Solution of the Inverse Heat Conduction Problem With a Time-Variable Number of Future Temperatures

Blanc, Gilles Le; Beck, James V.; Raynaud, M.

doi:10.1080/10407799708915018

Cited by 39 publications

(29 citation statements)

References 10 publications

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“…and the matrices are (13) where the previous history is stored in matrix [H] and vector q hist . The vectors and matrix related with future temperatures are: T fut , q fut and [X fut ].…”

Section: Sequential Svd Algorithmmentioning

confidence: 99%

“…Zabaras and Lyu [12] combine the Boundary Element Method (BEM) in conjunction with Beck's sensitivity analysis and least-squares method. Blanc et al [13], introduced a modification in the FSM, so that the new algorithm uses a time-variable number of future temperatures. Beck et al [14] compare the FSM, the Tikhonov regularization and the iterative regularization, using experimental data.…”

Section: Introductionmentioning

confidence: 99%

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A sequential algorithm of inverse heat conduction problems using singular value decomposition

Cabeza

García

Rodríguez

2005

International Journal of Thermal Sciences

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“…and the matrices are (13) where the previous history is stored in matrix [H] and vector q hist . The vectors and matrix related with future temperatures are: T fut , q fut and [X fut ].…”

Section: Sequential Svd Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A sequential algorithm of inverse heat conduction problems using singular value decomposition

Cabeza

García

Rodríguez

2005

International Journal of Thermal Sciences

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“…The inverse calculations have been applied to find the solution of heat transfer [2][3][4][5], but their application in manufacturing processes has been reported in only a few cases. Huang et al [6] used the conjugate gradient method to inversely calculate the unknown conductivities in metal castings.…”

Section: Introductionmentioning

confidence: 99%

Friction coefficient investigation on IC dam-bar trimming process by inverse method with experimental trimmed geometric profiles

Lin

Chen²

2007

International Journal of Machine Tools and Manufacture

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“…This method underwent different improvements. It was combined by Osman et al in [13] with a regularization technique, then modified by Blanc et al in [5] using a time-variable number of future temperatures. Raynaud and Bransier have also introduced in [16] future time temperatures in the analysis of the IHCP using a space-marching finite-difference procedure which is as precise as the Beck's method.…”

Section: Introductionmentioning

confidence: 99%

Experimental validation of an extended Kalman smoothing technique for solving nonlinear inverse heat conduction problems

Daouas

Radhouani

2007

Inverse Problems in Science and Engineering

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-A new approach combining the use of the Kalman filter with an extended version of a smoothing technique and introducing the use of future time measurements is developed in order to improve the solution of a nonlinear Inverse Heat Conduction Problem (IHCP). The behavior of the proposed algorithm is analyzed in presence of a real set of experimental noisy temperature measurements. Estimation results are validated by using a space marching technique proposed by Raynaud and Bransier whose performance is already known for the solution of the nonlinear IHCP. The influence of the number of future time data on the precision and the stability of the solution is analyzed according to the inverse time step, the location of measurement sensor and the standard deviation associated with the modeling error. INTRODUCTIONDue to the diffusive nature of the heat conduction, surface temperature changes are damped and lagged in the interior of the solid. So small inaccuracies in the measured interior temperatures can cause large oscillations in the estimated surface conditions which can show a time lag dependent on the measurement location. Based on the fact that the response of a temperature sensor placed at a distance below a heated surface can continue to rise even after the applied surface heat flux returns to zero, Beck was the first to recognize that a precise estimation of surface conditions requires the use of temperatures measured at times ulterior to the time of estimation and known as future time measurements, [12].The use of future temperatures was first applied by Beck in In this study, we introduce the use of future time measurements in a new approach combining the Kalman filter, [6] with an extended version of a smoothing technique. The proposed algorithm is developed in order to improve the solution of a nonlinear transient one-dimensional IHCP involving reconstruction of the heat flux density and the temperature at the surface of a cylindrical heat conducting solid. The aim of this work is to analyze the behavior of the extended Kalman smoothing technique in presence of a real set of experimental noisy temperature measurements.The influence of the number of future time data on the accuracy and the stability of the solution is studied according to the location of measurement sensors, the standard deviation associated with the modeling error and the inverse time step. Estimation results are validated with the solution of the space marching technique proposed by Raynaud and Bransier in [16], which is simple, rapid and easily adapt to nonlinear problems and whose performance is already known as shown in [15].

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Solution of the Inverse Heat Conduction Problem With a Time-Variable Number of Future Temperatures

Cited by 39 publications

References 10 publications

A sequential algorithm of inverse heat conduction problems using singular value decomposition

A sequential algorithm of inverse heat conduction problems using singular value decomposition

Friction coefficient investigation on IC dam-bar trimming process by inverse method with experimental trimmed geometric profiles

Experimental validation of an extended Kalman smoothing technique for solving nonlinear inverse heat conduction problems

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