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Ill-Posed Inverse Problems in Electrical Engineering Applications

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Numerical Methods for Energy Applications

Part of the book series: Power Systems ((POWSYS))

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Abstract

In this chapter some ill-posed inverse electromagnetic and power engineering problems are introduced, both at a theoretical introductory and mathematical modelling level and detailed regarding their numerical solving case studies based, by the application of several regularization techniques starting from classical Tikhonov approach up to singular values decomposition procedures. Fredholm integral equation mathematical modelling is presented in the physical definition of the inverse electromagnetic and/or power engineering problems, accompanied by explanations regarding the physical significance.

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Abbreviations

ART:

Algebraic reconstruction technique

IEP:

Inverse electromagnetic problem

IPIEP:

Ill posed inverse electromagnetic problem

HVPL:

High voltage power line

SVD:

Singular value decomposition

TSVD:

Truncated singular value decomposition

References

  1. Sykulski Jan K (ed) (1995) Pawluk Krystyn, Computational magnetics (field synthesis). Chapman & Hall, London

    Google Scholar 

  2. Tikhonov AN, Glasko VB (1965) Use of the regularization method in non-linear problems. USSR Comput Math Math Phys 3:93–107

    Article  Google Scholar 

  3. Hansen PC (2008) Regularization tools, a matlab package for analysis and solution of discrete ill posed problems, Denmark. www.imm.dtu.dk/~pch

  4. Bronshtein IN et al (2004) Handbook of mathematics. Springer, New-York

    Google Scholar 

  5. Lavrentiev M et al (1986) Ill-posed problems of mathematical physics and analysis. American Mathematical Society

    Google Scholar 

  6. Sadiku Matthew NO (2000) Numerical techniques in electromagnetics, 2nd edn. CRC Press, New York

    Book  Google Scholar 

  7. Palka R (1985) Synthesis of electrical fields by optimization of the shape of region boundaries. IEE Proc 132, Pt. A(1):28–32

    Google Scholar 

  8. Morozov VA (1966) Regularization of incorrectly posed problems and the choice of regularization parameter. USSR Comput Math Math Phys 1:242–251

    Article  Google Scholar 

  9. Micu A, Micu Dan O (2002) Electromagnetic field synthesis. Ed. Dacia, Cluj-Napoca

    Google Scholar 

  10. Micu Dan O (1993) Contributions to the synthesis of the stationary electric and magnetic field. PhD thesis, Cluj-Napoca

    Google Scholar 

  11. Michael J (2004) Modular regularization algorithms. PhD thesis, Denmark

    Google Scholar 

  12. Ştefan K (2004) Metode numerice, Algoritme, Programe de calcul, Aplicaţii în Energetică, Ediţia a 3-a, Ed. Orizonturi Universitare, Timişoara

    Google Scholar 

  13. Hansen PC (1992) Analysis of discrete Ill-posed problems by means of the L-curve. SIAM Rev 34(4):561–580

    Article  MathSciNet  Google Scholar 

  14. Hansen PC (1992) Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Inverse Probl 8:849–871

    Article  MathSciNet  Google Scholar 

  15. James Epperson (2002) An Introduction on Numerical Methods and Analysis. Wiley, New York

    Google Scholar 

  16. Chadebec O et al (2002) Recent improvements for solving inverse magnetostatic problem applied to thin shells. IEEE Trans Magn 38(3):1005–1009

    Google Scholar 

  17. Chadebec O et al (2003) How to well pose a magnetization identification problem. IEEE Trans Magn 39(3):1634–1637

    Google Scholar 

  18. Chadebec O et al (2004) Magnetization identification problem: illustration of an effective approach. COMPEL 23(2):518–530

    Google Scholar 

  19. Bărbulescu C, Ceclan A, Kilyeni Ş, Micu DD (2007) Power flow calculation for ill-conditioned systems. Simplified Newton method with SVD partial regularization, EUROCON, Varsovia

    Google Scholar 

  20. Tikhonov Andrev N (1981) Solution of incorrectly formulated problems. Mir, Wiley, New-York

    Google Scholar 

  21. Lamm Patricia K, Scofield Thomas L (2000) Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems. Inverse Probl 16:373–399

    Article  MathSciNet  Google Scholar 

  22. Lavrentiev M (1967) Some improperly posed problems of mathematical physics. Springer, New-York

    Book  Google Scholar 

  23. Gottvald A (1997) A survey of inverse methodologies, meta-evolutionary optimization and Bayesian statistics: applications to in vivo MRS. Int J Appl Electromagnet Mech 1:17–44

    Google Scholar 

  24. Strohmer T, Vershynin R (2006) A randomized solver for linear systems with exponential convergence. Random-Approx 4110:499–507

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Numerical Methods Research Center, Electrical Engineering Department, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Andrei Ceclan, Dan D. Micu & Levente Czumbil

  2. Doctoral School of Engineering Sciences, University Valahia, Targoviste, Romania

    Horia Andrei

  3. Department of Electrical Engineering, University Politehnica Bucharest, Bucharest, Romania

    Marian Gaiceanu, Marilena Stanculescu & Paul Cristian Andrei

Authors
  1. Andrei Ceclan
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  2. Dan D. Micu
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  3. Levente Czumbil
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  4. Horia Andrei
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  5. Marian Gaiceanu
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  6. Marilena Stanculescu
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  7. Paul Cristian Andrei
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Corresponding author

Correspondence to Dan D. Micu .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Seraj Higher Education Institute, Tabriz, Iran

    Naser Mahdavi Tabatabaei

  2. Faculty of Electronics, Communications and Computers, University of Pitesti, Pitesti, Romania

    Nicu Bizon

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Ceclan, A. et al. (2021). Ill-Posed Inverse Problems in Electrical Engineering Applications. In: Mahdavi Tabatabaei, N., Bizon, N. (eds) Numerical Methods for Energy Applications. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-62191-9_9

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  • DOI: https://doi.org/10.1007/978-3-030-62191-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62190-2

  • Online ISBN: 978-3-030-62191-9

  • eBook Packages: EnergyEnergy (R0)

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