Gegenstand dieser Arbeit ist die Forschungsdisziplin, welche in der Strukturmechanik als Modellordnungsreduktion bekannt ist. Im Mittelpunkt stehen Kopplungsprozesse von starren und elastischen Mehrkörpersystemen - sowohl in theoretischer Hinsicht als auch bezüglich der praktischen Realisation im Rahmen des Finite-Elemente-Programms ANSYS und des Mehrkörpersimulationsprogramms SIMPACK. Eine Vielfalt von strukturerhaltendenMOR-Methoden wurde zum Zwecke des Überblicks dargestellt. Darüber hinaus findet sich eine Kategorisierungsmethodik in Hinsicht auf den später beschriebenen FEM-MKS-Kopplungsprozess. Die Effizienz der MOR-Methoden wird sowohl hinsichtlich der Qualität der ROM als auch bezogen auf die hierfür benötigte Rechenzeit bemessen. Aus diesem Grunde wurden etliche MOR Schemata dargelegt, mit dem Ziel, den Effizienzfaktor während der Berechnung eines ROMs zu maximieren, das heißt maximale Qualität und minimale Rechenzeit zu erzielen. Die Validierung der dynamischen ROM-Eigenschaften basiert auf der Anwendung der sogenannten Modellkorrelationskriterien. Dies wurde an vier Anwendungsbeispielen aus dem Feld der Strukturmechanik getestet: der 3D-Balkenstruktur, der UIC60-Schiene, dem Pleuel und der Kurbelwelle. Die Anwendung der diagonal perturbation-Methodik verbessert die Kondition der Steifigkeitsmatrix eines Modells, von beiden Arten von Lösungsprozeduren, d.h. direkte und iterative Verfahren, betroffen sind. Die dynamische Bewegung mechanischer MKS wird als ein Index-3-DAE-Systemformuliert und die Information über die elastischen Körper wird in Form der sogenannten Standard Input Datei in einen MKS-Code transferriert. Die Einführung des Back-projection-Ansatzes ermöglicht die weitere Verwendung bestimmter ROM-Typen, derren assoziierten physikalische Eigenschaften unangemessen definiert wurden. Zum Abschluss werden die theoretischen, modellierenden und numerischen Fortschritte der Arbeit resümiert und kombiniert im Sinne der Model Order Reduction Package Toolbox (MORPACK). Die Matlab-basierte MORPACK-Toolbox ermöglicht den FEM-MKS-Kopplungsprozess für die Verwendung von ANSYS und SIMPACK. Hierin sind ein Großteil der zuvor erläuterten Erweiterungen eingeschlossen. Mit Hilfe der zwei integrierten inneren MOR- und SID-Schnittstellen als auch der vier Anwendungsebenen wird der Import von freien oder eingespannten ROM in SIMPACK ermöglicht. / The research discipline referred to as the Model Order Reduction in structural mechanics is the topic of this Thesis. Special emphasis is given to the coupling process of rigid and elastic Multi Body Dynamics in terms of both the theoretical aspects and the practical realization within the environment of the commercial Finite Element and the Multi Body Systems software packages, ANSYS and SIMPACK respectively. In this regard, a variety of structure preserving Model Order Reduction methods is presented and a categorization methodology is provided in view of the later FEM-MBS coupling process. The algorithmic scheme of several of the MOR methods indicates the capability of generating qualitatively better Reduced Order Models than the standardized Guyan and Component Mode Synthesis approaches. The efficiency of a MOR method is measured in terms of both the quality of the ROM and the associated time required for the .computation Based on the application of the, so called, Model Correlation Criteria the efficiency of the MOR schemes is tested on four application examples originating from the area of structural mechanics, i.e. the 3D elastic solid bar structure, the UIC60 elastic rail, the elastic piston rod, and the elastic crankshaft model. Herewith, the superiority of alternative MOR schemes in comparison to Guyan or CMS methods is demonstrated in terms of the ROM?s quality and the computation time by the use of either the one-step or the two-step MOR algorithms. Numerous of the FE discretized structures suffer from the, so called, ill-conditioned properties regarding the associated stiffness matrix. On one hand, the direct solution of a MOR method might produce erroneous ROMs due to the associated truncation phenomenon and on the other hand, any kind of iterative approach suffers from vast computation times. The application of the diagonal perturbation methodology improves the condition properties of the model?s stiffness matrix and thus, both kinds of the aforementioned solution procedures are affected. The back-projection approach is introduced, which projects the ROM belonging to the Non physical subspace reduction-expansion methods category back onto the physical configuration space and thus, enabling its further usage in a MBS code, e.g. SIMPACK. Finally, the theoretical, modelling, and numerical advancements are combined in terms of the Model Order Reduction Package. The Matlab-based MORPACK toolbox enables the FEM-MBS coupling process for the ANSYS-SIMPACK utilization and herewith, several of the aforementioned enhancements are included. With the help of the two integrated inner interfaces, i.e. MOR and SID, as well as four application levels, the import into SIMPACK of alternatively free or fixed ROMs is enabled. The functionality of MORPACK is demonstrated based on two application examples, namely, the 3D elastic solid bar and the UIC60 elastic rail, the dynamic properties of which are validated prior to their import into SIMPACK.

