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

Abstract

-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].

Finite Element Method for Heat Transfer Phenomenon on a Closed Rectangular Plate

“…Many improvements had been proposed on the work or method of Beck [4][5][6]. Many authors [2,[7][8][9][10][11][12][13] had improved on the solution to IHCP especially with the introduction of future time measurement concepts.…”