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Computational Intelligence and Tikhonov Regularization with Reduced Dimension Model: Applications in Health, Renewable Energy and Climate Heat Transfer Inverse Problems

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Computational Intelligence Methodologies Applied to Sustainable Development Goals

Abstract

In this chapter we present a method to predict the optimal value of the Tikhonov’s regularization parameter by solving simplified versions of the inverse problems considered. This can be of great benefit since methods such as the L-curve and the Fixed Point Iteration require the inverse problem to be solved several times in order to determine the optimal value for the regularization parameter. The main idea that supports the proposed approach is to solve the problem of interest using a low set of dimensions to represent the function to be estimated and, then, this solution is used to obtain an estimate for the regularization parameter of the complete model, based on the Fixed Point Iteration method. Tests are performed on three inverse heat transfer problems: estimation of the variable thermal conductivity of a biological tissue, estimation of the inlet temperature in parallel plates channel, and the estimation of the variable scattering albedo of a radiative transfer participating medium. The results obtained demonstrate the feasibility of the technique in three problems with potential practical applications in bioengineering, renewable energy and climate in alignment with the Sustainable Development Goals (SDG) 3, 4, 7, 9, 13, and 17 of the United Nations 2030 Agenda established in 2015.

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References

  1. Aucejo, M., De Smet, O.: A generalized multiplicative regularization for input estimation. Mech. Syst. Signal Process. 157, 107637 (2021)

    Article  Google Scholar 

  2. Bazán, F.S.V.: Fixed-point iterations in determining the Tikhonov regularization parameter. Inverse Probl. 24(3), 035001 (2008)

    Google Scholar 

  3. Beck, J.V., Arnold, K.J.: Parameter Estimation in Engineering and Science. Wiley, New York (1977)

    MATH  Google Scholar 

  4. Beck, J.V., Blackwell, B., Clair, C.R.S., Jr.: Inverse Heat Conduction: Ill-Posed Problems. Wiley, New York, NY (1985)

    MATH  Google Scholar 

  5. Bejan, A.: Convection Heat Transfer, 4th edn. Wiley, Hoboken, NJ (2013)

    Google Scholar 

  6. Benning, M., Burger, M.: Modern regularization methods for inverse problems 27, 1–111 (2018)

    Google Scholar 

  7. Bokar, J.C., Özisik, M.N.: An inverse analysis for estimating the time-varying inlet temperature in laminar flow inside a parallel plate duct. Int. J. Heat Mass Transf. 38(1), 39–45 (1995)

    Article  Google Scholar 

  8. Bozzoli, F., Cattani, L., Rainieri, S., Bazán, F.S.V., Borges, L.S.: Estimation of the local heat-transfer coefficient in the laminar flow regime in coiled tubes by the Tikhonov regularisation method. Int. J. Heat Mass Transf. 72, 352–361 (2014)

    Article  Google Scholar 

  9. Chalhoub, E.S., Campos Velho, H.F.: Estimation of the optical properties of seawater from measurements of exit radiance. J. Quant. Spectrosc. Radiat. Transf. 72, 551–565 (2002)

    Article  Google Scholar 

  10. Chandrasekhar, S.: Radiative Transfer. Dover Publications, Inc., New York, NY (1960)

    MATH  Google Scholar 

  11. Cotta, R.M., Cotta, B.P., Naveira-Cotta, C.P., Cotta-Pereira, G.: Hybrid integral transforms analysis of the bioheat equation with variable properties. Int. J. Therm. Sci. 49(9), 1510–1516 (2010)

    Article  Google Scholar 

  12. Elwassif, M.M., Kong, Q., Vazquez, M., Bikson, M.: Bio-heat transfer model of deep brain stimulation-induced temperature changes. J. Neural Eng. 3(4), 306 (2006)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia (1998)

    Book  Google Scholar 

  15. Hansen, P.C., O’Leary, D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14(6), 1487–1503 (1993)

    Article  MathSciNet  Google Scholar 

  16. Horvath, H., Alados Arboledas, L., Olmo, F.J., Jovanovic, O., Gangl, M., Kaller, W., Sánchez, C., Sauerzopf, H., Seidl, S.: Optical characteristics of the aerosol in Spain and Austria and its effect on radiative forcing. J. Geophys. Res. Atmos. 107, 4386 (2002)

