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However, the problem of severe system parameter coupling in a conventional tri-stable stochastic resonance model leads to difficulty in potential function regulation. In this paper, a new compound tri-stable stochastic resonance (CTSR) model is proposed to address this problem by combining a Gaussian Potential model and the mixed bi-stable model. The weak magnetic anomaly signal detection system consists of the CTSR system and judgment system based on statistical analysis. The system parameters are adjusted by using a quantum genetic algorithm (QGA) to optimize the output signal-to-noise ratio (SNR). The experimental results show that the CTSR system performs better than the traditional tri-stable stochastic resonance (TTSR) system and BSR system. When the input SNR is -8 dB, the detection probability of the CTSR system approaches 80%. Moreover, this detection system not only detects the magnetic anomaly signal but also retains information on the relative motion (heading) of the ferromagnetic target and the magnetic detection device.<\/jats:p>","DOI":"10.3390\/s23229293","type":"journal-article","created":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T01:48:45Z","timestamp":1700531325000},"page":"9293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Magnetic Anomaly Detection Based on a Compound Tri-Stable Stochastic Resonance System"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0059-6926","authenticated-orcid":false,"given":"Jinbo","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Zhen","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Yu","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Yuran","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Chengjun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4197-6734","authenticated-orcid":false,"given":"Guangbo","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Bingting","family":"Zha","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"},{"name":"China and the Science and Technology on Electromechanical Dynamic Control Laboratory, Xi\u2019an 710065, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.19026\/rjaset.7.536","article-title":"Detect Adjacent Well by Analyzing Geomagnetic Anomalies","volume":"7","author":"Zhang","year":"2014","journal-title":"Res. J. Appl. Sci. Eng. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17043","DOI":"10.1109\/JSEN.2022.3192668","article-title":"The Novel Method of Magnetic Anomaly Recognition Based on the Fourth Order Aperiodic Stochastic Resonance","volume":"22","author":"Qin","year":"2022","journal-title":"IEEE Sens J."},{"key":"ref_3","unstructured":"Clem, T., Allen, G., Bono, J., McDonald, R.J., Overway, D., Sulzberge, G., Kumarb, S., and King, D. (2004, January 9\u201312). Magnetic sensors for buried minehunting from small unmanned underwater vehicles. Proceedings of the Oceans\u201904 MTS\/IEEE Techno-Ocean \u201904 (IEEE Cat. No.04CH37600), Kobe, Japan."},{"key":"ref_4","first-page":"319","article-title":"The effect of magnetic anomaly detection technique in eddy current non-destructive testing","volume":"25","author":"Kosmas","year":"2007","journal-title":"Int. J. Appl. Electrom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.tecto.2009.12.004","article-title":"Relationship between characteristics of gravity and magnetic anomalies and the earthquakes in the Longmenshan range and adjacent areas","volume":"491","author":"Zhang","year":"2010","journal-title":"Tectonophysics"},{"key":"ref_6","first-page":"042002","article-title":"A brief review of magnetic anomaly detection","volume":"32","author":"Zhao","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3172","DOI":"10.1109\/TSP.2007.893757","article-title":"Theory of the Stochastic Resonance Effect in Signal Detection: Part I\u2014Fixed Detectors","volume":"55","author":"Chen","year":"2007","journal-title":"IEEE T Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1088\/0305-4470\/14\/11\/006","article-title":"The mechanism of stochastic resonance","volume":"14","author":"Benzi","year":"1981","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0375-9601(83)90086-5","article-title":"Stochastic resonance in a bistable system","volume":"97","author":"Fauve","year":"1983","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1142\/S0218127492000379","article-title":"Stochastic resonance in Chua\u2019s circuit","volume":"2","author":"Anishchenko","year":"1992","journal-title":"Int. J. Bifurc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3250","DOI":"10.1103\/PhysRevA.46.3250","article-title":"Stochastic resonance in a nonlinear system driven by an aperiodic force","volume":"46","author":"Gang","year":"1992","journal-title":"Phys. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1587\/transfun.E99.A.323","article-title":"Stochastic resonance of signal detection in mono- threshold system using additive and multiplicative noises","volume":"99","author":"Liu","year":"2016","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevE.94.052214","article-title":"Stochastic resonance subject to multiplicative and additive noise: The influence of potential asymmetries","volume":"94","author":"Qiao","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, H.B., Kong, F., Lu, S.L., and He, Q.B. (2013, January 9\u201311). A tri-stable stochastic resonance model and its applying in detection of weak signal. Proceedings of the 2013 ICICIP, Beijing, China.","DOI":"10.1109\/ICICIP.2013.6568067"},{"key":"ref_15","first-page":"1","article-title":"Note: Signal amplification and filtering with a tri-stable stochastic resonance cantilever","volume":"84","author":"Lu","year":"2013","journal-title":"Rev. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1869","DOI":"10.1007\/s42417-021-00332-8","article-title":"Piecewise Unsaturated Under-Damped Tri-stable Stochastic Resonance System and Its Application in Bearing Fault Diagnosis","volume":"9","author":"Zhang","year":"2021","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_17","first-page":"1","article-title":"Adaptive cancellation of geomagnetic background noise for magnetic anomaly detection using coherence","volume":"26","author":"Liu","year":"2014","journal-title":"Meas. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.4028\/www.scientific.net\/AMM.368-370.1860","article-title":"Decreasing Noise in Magnetic Anomaly Detection Basing on Wavelet Denoising","volume":"368\u2013370","author":"Zhou","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.sna.2018.05.009","article-title":"Magnetic anomaly detection based on stochastic resonance","volume":"278","author":"Wan","year":"2018","journal-title":"Sensor Actuat. A Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"162230","DOI":"10.1109\/ACCESS.2020.3020881","article-title":"Magnetic Anomaly Signal Detection Using Parallel Monostable Stochastic Resonance System","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, Z.Y., Xu, Y.J., Liu, W., Zhang, Q., Hu, J.F., and Pan, M.C. (2021, January 16\u201318). Magnetic anomaly signal detection using adaptive stochastic resonance system. Proceedings of the International Conference on Mechanical Engineering, Measurement Control, and Instrumentation, Guangzhou, China.","DOI":"10.1117\/12.2611100"},{"key":"ref_22","first-page":"1","article-title":"Magnetic Anomaly Detection Using a Parallel Stochastic Resonance System","volume":"71","author":"Wan","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/9.0000593","article-title":"Adaptive cascade detection of weak magnetic anomalies based on marine predators","volume":"13","author":"Sun","year":"2023","journal-title":"Aip Adv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1103\/RevModPhys.70.223","article-title":"Stochastic resonance","volume":"70","author":"Gammaitoni","year":"1998","journal-title":"Rev. Mod. Phys."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9293\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:25:30Z","timestamp":1760131530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/22\/9293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,20]]},"references-count":24,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["s23229293"],"URL":"https:\/\/doi.org\/10.3390\/s23229293","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,20]]}}}