Abstract—
Inverse problems of magnetostatics for continuity defects can be formulated in different ways. One can set the task of determining defects with high accuracy and resolution or limit the task to revealing several specified types of (“hazardous”) defects with varying degrees of probability. In this case, other real (“minor”) defects will be either skipped by the program or “replaced” by defects from among the ones specified. Minimizing the residual functional between experimental and calculated data is the main task when solving any inverse problems, both in real time and off-line. The paper considers an approach to calculating a simplified inverse problem in real time without accumulating experimental data bases.
This is a preview of subscription content, access via your institution.



REFERENCES
- 1
Dyakin, V.V., Matematicheskie osnovy klassicheskoi magnitostatiki (Mathematical Foundations of Classical Magnetostatics), Yekaterinburg: Ural Branch, Russ. Acad. Sci., 2016.
- 2
Dyakin, V.V., Umergalina, O.V., and Raevskii, V.Ya., The field of a finite defect in a 3D semispace, Russ. J. Nondestr. Test., 2005, vol. 41, no. 8, pp. 502–513.
- 3
Dyakin, V.V., Raevskii, V.Ya., and Kudryashova, O.V., The field of a finite defect in a plate, Russ. J. Nondestr. Test., 2009, vol. 45, no. 3, pp. 199–209.
- 4
Pechenkov, A.N. and Scherbinin, V.E., Influence of calculation accuracy on the time and results of solving the inverse problem of magnetostatic nondestructive testing. Need of parallel computations, Diagn. Resour. Mech. Mater. Struct., 2015, no. 5, p. 22–30.
- 5
Dyakin, V.V., Kudryashova, O.V., and Raevskii, V.Ya., Inverse problem of magnetostatics in saturation fields, Russ. J. Nondestr. Test., 2019, vol. 55, no. 10, pp. 746–755.
- 6
Pechenkov, A.N. and Shcherbinin, V.E., Nekotorye pryamye i obratnye zadachi tekhnicheskoi magnitostatiki (Some Direct and Inverse Problems in Technical Magnetostatics), Yekaterinburg: Ural Branch, Russ. Acad. Sci., 2004.
- 7
Pechenkov, A.N., Scherbinin, V.E., Shleenkov, S.A., and Bulychev, O.A., Computational relationships for the development of software for calculating magnetostatic fields from flaws in arbitrarily shaped ferromagnetic products, Russ. J. Nondestr. Test., 2017, vol. 53, no. 11, pp. 755–764.
- 8
Jiang Feng and Liu Shulin, Evaluation of cracks with different hidden depths and shapes using surface magnetic field measurements based on semi-analytical modeling, J. Phys. D: Appl. Phys., 2018, vol. 51, p. 125002–125011.
- 9
Wautischer, G., Bruckner, F., Abert, C., Suess, D., Koeck, H., and Eizaguirre, S.M., Solving the inverse magnetostatic problem using fictitious magnetic charges, AIP Adv., 2018, vol. 8, p. 056005.
- 10
Ravan, M., Khalaj, A.R., Koziel, S., Nikolova, N.K., and Reilly, J.P., Sizing of 3-D arbitrary defects using magnetic flux leakage measurements, IEEE Trans. Magn., 2010, vol. 46, no. 4, pp. 1024–1033.
- 11
Calvetti, D., Morigi, S., Reichel, L., and Sgallari, F., Tikhonov regularization and the L-curve for large discrete ill-posed problems, J. Comput. Appl. Math., 2000, vol. 123, pp. 423–446.
Funding
This work was carried out within the framework of the state order on topic “Diagnostics”, project no. АААА-А18-118020690196-3.
Author information
Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pechenkov, A.N. Method for Processing Results of Magnetic Testing for Reliable Real-Time Detection of Critical Continuity Defects. Russ J Nondestruct Test 56, 1050–1055 (2020). https://doi.org/10.1134/S1061830920120074
Received:
Revised:
Accepted:
Published:
Issue Date:
Keywords:
- inverse problem of magnetostatics
- pattern recognition methods
- integral equation of magnetostatics
- calculation of magnetic field
- “continuity” defects
- minimization problem
- brute force method