{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T18:00:35Z","timestamp":1777572035158,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T00:00:00Z","timestamp":1587686400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFC0805005-1"],"award-info":[{"award-number":["2017YFC0805005-1"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The non-contact detection of buried ferromagnetic pipeline is a long-standing problem in the field of inspection of outside pipelines, and the extraction of magnetic anomaly signal is a prerequisite for accurate detection. Pipeline defects can cause the fluctuation of magnetic signals, which are easily submerged in wide-band background noise without external excitation sources. Previously, Variational Mode Decomposition (VMD) was used to separate modal components; however, VMD is based on narrow-band signal processing algorithm and the calculation is complex. In this article, a method of pipeline defect signal based on Variational Specific Mode Extraction (VSME) is employed to extract the signal of a specific central frequency by signal modal decomposition, i.e., the specific mode is weak magnetic anomaly signal of pipeline defects. VSME is based on the fact that a wide-band signal can be converted into a narrow-band signal by demodulation method. Furthermore, the problem of wide-band signal decomposition is expressed as an optimal demodulation problem, which can be solved by alternating direction method of multipliers. The proposed algorithm is verified by artificially synthesized signals, and its performance is better than that of VMD. The results showed that the VSME method can extract the magnetic anomaly signal of pipeline damage using experimental data, while obtaining a better accuracy.<\/jats:p>","DOI":"10.3390\/a13040105","type":"journal-article","created":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T11:42:14Z","timestamp":1587728534000},"page":"105","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Variational Specific Mode Extraction: A Novel Method for Defect Signal Detection of Ferromagnetic Pipeline"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0729-7065","authenticated-orcid":false,"given":"Haiyang","family":"Ju","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinhua","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yizhen","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1109\/JSEN.2011.2176484","article-title":"A new method for detecting leaks in underground water pipelines","volume":"12","author":"Cataldo","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ijpvp.2016.11.007","article-title":"A review on pipeline corrosion, in-line inspection (ILI), and corrosion growth rate models International","volume":"149","author":"Vanaei","year":"2017","journal-title":"J. Press. Vessel. & Pip."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/TIM.2017.2775404","article-title":"Sensor motes for the exploration and monitoring of operational pipelines","volume":"67","author":"Duisterwinkel","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1243\/0954408JPME108","article-title":"A Review of Fluid-Driven Pipeline Pigs and their Applications","volume":"221","author":"Quarini","year":"2007","journal-title":"Proc. Inst. Mech. Eng.-Part E"},{"key":"ref_5","first-page":"1","article-title":"Highly sensitive planar hall magnetoresistive sensor for magnetic flux leakage pipeline inspection","volume":"54","author":"Pham","year":"2018","journal-title":"IEEE Trans. Magn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"012004","DOI":"10.1088\/1742-6596\/1249\/1\/012004","article-title":"Video processing techniques for the contactless investigation of large oscillations","volume":"1249","author":"Civera","year":"2019","journal-title":"J. Phys. Conf. Ser. IOP Publ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e12336","DOI":"10.1111\/str.12336","article-title":"An experimental study of the feasibility of phase-based video magnification for damage detection and localisation in operational deflection shapes","volume":"56","author":"Civera","year":"2020","journal-title":"Strain"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.sna.2015.12.026","article-title":"Gradient-field pulsed eddy current probes for imaging of hidden corrosion in conductive structures","volume":"238","author":"Li","year":"2016","journal-title":"Sens. & Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.ndteint.2016.03.006","article-title":"Current deflection NDE for the inspection and monitoring of pipes","volume":"81","author":"Jarvis","year":"2016","journal-title":"NDT & E Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1016\/j.ultras.2013.03.007","article-title":"Ultrasonic monitoring of erosion\/corrosion thinning rates in industrial piping systems","volume":"53","author":"Honarvar","year":"2013","journal-title":"Ultrasonics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1108\/ACMM-10-2014-1444","article-title":"Experimental study on the corrosion testing of a buried metal pipeline by transient electromagnetic method","volume":"63","author":"Hu","year":"2016","journal-title":"Anti-Corros. Methods Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ndteint.2016.12.007","article-title":"Defect characterisation from limited view pipeline radiography","volume":"86","author":"Haith","year":"2017","journal-title":"NDT & E Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.jmmm.2015.12.035","article-title":"Metal magnetic memory technique used to predict the fatigue crack propagation behavior of 0.45% C steel","volume":"405","author":"Chongchong","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_14","first-page":"1","article-title":"Coupled magneto-mechanical analysis of iron sheets under biaxial stress","volume":"52","author":"Aydin","year":"2015","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s40194-012-0011-5","article-title":"The metal magnetic memory method application for online monitoring of damage development in steel pipes and welded joints specimens","volume":"57","author":"Dubov","year":"2013","journal-title":"Weld. World"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10921-015-0292-x","article-title":"Discussion of Derivability of Local Residual Stress Level from Magnetic Stray Field Measurement","volume":"34","author":"Augustyniak","year":"2015","journal-title":"J. Nondestruct. Eval."