    Article  Google Scholar 

  17. Jardim, L.C.S., Knupp, D.C., Sacco, W.F., Silva Neto, A.J.: Solution of a coupled conduction—radiation inverse heat transfer problem with the topographical global optimization method. In: Computational Intelligence in Emerging Technologies for Engineering Applications, pp. 53–71. Springer (2020)

    Google Scholar 

  18. Jiang, S.C., Ma, N., Li, H.J., Zhang, X.X.: Effects of thermal properties and geometrical dimensions on skin burn injuries. Burns 28(8), 713–717 (2002)

    Article  Google Scholar 

  19. Ke, H., Tai, S., Wang, L.V.: Photoacoustic thermography of tissue. J. Biomed. Opt. 19(2), 026003 (2014)

    Article  Google Scholar 

  20. Kengne, E., Lakhssassi, A., Vaillancourt, R.: Temperature distributions for regional hypothermia based on nonlinear bioheat equation of Pennes type: dermis and subcutaneous tissues. Appl. Math. 3(3) (2012)

    Google Scholar 

  21. Khanday, M.A., Nazir, K.: Mathematical and numerical analysis of thermal distribution in cancerous tissues under the local heat therapy. Int. J. Biomath. 10(7), 1750099 (2017)

    Article  Google Scholar 

  22. Knupp, D.C., Canato, J.V.M., Silva Neto, A.J., Soeiro, F.J.C.P.: Radiative properties estimation and construction of confidence regions with a combination of the differential evolution algorithm and the likelihood method. Proc. Ser. Braz. Soc. Comput. Appl. Math. 5(1) (2017)

    Google Scholar 

  23. Knupp, D.C., Silva Neto, A.J.: Solution of the inverse radiative transfer problem of simultaneous identification of the optical thickness and space-dependent Albedo using Bayesian inference. Comput. Model. Eng. Sci. 96(5), 339–360 (2013)

    MathSciNet  MATH  Google Scholar 

  24. Knupp, D.C., Silva Neto, A.J., Sacco, W.F.: Radiative properties estimation with the Luus-Jaakola and the particle collision algorithm. Comput. Model. Eng. Sci. (CMES) 54(2), 121 (2009)

    MathSciNet  MATH  Google Scholar 

  25. Mellal, I., Oukaira, A., Kengene, E., Lakhssassi, A.: Thermal therapy modalities for cancer treatment: a review and future perspectives. Int. J. Appl. Sci. Res. Rev. 4(2), 14 (2017)

    Article  Google Scholar 

  26. Momenroodaki, P., Haines, W., Fromandi, M., Popovic, Z.: Noninvasive internal body temperature tracking with near-field microwave radiometry. IEEE Trans. Microw. Theory Tech. 66(5), 2535–2545 (2017)

    Article  Google Scholar 

  27. Morozov, V.A.: Regularization Methods for Solving Incorrectly Posed Problems. Springer, New York, NY (1984)

    Book  Google Scholar 

  28. Moura Neto, F.D., Silva Neto, A.J.: Two equivalent approaches to obtain the gradient in algorithms for function estimation in heat conduction problems. In: Proceedings of the 34th National Heat Transfer Conference, Pittsburgh, PA (2000)

    Google Scholar 

  29. Moura Neto, F.D., Silva Neto, A.J.: An Introduction to Inverse Problems with Applications. Springer-Verlag, Berlin (2013)

    Book  Google Scholar 

  30. Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)

    Article  MathSciNet  Google Scholar 

  31. Ng, E.Y.K., Tan, H.M., Ooi, E.H.: Boundary element method with bioheat equation for skin burn injury. Burns 35(7), 987–997 (2009)

    Article  Google Scholar 

  32. Oliva Soares, P., Silva Neto, A.J., Campos Velho, H.F., Soeiro, F.J.C.P.: A two step inverse problem for vertical temperature profile retrieval in cloudy atmosphere using artificial neural networks. In: Proceedings of the 22nd International Congress of Mechanical Engineering, Ribeirão Preto, Brazil, pp. 4364–4375 (2013)

    Google Scholar 

  33. Özen, Ş., Helhel, S., Cerezci, O.: Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT). Burns 34(1), 45–49 (2008)

    Google Scholar 

  34. Özişik, M.N.: Radiative Transfer and Interactions with Conduction and Convection. Wiley, New Jersey (1973)

