{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T09:03:09Z","timestamp":1772355789387,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T00:00:00Z","timestamp":1611878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The effect of temperature on magnetic Barkhausen noise (MBN) can be divided into two types: the direct effect of temperature itself and the indirect effect of thermally induced stress. The theoretical model is proposed in this paper to describe the effects of temperature on the MBN signal. For the case considering the direct effect of temperature only, the analytical model allows the prediction of the effect of temperature on MBN profile, and, based on the model, a simple linear calibration curve is presented to evaluate the effect of temperature on MBN amplitude quantitatively. While for the case where the indirect effect of thermal stress is taken into account in addition to the direct effect, the proposed theoretical model allows the deduction of parabolic function for quantitative evaluation of the combined effect on MBN. Both effects of temperature on MBN, i.e., the direct only and the combined one, have been studied experimentally on 0.5 mm thickness non-oriented (NO) electrical steel and the adhesive structure of NO steel and ceramic glass, respectively. The reciprocal of the measured MBN peak amplitude (1\/MBNp) in the first case shows a linear function of temperature, which agrees with the proposed linear calibration curve. While in the experiments considering the combined effects, 1\/MBNp shows parabolic dependence on temperature, which is further simplified as a piecewise function for the practical applications.<\/jats:p>","DOI":"10.3390\/s21030898","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T05:53:43Z","timestamp":1611899623000},"page":"898","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Quantitative Evaluation of the Effect of Temperature on Magnetic Barkhausen Noise"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5547-2238","authenticated-orcid":false,"given":"Yujue","family":"Wang","sequence":"first","affiliation":[{"name":"Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Cardiff CF24 3AA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4608-0507","authenticated-orcid":false,"given":"Turgut","family":"Meydan","sequence":"additional","affiliation":[{"name":"Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Cardiff CF24 3AA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9787-5238","authenticated-orcid":false,"given":"Yevgen","family":"Melikhov","sequence":"additional","affiliation":[{"name":"Wolfson Centre for Magnetics, School of Engineering, Cardiff University, Cardiff CF24 3AA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ndteint.2006.09.003","article-title":"Analysis of the stress dependent magnetic easy axis in ASTM 36 steel by the magnetic Barkhausen noise","volume":"40","author":"Padovese","year":"2007","journal-title":"NDT E Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1007\/s10921-018-0486-0","article-title":"Quantitative Prediction of Surface Hardness in 12CrMoV Steel Plate Based on Magnetic Barkhausen Noise and Tangential Magnetic Field Measurements","volume":"37","author":"Liu","year":"2018","journal-title":"J. Nondestruct. Eval."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.ndteint.2009.08.003","article-title":"Non-destructive determination of residual stress state in steel weldments by Magnetic Barkhausen Noise technique","volume":"43","author":"Yelbay","year":"2010","journal-title":"NDT E Int."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1109\/TMAG.2009.2032417","article-title":"Determination of Hardness and Residual-Stress Variations in Hardened Surface Layers With Magnetic Barkhausen Noise","volume":"46","author":"Zerovnik","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"102138","DOI":"10.1016\/j.ndteint.2019.102138","article-title":"Non-destructive hardness prediction for 18CrNiMo7-6 steel based on feature selection and fusion of Magnetic Barkhausen Noise","volume":"107","author":"Ding","year":"2019","journal-title":"NDT E Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jmmm.2018.01.023","article-title":"Through-process characterization of local anisotropy of Non-oriented electrical steel using magnetic Barkhausen noise","volume":"453","author":"He","year":"2018","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Maciusowicz, M., and Psuj, G. (2020). Time-Frequency Analysis of Barkhausen Noise for the Needs of Anisotropy Evaluation of Grain-Oriented Steels. Sensors, 20.","DOI":"10.3390\/s20030768"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.sna.2013.01.027","article-title":"Investigation of temperature effect of stress detection based on Barkhausen noise","volume":"194","author":"Wang","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.jmmm.2016.01.065","article-title":"The effect of temperature on the average volume of Barkhausen jump on Q235 carbon steel","volume":"407","author":"Guo","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BF00729134","article-title":"Nondestructive evaluation of cementite content in steel and white cast iron using inductive Barkhausen noise","volume":"15","author":"Altpeter","year":"1996","journal-title":"J. Nondestruct. Eval."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5830","DOI":"10.1063\/1.353541","article-title":"Modeling of micromagnetic Barkhausen activity using a stochastic process extension to the theory of hysteresis","volume":"73","author":"Jiles","year":"1993","journal-title":"J. Appl. