A New Approach of the Kalman Filter Using Future Temperature Measurements for Nonlinear Inverse Heat Conduction Problems

Daouas, Naouel; Radhouani, Mohamed-Sassi

doi:10.1080/10407790490430598

Cited by 52 publications

(17 citation statements)

References 12 publications

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“…As shown in Figures 4 and 5, a farther sensor from the surface requires a larger number n f of future time measurements. An optimal value of this number is obtained by increasing it progressively until it provides only a negligible improvement on the estimates as described in [8]. These results are also illustrated by calculating values of the global relative error (ERR) and the maximum relative error shown in Table 1.…”

Section: Resultsmentioning

confidence: 81%

“…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%

“…We adopt the same linearization used with the extended Kalman filter in [6], whose reference vector is updated with the filter's estimates getting at each time the value of the last available estimation. So the fixed interval smoothing technique leads to the following recursive relation, [8]:…”

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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Section: Resultsmentioning

confidence: 81%

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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“…As a result, the heat conduction problem will become nonlinear. The estimat ion of the unknown boundary conditions for the nonlinear IHCP is more co mp licated than those for the linear IHCP [11][12]. Among the well-known methods for boundary estimat ion problems, the gradient methods have received the most attention.…”

Section: Introductionmentioning

confidence: 99%

“…The unknown thermal coefficients on the mathematical model (i.e., thermal properties, boundary or initial conditions) that lead to an acceptable value for the aforementioned error function, based on the iterative regularization method, are the solution of the IHCP. In addit ion to textbooks [1,2] available in the literature, nu merous recent published researches have discussed the estimat ion of boundary conditions in IHCP [3][4][5][6][7][8][9][10][11][12]. Most of the previous work was restricted to problems with constant thermophysical properties.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for nonlinear inverse heat conduction problem

Qian¹,

Wang²

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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Abstract-Inverse Heat Conduction Problems(IHCPs) have been extensi vely studied over the last 60 years. They have numerous applications in many branches of science and technol ogy.The problem consists in determining the temperature and heat flux at inaccessible parts of the boundary of a 2-or 3-di mension al body from correspondi ng data-called " Cauchy data" on accessible parts of the boundary. It is well-known that IHCPs are severely ill-posed which means that small perturbations in the data may cause extremely large errors in the soluti on. In this contri buti on, I present an anal ysis of numerical soluti on of nonlinear inverse heat conduction problem in a region wi th movi ng boundaries, a regul arizati on method is used to construct an algorithm for smoothing the experi mental data in a complication of the input data for the i nverse problem.

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Rapid Online Estimation of Time-Varying Thermal Boundary Conditions in Convective Heat Transfer Problem by ANN-Based Extended Kalman Smoothing Algorithm

Zhang,

Li,

Cheng

et al. 2024

Mechanisms and Machine Science

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A New Approach of the Kalman Filter Using Future Temperature Measurements for Nonlinear Inverse Heat Conduction Problems

Cited by 52 publications

References 12 publications

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

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

A numerical method for nonlinear inverse heat conduction problem

Rapid Online Estimation of Time-Varying Thermal Boundary Conditions in Convective Heat Transfer Problem by ANN-Based Extended Kalman Smoothing Algorithm

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