Dissertations / Theses on the topic 'Multiscale Representation'

Thesis (Ph.D.) -- University of Maryland, College Park, 2009.
Thesis research directed by: Applied Mathematics & Statistics, and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

It was analyzed multiple images. The results in the first approximation show a 2-fold increase in speed when using our implementation of active contours. At the same time, the segmented areas of crystals correspond to the approach without the use of multi-scale image representation.

Atmospheric boundary layer flows are characterized by the coexistence of a broad range of scales. These scales cover from synoptic- (100-5000 km) and meso-scales (1-100 km) up to three-dimensional micro-scale turbulence (less than a few kilometers). This multiscale nature inherent to atmospheric flows clearly determines the behaviour of the atmospheric boundary layer, whose structure and evolution are of major importance for the wind energy community. This PhD thesis is focused on the development of a numerical methodology that allows to include contribution from all the above mentioned scales, with the purpose of improving the representation of boundary layer processes. The multiscale numerical methodology is developed based on a numerical weather prediction (NWP) model, the Weather Research and Forecasting (WRF) model.

Prior to the development of the multiscale numerical methodology, one-year of sonic anemometer and wind LiDAR measurements from the FINO1 offshore platform are analyzed. A comprehensive database of offshore measurements in the lowest 250 m of the boundary layer is developed after quality data check and correction for flow distortion effects by the measurement mast, allowing the characterization of the offshore conditions at FINO1. Spectral analysis of high frequency sonic anemometer measurements is used to estimate a robust averaing time for the turbulent fluxes that minimizes non-universal contributions from mesoscale structures but captures the contribution from boundary layer turbulence, employing the Ogive function concept. A stability classification of the measurements is carried out based on the Obukhov length. Results compare well to other surface layer observational studies while vertical wind speed profiles exhibit the expected stability-dependency.

Although NWP models have been extensively used for weather forecasting purposes, a comprehensive analysis of its suitability to meet the wind energy requirements needs to be carried out. The applicability of the WRF mesoscale model to reproduce offshore boundary layer characteristics is evaluated and validated against field measurements from FINO1. The ability of six planetary boundary layer (PBL) parameterizations to account for stability effects is analyzed. Overall, PBL parameterizations are rather accurate in reproducing the vertical structure of the boundary layer for convective and neutral stabilities. However, difficulties are found under stable stratifications, due to the general tendency of PBL formulations to be overdiffusive and therefore, not capable to develope the strong vertical gradients found in the observations. A low-level jet and a very shallow boundary layer cases are simulated to provide further insights into the limits of the parameterizations.

Large-eddy simulations (LES) based on averaged conditions from a convective episode at FINO1 are conducted to understand the mechanisms of transition and equilibration that occur in turbulent one-way nested simulations. The nonlinear backscatter and anisotropy subgrid scale model with a prognostic turbulent kinetic energy equation is found to be capable of providing similar results when performing one-way nested large-eddy simulations to a reference stand-alone domain using periodic lateral boundary conditions. A good agreement is obtained in terms of velocity shear and turbulent fluxes of heat and momentum, while velocity variances are overestimated. A considerable streamwise fetch is needed following each domain transition for appropriate energy levels to be reached at high wavelengths and for the solution to reach quasi-stationary results. A pile-up of energy is observed at low wavelengths on the first nested domain, mitigated by the inclusion of a second nested domain with higher resolution that allows the development of an appropriate turbulent energy cascade.

