## 4 Results and Analysis
### Experimental Results
#### 4.2.2 Results Analysis  
Buried pipelines are affected by external factors, thus the algorithm for extracting defect signals should have a certain anti-noise performance, and it should also have the ability to extract abnormal signal of subtle change. Therefore, we compare the performance of band-pass filter (BPF), EWT, VMD, and VSME for pipeline defect signals. Before extracting the pipeline defect signal in original signal, as shown in Figure 10a, we first use STFT to carry out time-frequency spectrum analysis of the signal. Figure 10b shows that the main energy of acquired signal is concentrated in the low-frequency component, and the frequency spectrum changes abnormally in the middle of detected pipeline. According to the actual pipeline being tested, as shown in Figure 9, the position of through hole defect in pipeline is just detected at about 10 th second of constant speed detection, where pipeline damage is relatively serious. This situation is usually not effective for the BPF method, and its response contains some additional fluctuations, which increase with the increase of noise level. Figure 10d-f show that analysis results of EWT, VMD, and VSME are satisfactory, and it is difficult to identify the subtle differences manually. In the following analysis, we use quantitative indicators to measure the filtering effect. Considering the length of article, only one group data of analysis figures was listed, and other groups of data gave the calculation results. To analyze the accuracy of mentioned algorithms in extracting MAD signal, frequency band of magnetic anomaly signal is obtained from the defect signal of experimental pipeline, and then detection results are analyzed statistically. We use SNR, normalized cross correlation coefficient (NCCC), and root mean square error (RMSE) to evaluate the performance difference between VME detectors and other techniques. The calculation equations of the two indexes are in Equations (40) and (41), and the NCCC is as follows:  
\[NCCC=\sqrt{\frac{\sum_{n=0}^{N-1}\hat{x}(n)x(n)}{\left[\sum_{n=0}^{N-1}\hat{x} ^{2}(n)\sum_{n=0}^{N-1}x^{2}(n)\right]^{1/2}}} \tag{43}\]  
Figure 9: Images of defects in the ferromagnetic pipeline. (**a**) The size of axial crack is 30 mm \(\times\) 1 mm \(\times\) 1 mm; (**b**) The size of axial crack is 1 mm \(\times\) 20 mm \(\times\) 1 mm; (**c**) The size of axial crack is 12 mm \(\times\) 20 mm \(\times\) 1 mm; (**d**) The diameter of through hole is 10 mm; (**e**) The diameter and depth of blind hole are 10 mm and 1 mm; (**f**) The size of 45-degree crack is 1 mm \(\times\) 20 mm \(\times\) 1 mm. where \(\hat{x}(n)\) is filtered output signal, \(x(n)\) is input signal, and \(N\) is signal dimension. The three mentioned indexes were calculated for Figure 11, and the average value is shown in Table 2.  
Figure 11: Performance evaluation for the defect signals at different lift-off distances. (**a**) SNR plot, (**b**) RMSE plot, (**c**) NCCC plot. Figure 10: Analysis results for the Lab. 1 signal. (**a**) Acquired original magnetic field signal; (**b**) Fourier spectrum of original signal by STFT; (**c**) Pipeline defect signal extracted by band-pass filter; (**d**) Pipeline defect signal extracted by EWT; (**e**) Pipeline defect signal extracted by VMD; (**f**) Pipeline defect signal extracted by VSME. To further evaluate the detection effect of pipeline defects at different lift-off distances, the SNR, RMSE, and NCCC of defect signals were computed using these algorithms. Figure 11 plots the evaluation indicators for the six sets of data, which are obtained at different lift-off distances. SNR of extracted defect signal gradually decreases as the lift-off distance increases, as shown in Figure 11a. The performance of VSME is slightly higher than VMD and EWT, but significantly higher than BPF. RMSE of the VSME-processed signal is generally lower than the other three methods, indicating that the proposed algorithm is more reliable, as shown in Figure 11b.