Incorporating engineering intuition for parameter estimation in thermal sciences
Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic...
Ausführliche Beschreibung
Autor*in: |
Balaji, C. [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2013 |
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Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2013 |
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Übergeordnetes Werk: |
Enthalten in: Heat and mass transfer - Berlin : Springer, 1968, 49(2013), 12 vom: 17. Aug., Seite 1771-1785 |
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Übergeordnetes Werk: |
volume:49 ; year:2013 ; number:12 ; day:17 ; month:08 ; pages:1771-1785 |
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DOI / URN: |
10.1007/s00231-013-1213-0 |
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Katalog-ID: |
SPR002629453 |
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520 | |a Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. | ||
650 | 4 | |a Nusselt Number |7 (dpeaa)DE-He213 | |
650 | 4 | |a Asymptotic Variant |7 (dpeaa)DE-He213 | |
650 | 4 | |a Posterior Probability Density Function |7 (dpeaa)DE-He213 | |
650 | 4 | |a Transient Heating |7 (dpeaa)DE-He213 | |
650 | 4 | |a Thermochromic Liquid Crystal |7 (dpeaa)DE-He213 | |
700 | 1 | |a Reddy, B. Konda |4 aut | |
700 | 1 | |a Herwig, H. |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Heat and mass transfer |d Berlin : Springer, 1968 |g 49(2013), 12 vom: 17. Aug., Seite 1771-1785 |w (DE-627)27012635X |w (DE-600)1476367-9 |x 1432-1181 |7 nnns |
773 | 1 | 8 | |g volume:49 |g year:2013 |g number:12 |g day:17 |g month:08 |g pages:1771-1785 |
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10.1007/s00231-013-1213-0 doi (DE-627)SPR002629453 (SPR)s00231-013-1213-0-e DE-627 ger DE-627 rakwb eng Balaji, C. verfasserin aut Incorporating engineering intuition for parameter estimation in thermal sciences 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 Reddy, B. Konda aut Herwig, H. aut Enthalten in Heat and mass transfer Berlin : Springer, 1968 49(2013), 12 vom: 17. Aug., Seite 1771-1785 (DE-627)27012635X (DE-600)1476367-9 1432-1181 nnns volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 https://dx.doi.org/10.1007/s00231-013-1213-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2013 12 17 08 1771-1785 |
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10.1007/s00231-013-1213-0 doi (DE-627)SPR002629453 (SPR)s00231-013-1213-0-e DE-627 ger DE-627 rakwb eng Balaji, C. verfasserin aut Incorporating engineering intuition for parameter estimation in thermal sciences 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 Reddy, B. Konda aut Herwig, H. aut Enthalten in Heat and mass transfer Berlin : Springer, 1968 49(2013), 12 vom: 17. Aug., Seite 1771-1785 (DE-627)27012635X (DE-600)1476367-9 1432-1181 nnns volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 https://dx.doi.org/10.1007/s00231-013-1213-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2013 12 17 08 1771-1785 |
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10.1007/s00231-013-1213-0 doi (DE-627)SPR002629453 (SPR)s00231-013-1213-0-e DE-627 ger DE-627 rakwb eng Balaji, C. verfasserin aut Incorporating engineering intuition for parameter estimation in thermal sciences 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 Reddy, B. Konda aut Herwig, H. aut Enthalten in Heat and mass transfer Berlin : Springer, 1968 49(2013), 12 vom: 17. Aug., Seite 1771-1785 (DE-627)27012635X (DE-600)1476367-9 1432-1181 nnns volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 https://dx.doi.org/10.1007/s00231-013-1213-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2013 12 17 08 1771-1785 |
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10.1007/s00231-013-1213-0 doi (DE-627)SPR002629453 (SPR)s00231-013-1213-0-e DE-627 ger DE-627 rakwb eng Balaji, C. verfasserin aut Incorporating engineering intuition for parameter estimation in thermal sciences 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 Reddy, B. Konda aut Herwig, H. aut Enthalten in Heat and mass transfer Berlin : Springer, 1968 49(2013), 12 vom: 17. Aug., Seite 1771-1785 (DE-627)27012635X (DE-600)1476367-9 1432-1181 nnns volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 https://dx.doi.org/10.1007/s00231-013-1213-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2013 12 17 08 1771-1785 |
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10.1007/s00231-013-1213-0 doi (DE-627)SPR002629453 (SPR)s00231-013-1213-0-e DE-627 ger DE-627 rakwb eng Balaji, C. verfasserin aut Incorporating engineering intuition for parameter estimation in thermal sciences 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 Reddy, B. Konda aut Herwig, H. aut Enthalten in Heat and mass transfer Berlin : Springer, 1968 49(2013), 12 vom: 17. Aug., Seite 1771-1785 (DE-627)27012635X (DE-600)1476367-9 1432-1181 nnns volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 https://dx.doi.org/10.1007/s00231-013-1213-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2013 12 17 08 1771-1785 |
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Enthalten in Heat and mass transfer 49(2013), 12 vom: 17. Aug., Seite 1771-1785 volume:49 year:2013 number:12 day:17 month:08 pages:1771-1785 |
