Version étendue du filtre de Kalman discret appliquée à un problème inverse de conduction de chaleur non linéaire

Daouas, Naouel; Radhouani, Mohamed-Sassi

doi:10.1016/s1290-0729(00)00239-8

Cited by 25 publications

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“…), and have also been applied successfully in IHCP in order to get a stable estimation. In this frame, the well-known Kalman filtering technique [15] has been used to resolve linear and non-linear IHCP [16,17]. The use of an artificial neural network (ANN) has also been considered in the IHCP [18].…”

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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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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“…On the other hand, one can note reduction of oscillations which means that the solution becomes less sensitive to measurement errors. So the choice of σ q must satisfy a compromise between stability and precision as explained in [9]. The use of the extended Kalman filter smoothing technique with an optimal number of future time data provides a symmetrical and more stable solution that is in good agreement with the heat flux density estimated with the Raynaud method (see Figure 6b).…”

Section: Resultsmentioning

confidence: 96%

“…The inverse time step (time interval separating two successive measurements) is taken as ∆t=0.1s. The standard deviation of the modeling error which is a stabilizing parameter in the Kalman filter algorithm [7,9], is assumed to be constant and is taken as σ q =100W/m². This parameter is associated with the diagonal covariance matrix Q whose only element different from zero is the variance 2 q σ so as to compensate the model mismatch caused by the unknown heat flux approximation with a piecewise constant function.…”

Section: Resultsmentioning

confidence: 99%

“…The proposed algorithm is a combination of the extended Kalman filter [9] with a new version of the fixed interval smoothing technique [8] capable of handling the nonlinear inverse heat conduction problem under study. Nonlinear equations of the problem are modified by linearization about some reference state vector.…”

Section: The Extended Kalman Smoothing Techniquementioning

confidence: 99%

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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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“…6c page 2676 in [4]). Recursive methods have also been used [8][9][10], but the solution is not totally satisfactory for sharp variations ( fig. 4d page 279 in [10]).…”

Section: Introductionmentioning

confidence: 99%

Evaluating time-dependent heat fluxes using artificial neural networks

Lecœuche

Mercère

Lalot

2006

Inverse Problems in Science and Engineering

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The inverse heat conduction problem (IHCP) is still challenging. Here is presented a new application of recurrent neural networks to estimate the heat flux applied on one side of a structure from the knowledge of the temperature measured at the other side of the structure (standard one-dimensional conducting bar). In the first part of the article the direct problem is solved and a model is determined. The mathematical inversion of this model leading to unsatisfactory results, a second approach is given in the second part of the study: to directly determine a representation of the mapping between the temperatures and the heat fluxes. After showing that satisfactory results are obtained when noisy data are considered, a final validation is carried out by coupling the direct model and the inverse model. The results are promising and it can be considered that recurrent neural networks are helpful tools to approach the solution of an inverse heat conduction problem.

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Version étendue du filtre de Kalman discret appliquée à un problème inverse de conduction de chaleur non linéaire

Cited by 25 publications

References 0 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

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

Evaluating time-dependent heat fluxes using artificial neural networks

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