Identification strategies for model-based control
Identifieur interne : 004E95 ( Main/Exploration ); précédent : 004E94; suivant : 004E96Identification strategies for model-based control
Auteurs : Laurent Cordier [France] ; Bernd R. Noack [France] ; Gilles Tissot [France] ; Guillaume Lehnasch [France] ; Joël Delville [France] ; Maciej Balajewicz [États-Unis] ; Guillaume Daviller [France] ; Robert K. Niven [Australie]Source :
- Experiments in fluids [ 0723-4864 ] ; 2013.
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Abstract
A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To understand more deeply this behaviour, a hierarchy of POD ROMs is studied and compared for a two-dimensional uncontrolled mixing layer. First, dynamical models based on POD are derived from the Navier-Stokes and the vorticity equations. It is shown that these models can exhibit for some truncation level finite-time blow-ups. A symmetrized quadratic model is then proposed to enforce the preservation of energy in the model. This formulation improves considerably the behaviour of the model, but the energy level is still overestimated. Subsequently, a nonlinear eddy-viscosity model with guaranteed stability is proposed. This model still leads to an imperfect description of the energy. Different 4D-Var identification strategies are then considered to improve the nonlinear eddy-viscosity model. It is shown that penalizing the time variation in the eddy-viscosity parameter leads to the best compromise in terms of description of the energy and of physical relevance of the eddy viscosity. Lastly, a statistical inference procedure is used to take into account the bias inherent of the sampling employed in the identification procedure. Joined probability density functions are then determined empirically for all the coefficients of the model, and a stochastic dynamical model is finally derived to study the influence on the long-term solution of different equiprobable sets of coefficients.
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Niven</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>School of Engineering and Information Technology, The University of New South Wales at ADFA</s1><s2>Canberra, ACT 2600</s2><s3>AUS</s3><sZ>8 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra, ACT 2600</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">13-0309817</idno><date when="2013">2013</date><idno type="stanalyst">PASCAL 13-0309817 INIST</idno><idno type="RBID">Pascal:13-0309817</idno><idno type="wicri:Area/PascalFrancis/Corpus">000810</idno><idno type="wicri:Area/PascalFrancis/Curation">005678</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000894</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000894</idno><idno type="wicri:doubleKey">0723-4864:2013:Cordier L:identification:strategies:for</idno><idno type="wicri:Area/Main/Merge">005068</idno><idno type="wicri:Area/Main/Curation">004E95</idno><idno type="wicri:Area/Main/Exploration">004E95</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Identification strategies for model-based control</title><author><name sortKey="Cordier, Laurent" sort="Cordier, Laurent" uniqKey="Cordier L" first="Laurent" last="Cordier">Laurent Cordier</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region><region type="old region" nuts="2">Poitou-Charentes</region><settlement type="city">Poitiers</settlement></placeName></affiliation></author><author><name sortKey="Noack, Bernd R" sort="Noack, Bernd R" uniqKey="Noack B" first="Bernd R." last="Noack">Bernd R. Noack</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region><region type="old region" nuts="2">Poitou-Charentes</region><settlement type="city">Poitiers</settlement></placeName></affiliation></author><author><name sortKey="Tissot, Gilles" sort="Tissot, Gilles" uniqKey="Tissot G" first="Gilles" last="Tissot">Gilles Tissot</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region><region type="old region" nuts="2">Poitou-Charentes</region><settlement type="city">Poitiers</settlement></placeName></affiliation></author><author><name sortKey="Lehnasch, Guillaume" sort="Lehnasch, Guillaume" uniqKey="Lehnasch G" first="Guillaume" last="Lehnasch">Guillaume Lehnasch</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region><region type="old region" nuts="2">Poitou-Charentes</region><settlement type="city">Poitiers</settlement></placeName></affiliation></author><author><name sortKey="Delville, Joel" sort="Delville, Joel" uniqKey="Delville J" first="Joël" last="Delville">Joël Delville</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Nouvelle-Aquitaine</region><region type="old region" nuts="2">Poitou-Charentes</region><settlement type="city">Poitiers</settlement></placeName></affiliation></author><author><name sortKey="Balajewicz, Maciej" sort="Balajewicz, Maciej" uniqKey="Balajewicz M" first="Maciej" last="Balajewicz">Maciej Balajewicz</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Mechanical Engineering and Materials Sciences, Duke University</s1><s2>Durham, NC 27708-0287</s2><s3>USA</s3><sZ>6 aut.