Le développement de la fabrication additive permet d'élaborer des pièces de forme extrêmement complexes, en particulier des structures alvéolaires ou "lattices", où l'allégement est recherché. Toutefois, cette technologie, en très forte croissance dans de nombreux secteurs d'activités, n'est pas encore totalement mature, ce qui ne facilite pas les corrélations entre les mesures expérimentales et les simulations déterministes. Afin de prendre en compte les variations de comportement, les approches multiparamétriques sont, de nos jours, des solutions pour tendre vers des conceptions fiables et robustes. L'objectif de cette thèse est d'intégrer des incertitudes matérielles et géométriques, quantifiées expérimentalement, dans des analyses de flambement. Pour y parvenir, nous avons, dans un premier temps, évalué différentes méthodes de substitution, basées sur des régressions et corrélations, et différentes réductions de modèles afin de réduire les temps de calcul prohibitifs. Les projections utilisent des modes issus soit de la décomposition orthogonale aux valeurs propres, soit de développements homotopiques ou encore des développements de Taylor. Dans un second temps, le modèle mathématique, ainsi créé, est exploité dans des analyses ensemblistes et probabilistes pour estimer les évolutions de la charge critique de flambement de structures lattices. / The development of additive manufacturing allows structures with highly complex shapes to be produced. Complex lattice shapes are particularly interesting in the context of lightweight structures. However, although the use of this technology is growing in numerous engineering domains, this one is not enough matured and the correlations between the experimental data and deterministic simulations are not obvious. To take into account observed variations of behavior, multiparametric approaches are nowadays efficient solutions to tend to robust and reliable designs. The aim of this thesis is to integrate material and geometric uncertainty, experimentally quantified, in buckling analyses. To achieve this objective, different surrogate models, based on regression and correlation techniques as well as different reduced order models have been first evaluated to reduce the prohibitive computational time. The selected projections rely on modes calculated either from Proper Orthogonal Decomposition, from homotopy developments or from Taylor series expansion. Second, the proposed mathematical model is integrated in fuzzy and probabilistic analyses to estimate the evolution of the critical buckling load for lattice structures.

In der vorliegenden Arbeit wird die Entwicklung eines effizienten Verfahrens zur parametrischen Finite Elemente Simulation von Mikrosystemen und zum Export dieser Modelle in Elektronik- und Systemsimulationswerkzeuge vorgestellt. Parametrische FE-Modelle beschreiben den Einfluss von geometrischen Abmessungen, Schwankungen von Materialeigenschaften und veränderten Umgebungsbedingungen auf das Funktionsverhalten von Sensoren und Aktuatoren. Parametrische FE-Modelle werden für die Auswahl geeigneter Formelemente und deren Dimensionierung während des Entwurfsprozesses in der Mikrosystemtechnik benötigt. Weiterhin ermöglichen parametrische Modelle Sensitivitätsanalysen zur Bewertung des Einflusses von Toleranzen und Prozessschwankungen auf die Qualität von Fertigungsprozessen. In Gegensatz zu üblichen Sample- und Fitverfahren wird in dieser Arbeit eine Methode entwickelt, welche die Taylorkoeffizienten höherer Ordnung zur Beschreibung des Einflusses von Designparametern direkt aus der Finite-Elemente- Formulierung, durch Ableitungen der Systemmatrizen, ermittelt. Durch Ordnungsreduktionsverfahren werden die parametrischen FE-Modelle in verschiedene Beschreibungssprachen für einen nachfolgenden Elektronik- und Schaltungsentwurf überführt. Dadurch wird es möglich, neben dem Sensor- und Aktuatorentwurf auch das Zusammenwirken von Mikrosystemen mit elektronischen Schaltungen in einer einheitlichen Simulationsumgebung zu analysieren und zu optimieren. / The thesis deals with advanced parametric modeling technologies based on differentiation of the finite element equations which account for parameter variations in a single FE run. The key idea of the new approach is to compute not only the governing system matrices of the FE problem but also high order partial derivatives with regard to design parameters by means of automatic differentiation. As result, Taylor vectors of the system’s response can be expanded in the vicinity of the initial position capturing dimensions and physical parameter. A novel approaches for the parametric MEMS simulation have been investigated for mechanical, electrostatic and fluidic domains in order to improve the computational efficiency. Objective of reduced order modeling is to construct a simplified model which approximates the original system with reasonable accuracy for system level design of MEMS. The modal superposition technique is most suitable for system with flexible mechanical components because the deformation state of any flexible system can be accurately described by a linear combination of its lowest eigenvectors. The developed simulation approach using parametric FE analyses to extract basis functions have been applied for parametric reduced order modeling. The successful implementation of a derivatives based technique for parameterization of macromodel by the example of microbeam and for exporting this macromodel into MATLAB/Similink to simulate dynamical behavior has been reported.

Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.

Scannende MEMS-Mikrospiegel stellen eine vielversprechende technologische Entwicklung mit potentiellen Anwendungen im Bereich der miniaturisierten Bildprojektion und Umgebungssensierung dar. Im Regelfall oszilliert das Spiegelelement hierbei resonant um die horizontale Achse, während die vertikale Achse statisch ausgelenkt wird. Somit ergibt sich ein sogenannter Raster-Scan. Während eine resonante Aktuierung in MEMS-Technologie im Frequenzbereich mehrerer kHz effizient umgesetzt werden kann, stellt die Implementierung statischer Antriebe eine Herausforderung dar. In dieser Arbeit wird ein neuartiges Aktuierungskonzept vorgestellt, das effizientere quasi-statische Auslenkung ermöglicht. Hierfür wird der Drehimpuls, der durch die hochfrequente horizontale Schwingung erzeugt wird, durch eine weitere resonante Oszillation ähnlicher Frequenz gestört, wodurch sich ein für die quasi-statische Auslenkung nutzbares Drehmoment ergibt. Da gyroskopische Effekte ausgenutzt werden, die nicht in aktuellen auf Modalanalyse basierenden Simulationsmethoden berücksichtigt sind, werden Starrkörper- und transiente FEM-Modelle entwickelt, um die Realisierbarkeit des Antriebskonzepts simulatorisch zu verifizieren. Im Rahmen der durch den genutzten Prozess gegebenen Randbedingungen werden daraufhin Aktuierungselemente für die resonanten Achsen erarbeitet und mit diesen zwei Designvarianten eines 2D-Mikrospiegels erstellt. Nach modellbasierter Verifikation werden diese in einer MEMS-Fertigungslinie prozessiert. Mit den generierten Mustern wird dann eine vollständige experimentelle Charakterisierung unter Nutzung eines speziell erstellten FPGA-basierten Evaluations-Boards durchgeführt. Beide Design-Varianten zeigen hierbei voll funktionsfähige Sensierungs- und Aktuierungselemente. Es kann ein erfolgreicher Nachweis der Funktionsfähigkeit des neuartigen Antriebskonzepts vollbracht werden. Die dabei gezeigte 2D-Projektion erreicht Winkel von 12° x 1.8° / Scanning MEMS micromirrors are an emergent technology for compact form factor image projection and environment sensing applications. Commonly the mirror element oscillates resonantly along the horizontal axis, whereas it is deflected statically along the vertical axis, performing a so called raster scan. While resonant actuation can be implemented efficiently in MEMS, static deflection however remains challenging. In this thesis a novel actuation concept for 2D MEMS micromirrors is introduced that potentially enables efficient quasi-static actuation. Therefore the angular momentum that is generated by the high frequency resonant axis is disturbed by an orthogonal resonant oscillation of similar frequency, leading to a torque that can be utilized to achieve an indirect quasi-static deflection. As in this case gyroscopic effects are exploited that are usually not considered in state of the art modal finite element based MEMS simulation, in order to validate the feasibility of the actuation concept rigid body and transient finite element based models are developed and simulation studies conducted. Using an existing manufacturing process as a framework, actuation schemes for the resonant axes are introduced and two distinct micromirror designs are developed and verified by simulation. These are processed in a MEMS manufacturing line. A thorough characterization study is then carried out using a custom FPGA based evaluation board with closed loop control capabilities. Both design variants are functional with regard to all actuation and tilt angle detection elements. A successful implementation of the proposed actuation concept is shown achieving 2D projection of a laser beam with tilt angles of 12 ◦ × 1.8 ◦ in frequency and amplitude controlled operation.