As the final step towards developing the multiscale capabilities of WRF, the specific problem of the transition from meso- to micro-scales in atmospheric models is addressed. The challenge is to generate turbulence on inner LES domain from smooth mesoscale inflow. Several new methods are proposed to trigger the development of turbulent features. The inclusion of adequate potential temperature perturbations near the inflow boundaries of the LES domain results in a very good agreement of mean velocity profiles, variances and turbulent fluxes, as well as velocity spectra, when compared to periodic stand-alone simulations. This perturbation method allows an efficient generation of fully developed turbulence and is tested under a broad range of atmospheric stabilities: convective, neutral and stable conditions, showing successful results in all the regimes.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

L'asservissement visuel est un procédé consistant à utiliser l'information visuelle obtenue par un capteur afin de commander un système robotique. Ces informations, appelées primitives visuelles peuvent être d'ordre 2D ou 3D. Le travail présenté ici porte sur une nouvelle approche 2D utilisant des primitives directes : les décompositions de l'image en ondelettes ou en shearlets. Ces représentations présentent en effet l'avantage de décrire l'image sous différentes formes, mettant l'accent soit sur les basses fréquences de l'image, soit sur les hautes fréquences selon plusieurs directions. Les zones de l'image contenant beaucoup d'information, comme les contours ou les points singuliers, possèdent alors de forts coefficients dans la transformée en ondelettes ou en shearlets de l'image, tandis que les zones uniformes possèdent des coefficients proches de zéro. Les travaux de cette thèse montrent la précision et la robustesse de l'approche utilisant la décomposition en shearlets dans le cadre de l'imagerie échographique. Néanmoins, sa contribution majeure est l'élaboration d'une commande permettant d'utiliser au choix les ondelettes ou les shearlets ainsi que la validation de cette méthode sur caméra monoculaire et sur capteur de type tomographie par cohérence optique dans différentes conditions d'utilisation. Cette méthode présente des performances significatives en termes de précision et de robustesse et ouvre la porte vers une utilisation couplée de l'asservissement visuel et de l'acquisition comprimée
A visual servoing scheme consists of a closed-loop control approach which uses visual information feedback to control the movement of a robotic system. This data, called visual features, can be 2D or 3D. This thesis deals with the development of a new generation of 2D direct visual servoing methods in which the signal control inputs are the coefficients of a multiscale image representation. Specially, we consider the use of multiscale image representations that are based on discrete wavelet and shearlet transformations. This kind of representations allows us to obtain several descriptions of the image based on either low or high frequencies levels. Indeed, high coefficients in the wavelet or in the shearlet transformation of the image correspond to image singularities. This thesis has begun with the development of a shearlet-based visual servoing for ultrasound imaging that has performed well in precision and robustness for this medical application. Nevertheless, the main contribution is a framework allowing us to use several multi-scale representations of the image. It was then tested with conventional white light camera and with an optical coherence tomography imaging system with nominal and unfavorable conditions. Then, the wavelet and the shearlet based methods showed their accuracy and their robustness in several conditions and led to the use of both visual servoing and compressed sensing as the main perspective of this work

Afin d'améliorer la sûreté (dose plus faible) et la productivité (acquisition plus rapide) du système de la tomographie par rayons X (CT), nous cherchons à reconstruire une image de haute qualitée avec un faible nombre de projections. Les algorithmes classiques ne sont pas adaptés à cette situation et la reconstruction est instable et perturbée par des artefacts. L'approche "Compressed Sensing" (CS) fait l'hypothèse que l'image inconnue est "parcimonieuse" ou "compressible", et la reconstruit via un problème d'optimisation (minimisation de la norme TV/L1) en promouvant la parcimonie. Pour appliquer le CS en CT, en utilisant le pixel/voxel comme base de representation, nous avons besoin d'une transformée parcimonieuse, et nous devons la combiner avec le "projecteur du rayon X" appliqué sur une image pixelisée. Dans cette thèse, nous avons adapté une base radiale de famille Gaussienne nommée "blob" à la reconstruction CT par CS. Elle a une meilleure localisation espace-fréquentielle que le pixel, et des opérations comme la transformée en rayons-X, peuvent être évaluées analytiquement et sont facilement parallélisables (sur plateforme GPU par exemple). Comparé au blob classique de Kaisser-Bessel, la nouvelle base a une structure multi-échelle : une image est la somme des fonctions translatées et dilatées de chapeau Mexicain radiale. Les images médicales typiques sont compressibles sous cette base. Ainsi le système de representation parcimonieuse dans les algorithmes ordinaires de CS n'est plus nécessaire. Des simulations (2D) ont montré que les algorithmes TV/L1 existants sont plus efficaces et les reconstructions ont des meilleures qualités visuelles que par l'approche équivalente basée sur la base de pixel-ondelettes. Cette nouvelle approche a également été validée sur des données expérimentales (2D), où nous avons observé que le nombre de projections en général peut être réduit jusqu'à 50%, sans compromettre la qualité de l'image.