A análise modal experimental tem contribuído de forma decisiva para caracterização e solução de problemas de engenharia, relacionados à vibração estrutural. Uma das áreas fundamentais da análise modal experimental é a identificação de sistemas, cujo objetivo é determinar as propriedades dinâmicas de uma estrutura, descritas através das freqüências naturais, fatores de amortecimento e modos de vibrar do sistema em análise. Neste trabalho é realizado um estudo sobre as técnicas paramétricas de identificação de sistemas no domínio do tempo utilizando o modelo auto-regressivo de média móvel vetorial (ARMAV) e o modelo auto-regressivo vetorial (ARV). Em ambos os modelos, os procedimentos de identificação dos parâmetros auto-regressivos, responsáveis pela dinâmica do sistema, são estimados utilizando a aproximação dos mínimos quadrados. A partir desses coeficientes um modelo em espaço de estado do sistema é construído, a fim de estimar os parâmetros modais do sistema dinâmico. A ordem do modelo ARMAV, necessária para determinar as características dinâmicas do sistema, é estimada através do critério de informação Bayesiana (BIC). Para o caso do procedimento baseado no modelo ARV, onde apenas as respostas do sistema são consideradas no processo de identificação, uma nova técnica é proposta para solucionar o problema da identificação da ordem do modelo dinâmico. Essa técnica, baseada na estabilidade das freqüências naturais estimadas em várias identificações, contribuiu também para automação do procedimento de identificação. O desempenho dos algoritmos de identificação utilizando o modelo ARMAV, e o modelo ARV juntamente com a nova metodologia desenvolvida, é verificado através de aplicações a dados provenientes de simulações numéricas e de um ensaio experimental realizado em uma placa de alumínio. / The experimental modal analysis has contribued in a decisive way to characterization and solution of engineering problems, related to structural vibration. One of the fundamental areas of the experimental modal analysis is the mechanical systems identification, whose objective is to identify the dynamic properties of a structure, described through the natural frequencies, damping ratios and mode shapes of the system in analysis. In this work a study is accomplished on the parametric techniques of systems identification in time domain using the Auto-Regressive Moving Average Vector (ARMAV) and the Auto-Regressive Vector (ARV) models. In these models, the procedures of the auto-regressive parameters identification that describes the dynamics of the system are estimated using the least square approach. Trough these coefficients a model in state space is built, in order to identify the modal parameters of the dynamic system. The order of the ARMAV model, necessary to determine the dynamic characteristics of the system, is estimated through Bayesian Information Criterion (BIC). For the procedure based on the model ARV, where only the system responses are considered in the identification process, a new technique is proposed to solve the identification problem of the order of the dynamic model. This technique, based on the stability of the natural frequencies in several identifications, also contributed to automation of the identification procedure. The performance of these identification algorithms using the ARMAV model, and the ARV model together with the new developed methodology, is verified using data from numerical simulations and from an experimental test accomplished in an aluminum plate.