<h4>A generalized physics-based modeling framework is presented to analyze: (a) the effects of temperature on identified degradation mechanisms, (b) interfacial debonding processes, including deterministic and stochastic mechanisms, and (c) establishing model performance benchmarks of electrochemical porous electrode theory models, as a necessary stepping stone to perform valid battery degradation analyses and designs. Specifically, the effects of temperature were incorporated into a physics-based, reduced-order model and extended for a LiCoO₂ -graphite 18650 cell. Three dimensionless driving forces were identified, controlling the temperature-dependent reversible charge capacity. The identified temperature-dependent irreversible mechanisms include homogeneous SEI, at moderate to high temperatures, and the chemomechanical degradation of the cathode at low temperatures. Also, debonding of a statistically representative electrochemically active particle from the surrounding binder-electrolyte matrix in a porous electrode was modeled analytically, for the first time. The proposed framework enables to determine the space of C-Rates and electrode particle radii that suppresses or enhances debonding and is graphically summarized into performance–microstructure maps where four debonding mechanisms were identified, and condensed into power-law relations with respect to the particle radius. Finally, in order to incorporate existing or emerging degradation models into porous electrode theory (PET) implementations, a set of benchmarks were proposed to establish a common basis to assess their physical reaches, limitations, and accuracy. Three open source models: dualfoil, MPET, and LIONSIMBA were compared, exhibiting significant qualitative differences, despite showing the same macroscopic voltage response, leading the user to different conclusions regarding the battery performance and possible degradation mechanisms of the analyzed system.</h4>

<p dir="ltr">For additive manufacturing to be a viable method to build metal parts for industries such as nuclear, the manufactured parts must be of higher quality and have lower variation in said quality than what can be achieved today. This high variation in quality bars the techniques from being used in high safety tolerance fields, such as nuclear. If this obstacle could be overcome, the benefits of additive manufacturing would be in lower cost for complex parts, as well as the ability to design and test parts in a very short timeframe, as only the CAD model needs to be created to manufacture the part. In this study, work to achieve this lower variation of quality was approached in two ways. The first was in the development of surrogate models, utilizing machine learning, to predict the end quality of additively manufactured parts. This was done by using experimental data for the mechanical properties of built parts as outputs to be predicted, and in-situ signals captured during the manufacturing process as inputs to the model. To capture the in-situ signals, cameras were used for thermal and optical imaging, leveraging the natural layer-by-layer manufacturing method used in AM techniques. The final models were created using support vector machine and gaussian process regression machine learning algorithms, giving high correlations between the insitu signals and mechanical properties of relative density, elongation to fracture, uniform elongation, and the work hardening exponent. The second approach to this study was in the development of a reduced order model for a computer simulation of an AM build. For project, a ROM was built inside the MOOSE framework, and was developed for an AM model designed by the MOOSE team, using proper orthogonal decomposition to project the problem onto a lower dimensional subspace, using POD to design the reduced basis subspace. The ROM was able to achieve a reduction to 1% the original dimensionality of the problem, while only allowing 2-5% relative error associated with the projection.</p>

L’objet de la thèse est la modélisation de systèmes hétérogènes intégrant différents domaines de la physique et à signaux mixtes, numériques et analogiques (AMS). Une étude approfondie de différentes techniques d’extraction et de calibration de modèles comportementaux de composants analogiques à différents niveaux d’abstraction et de précision est présentée. Cette étude a mis en lumière trois approches principales qui ont été validées par la modélisation de plusieurs applications issues de divers domaines: un amplificateur faible bruit (LNA), un capteur chimique basé sur des ondes acoustiques de surface (SAW), le développement à plusieurs niveaux d’abstraction d’un capteur CMOS vidéo, et son intégration dans une plateforme industrielle. Les outils développés sont basés sur les extensions AMS du standard IEEE 1666 SystemC mais les techniques proposées sont facilement transposables à d’autres langages tels que VHDL-AMS ou Verilog-AMS utilisés en conception de dispositifs mixtes. / The thesis objective is the modeling of heterogeneous systems. Such systems integrate different physical domains (mechanical, chemical, optical or magnetic) therefore integrate analog and mixed- signal (AMS) parts. The aim is to provide a methodology based on high-level modeling for assisting both the design and the verification of AMS systems. A study on different techniques for extracting behavioral models of analog devices at different abstraction levels and computational weights is presented. Three approaches are identified and regrouped in three techniques. These techniques have been validated through the virtual prototyping of different applications issued from different domains: a low noise amplifier (LNA), a surface acoustic wave-based (SAW) chemical sensor, a CMOS video sensor with models developed at different abstraction levels and their integration within an industrial platform. The flows developed are based on the AMS extensions of the SystemC (IEEE 1666) standard but the methodologies can be implemented using other Analog Hardware Description Languages (VHDL-AMS, Verilog-AMS) typically used for mixed-signal microelectronics design.

