## 4 Results and Analysis
### Experimental Results
#### 4.2.2 Results Analysis
When the lift-off distance increased from 0.5 m to 2 m, the value of RMSE showed a trend of increasing first and then decreasing. Through experimental analysis, when the lift-off distance is 1 m-1.5 m, the excessive RMSE fluctuation is due to the joint effect of the pipeline magnetic field signal and the surrounding interference, which leads to the instability of the magnetic field. As the lift-off height increases, the pipeline magnetic field signal weakens, thus the value of RMSE decreases. Figure 11c shows the NCCC, the performance of BPF is the worst, and VSME is slightly better than the other two methods. The analysis of the mentioned three filtering indicators shows that the VSME algorithm has good performance in the extraction of pipeline defect signals. Calculation time of the same data set is an important index to measure algorithm. To compare the computational complexity of different algorithms, average time required to extract the MAD signal from the 100,000 sample points of experimental data is given in Table 3. According to the table, the calculation time of VSME is less than one-tenth that of VMD and EWT, and it can be compared with the computational complexity of BPF. Results showed that VSME has a good performance by evaluating the index of filtered experimental data. Computational time for processing a segment of 100,000 samples (100 s) of acquired signal (in second). Computing platform adopts DELL-EQVS5M4, the hardware configuration is Intel (R) core (TM) i5-4430 CPU @ 3.0 GHz and the memory is 8.0 GB. The system version is Windows 10 professional, and we use Matlab 2016b as signal processing software. Comparing defect signals at different lift-off distances, we transformed the extracted MAD signal into a normalized gradient energy operator. By analyzing the test data of pipeline in laboratory, it is found that with the increase of the lift-off distance, the signal of the less damaged location becomes weaker. Six defects are easily detected when the lift-off distance is 0.5 m, as shown in Figure 7b. When lift-off distance is 2.0 m, six defects can still be detected. However, the signal with larger damage degree has a certain submergence effect on the position with smaller damage degree. Figure 12d shows that the signals are weak at the axial crack and 45-degree crack positions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{2}{c}{**SNR/dB**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**NCCC**} \\ \cline{2-7}  & **M** & **SD** & **M** & **SD** & **M** & **SD** \\ \hline BPF & 2.23 & 0.20 & 0.15 & 0.10 & 0.81 & 0.46 \\ EWT & 2.61 & 0.12 & 0.18 & 0.06 & 0.89 & 0.26 \\ VMD & 3.08 & 0.89 & 0.11 & 0.68 & 0.94 & 0.16 \\ VSME & 3.26 & 0.05 & 0.13 & 0.02 & 0.95 & 0.04 \\ \hline \hline \end{tabular} \(M\) is the mean and \(SD\) is the standard deviation of the filtered signal.  
\end{table} 
Table 2: Mean and standard deviation (SD) of the three indexes used for comparing different algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **BPF** & **EMD** & **VMD** & **VSME** \\ \hline Mean/s & 5.69 & 146.82 & 108.36 & 10.63 \\ SD & 0.04 & 16.78 & 8.29 & 1.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and standard deviation (SD) of calculation time. In this section, we concentrate on the performance of VSME in extracting MAD signals of pipeline defects. As mentioned, variational theory can provide effective solutions for pipeline defect signal extraction. Herein, we used and VSME to extract pipeline defect signals, and compared with BPF, EWT, and VMD. To ensure the performance of MAD signal extraction, we randomly selected six sets of experimental data, and extracted the MAD of defect signals by four algorithms on the same computing platform for several times. Then, the acquired MAD signals were evaluated by calculating the cross correlation coefficients with the reference pipeline defect signals. The results showed that VSME has certain advantages.