Cette thèse traite de modélisation des systèmes complexes. Dans ce cadre, l'approche est basée sur les Modèles Structurés en Second Ordre (MSSO). Afin d'utiliser cette classe de modèles, les propriétés telles que l'atteignabilité, l'observabilité et les grammiens, bien connues pour les réalisations d'états, sont étendues aux MSSO.Lors de la co-simulation d'un système, des éléments de natures différentes (physiques et logicielles) sont intégrés et la simulation est effectuée en temps réel. Or, les modèles d'ordre élevés sont couteux en temps de calcul, ce qui rend difficile ce type de simulation. Ainsi, des méthodes de réduction de modèle sont explorées. En particulier, de nouvelles méthodes, permettant de préserver la structure des modèles avec une bonne erreur d'approximation sont présentées.Ces développements sont appliqués à la co-simulation de modèles véhicules sous forme de MSSO. Le modèle créé est un modèle par blocs, complexe et non-linéaire. Afin d'appliquer les méthodes de réduction de modèle il est nécessaire de le linéariser. La structure par blocs permet de linéariser l'ensemble du modèle ou de ne linéariser que certaines sous parties du modèle.Ensuite, l'identification des paramètres est effectuée pour chaque sous-systèmes du véhicule. Une méthode d'interconnexion est ensuite proposée pour créer une représentation monobloc du modèle afin de réduire ce dernier. Au final, des essais en co-simulation de la partie arrière du véhicule sous forme de modèle interconnectée avec la partie avant du véhicule physiquement présente sur un banc de test, valide notre approche pour effectuer de la co-simulation temps réel avec matériel.x / This thesis studies the modeling of complex systems. In this framework, the approach is based on Second Order Form Model (SOFM). In order to use this kind of models, properties such as the reachability, the observability, the gramians and the Markov parameters, well known for state-space representation, are extended to the SOFM. During the co-simulation of a system, its physical parts are interconnected to models which simulate the system environement and the simulation is performed in real time. However, the simulation of high order models consumes to much time to be performed in real time. Therefore, model order reduction methods are studied. Particularly, new methods preserving SOFM structure with a good approximation error are presented. These developments are applied to the vehicle dynamic. Hence, a vehicle SOFM model is developed. The created model is a blockwise model where each blocks describes a part of the vehicle. This model is complex and non-linear. In order to apply the model order reduction methods, model linearisation is necessary. The block modeling allows to linearise the full model or allows to linearise some part of the model. Then, the identification of the model parameters is done by vehicle sub-system. In addition, an interconnection method is proposed to build a monobloc model in order to reduce it. Finally, co-simulations of the model vehicle rear part interconnected to the physical front part of the vehicle show the capacity to make co-simulation with the reduced models.

Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. Both methods are designed for generalised state space systems---the former for multiple-input-multiple-output (MIMO) systems from finite element discretisations and the latter for single-input-single-output (SISO) systems---and applied to relevant test problems. The dual rational Arnoldi method is designed for generating real reduced order systems using complex shift points and stabilising a system that happens to be unstable. For the rational Krylov method, a forward error in the recursion and an estimate of the error in the approximation of the transfer function are studie. A stability analysis of a heat exchanger model is made. The model is a nonlinear partial differential-algebraic equation (PDAE). Its well-posedness and how to prescribe boundary data is investigated through analysis of a linearised PDAE and numerical experiments on a nonlinear DAE. Four methods for generating reduced order models are applied to the nonlinear DAE and compared: a Krylov based moment matching method, balanced truncation, Galerkin projection onto a proper orthogonal decomposition (POD) basis, and a lumping method. / QC 20101013