L'objectif de cette thèse est de proposer l'approche la plus appropriée afin de minimiser le coût d'intégration de petite éolienne dans un micro-réseau DC urbain. Une petit éolienne basé sur un machine synchrone à aimant permanent (MSAP) est considéré à étudier. Un état de l'art concernant les énergies renouvelables, micro-réseau DC, et la production d'énergie éolienne, est fait. Comme le capteur mécanique de cette structure est relativement d'un coût élevé, les différents types de contrôle pour un système de conversion éolienne sont présentés afin de choisir une structure active de conversion d'énergie et un MSAP sans capteur. Par conséquent, un estimateur de vitesse/position est nécessaire pour contrôler le système. Ainsi, les méthodes différentes proposées dans la littérature sont considérées et classifiées à étudier dans les détails, puis les plus efficaces et largement utilisés sont à vérifier dans la simulation et expérimentalement pour le système étudié. Les méthodes choisies sont: estimation de la flux de rotor avec boucle à verrouillage de phase (PLL), observateur à mode glissement (SMO), observateur de Luenberger d'ordre réduit, et filtre de Kalman étendu (EKF). Face à d'autres méthodes, l'estimateur basé sur un modèle EKF permet une commande sans capteur dans une large plage de vitesse et estime la vitesse de rotation avec une réponse rapide. Le réglage des paramètres EKF est le problème principal à sa mise en œuvre. Par conséquent, pour résoudre ce problème, la thèse présente une méthode adaptative, à savoir réglage-adaptatif d’EKF. En conséquence, et grâce à cette approche, le coût total du système de conversion est réduite et la performance est garantie et optimisée. / The aim of this thesis is to propose the most appropriate approach in order to minimize the cost of integration of a wind generator into a DC urban microgrid. A small-scale wind generator based on a permanent magnet synchronous machine (PMSM) is considered to be studied. A state of the art concerning the renewable energies, DC microgrid, and wind power generation is done. As the mechanical sensor for this structure is relatively of high cost, various types of wind conversion system control are presented in order to choose an energy conversion active structure and a sensorless PMSM. Therefore, a speed/position estimator is required to control the system. Thus, different methods proposed in literatures are considered and classified to be studied in details, and then the most effective and widely used ones are to be verified in simulation and experimentally for the studied system. The methods which are chosen are: rotor flux estimation with phase locked loop (PLL), sliding mode observer (SMO), Luenberger observer of reduced order, and extended Kalman filter (EKF). Facing to other methods, the EKF model-based estimator allows sensorless drive control in a wide speed range and estimates the rotation speed with a rapid response. The EKF parameters tuning is the main problem to its implementation. Hence, to solve this problem, the thesis introduces an adaptive method, i.e. adaptive-tuning EKF. As a result and grace to this approach, the total cost of conversion system is reduced and the performance is guaranteed and optimized.

Im Zuge der Miniaturisierung werden mechanische Nichtlinearitäten immer wichtiger für die Auslegung und Optimierung von mikromechanischen Drehratensensoren. Die vorliegende Arbeit beschäftigt sich mit neuen Simulationsmethoden zur Beschreibung dieser mechanischen Nichtlinearitäten. Die Methoden werden mit Benchmark-Simulationen und Messergebnissen validiert. Die Genauigkeit der neuen Simulationsmethoden erlaubt den Einsatz in der Designoptimierung von kommerziellen MEMS Drehratensensoren. / In this thesis, new simulation methods for the mechanical nonlinearities in microelectromechanical gyroscopes are developed and validated with benchmark simulations and experimental results. The benchmark simulations use transient finite element analysis that consider geometric nonlinear effects. Experimental results are from Laser Doppler Vibrometry and electrical measurements on wafer level. Two different simulation methods, the energy- and stiffness-based approach, are compared with respect to numerical performance and accuracy. In order to evaluate these methods, four different mechanical structures are taken into account: a doubly-clamped beam, a gyroscope test structure and two state-of-the-art gyroscopes with 1 and 2 axes. For the accuracy measurement, the simulated frequency shifts of modes are compared to the true frequency shifts that are developed from either benchmark simulation, Laser Doppler Vibrometry or electrical measurement. The presented methods allow to predict the frequency shift of modes accurately and with a minimum of computational cost. Furthermore, the methodologies allow to generate modal reduced order models which are compatible with common model order reduction in the field. This makes it possible to incorporate mechanical nonlinearity in already established reduced order models of gyroscopes. The simulation and modeling strategies are applicable for generic actuated structures that can be also in different fields of study such as the aerospace and earthquake engineering.