With the recent advent of neuroimaging techniques, the majority of the research studying the neural basis of language processing has focused on the localization of various lexical and semantic functions. Unfortunately, the limited time resolution of functional neuroimaging prevents a detailed analysis of the dynamics involved in word recognition, and the hemodynamic basis of these techniques prevents the study of the underlying neurophysiology. Compounding this problem, current techniques for the analysis of high-dimensional neural data are mainly sensitive to large effects in a small area, preventing a thorough study of the distributed processing involved for representing semantic knowledge. This thesis demonstrates the use of multivariate machine-learning techniques for the study of the neural representation of semantic and speech information in electro/magneto-physiological recordings with high temporal resolution. Support vector machines (SVMs) allow for the decoding of semantic category and word-specific information from non-invasive electroencephalography (EEG) and magnetoenecephalography (MEG) and demonstrate the consistent, but spatially and temporally distributed nature of such information. Moreover, the anteroventral temporal lobe (avTL) may be important for coordinating these distributed representations, as supported by the presence of supramodal category-specific information in intracranial recordings from the avTL as early as 150ms after auditory or visual word presentation. Finally, to study the inputs to this lexico-semantic system, recordings from a high density microelectrode array in anterior superior temporal gyrus (aSTG) are obtained, and the recorded spiking activity demonstrates the presence of single neurons that respond specifically to speech sounds. The successful decoding of word identity from this firing rate information suggests that the aSTG may be involved in the population coding of acousto-phonetic speech information that is likely on the pathway for mapping speech-sounds to meaning in the avTL. The feasibility of extracting semantic and phonological information from multichannel neural recordings using machine learning techniques provides a powerful method for studying language using large datasets and has potential implications for the development of fast and intuitive communication prostheses.
Engineering and Applied Sciences

Coarse-graining and multi-scale approaches are rapidly becoming important tools for computer simulations of large complex molecular systems. Such theoretical models are powerful tools because they allow one to probe the essential features of a complex, many-bodied system on length and time scales over which emergent phenomena may occur. Because of the computational advantages and fundamental insight made available through coarse-grained methods, a vast array of various phenomenological potentials to describe coarse-grained interactions have been developed; nonetheless, the ability of these potentials to provide quantitative information about several different properties of the same system is not evident. On a theoretical level, it is not well-understood how small correlations in the long-range structure propagate through the coarse-graining procedure into the effective potential and lead to incorrect thermodynamics. Taking an alternative approach, this dissertation will discuss an analytical coarse-graining method for synthetic polymer chains of specific chemical structure, where a group of atoms on a polymer chain are represented by a variable number of soft interacting effective sites. The approach is based in liquid-state theory, providing a theoretical framework to address questions of thermodynamic consistency. It will be shown that the proposed method of coarse-graining maintains thermodynamic consistency for a variety of polymer models. In a multi-scale modeling scheme simulations of the same system represented by several different levels of detail may be joined to provide a complete description of the system at all length and time scales of interest. This dissertation includes previously published and unpublished co-authored material.

