Abstract—Thermal efficiency prediction for heat exchangers is a great challenge for environmental purposes. In spite of technological developments in order to optimize materials or design, fouling phenomena are quite difficult to take into account. This important constraint for heat exchangers efficiency has to be carefully estimated and new sensors are developed in order to inform experimenters about fouling thickness evolution. In this communication, a mathematical model for fouling state prediction is proposed. Thermal system analysis is performed and from experimental observations, identification methodologies are carried out and lead to the identification of unknown model parameters. I. INTRODUCTION HIS communication is dedicated to parameters identification for a thermal system encountered in an industrial framework. The application purpose is the design of a new probe in order to accurately estimate in situ not only the exchange coefficient but also the fouling thickness of cross flow tubular heat exchangers from reliable transient state identification methods. Frequently, in industrial gaseous systems, the effectiveness of heat exchangers can decrease because of fouling deposition onto the heat transfer surface. Some gas-side fouling measuring devices have been envisaged. All of them allow to obtain physical information on fouling. Nevertheless, they are still far from giving thermal information and taking into account the deposit phenomena involved. Investigating heat transfer in an heat exchanger is crucial to determine optimal condition and to ensure safety processes. In fouling conditions, the formulation of a predictive mathematical model requires the identification of unknown model parameters. The non-stationary state and non-linearity of the studied process reduce the possibility of using many traditional design-and-theoretical and experimental methods. The approach based on observations of the system state to specify the unknown parameters is known as inverse method (in other words, to find not causal- sequential, as in direct problems, but rather sequential-causal quantitative relations). Inverse heat transfer problems are Manuscript received February 28, 2005. This work was supported in part by the University of Perpignan. Laetitia Perez was with the ENSTIMAC, 81013 Albi cedex, France. She is now with the PROMES Institute, Rambla de la thermodynamique, 66000 Perpignan, FRANCE (e-mail: laetitia.perez@univ-perp.fr). Laurent Autrique is with GHF, 10 rue des fours solaires BP 6, 66125 Font-Romeu Odeillo, France (e-mail: autrique@univ-perp.fr). Jean-Christophe Batsale is with TREFLE-ENSAM, esplanade des arts et métiers, 33405 Talence, cedex, France (email: batsale@u- bordeaux.ensam.fr). widely investigated (see [1]) since the formulation of ill- posed inverse problem by Hadamard: an inverse problem is well-posed if it satisfies the three Hadamard’s conditions of existence, uniqueness and stability. If any of the previous conditions are not satisfied, then the problem is ill-posed. For continuous diffusive systems such the thermal process studied in this paper, the inverse operator is ill-conditioned and the presence of measurement noises in the observed data makes the problem unstable; the inverse problem is then ill posed. Overcoming the ill-posedness of inverse problem is known as regularization. The key issue in solving inverse problems, is how to introduce just enough prior information to obtain a satisfactory result [2]. Several techniques for regularizing and solving ill-posed problems have been proposed and used. One first simple idea consisted on choosing a restricted class of inputs : steps, band limited signals, polynomial bases … A more attractive technique, however, does not use constraint on the input signal structure but build a regularization operator depending on a numerical parameter called the regularization parameter. Tikhonov first suggests the use a smoothing function to account for prior information. The determination of the optimal value for the smoothing parameter remains an open problem. A commonly used procedure is based on the Morozov's discrepancy principle ([3] and the references therein) assuming that a bound on measurement errors statistics is known. In other situations, a Bayesian inference is preferred and the maximum entropy principle makes it possible to take into account any prior knowledge on the unknown parameters and measurement noises. In the specific framework of inverse heat transfer problem, three classes can be considered: - inverse problems that arise in the diagnostic and identification of physical processes, - inverse problems that arise in the design of engineering products, - inverse problems that arise in the control of processes and systems. The problem of the determination of a model for predicting fouling state evolution in a heat exchanger depends on the previous first class. In the following, the experimental situation and the partial differential equations system describing the process state evolution are exposed. Then a sensitivity analysis is performed in order to ensure efficient identification conditions. State observations are then exposed and several identification methods are investigated. Finally, model prediction is compared to experimental measurements. Parameters identification in a physical system for thermal efficiency prediction L. Perez, L. Autrique and J.C. Batsale T Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 Seville, Spain, December 12-15, 2005 WeC04.5 0-7803-9568-9/05/$20.00 ©2005 IEEE 5722