    Google Scholar 

  35. Özişik, M.N., Orlande, H.R.B.: Inverse Heat Transfer: Fundamentals and Applications. Taylor & Francis, New York (2000)

    Google Scholar 

  36. Pennes, H.H.: Analysis of tissue and arterial blood temperatures in the resting human forearm. J. Appl. Physiol. 1, 93–122 (1948)

    Article  Google Scholar 

  37. Pradere, C., Joanicot, M., Batsale, J.C., Toutain, J., Gourdon, C.: Processing of temperature field in chemical microreactors with infrared thermography. Quant. InfraRed Thermogr. J. 3(1), 117–135 (2006)

    Article  Google Scholar 

  38. Schena, E., Saccomandi, P., Fong, Y.: Laser ablation for cancer: past, present and future. J. Funct. Biomater. 8(2), 19 (2017)

    Article  Google Scholar 

  39. Shah, R.K.E., London, A.L.: Laminar Flow Forced Convection in Ducts. Advances in Heat Transfer, vol. 1, p. 1. Academic Press, New York (1978)

    Google Scholar 

  40. Shah, J., Park, S., Aglyamov, S.R., Larson, T., Ma, L., Sokolov, K.V., Johnston, K., Milner, T., Emelianov, S.Y.: Photoacoustic imaging and temperature measurement for photothermal cancer therapy. J. Biomed. Opt. 13(3), 034024 (2008)

    Article  Google Scholar 

  41. Silva Neto, C.A., Silva Neto, A.J.: Estimation of optical thickness, single scattering albedo and diffuse reflectivities with a minimization algorithm based on an interior points method. In: Proceedings of 17th International Congress of Mechanical Engineering, ABCM, São Paulo, SP, Brazil (2003)

    Google Scholar 

  42. Silva Neto, A.J., Özişik, M.N.: An inverse problem of simultaneous estimation of radiation phase function, albedo and optical thickness. J. Quant. Spectrosc. Radiat. Transf. 53(4), 397–409 (1995)

    Article  Google Scholar 

  43. Stephany, S., Becceneri, J.C., Souto, R.P., Campos Velho, H.F., Silva Neto, A.J.: A pre-regularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation. Appl. Math. Model. 34(3), 561–572 (2010)

    Article  MathSciNet  Google Scholar 

  44. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  Google Scholar 

  45. Tikhonov, A.N.: On the solution of ill-posed problems and the method of regularization. Dokl. Akad. Nauk SSSR 151(3), 501–504 (1963)

    MathSciNet  Google Scholar 

  46. Wang, J., Silva Neto, A.J., Moura Neto, F.D., Su, J.: Function estimation with Alifanov’s iterative regularization method in linear and nonlinear heat conduction problems. Appl. Math. Model. 26(11), 1093–1111 (2002)

    Article  Google Scholar 

  47. Wolfram Documentation Center. https://reference.wolfram.com/. Accessed 15 Mar 2021

  48. Zhang, K., Li, W., Eide, H., Stamnes, K.: A bio-optical model suitable for use in forward and inverse coupled atmosphere-ocean radiative transfer models. J. Quant. Spectrosc. Radiat. Transf. 103, 411–423 (2007)

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge the financial support provided by CAPES—Coordination of Superior Level Staff Improvement (Finance Code 001), CNPq—National Council for Scientific and Technological Development, and FAPERJ—Carlos Chagas Filho Foundation for Supporting Research in the State of Rio de Janeiro. The authors acknowledge also the CAPES PrInt program grants (Process Code 88887.469279/2019-00 and 88887.311757/2018-00). This work has been also partially funded by the Spanish Ministry of Economy and Competitiveness with the support of the project TIN2017-86647-P (including funds from the European Regional Development Fund, ERDF).

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Correspondence to Lucas Correia da Silva Jardim .

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da Silva Jardim, L.C., Knupp, D.C., de Souza Monteiro de Barros, T.M., da Silva Abreu, L.A., Corona, C.C., Neto, A.J.S. (2022). Computational Intelligence and Tikhonov Regularization with Reduced Dimension Model: Applications in Health, Renewable Energy and Climate Heat Transfer Inverse Problems. In: Verdegay, J.L., Brito, J., Cruz, C. (eds) Computational Intelligence Methodologies Applied to Sustainable Development Goals. Studies in Computational Intelligence, vol 1036. Springer, Cham. https://doi.org/10.1007/978-3-030-97344-5_8

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