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Nusselt Number Asymptotic Variant Posterior Probability Density Function Transient Heating Thermochromic Liquid Crystal |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR002629453</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327155846.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2013 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00231-013-1213-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR002629453</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00231-013-1213-0-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Balaji, C.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Incorporating engineering intuition for parameter estimation in thermal sciences</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nusselt Number</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic Variant</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Posterior Probability Density Function</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transient Heating</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thermochromic Liquid Crystal</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Reddy, B. Konda</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Herwig, H.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Heat and mass transfer</subfield><subfield code="d">Berlin : Springer, 1968</subfield><subfield code="g">49(2013), 12 vom: 17. 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Balaji, C. |
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Balaji, C. misc Nusselt Number misc Asymptotic Variant misc Posterior Probability Density Function misc Transient Heating misc Thermochromic Liquid Crystal Incorporating engineering intuition for parameter estimation in thermal sciences |
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Incorporating engineering intuition for parameter estimation in thermal sciences Nusselt Number (dpeaa)DE-He213 Asymptotic Variant (dpeaa)DE-He213 Posterior Probability Density Function (dpeaa)DE-He213 Transient Heating (dpeaa)DE-He213 Thermochromic Liquid Crystal (dpeaa)DE-He213 |
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misc Nusselt Number misc Asymptotic Variant misc Posterior Probability Density Function misc Transient Heating misc Thermochromic Liquid Crystal |
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misc Nusselt Number misc Asymptotic Variant misc Posterior Probability Density Function misc Transient Heating misc Thermochromic Liquid Crystal |
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incorporating engineering intuition for parameter estimation in thermal sciences |
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Incorporating engineering intuition for parameter estimation in thermal sciences |
abstract |
Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. © Springer-Verlag Berlin Heidelberg 2013 |
abstractGer |
Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. © Springer-Verlag Berlin Heidelberg 2013 |
abstract_unstemmed |
Abstract This paper proposes a new method of incorporating priors based on engineering intuition for solving inverse problems. The thesis of this paper is that if an asymptote can be found to a problem in applied sciences or engineering, estimation of parameters can be first done for this asymptotic variant, which in principle should be simpler, since one or more parameters of the original problem may vanish for the asymptotic variant. Even so, by solving the inverse problem associated with the asymptotic variant, estimates of key parameters of the full problem can be obtained. This information can then be quantitatively incorporated as priors in the estimation of parameters for the full version of the problem which we call as prior generation through asymptotic variant. The goal is to see if this methodology will significantly reduce the uncertainties in the resulting estimates. To demonstrate this methodology, the classic problem of unsteady heat transfer from a one dimensional fin is chosen. The inverse problem is posed as the simultaneous estimation of the temperature dependent transfer coefficient ($ h_{θ} $) and the thermal diffusivity (α) of the fin material, given experimentally measured temperature–time histories at various locations along the fin. The asymptotic variant θ(x,t) is the steady state problem where the influence of thermal diffusivity vanishes. Using surrogate temperature data generated from assumed values of $ h_{θ} $, first the asymptotic variant of the problem is solved using the Markov Chain Monte Carlo method in a Bayesian framework to generate an estimate of $ h_{θ} $. The estimate of $ h_{θ} $ is then used as an informative prior for solving the inverse problem of determining $ h_{θ} $ and α from θ(x,t), and the effect of prior is quantitatively assessed by performing estimation with and without the prior. Finally, for purposes of validation, in-house experiments have been done where θ(x,t) is generated using liquid crystal thermography and these data are used to estimate $ h_{θ} $ and α. A comparison of experimentally measured temperatures with those that are simulated by using estimated values of ($ h_{θ} $, α) to solve the governing equation to the problem is also done. © Springer-Verlag Berlin Heidelberg 2013 |
collection_details |
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container_issue |
12 |
title_short |
Incorporating engineering intuition for parameter estimation in thermal sciences |
url |
https://dx.doi.org/10.1007/s00231-013-1213-0 |
remote_bool |
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author2 |
Reddy, B. Konda Herwig, H. |
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Reddy, B. Konda Herwig, H. |
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doi_str |
10.1007/s00231-013-1213-0 |
up_date |
2024-07-03T14:10:45.181Z |
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|
score |
7.398595 |