{"id":5067,"date":"2018-06-16T08:16:24","date_gmt":"2018-06-16T07:16:24","guid":{"rendered":"https:\/\/l2ep.univ-lille.fr\/?p=5067"},"modified":"2018-11-06T12:57:36","modified_gmt":"2018-11-06T11:57:36","slug":"these-laurent-montier-16-juillet-2018","status":"publish","type":"post","link":"https:\/\/l2ep.univ-lille.fr\/en\/these-laurent-montier-16-juillet-2018\/","title":{"rendered":"Th\u00e8se : Laurent MONTIER, 16 Juillet 2018"},"content":{"rendered":"

Titre :\u00a0Application de m\u00e9thodes de r\u00e9duction de mod\u00e8les aux probl\u00e8mes d\u2019\u00e9lectromagn\u00e9tisme basse fr\u00e9quence<\/span><\/strong><\/p>\n

Date<\/strong> : Lundi 16 juillet 2018
\nHeure<\/strong> : 14h00
\nLieu<\/strong> : ENSAM Lille, salle La Rochefoucauld<\/p>\n

R\u00e9sum\u00e9 :\u00a0<\/strong><\/p>\n

\nDans le domaine de l\u2019\u00e9lectrotechnique, la simulation num\u00e9rique permet de s\u2019affranchir d\u2019essais qui peuvent \u00eatre co\u00fbteux ou difficiles \u00e0 r\u00e9aliser. La M\u00e9thode des \u00c9l\u00e9ments Finis est ainsi devenue une approche de r\u00e9f\u00e9rence dans ce contexte car elle permet d\u2019obtenir des r\u00e9sultats pr\u00e9cis sur des syst\u00e8mes aux g\u00e9om\u00e9tries complexes. Or, la simulation num\u00e9rique d\u2019un dispositif \u00e9lectrotechnique peut s\u2019av\u00e9rer co\u00fbteuse en temps de calcul du fait d\u2019un nombre d\u2019inconnues et de pas de temps important, ainsi que de fortes non-lin\u00e9arit\u00e9s des mat\u00e9riaux ferromagn\u00e9tiques. Il est alors n\u00e9cessaire de mettre en \u0153uvre des techniques permettant de r\u00e9duire les temps de calcul n\u00e9cessaires \u00e0 la r\u00e9solution de tels mod\u00e8les num\u00e9riques. Les m\u00e9thodes de r\u00e9duction de mod\u00e8les semblent bien adapt\u00e9es \u00e0 ce type de probl\u00e8mes car elles ont d\u00e9j\u00e0 \u00e9t\u00e9 appliqu\u00e9es avec succ\u00e8s dans de nombreux domaines de l\u2019ing\u00e9nierie, notamment en m\u00e9canique des fluides et du solide. Une premi\u00e8re cat\u00e9gorie de m\u00e9thodes permet de rechercher la solution dans une base r\u00e9duite afin de diminuer le nombre d\u2019inconnues du mod\u00e8le num\u00e9rique. Pour ce type d\u2019approche, les m\u00e9thodes les plus connues sont la Proper Orthogonal Decomposition, la Proper Generalized Decomposition et la Projection d\u2019Arnoldi. Une seconde cat\u00e9gorie regroupe les approches permettant de r\u00e9duire le co\u00fbt de calcul d\u00fb aux ph\u00e9nom\u00e8nes non lin\u00e9aires, gr\u00e2ce \u00e0 des m\u00e9thodes d\u2019interpolation telles que l\u2018Empirical Interpolation Method et la Gappy POD. Cette th\u00e8se CIFRE a ainsi \u00e9t\u00e9 effectu\u00e9e dans le cadre du LAMEL (laboratoire commun entre le L2EP et EDF R&D) avec pour but d\u2019identifier et d\u2019impl\u00e9menter les m\u00e9thodes de r\u00e9duction les mieux adapt\u00e9es \u00e0 l\u2019\u00e9lectrotechnique. Celles-ci devront \u00eatre capables de r\u00e9duire le co\u00fbt de calcul tout en prenant en compte le mouvement du rotor, les non-lin\u00e9arit\u00e9s des mat\u00e9riaux ferromagn\u00e9tiques mais aussi l\u2019environnement \u00e9lectrique et m\u00e9canique du dispositif. Enfin, un indicateur \u00e9valuant l\u2019erreur commise par le mod\u00e8le r\u00e9duit a \u00e9t\u00e9 d\u00e9velopp\u00e9, offrant ainsi la garantie d\u2019une pr\u00e9cision suffisante sur les r\u00e9sultats.<\/p>\n