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1109\/TMAG.2002.803612","article-title":"Modeling stress effects on magnetic hysteresis and Barkhausen emission using a hysteretic-stochastic model","volume":"38","author":"Lo","year":"2002","journal-title":"IEEE Trans. Magn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1109\/TMAG.2010.2091418","article-title":"A New Method for Evaluation of Mechanical Stress Using the Reciprocal Amplitude of Magnetic Barkhausen Noise","volume":"47","author":"Mierczak","year":"2011","journal-title":"IEEE Trans. Magn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TMAG.2014.2335204","article-title":"Analysis of Barkhausen Noise Emissions and Magnetic Hysteresis in Multi-Phase Magnetic Materials","volume":"50","author":"Gaunkar","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3954","DOI":"10.1109\/TMAG.2009.2022744","article-title":"Modeling the Temperature Dependence of Hysteresis Based on Jiles\u2013Atherton Theory","volume":"45","author":"Raghunathan","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1109\/TMAG.2010.2045351","article-title":"Theoretical Model of Temperature Dependence of Hysteresis Based on Mean Field Theory","volume":"46","author":"Raghunathan","year":"2010","journal-title":"IEEE Trans. Magn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.measurement.2018.02.041","article-title":"Reduction of thermal effect on rail stress measurement based on magnetic Barkhausen noise anisotropy","volume":"125","author":"Ding","year":"2018","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.jsv.2004.02.055","article-title":"Laser vibrometry technique for measurement of contained stress in railroad rail","volume":"282","author":"Weaver","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5355","DOI":"10.1063\/1.342370","article-title":"Phenomenology and interpretation of the Barkhausen effect in ferromagnetic materials (invited)","volume":"64","author":"Alessandro","year":"1988","journal-title":"J. Appl. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1023\/A:1022846128461","article-title":"Dynamics of domain magnetization and the Barkhausen effect","volume":"50","author":"Jiles","year":"2000","journal-title":"Czechoslov. J. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.1088\/0022-3727\/28\/8\/001","article-title":"Theory of the magnetomechanical effect","volume":"28","author":"Jiles","year":"1995","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jmmm.2007.02.157","article-title":"An alternative method to estimate the parameters of Jiles\u2013Atherton model","volume":"314","author":"Chwastek","year":"2007","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"043916","DOI":"10.1063\/1.4747915","article-title":"On physical aspects of the Jiles-Atherton hysteresis models","volume":"112","author":"Zirka","year":"2012","journal-title":"J. Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"172510","DOI":"10.1063\/1.3249581","article-title":"Generalized form of anhysteretic magnetization function for Jiles-Atherton theory of hysteresis","volume":"95","author":"Raghunathan","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1109\/20.996206","article-title":"An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations","volume":"38","author":"Sadowski","year":"2002","journal-title":"IEEE Trans. Magn."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hussain, S., Ghorbanian, V., Benabou, A., Clenet, S., and Lowther, D.A. (2016, January 4\u20137). A Study of the Effects of Temperature on Magnetic and Copper Losses in Electrical Machines. Proceedings of the XXII International Conference on Electrical Machines (ICEM), Ecublens, Switzerland.","DOI":"10.1109\/ICELMACH.2016.7732689"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ndteint.2018.01.004","article-title":"Dipole modeling of stress-dependent magnetic flux leakage","volume":"95","author":"Wang","year":"2018","journal-title":"NDT E Int."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10921-019-0643-0","article-title":"Stress-Dependent Magnetic Flux Leakage: Finite Element Modelling Simulations Versus Experiments","volume":"39","author":"Wang","year":"2019","journal-title":"J. Nondestruct. Eval."},{"key":"ref_29","unstructured":"Cengel, Y.A., and Boles, M.A. (2007). Thermodynamics: An Engineering Approach, The McGraw-Hill Companies Inc.. [6th ed.]."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Timoshenko, S., and Goodier, J. (1970). Theory of Elasticity, The McGraw Hill Education. [3rd ed.].","DOI":"10.1115\/1.3408648"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.jmmm.2016.08.030","article-title":"Analysis of domain wall dynamics based on skewness of magnetic Barkhausen noise for applied stress determination","volume":"421","author":"Ding","year":"2017","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_32","unstructured":"(2020, November 25). Grain-Oriented Electrical Steel (Technical Information). Available online: https:\/\/www.spacematdb.com\/spacemat\/manudatasheets\/crgo.pdf."},{"key":"ref_33","unstructured":"(2020, November 01). Ultra-Low Expansion Glass-Ceramics (Technical Information). Available online: https:\/\/www.sydor.com\/wp-content\/uploads\/2019\/05\/Ohara-CLEARCERAM-Z-Low-Expansion-Glass.pdf."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4744","DOI":"10.1109\/TMAG.2009.2022320","article-title":"Effect of Magnetostriction Anisotropy in Nonoriented Electrical Steels on Deformation of Induction Motor Stator Cores","volume":"45","author":"Somkun","year":"2009","journal-title":"IEEE Trans. Magn."},{"key":"ref_35","first-page":"233","article-title":"Electrical steels: Past, present and future developments","volume":"137","author":"Moses","year":"1990","journal-title":"IEE Proc. A Phys. Sci. Meas. Instrum. Manag. Educ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0963-8695(96)00028-X","article-title":"Effect of applied stresses on magnetostriction of low carbon steel","volume":"29","author":"Yamasaki","year":"1996","journal-title":"NDT E Int."},{"key":"ref_37","unstructured":"Klimczyk, P. (2012). Novel techniques for characterisation and control of magnetostriction in G.O.S.S. [Ph.D. Thesis, Cardiff University]."},{"key":"ref_38","unstructured":"Somkun, S. (2010). Magnetostriction and Magnetic Anisotropy in Non-Oriented Electrical Steels and Stator Core Laminations. [Ph.D. Thesis, Cardiff University]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/3\/898\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:17:02Z","timestamp":1760159822000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/3\/898"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,29]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["s21030898"],"URL":"https:\/\/doi.org\/10.3390\/s21030898","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,29]]}}}