on Orthogonal Matching Pursuit and Pseudo Wigner-Ville Distribution

The time-frequency domain reflection method (TFDR) uses the time-frequency joint method to locate the defects, and the traditional time-frequency analysis method is used to obtain the location signal. There is cross-term interference in the time spectrum, resulting in interference peaks in the final positioning curve, which can not accurately locate the local defects of the cable. The orthogonal matching pursuit (OMP) algorithm is proposed to reconstruct the acquired superimposed signal, and the pseudo-Wegner distribution (PWVD) algorithm is used to obtain the time-frequency distribution of the reconstructed sub-signal, so as to obtain the optimal feature distribution in the time-frequency domain of the signal, so as to achieve the feature extraction of the measured cable positioning signal and the suppression of cross-term interference in the signal time-frequency spectrum. Firstly, the Gaussian envelope linear frequency modulation signal is used as the incident signal, and the reflected superimposed signal is obtained according to the transfer function of the single defect cable model. Because the traditional time-frequency domain reflection method uses Wigner distribution (WVD) to calculate the time-frequency spectrum of superimposed signals, the Wigner distribution is no longer an ideal banded impulse function, and the cross terms are more complex. To solve this problem, the OMP algorithm is used to decompose the original superimposed signal, and the PWVD time-frequency distribution is obtained for the decomposed sub-signals; Then the time-frequency spectrum of the obtained sub-signal is linearly superimposed to obtain a more accurate time-frequency expression of the positioning signal, so as to eliminate the cross-term interference; Finally, time-frequency cross-correlation function (TFCC) is used to accurately locate the defect location. The power cable defect model with a total length of 800 m and defects at 300 m is simulated. The OMP-WVD, OMP-PWVD and OMP-SPWVD algorithms are used to process the data respectively. The positioning results are shown in Figure 9. Comparing the positioning results of the three methods, it is shown that the three original time-frequency analysis methods can effectively eliminate the influence of the cross term after the OMP algorithm is processed, but compared with the two time-frequency analysis methods of WVD and SPWVD, PWVD has higher positioning accuracy while maintaining better resolution. Then, under the condition of white noise with signal-to-noise ratio of 10, 5 and 0 dB respectively, the OMP-PWVD algorithm is used for processing, and the positioning results are shown in Figure 12. The results show that under different SNR conditions, the OMP algorithm realizes the atomic reconstruction of the signal, eliminates the interference of some noise signals on the original signal, and makes the OMP-PWVD algorithm improve the defect location effect while suppressing the cross terms, and has strong anti-interference ability. Finally, an experimental platform for defect location of 10 kV XLPE cable with a length of 40 m and two intermediate joints, 105 m with corrosion defects of copper shielding layer and 500 m with intermediate joints was built in the laboratory to verify the proposed algorithm. The experimental results show that the improved OMP-PWVD algorithm can effectively suppress cross-term interference, and has strong anti-interference ability. It can effectively locate single defect and multiple defects, and improves the positioning accuracy of time-frequency domain reflection method. © 2023 Chinese Machine Press. All rights reserved.