MODIFIED DYNAMIC OBSERVERS BASED ON GREEN FUNCTIONS METHOD TO SOLVE A 3 D TRANSIENT IHCP

Abstract. The inverse problem can be found in a large area of science and engineering and can be applied in different ways. The great advantage of this technique is the ability of obtaining the solution of a physical problem that cannot be solved directly. Different techniques of the inverse heat conduction problem (IHCP) can be found in literature. In the dynamic observer technique, the IHCP solution algorithms are interpreted as filters passing low-frequency components of the true boundary heat flux signal while rejecting highfrequency components in order to avoid excessive amplification of measurement noise [1]. The dynamic observers technique proposed by Blum and Marquardt [1], focused on the onedimensional linear case, is here extended to solve an inverse multidimensional heat conduction problem. In order to deal with multidimensional thermal models, this work proposes an alternative way of obtaining the heat transfer function, GH. The obtaining of this function represents an important role in the observer method and is crucial to allow that the technique be directly applied to three dimensional heat conduction problems. In this work, the heat conductor transfer function GH is obtained by using the Green function concept. This new procedure allows flexibility and efficiency to solve multidimensional inverse problems. The inverse heat conduction problem is represented by an unknown heat flux heat that is partially imposed at a front surface of a sample while the other surface is kept at constant temperature. The reminiscent surfaces are exposed to convective medium. The heat flux is then estimated by using the modified dynamic observer techniques and temperature data from a sensor located at the sample far from the heat source. The novelty is the procedure used to obtain the heat transfer function. This work uses a polynomial fitting of the transfer function model GH in time domain instead the linear adjust method. The technique is evaluated in two experimental cases.