## 5 Conclusions  
In the process of the defect detection of long-distance pipelines, noise interference will inevitably distort the detection signal and affect the detection result. Therefore, the ICEEMDAN-LMS pipeline defect signal denoising method is proposed in this study. The field pipeline defect signal is denoised, and the signal-to-noise ratio and root-mean-squared error are used to evaluate the signal denoising performance.  
The contributions of this paper are as follows:  
1. In this study, by adjusting and improving the step size of LMS, the convergence speed of weights is accelerated and the steady-state error of the algorithm is reduced.
2. The superior performance of this method compared with existing methods is verified by simulating pipeline defect signals. The experimental results show that the proposed algorithm can effectively preserve the defect signal and suppress the pipeline noise.
3. Compared with the traditional pipeline signal denoising method, the ICEEMDAN-LMS method can improve the signal-to-noise ratio by 6.74% and reduce the root-mean-squared error by 4.36%. The ICEEMDAN-LMS denoising method has the highest signal-to-noise ratio and the lowest RMSE. As a result, ICEEMDAN-LMS improves the signal-to-noise ratio and root-mean-squared error, resulting in a better pipeline noise reduction.  
This paper provides a new concept for the noise reduction method and the defect identification of natural gas pipelines and has certain reference value in engineering applications and scientific research experiments. Although this study carried out the field collection and research of defect data and achieved specific results, pipeline leakage caused by pipeline defects is complicated and changeable, and it is necessary to further enrich the signal data of natural gas pipeline defect detection under various circumstances to lay a solid foundation for the realization of big data identification. In addition, how to build a more refined noise reduction model for natural gas pipelines and fully realize the intelligent recognition of pipeline defect signals are challenging tasks. In future studies, the performance of this method will be evaluated from the perspective of the intelligent diagnosis of pipeline defects. We aim to strengthen the emergency analysis and management of long-distance natural gas pipelines and improve the emergency support capacity of natural gas pipeline enterprises.  
Conceptualization, Y.G. and A.B.; methodology, Y.W.; software, Y.G. and A.B.; validation, Q.W.; formal analysis, Z.L.; investigation, Y.W. and Q.W.; resources, A.B. and X.W.; data curation, Y.G.; writing--original draft preparation, Y.G. and A.B.; writing--review and editing, Z.L.; visualization, X.W.; supervision, A.B.; project administration, Z.L.; funding acquisition, A.B. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by National Natural Science Foundation of China (41877527), the Philosophy and Social Science Foundation of the Jiangsu Higher Education Institutions of China (no. 2022 SJYB1931), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no. 21 KJB620008).  
Not applicable for studies not involving humans or animals.  
Not applicable for studies not involving humans.  
The data used to support the findings of the study are available from the corresponding author upon request. The author's email address is [EMAIL_ADDRESS].  
The authors declare no conflict of interest.