文章基本信息

标题：Heat equation parameter estimation based on the POD-Galerkin approach
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作者：Duc-Cuong Pham ; Guillaume Mercère ; Régis Ouvrard 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：15
页码：245-250
DOI：10.1016/j.ifacol.2018.09.142
语种：English
出版社：Elsevier
摘要：AbstractThe proper orthogonal decomposition (POD), a mathematical procedure initially developed to determine low-dimensional approximated descriptions of high-dimensional functions, has already proved its efficiency for model reduction of linear and non-linear systems. In this paper, the POD and the Galerkin projection methods are combined to estimate the thermal diffusivity parameter of a wall, the behavior of which is assumed to be modeled by the famous heat partial differential equation (PDE). According to this approach, empirical orthogonal functions are first extracted from the POD, then used by the Galerkin method to transform the initial PDE into a set of ordinary differential equations (ODEs). These ODEs explicitly contain the parameter to be identified which is estimated in this contribution by using the Levenberg-Marquardt algorithm. Simulation results are provided to illustrate the effectiveness of this multi-step approach.
关键词：KeywordsSystem identificationPartial differential equationHeat equationProper orthogonal decompositionGalerkin method