<p>Rational Krylov methods for model order reduction are studied. A dual rational Arnoldi method for model order reduction and a rational Krylov method for model order reduction and eigenvalue computation have been implemented. It is shown how to deflate redundant or unwanted vectors and how to obtain moment matching. Both methods are designed for generalised state space systems---the former for multiple-input-multiple-output (MIMO) systems from finite element discretisations and the latter for single-input-single-output (SISO) systems---and applied to relevant test problems. The dual rational Arnoldi method is designed for generating real reduced order systems using complex shift points and stabilising a system that happens to be unstable. For the rational Krylov method, a forward error in the recursion and an estimate of the error in the approximation of the transfer function are studie.</p><p>A stability analysis of a heat exchanger model is made. The model is a nonlinear partial differential-algebraic equation (PDAE). Its well-posedness and how to prescribe boundary data is investigated through analysis of a linearised PDAE and numerical experiments on a nonlinear DAE. Four methods for generating reduced order models are applied to the nonlinear DAE and compared: a Krylov based moment matching method, balanced truncation, Galerkin projection onto a proper orthogonal decomposition (POD) basis, and a lumping method.</p>

Für die elastische Mehrkörpersimulation bzw. die FEM-MKS-Kopplung sind reduzierte FE-Modelle von großer Bedeutung. Die Erstellung reduzierter Modelle mit hoher Abbildungsgüte im Rahmen einer Modellordnungsreduktion erfordert einerseits ein geeignetes Reduktions-verfahren und andererseits zuverlässige Korrelationsmethoden. Beides wird durch die Soft-ware MORPACK bereitgestellt. Die Korrelation reduzierter FE-Modelle basiert in MORPACK derzeit ausschließlich auf modalen Eigenschaften. Ausgehend von der Annahme, dass sich die Abbildungsgüte eines reduzierten FE-Modells erst im Rahmen einer Zeitbereichssimula-tion vollständig beurteilen lässt, ist eine dahingehende Erweiterung von MORPACK geplant. Für einfache Topologien muss die Möglichkeit bestehen, das dynamische Verhalten, redu-zierter Modelle, direkt in MORPACK zu simulieren. Mit Hilfe der resultierenden Zeitsignale werden die reduzierten Modelle bewertet. Für die Umsetzung dieser Idee muss in MORPACK zunächst ein eigenständiges EMKS-Programm implementiert werden. Die Implementierung des EMKS-Programms in MORPACK (bzw. MATLAB) stellt den Schwerpunkt dieser Arbeit dar. Es werden zunächst die Anforderungen an das EMKS-Programm formuliert. Nach der Behandlung aller erforderlichen theoretischen Grundlagen werden die Systemgleichungen hergeleitet. Anschließend wird ein Formalismus bereitgestellt, der den Aufbau der Systemgleichungen, auf Basis der Nutzereingaben ermöglicht. Nach der Implementierung des Formalismus wird das EMKS-Programm verifiziert und erprobt. / Reduced FE-Models are very important for elastic multibody simulation and FEM-MKS-coupling. The generation of reduced FE-models with high approximation quality in a model order reduction requires on the one hand a suitable reduction method and on the other hand reliable correlation methods. Both are provided by the MORPACK software. In MORPACK the correlation of reduced FE models based currently only on modal properties. An extension of the MORPACK software is planned on the assumption, that the approximation quality of a reduced FE-model can be completely assessed only in a time domain simulation. For simple topologies, it must be possible to simulate the dynamic behavior of reduced models directly into MORPACK. With the correlation of resulting time signals, the reduced models are as-sessed. To realize this idea, an independent EMKS program must be implemented in MORPACK. The implementation of the EMKS program in MORPACK (respectively MATLAB) represents the focus of this thesis. The first part is to formulate the necessary requirements for the EMKS program. After handling of all the necessary theoretical foundations, the system equa-tions are derived. Subsequently, formalism is provided that allows a construction of the sys-tem equations based on the user input. After the implementation of the formalism, the EMKS program will verify and tested.

No description available.

