1 Copyright © 1999 by ASME Inverse Problems in Engineering: Theory and Practice 3rd Int. Conference on Inverse Problems in Engineering June 13-18, 1999, Port Ludlow, WA, USA HT14 A COMPARISON OF DIFFERENT PARAMETER ESTIMATION TECHNIQUES FOR THE IDENTIFICATION OF THERMAL CONDUCTIVITY COMPONENTS OF ORTHOTROPIC SOLIDS M. M. Mejias and H. R. B. Orlande Department of Mechanical Engineering, EE/COPPE Federal University of Rio de Janeiro, UFRJ Cid. Universitária, Cx. Postal:68503 Rio de Janeiro, RJ, 21945-970 Brasil M. N. Ozisik Department of Mechanical and Aerospace Engineering North Carolina State University, NCSU PO Box: 7910 Raleigh, NC, 27695-7910 USA ABSTRACT In this paper we examine the inverse problem of identification of the three thermal conductivity components of an orthotropic cube. For the solution of such parameter estimation problem, we consider two different versions of the Levenberg-Marquardt method and four different versions of the conjugate gradient method. The techniques are compared in terms of rate of reduction of the objective function with respect to the number of iterations, CPU time and accuracy of the estimated parameters. Simulated measurements with and without measurement errors are used in the analysis, for three different sets of exact values for the parameters. NOMENCLATURE I number of transient measurements per sensor J sensitivity coefficients J sensitivity matrix defined by equation (7) k 1 ,k 2 ,k 3 thermal conductivities in the x, y and z directions, respectively M number of sensors P vector of unknown parameters S least-squares norm defined by equation (5) T vector of estimated temperatures t h , t f heating time and final time Y vector of measured temperatures GREEKS σ standard deviation of the measurement errors INTRODUCTION In nature, several materials have direction-dependent thermal conductivities including, among others, woods and crystals. This is also the case for some man-made materials, for example, composites. Such kind of materials is denoted anisotropic, as an opposition to isotropic materials, in which the thermal conductivity does not vary with direction. A special case of anisotropic materials involve those where the off- diagonal elements of the conductivity tensor are null and the diagonal elements are the principal conductivities along three mutually orthogonal directions. They are referred to as orthotropic materials (Ozisik, 1993). As a result of the importance of orthotropic materials in nowadays engineering, a lot of attention has been devoted in the recent past to the estimation of their thermal properties, by using inverse analysis techniques of parameter estimation (Sawaf and Ozisik, 1995, Sawaf et al, 1995, Taktak et al, 1993, Taktak, 1992, Dowding et al, 1995, 1996, Mejias et al, 1999). In this paper we present a comparison of different methods of parameter estimation, as applied to the identification of the three thermal conductivity components of an orthotropic solid, by using simulated experimental data. Such a physical problem was chosen for comparison of the methods because it requires non-linear estimation procedures, since the sensitivity coefficients are functions of the unknown parameters. Experimental variables used in the analysis, such as the duration of the experiment, location of sensors and boundary conditions, were optimally chosen (Mejias et al, 1999). The methods examined in this work include: the Levenberg-Marquardt Method (Levenberg, 1944, Marquardt, 1963, Beck and Arnold, 1977, Moré, 1977, Mejias et al, 1999, Ozisik and Orlande,