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Real‐time monitoring of thermal processes by reduced‐order modeling
Author(s) -
Aguado José V.,
Huerta Antonio,
Chinesta Francisco,
Cueto Elías
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4784
Subject(s) - transfer function , computer science , reciprocity (cultural anthropology) , reduction (mathematics) , time domain , process (computing) , model order reduction , function (biology) , algorithm , mathematical optimization , control theory (sociology) , mathematics , engineering , artificial intelligence , control (management) , electrical engineering , computer vision , operating system , evolutionary biology , biology , psychology , social psychology , projection (relational algebra) , geometry
Summary This work presents a simple technique for real‐time monitoring of thermal processes. Real‐time simulation‐based control of thermal processes is a big challenge because high‐fidelity numerical simulations are costly and cannot be used, in general, for real‐time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real time the transient heat equation at the monitored point. In order to apply the reciprocity principle , harmonic analysis is used in the space‐frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre‐computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post‐processing step. This last step can be performed online for real‐time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems. Copyright © 2014 John Wiley & Sons, Ltd.