},{"key":"ref_17","first-page":"447","article-title":"Calibration and Compensation of Geomagnetic Vector Measurement System and Improvement of Magnetic Anomaly Detection","volume":"13","author":"Liu","year":"2016","journal-title":"IEEE Geosci. & Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"45104","DOI":"10.1088\/0957-0233\/27\/4\/045104","article-title":"Magnetic anomaly detection (MAD) of ferromagnetic pipelines using principal component analysis (PCA)","volume":"27","author":"Sheinker","year":"2016","journal-title":"Meas. Sci. & Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1109\/JSEN.2018.2879348","article-title":"Microwave-Based SAR Technique for Pipeline Inspection Using Autofocus Range-Doppler Algorithm","volume":"19","author":"Buhari","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1109\/TAP.2013.2287024","article-title":"Piecewise and Wiener filter-based SAR techniques for monostatic microwave imaging of layered structures","volume":"62","author":"Fallahpour","year":"2013","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1109\/TGRS.2006.870402","article-title":"Derivation and comparison of SAR and frequency-wavenumber migration within a common inverse scalar wave problem formulation","volume":"44","author":"Gilmore","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/TAP.2009.2035997","article-title":"A sparsity regularization approach to the electromagnetic inverse scattering problem","volume":"58","author":"Winters","year":"2009","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3279","DOI":"10.1109\/TAP.2007.908824","article-title":"Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method-Theory and experiment","volume":"55","author":"Franchois","year":"2007","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1109\/TAP.2009.2015823","article-title":"A new value picking regularization strategy\u2014Application to the 3-D electromagnetic inverse scattering problem","volume":"57","author":"Franchois","year":"2009","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1109\/TGRS.2011.2164086","article-title":"Magnetic Anomaly Detection Using High-Order Crossing Method","volume":"50","author":"Sheinker","year":"2012","journal-title":"IEEE Trans. Geosci. & Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"45205","DOI":"10.1088\/0957-0233\/19\/4\/045205","article-title":"Magnetic anomaly detection using entropy filter","volume":"19","author":"Sheinker","year":"2008","journal-title":"Meas. Sci. & Technol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhou, H., Pan, Z., and Zhang, Z. (2017). Magnetic Anomaly Detection with Empirical Mode Decomposition Trend Filtering. IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 2503\u20132506.","DOI":"10.1587\/transfun.E100.A.2503"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. Math. Phys. & Eng. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1142\/S1793536910000422","article-title":"Complementary Ensemble Empirical Mode Decomposition: A Novel Noise Enhanced Data Analysis Method","volume":"2","author":"Yeh","year":"2010","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3999","DOI":"10.1109\/TSP.2013.2265222","article-title":"Empirical Wavelet Transform","volume":"61","author":"Gilles","year":"2013","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6024","DOI":"10.1109\/TSP.2017.2731300","article-title":"Nonlinear Chirp Mode Decomposition: A Variational Method","volume":"65","author":"Chen","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"35109","DOI":"10.1063\/1.4978029","article-title":"Variational mode decomposition denoising combined with the Hausdorff distance","volume":"88","author":"Ma","year":"2017","journal-title":"Rev. Sci. Instrum."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1109\/JBHI.2017.2734074","article-title":"Variational Mode Extraction: A New Efficient Method to Derive Respiratory Signals from ECG","volume":"22","author":"Nazari","year":"2018","journal-title":"IEEE J. Biomed. Health Inf."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TSP.2013.2276393","article-title":"Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis","volume":"62","author":"Wang","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers","volume":"3","author":"Boyd","year":"2010","journal-title":"Found. & Trends\u00ae Mach. Learn."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5185","DOI":"10.1109\/TGRS.2018.2811245","article-title":"Appraisal of instantaneous phase-based functions in adjoint waveform inversion","volume":"56","author":"Tejero","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.jsv.2016.03.015","article-title":"Decomposing a signal into short-time narrow-banded modes","volume":"373","author":"Mcneill","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.sigpro.2014.03.014","article-title":"Empirical mode decomposition revisited by multicomponent non-smooth convex optimization","volume":"102","author":"Pustelnik","year":"2014","journal-title":"Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1137\/120896219","article-title":"Fast alternating direction optimization methods","volume":"7","author":"Goldstein","year":"2014","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5994","DOI":"10.1109\/JSEN.2017.2737467","article-title":"Separation of overlapped non-stationary signals by ridge path regrouping and intrinsic chirp component decomposition","volume":"17","author":"Chen","year":"2017","journal-title":"IEEE Sens. J."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/4\/105\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:51:13Z","timestamp":1760363473000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/4\/105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,24]]},"references-count":42,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["a13040105"],"URL":"https:\/\/doi.org\/10.3390\/a13040105","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,24]]}}}