A análise modal experimental tem contribuído de forma decisiva para caracterização e solução de problemas de engenharia, relacionados à vibração estrutural. Uma das áreas fundamentais da análise modal experimental é a identificação de sistemas, cujo objetivo é determinar as propriedades dinâmicas de uma estrutura, descritas através das freqüências naturais, fatores de amortecimento e modos de vibrar do sistema em análise. Neste trabalho é realizado um estudo sobre as técnicas paramétricas de identificação de sistemas no domínio do tempo utilizando o modelo auto-regressivo de média móvel vetorial (ARMAV) e o modelo auto-regressivo vetorial (ARV). Em ambos os modelos, os procedimentos de identificação dos parâmetros auto-regressivos, responsáveis pela dinâmica do sistema, são estimados utilizando a aproximação dos mínimos quadrados. A partir desses coeficientes um modelo em espaço de estado do sistema é construído, a fim de estimar os parâmetros modais do sistema dinâmico. A ordem do modelo ARMAV, necessária para determinar as características dinâmicas do sistema, é estimada através do critério de informação Bayesiana (BIC). Para o caso do procedimento baseado no modelo ARV, onde apenas as respostas do sistema são consideradas no processo de identificação, uma nova técnica é proposta para solucionar o problema da identificação da ordem do modelo dinâmico. Essa técnica, baseada na estabilidade das freqüências naturais estimadas em várias identificações, contribuiu também para automação do procedimento de identificação. O desempenho dos algoritmos de identificação utilizando o modelo ARMAV, e o modelo ARV juntamente com a nova metodologia desenvolvida, é verificado através de aplicações a dados provenientes de simulações numéricas e de um ensaio experimental realizado em uma placa de alumínio. / The experimental modal analysis has contribued in a decisive way to characterization and solution of engineering problems, related to structural vibration. One of the fundamental areas of the experimental modal analysis is the mechanical systems identification, whose objective is to identify the dynamic properties of a structure, described through the natural frequencies, damping ratios and mode shapes of the system in analysis. In this work a study is accomplished on the parametric techniques of systems identification in time domain using the Auto-Regressive Moving Average Vector (ARMAV) and the Auto-Regressive Vector (ARV) models. In these models, the procedures of the auto-regressive parameters identification that describes the dynamics of the system are estimated using the least square approach. Trough these coefficients a model in state space is built, in order to identify the modal parameters of the dynamic system. The order of the ARMAV model, necessary to determine the dynamic characteristics of the system, is estimated through Bayesian Information Criterion (BIC). For the procedure based on the model ARV, where only the system responses are considered in the identification process, a new technique is proposed to solve the identification problem of the order of the dynamic model. This technique, based on the stability of the natural frequencies in several identifications, also contributed to automation of the identification procedure. The performance of these identification algorithms using the ARMAV model, and the ARV model together with the new developed methodology, is verified using data from numerical simulations and from an experimental test accomplished in an aluminum plate.

Abstract Functional communication between brain regions is likely to play a key role in complex cognitive processes that require continuous integration of information across different regions of the brain. This makes the studying of functional connectivity in the human brain of high importance. It also provides new insights into the hierarchical organization of the human brain regions. Resting-state networks (RSNs) can be reliably and reproducibly detected using independent component analysis (ICA) at both individual subject and group levels. A growing number of ICA studies have reported altered functional connectivity in clinical populations. In the current work, it was hypothesized that ICA model order selection influences characteristics of RSNs as well as their functional connectivity. In addition, it was suggested that high ICA model order could be a useful tool to provide more detailed functional connectivity results. RSNs’ characteristics, i.e. spatial features, volume and repeatability of RSNs, were evaluated, and also differences in functional connectivity were investigated across different ICA model orders. ICA model order estimation had a significant impact on the spatial characteristics of the RSNs as well as their parcellation into sub-networks. Notably, at low model orders neuroanatomically and functionally different units tend to aggregate into large singular RSN components, while at higher model orders these units become separate RSN components. Disease-related differences in functional connectivity also seem to alter as a function of ICA model order. The volume of between-group differences reached maximum at high model orders. These findings demonstrate that fine-grained RSNs can provide detailed, disease-specific functional