</sZ></inist:fA14><country>États-Unis</country><wicri:noRegion>Durham, NC 27708-0287</wicri:noRegion></affiliation></author><author><name sortKey="Daviller, Guillaume" sort="Daviller, Guillaume" uniqKey="Daviller G" first="Guillaume" last="Daviller">Guillaume Daviller</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Institut Pprime, CNRS - Université de Poitiers - ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l'Aérodrome</s1><s2>86036 Poitiers</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>86036 Poitiers</wicri:noRegion><wicri:noRegion>43 rue de l'Aérodrome</wicri:noRegion><wicri:noRegion>86036 Poitiers</wicri:noRegion></affiliation></author><author><name sortKey="Niven, Robert K" sort="Niven, Robert K" uniqKey="Niven R" first="Robert K." last="Niven">Robert K. Niven</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>School of Engineering and Information Technology, The University of New South Wales at ADFA</s1><s2>Canberra, ACT 2600</s2><s3>AUS</s3><sZ>8 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra, ACT 2600</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Experiments in fluids</title><title level="j" type="abbreviated">Exp. fluids</title><idno type="ISSN">0723-4864</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Experiments in fluids</title><title level="j" type="abbreviated">Exp. fluids</title><idno type="ISSN">0723-4864</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Compressible fluid</term><term>Data assimilation</term><term>Digital simulation</term><term>Eddy viscosity</term><term>Eigenfunctions</term><term>Mixing layer</term><term>Modelling</term><term>Navier-Stokes equations</term><term>Orthogonal function</term><term>Reduced order model</term><term>Subgrid scale method</term><term>Turbulence structure</term><term>Two dimensional flow</term><term>Vorticity</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Structure turbulence</term><term>Ecoulement bidimensionnel</term><term>Fluide compressible</term><term>Vorticité</term><term>Couche mélange</term><term>Fonction orthogonale</term><term>Fonction propre</term><term>Méthode sous maille</term><term>Modélisation</term><term>Simulation numérique</term><term>Modèle ordre réduit</term><term>Viscosité tourbillonnaire</term><term>Equation Navier Stokes</term><term>Assimilation donnée</term><term>4727P</term><term>4727E</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To understand more deeply this behaviour, a hierarchy of POD ROMs is studied and compared for a two-dimensional uncontrolled mixing layer. First, dynamical models based on POD are derived from the Navier-Stokes and the vorticity equations. It is shown that these models can exhibit for some truncation level finite-time blow-ups. A symmetrized quadratic model is then proposed to enforce the preservation of energy in the model. This formulation improves considerably the behaviour of the model, but the energy level is still overestimated. Subsequently, a nonlinear eddy-viscosity model with guaranteed stability is proposed. This model still leads to an imperfect description of the energy. Different 4D-Var identification strategies are then considered to improve the nonlinear eddy-viscosity model. It is shown that penalizing the time variation in the eddy-viscosity parameter leads to the best compromise in terms of description of the energy and of physical relevance of the eddy viscosity. Lastly, a statistical inference procedure is used to take into account the bias inherent of the sampling employed in the identification procedure. Joined probability density functions are then determined empirically for all the coefficients of the model, and a stochastic dynamical model is finally derived to study the influence on the long-term solution of different equiprobable sets of coefficients.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li><li>États-Unis</li></country><region><li>Nouvelle-Aquitaine</li><li>Poitou-Charentes</li></region><settlement><li>Poitiers</li></settlement></list><tree><country name="France"><region name="Nouvelle-Aquitaine"><name sortKey="Cordier, Laurent" sort="Cordier, Laurent" uniqKey="Cordier L" first="Laurent" last="Cordier">Laurent Cordier</name></region><name sortKey="Daviller, Guillaume" sort="Daviller, Guillaume" uniqKey="Daviller G" first="Guillaume" last="Daviller">Guillaume Daviller</name><name sortKey="Delville, Joel" sort="Delville, Joel" uniqKey="Delville J" first="Joël" last="Delville">Joël Delville</name><name sortKey="Lehnasch, Guillaume" sort="Lehnasch, Guillaume" uniqKey="Lehnasch G" first="Guillaume" last="Lehnasch">Guillaume Lehnasch</name><name sortKey="Noack, Bernd R" sort="Noack, Bernd R" uniqKey="Noack B" first="Bernd R." last="Noack">Bernd R. Noack</name><name sortKey="Tissot, Gilles" sort="Tissot, Gilles" uniqKey="Tissot G" first="Gilles" last="Tissot">Gilles Tissot</name></country><country name="États-Unis"><noRegion><name sortKey="Balajewicz, Maciej" sort="Balajewicz, Maciej" uniqKey="Balajewicz M" first="Maciej" last="Balajewicz">Maciej Balajewicz</name></noRegion></country><country name="Australie"><noRegion><name sortKey="Niven, Robert K" sort="Niven, Robert K" uniqKey="Niven R" first="Robert K." last="Niven">Robert K. Niven</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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