## 4 Experimental Verification  
During gas pipeline defect detection, noise and human interference inevitably exist, which distorts the detection signal and affects the detection. Long-distance pipelines typically pass through complex geological environments. In this study, the magnetic flux leakage detection method was used to detect the pipeline defect signal, and ICEEMDAN-LMS was used to analyze the pipeline defect signal. The reference signals were taken from defect signals measured under normal pipeline working conditions, and the normal signals were filtered to remove high-frequency components. The speed of the detection device of the Shanjing DN250 pipeline was 0.1 m/s, and signals of 14,016 samples in length were obtained in the experiment. The signals were imported into MATLAB for noise removal using ICEEMDAN-LMS. The on-site detection and noise removal results are presented in Figure 6.  
Figure 5: Simulation signal denoising results. Figure 6: Noise reduction diagram of the field detection. ICEEMDAN was used to decompose the signal characteristics of the pipeline signals and compare them with three other EMD-based methods: EEMD, CEEMDAN, and ICEEMDAN [25; 33; 34]. Figure 7 shows the signal denoising decomposition results of the different methods. As Figure 7a-d show, all four noise reduction methods are suitable for reducing pipeline defect signal noise. Although different methods can eliminate some of the noise, no method performs sufficiently well. Figure 7a shows the decomposition results of the EMD. The original signal has not been completely decomposed, and noise remains in the signal after noise reduction. Moreover, when the signal is highly distorted, the final results are poor. As shown in Figure 7b, the EEMD method is superior to the EMD method in terms of noise reduction; however, the processing of signal distortion remains unsatisfactory, and the mode-aliasing problem still exists in the decomposed eigenmode components. The same problem occurs in the decomposition results of CEEMDAN. As shown in Figure 7c, the denoising performance is better, and progress has been made in the removal of pseudo-modes and residual noise. The results in Figure 7d reveal that the problem of residual noise modes is largely solved, the SNR is increased, and good noise reduction results have been obtained. This method is less effective at suppressing noise and is less robust. Nevertheless, this adaptive denoising method is particularly suitable for denoising pipeline defect signals. The defect signal is only a part of the pipeline detection results, most of which comprise the detected normal pipeline signal. To evaluate the effectiveness of the proposed denoising method, the EMD, EEMD, CEEMDAN, and ICEEMDAN-LMS methods, which are based on different optimization algorithms, were each used to reduce the noise of field signals. Figure 8 compares the traditional denoising methods and proposed method. First, the signal of a normal pipeline should be denoised; otherwise, the noise signal could be incorrectly identified as the defect signal. Therefore, to evaluate the noise reduction performance for the pipeline defect signal, noise signal, and normal pipeline signal, the SNR and RMSE were used as evaluation criteria:  
\[RMSE=\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\sum}}[x(t)-x^{\prime}(t)]^{2}} \tag{14}\]  
\[SNR=10\log\frac{\underset{t=1}{\overset{N}{\sum}}x^{2}(t)}{\underset{t=1}{ \overset{N}{\sum}}[x(t)-x^{\prime}(t)]^{2}} \tag{15}\]  
where \(x(t)\) represents the original signal, \(x\prime(t)\) is the denoised signal, and N is the signal length. The RMSE index measures the overall accuracy. The smaller the mean squared error, the better the approximation between the reconstructed and original signals. The SNR is the ratio of the effective signal to the interference signal. The SNR and RMSE were used to evaluate the denoising performance. A larger SNR and smaller RMSE indicate better denoising performance.