connectivity alterations. Finally, in order to overcome the multiple comparisons problem encountered at high ICA model orders, a new framework for group-ICA analysis was introduced. The framework involved concatenation of IC maps prior to permutation tests, which enables statistical inferences from all selected RSNs. In SAD patients, this new correction enabled the detection of significantly increased functional connectivity in eleven RSNs. / Tiivistelmä Toiminnallisten aivoalueiden välinen viestintä on todennäköisesti avainasemassa kognitiivisissa prosesseissa, jotka edellyttävät jatkuvaa tiedon integraatiota aivojen eri alueiden välillä. Tämä tekee ihmisaivojen toiminnallisen kytkennällisyyden tutkimuksesta erittäin tärkeätä. Kytkennälllisyyden tutkiminen antaa myös uutta tietoa ihmisaivojen osa-alueiden välisestä hierarkiasta. Aivojen hermoverkot voidaan luotettavasti ja toistettavasti havaita lepotilan toiminnasta yksilö- ja ryhmätasolla käyttämällä itsenäisten komponenttien analyysia (engl. Independent component analysis, ICA). Yhä useammat ICA-tutkimukset ovat raportoineet poikkeuksellisia toiminnallisen konnektiviteetin muutoksia kliinisissä populaatioissa. Tässä tutkimuksessa hypotetisoitiin, että ICA:lla laskettaujen komponenttien lukumäärä (l. asteluku) vaikuttaa tuloksena saatujen hermoverkkojen ominaisuuksiin kuten tilavuuteen ja kytkennällisyyteen. Lisäksi oletettiin, että korkea ICA-asteluku voisi olla herkempit tuottamaan yksityiskohtaisia toiminnallisen jaottelun tuloksia. Aivojen lepotilan hermoverkkojen ominaisuudet, kuten anatominen jakautuminen, volyymi ja lepohermoverkkojen havainnoinnin toistettavuus evaluoitin. Myös toiminnallisen kytkennällisyyden erot tutkitaan eri ICA-asteluvuilla. Havaittiin että asteluvulla on huomattava vaikutus aivojen lepotilan hermoverkkojen tilaominaisuuksiin sekä niiden jakautumiseen alaverkoiksi. Pienillä asteluvuilla hermoverkojen neuroanatomisesti erilliset yksiköt pyrkivät keräytymään laajoiksi yksittäisiksi komponenteiksi, kun taas korkeammilla asteluvuilla ne havaitaan erillisinä. Sairauksien aiheuttamat muutokset toiminnallisessa kytkennällisyydessä näyttävät muuttuvan myös ICA asteluvun mukaan saavuttaen maksiminsa korkeilla asteluvuilla. Korkeilla asteluvuilla voidaan havaita yksityiskohtaisia, sairaudelle ominaisia toiminnallisen konnektiviteetin muutoksia. Korkeisiin ICA asteluvun liittyvän tilastollisen monivertailuongelman ratkaisemiseksi kehitimme uuden menetelmän, jossa permutaatiotestejä edeltävien itsenäisten IC-karttoja yhdistämällä voidaan tehdä luotettava tilastollinen arvio yhtä aikaa lukuisista hermoverkoista. Kaamosmasennuspotilailla esimerkiksi kehittämämme korjaus paljastaa merkittävästi lisääntynyttä toiminnallista kytkennällisyyttä yhdessätoista hermoverkossa.

Les travaux de thèse visent à utiliser les modèles éléments finis pour l'optimisation de systèmes multidynamiques. Les modèles éléments finis sont en effet rarement utilisés en optimisation car ils génèrent des temps de calcul trop importants. Pour réduire le temps global d'optimisation, le temps de simulation du modèle lui-même peut être diminué, mais le nombre d'évaluations du modèle peut aussi être limité. Dans cette optique, les stratégies d'optimisation multigranularités sont appliquées, permettant de corriger ou de créer des modèles rapides pour l'optimisation à partir de quelques évaluations d'un modèle initial. Ce modèle est un système multidynamique intégrant un modèle éléments finis. La modélisation d'un tel système est effectuée via la méthode de relaxation des formes d'onde qui permet un couplage efficace en un temps raisonnable. Le temps de calcul est encore réduit par l'application aux modèles éléments finis électromagnétiques de méthodes de réduction de modèle. La méthode de relaxation des formes d'onde est appliquée à la modélisation d'un transformateur. Le transformateur est ensuite optimisé par des méthodes de space mapping et de krigeage. La méthode de relaxation des formes d'onde permet également le couplage d'un modèle électromagnétique non linéaire de type éléments finis avec un redresseur commandé et un modèle thermique éléments finis / These works aim at using finite element models in optimisation of multirate systems. Indeed, the finite element models are rarely used in optimisation because their computation time is too high. To reduce the duration of the optimisation process, simulation time of the model can be reduced, but the number of evaluations of the model can also be limited. In this perspective, multi-level optimisations are applied. They allow to correct or create fast models for the optimisation from a few number of evaluations of an initial model. The model is a multirate system including a finite element model. The modeling of such a system is done by waveform relaxation method which allows an efficient coupling in an acceptable computation time. Computation time is further reduced by applying model order reduction to the finite element models.The waveform relaxation method is applied to the modeling of a transformer. Then the transformer is optimised by space mapping and kriging techniques. The waveform relaxation method also allows the coupling of a finite element type electromagnetic non linear model with a rectifier and a finite element thermal model