Abstract
This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.
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References
Alifanov OM (1977) Determination of heat loads from a solution of the nonlinear inverse problem. High Temp 15(3):498–504
Alifanov OM (1994) Inverse heat transfer problems. Springer, New York
Beck JV, Blackwell B, St Clair CR (1985) Inverse heat conduction: Ill-posed problems. Wiley, New York
Green P, Silverman B (1994) Nonparametric regression and generalized linear models: a roughness penalty approach. Chapman & Hall/CRC Press, Boca Raton
Hadamard J (1923) Lectures on Cauchys problem in linear differential equations. In: Technical report. Yale University, New Haven
Jakubowska M (2011) Signal processing in electrochemistry. Electroanalysis 23:553–572
Kabala ZJ (1997) Inverse thermal problems. Am Sci 85(3):288
Kaipio JP, Fox C (2011) The Bayesian framework for inverse problems in heat transfer, vol 32
Kim HJ, Kim NK, Kwak JS (2006) Heat flux distribution model by sequential algorithm of inverse heat transfer determining workpiece temperature in creep feed grinding. Int J Mach Tool Man 46:2086–2093
Oliveira J, Santos J, Seleghim P Jr (2006) Inverse measurement method for detecting bubbles in a fluidized bed reactor-toward the development of an intelligent temperature sensor. Powder Technol 169:123–135
Orlande HRB (2011) Inverse heat transfer problems, vol 32. doi:10.1080/01457632.2011.525128
Özisik H, Orlande HRB (2000) Inverse heat transfer: fundamentals and applications. Taylor & Francis, New York
Park HM, Chung OY, Lee JH (1999) On the solution of inverse heat transfer problem using the Karhunen–loève Galerkin method. Int J Heat Mass Transf 42(1):127–142
Pollock DSG (1993) Smoothing with cubic splines. In: Technical report
Reinsch CH (1967) Smoothing by spline function. Numer Math 10:177–183
Tikhonov AN, Arsenin VY (1977) Solution of Ill—posed problems. Winston & Sons, Washington
Weinert HL (2009) A fast compact algorithm for cubic spline smoothing. Comput Stat Data Anal 53:932–940
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Communicated by Cristina Turner.
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Kubo, L.H., de Oliveira, J. Smoothing by cubic spline modified applied to solve inverse thermal problem. Comp. Appl. Math. 37, 1162–1174 (2018). https://doi.org/10.1007/s40314-016-0385-x
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DOI: https://doi.org/10.1007/s40314-016-0385-x