A Modal Identification Method To Reduce A High-Order Model: Application To Heat Conduction Modelling

Abstract

AbstractThis paper presents a model reduction method for linear multivariable systema. In order to reduce the high-order model, the authors use here a specific state-space representation including the input derivative with respect to time. This formulation emphasizes a static matrix, allowing description of the instantaneous asymptotic behaviour of the system. The dynamics of the Reduced Model (RM) intervenes to adjust this instantaneous behaviour. This formulation enables the preservation of any stationary state.The RM is made up of several Elementary Reduced Models (ERM): each is related to one stimulus of the system and is identified in a modal base with its corresponding order, eigenvalues, and matrices. Only numerical simulations executed with the Detailed Model (DM) are needed; it is not necessary to know DM equations.An application is given that illustrates the method applied to diffusive heat transfer modelling within an electronic component. From this three-dimensional model of order 1643 obtained through the finite element method, the authors show the possibility of obtaining a satisfactory RM of order 26 with 3 inputs (thermal sources) and 27 outputs (the more interesting node temperatures).This model allows the reduction of computational by a factor of 8,000 according to the 27 observed outputs. Different kinds of simulations are compared, demonstrating that RM is very close to DM.Keywords:: Multivariable linear systemsstate-space representationmodel reductionmodal analysisidentificationoptimizationfinite elementsheat conduction Additional informationNotes on contributorsD. PetitRémy Hachette was born in 1966. He received his Ph.D. degree in Mechanics - Heat Transfer in 1995. Actually doing post doctoral studies at Université de Quebec, Chicoutimi, Canada.R. HachetteDamien Veyret was born in 1966. He received his Ph.D. degree in Mechanics - Energy in 1991. Since 1992 he has been a Researcher for the CNRS (National Center for Scientific Research), specializing in numerical methods (finite element methods, model reduction, integration scheme, segregated solvers).D. VeyretDaniel Petit was born in 1950. Since 1995, he has been a Professor at the University of Poitiers, specializing in heat transfer, modelling, model reduction, inverse problems.