L'analyse des systèmes de grande taille est confrontée à des difficultés d'ordre syntaxique et sémantique : comment observer un million d'entités distribuées et asynchrones ? Comment interpréter le désordre résultant de l'observation microscopique de ces entités ? Comment produire et manipuler des abstractions pertinentes pour l'analyse macroscopique des systèmes ? Face à l'échec de l'approche analytique, le concept d'émergence épistémique - relatif à la nature de la connaissance - nous permet de définir une stratégie d'analyse alternative, motivée par le constat suivant : l'activité scientifique repose sur des processus d'abstraction fournissant des éléments de description macroscopique pour aborder la complexité des systèmes. Cette thèse s'intéresse plus particulièrement à la production d'abstractions spatiales et temporelles par agrégation de données. Afin d'engendrer des représentations exploitables lors du passage à l'échelle, il apparaît nécessaire de contrôler deux aspects essentiels du processus d'abstraction. Premièrement, la complexité et le contenu informationnel des représentations macroscopiques doivent être conjointement optimisés afin de préserver les détails pertinents pour l'observateur, tout en minimisant le coût de l'analyse. Nous proposons des mesures de qualité (critères internes) permettant d'évaluer, de comparer et de sélectionner les représentations en fonction du contexte et des objectifs de l'analyse. Deuxièmement, afin de conserver leur pouvoir explicatif, les abstractions engendrées doivent être cohérentes avec les connaissances mobilisées par l'observateur lors de l'analyse. Nous proposons d'utiliser les propriétés organisationnelles, structurelles et topologiques du système (critères externes) pour contraindre le processus d'agrégation et pour engendrer des représentations viables sur les plans syntaxique et sémantique. Par conséquent, l'automatisation du processus d'agrégation nécessite de résoudre un problème d'optimisation sous contraintes. Nous proposons dans cette thèse un algorithme de résolution générique, s'adaptant aux critères formulés par l'observateur. De plus, nous montrons que la complexité de ce problème d'optimisation dépend directement de ces critères. L'approche macroscopique défendue dans cette thèse est évaluée sur deux classes de systèmes. Premièrement, le processus d'agrégation est appliqué à la visualisation d'applications parallèles de grande taille pour l'analyse de performance. Il permet de détecter les anomalies présentes à plusieurs niveaux de granularité dans les traces d'exécution et d'expliquer ces anomalies à partir des propriétés syntaxiques du système. Deuxièmement, le processus est appliqué à l'agrégation de données médiatiques pour l'analyse des relations internationales. L'agrégation géographique et temporelle de l'attention médiatique permet de définir des évènements macroscopiques pertinents sur le plan sémantique pour l'analyse du système international. Pour autant, nous pensons que l'approche et les outils présentés dans cette thèse peuvent être généralisés à de nombreux autres domaines d'application.

Drought indices based on monthly precipitation and sometimes temperature are widely used due to their simple calculation with readily available climate data. The portrayal of drought through simple precipitation anomalies or water balances when accounting for temperature may not capture the potentially complex evolution of drought events due to the timing, intensity, and frequency of precipitation events at the daily scale. In this study, we present a new drought index that incorporates a deterministic soil model, HYDRUS-1D, and daily climate data to assess how representative simple drought indices are of soil moisture status in the Southwest. Specifically, we compare our drought index with two widely used drought indices: the Standardized Precipitation Index (SPI) and the Standardized Perception-Evapotranspiration Index (SPEI). Modeled soil moisture output was summed into monthly values for direct comparison between indices. SPI and SPEI proved to be representative of soil moisture status at shallow depths, correlating best at a two-month window. SPI correlated higher with our modeled drought index than SPEI in shallow settings across all study sites. Intense drought events were controlled by the magnitude and frequency of precipitation, with large events creating water surplus and then a slow decay in soil moisture until the next large event. Furthermore, heat map correlations indicate that monitoring drought at depth is dependent upon the previous years monsoon, with the best correlating window growing with distance from monsoon onset. Modeled soil moisture showed volumetric water content increased during monsoon season and remained high through the fall and into the winter months. Higher moisture content increased hydraulic conductivity, priming the soil profile for winter recharge. We believe that the addition of a soil physics based drought index greatly improves drought monitoring conditions for the southwest.