Mots cl\u00e9s :<\/strong> R\u00e9duction de mod\u00e8le ; Machines \u00e9lectriques ; Proper Orthogonal Decomposition ; Empirical Interpolation Method ; Estimation d\u2019erreur ; M\u00e9thode des \u00c9l\u00e9ments Finis<\/p>\n

Abstract :\u00a0<\/strong><\/p>\n

\nIn the electrical engineering field, numerical simulation allows to avoid experiments which can be expensive, difficult to carry out or harmful for the device. In this context, the Finite Element Method has become to be one of the most used approach since it allows to obtain precise results on devices with complex geometries. However, these simulations can be computationally expensive because of a large number of unknowns and time-steps, and of strong nonlinearities of ferromagnetic materials to take into account. Numerical techniques to reduce the computational effort are thus needed. In this context, model order reduction approaches seem well adapted to this kind of problem since they have already been successfully applied to many engineering fields, among others, fluid and solid mechanics. A first class of methods allows to seek the solution in a reduced basis, allowing to dramatically reduce the number of unknowns of the numerical model. The most famous technics are probably the Proper Orthogonal Decomposition, the Proper Generalized Decomposition and the Arnoldi Projection. The second class of approaches consists of methods allowing to reduce the computational cost associated to nonlinearities, using interpolation methods like the Empirical Interpolation Method and the Gappy POD. This Ph.D. has been done within the LAMEL, the joint laboratory between the L2EP and EDF R&D, in order to identify and implement the model order reduction methods which are the most adapted to electrical engineering models. These methods are expected to reduce the computational cost while taking into account the motion of an electrical machine rotor, the nonlinearities of the ferromagnetic materials and also the mechanical and electrical environment of the device. Finally, an error indicator which evaluates the error introduced by the reduction technic has been developed, in order to guarantee the accuracy of the results obtained with the reduced model.<\/p>\n

Keywords :<\/strong> Model-order reduction ; Electrical machines ; Proper Orthogonal Decomposition ; Empirical Interpolation Method ; Error Estimation ; Finite Element Method<\/p>\n","protected":false},"excerpt":{"rendered":"

Titre :\u00a0Application de m\u00e9thodes de r\u00e9duction de mod\u00e8les aux probl\u00e8mes d\u2019\u00e9lectromagn\u00e9tisme basse fr\u00e9quence Date : Lundi 16 juillet 2018 Heure : 14h00 Lieu : ENSAM Lille, salle La Rochefoucauld R\u00e9sum\u00e9 :\u00a0 Dans le domaine de l\u2019\u00e9lectrotechnique, la simulation num\u00e9rique permet de s\u2019affranchir d\u2019essais qui peuvent \u00eatre co\u00fbteux ou difficiles \u00e0 r\u00e9aliser. La M\u00e9thode des \u00c9l\u00e9ments […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34,3],"tags":[],"_links":{"self":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/posts\/5067"}],"collection":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/comments?post=5067"}],"version-history":[{"count":3,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/posts\/5067\/revisions"}],"predecessor-version":[{"id":5070,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/posts\/5067\/revisions\/5070"}],"wp:attachment":[{"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/media?parent=5067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/categories?post=5067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/l2ep.univ-lille.fr\/en\/wp-json\/wp\/v2\/tags?post=5067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}