Ce mémoire de thèse présente de nouvelles méthodologies pour l'analyse de données Poissoniennes sur la sphère, dans le cadre de la mission Fermi. Les objectifs principaux de la mission Fermi, l'étude du fond diffus galactique et l'établissement du catalogue de source, sont com pliqués par la faiblesse du flux de photons et les effets de l'instrument de mesure. Ce mémoire introduit une nouvelle représentation mutli-échelles des données Poissoniennes sur la sphère, la Transformée Stabilisatrice de Variance Multi-Echelle sur la Sphère (MS-VSTS), consistant à combiner une transformée multi-échelles sur la sphère (ondelettes, curvelets), avec une transformée stabilisatrice de variance (VST). Cette méthode est appliquée à la suppression du bruit de Poisson mono et multicanale, à l'interpolation de données manquantes, à l'extraction d'un modèle de fond et à la déconvolution multicanale. Enfin, ce mémoire aborde le problème de la séparation de composantes en utilisant des représentations parcimonieuses (template fitting).

碩士
國立成功大學
電機工程研究所
82
In this paper, a new shape representation and recognition method is proposed to identify single objects or overlapping objects from model objects. By using the wavelet transform, the boundary of an input object is decomposed into three signals, from which a new feature points selection and feature vectors assignmen scheme is used to extract magnitude and position change information. The shape recognition task is achieved through feeding these feature vectors of the feature points belonging to the input object and the model into a modified Hopfield neural network. The modified Hopfield neural network is employed to perform global and parallel feature matching. The modification of the network aim at achieving unique and stable matching result. Experiments were conducted to illustrate the performance of the proposed method for single or overlapping objects recognition.

H. Krim, J.-C. Pesquet, A.S. Willsky.
Caption title.
Includes bibliographical references (p. [4]).
Supported by the ARO. DAAL03-92-G-0115 Supported by the AFOSR. F49620-92-J-0002 Supported by the NSF. MIP-9015281

Many machine learning problems involve dealing with a large amount of high-dimensional data across diverse domains. In addition, annotating or labeling the data is expensive as it involves significant human effort. This dissertation explores a joint solution to both these problems by exploiting the property that high-dimensional data in real-world application domains often lies on a lower-dimensional structure, whose geometry can be modeled as a graph or manifold. In particular, we propose a set of novel manifold-alignment based approaches for transfer learning. The proposed approaches transfer knowledge across different domains by finding low-dimensional embeddings of the datasets to a common latent space, which simultaneously match corresponding instances while preserving local or global geometry of each input dataset. We develop a novel two-step transfer learning method called Procrustes alignment. Procrustes alignment first maps the datasets to low-dimensional latent spaces reflecting their intrinsic geometries and then removes the translational, rotational and scaling components from one set so that the optimal alignment between the two sets can be achieved. This approach can preserve either global geometry or local geometry depending on the dimensionality reduction approach used in the first step. We propose a general one-step manifold alignment framework called manifold projections that can find alignments, both across instances as well as across features, while preserving local domain geometry. We develop and mathematically analyze several extensions of this framework to more challenging situations, including (1) when no correspondences across domains are given; (2) when the global geometry of each input domain needs to be respected; (3) when label information rather than correspondence information is available. A final contribution of this thesis is the study of multiscale methods for manifold alignment. Multiscale alignment automatically generates alignment results at different levels by discovering the shared intrinsic multilevel structures of the given datasets, providing a common representation across all input datasets.

by Mark R. Luettgen ... [et al.].
Includes bibliographical references (p. 54-58).
Supported by the Draper Laboratory IR&D Program. DL-H-418524 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Army Research Office of Research. DAAL03-92-G-0115 Supported by the Air Force Office of Scientific Research. F49620-91-C-0047 AFOSR-92-J-0002

Hamid Krim.
Cover title.
Includes bibliographical references (p. 4).
Supported in part by the Army Research Office DAAL-03-92-G-115 Supported in part by the Air Force Office of Scientific Research. F49620-95-1-0083, BU GC12391NGD

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.

First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.

Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.

As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.