Com o aperfeiçoamento de materiais compósitos de alto desempenho, surge a possibilidade do desenvolvimento de estruturas inteligentes, onde atuadores e sensores piezelétricos estão integrados na estrutura com sistemas de controle adequados para a atenuação de vibrações. Projetos multidisciplinares se tornam cada vez mais complexos e sofisticados, envolvendo diversas fontes de incertezas que devem ser analisadas e quantificadas. O escopo principal desse trabalho visa o estudo da propagação de incertezas em estruturas de materiais compósitos laminados com atuadores e sensores piezelétricos, onde entradas e parâmetros do projeto podem ser fontes aleatórias e/ou nebulosas. Para atingir esse objetivo é adotada a metodologia fuzzy, com a aplicação de otimização de cortes-α. Essa técnica é utilizada na presença de informações vagas ou imprecisas acerca da aleatoriedade presente. Nesse estudo projetam-se, através do método dos elementos finitos, estruturas em forma de placa e casca de material compósito laminado com atuadores e sensores piezelétricos acoplados, controlados pelos reguladores Linear Quadratic Regulator (LQR) e Linear Quadratic Gaussian (LQG). Inicialmente são realizados estudos de otimização para encontrar a melhor localização dos componentes piezelétricos pelos Gramianos de controlabilidade e observabilidade, assim como os fatores de ponderação das leis de controle. O desenvolvimento é realizado no espaço modal reduzido visando um melhor desempenho computacional. As métricas escolhidas para avaliação do controle de vibração e análise das saídas incertas do sistema são baseadas nas energias cinética, potencial e elétrica. Também apresentam-se estudos de envelopes relacionados ao deslocamentos e às frequências naturais da estrutura devido às incertezas. Os resultados mostraram que as otimizações por corte-α para tratar números fuzzy nesse tipo de problema são robustas e eficientes, encontrando-se valores extremos das saídas desejadas. Além de ser um método não intrusivo, também pode ser utilizado em problemas com um número elevado de parâmetros incertos como entrada. / The possibility of developments of smart structures arises with high performance composite materials improvements, where piezoelectric actuators and sensors are embedded into the structures, following a suitable control laws for vibration attenuation. Multidisciplinary projects are becoming highly complex and sophisticated, involving several sources of uncertainty that should be analyzed and quantified. The main objective for this work is to study the uncertainty propagation in composite laminate structures with embedded piezoelectric actuators and sensors, considering random and/or fuzzy sources for the inputs and design parameters. To accomplish this objective, it is adopted the fuzzy α-cut optimizations methodology. This technique is used when the available information related to the actual randomness is vague or imprecise. In this study, laminated composite shells and plates structures are designed and analyzed by the finite element method, where embedded piezoelectric actuators and sensors controlled by Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) are present. Initially, optimization analyses are executed to find the best arrangement for the piezoelectric material using controllability and observability Gramians metrics, as well as the best controller parameters. This study is developed in the reduced modal space looking for computational costs savings. The chosen rating metrics for the vibration control and uncertainty analysis are based on kinetic, potential and electrical energies. Structural displacements and natural frequency envelopes due uncertainty are also studied and presented. The results have shown that the fuzzy α-cut optimizations methodology is robust and efficient to find extreme values for the sought outputs. In addition to being a non-intrusive method, it is also able to deal with a large number of uncertain input parameters.

As bombas de fluxo, além das aplicações clássicas em Engenharia, são instrumentos importantes em áreas como a biologia, farmácia e medicina. Um novo princípio para o bombeamento de fluidos está sendo estudado dentro do Departamento deEngenharia Mecatrônica e de Sistemas Mecânicos da Escola Politécnica da Universidade de São Paulo. O presente projeto trata deste princípio: a utilização de um atuador piezelétrico bilaminar inserido num meio fluido para geração de vazão. O objetivo deste projeto é verificar a viabilidade desta bomba piezelétrica através de simulações computacionais, estudando a sensibilidade do sistema a diversos parâmetros e realizando a otimização do mesmo de forma a maximizar seudesempenho. O software ANSYS é utilizado para a simulação computacional do problema de dinâmica de fluidos e para modelar o atuador piezelétrico bilaminar, e o software Altair Hyperstudy na etapa de otimização. O texto apresenta as metodologias empregadas e discute os resultados obtidos, de forma a analisar os fenômenos físicos em questão e validar este novo princípio proposto. / Flow pumps, besides their classical applications in Engineering, are important devices in areas such as Biology, Pharmacy and Medicine. A novel principle for fluid pumping has been studied at the Department of Mechatronic Engineering and Mechanical Systems of the Engineering School of the University of Sao Paulo. The current project deals with this principle: the use of a bimorph piezoelectric actuator in a fluid environment for flow generation. The objective of this project is to verify the viability of this pump through computational simulations, by performing a sensitivity analysis for various parameters and an optimization to maximize its performance. The ANSYS software is used for the computational fluid dynamics simulations and for modeling the bimorph piezoelectric actuator, and the Altair Hyperstudy software for the optimization. The text presents the employed methodologies and discusses the obtained data in order to analyze the physical phenomena involved and to validate this novel principle.

Notre environnement est de plus en plus peuplé de grandes quantités d’objets intelligents. Certains surveillent des places de stationnement disponibles, d’autres analysent les conditions matérielles dans les bâtiments ou détectent des niveaux de pollution dangereux dans les villes. Les quantités massives de capteurs et d’actionneurs constituent des infrastructures de grande envergure qui s’étendent sur des terrains de stationnement entiers, des campus comprenant plusieurs bâtiments ou des champs agricoles. Le développement d’applications pour de telles infrastructures reste difficile, malgré des déploiement réussis dans un certain nombre de domaines. Une connaissance considérable des spécificités matériel / réseau de l’infrastructure de capteurs est requise de la part du développeur. Pour remédier à ce problème, des méthodologies et des outils de développement logiciel permettant de relever le niveau d’abstraction doivent être introduits pour que des développeurs non spécialisés puissent programmer les applications. Cette thèse présente une méthodologie dirigée par la conception pour le développement d’applications orchestrant des quantités massives d’objets communicants. La méthodologie est basée sur un langage de conception dédié, nommé DiaSwarm qui fournit des constructions déclaratives de haut niveau permettant aux développeurs de traiter des masses d’objets en phase de conception, avant de programmer l’application. La programmation générative est utilisée pour produire des cadres de programmation spécifiques à la conception pour guider et soutenir le développement d’applications dans ce domaine. La méthodologie intègre le traitement parallèle de grandes quantités de données collectées à partir de masses de capteurs. Nous introduisons un langage de déclarations permettant de générer des cadres de programmation basés sur le modèle de programmation MapReduce. En outre, nous étudions comment la conception peut être utilisée pour rendre explicites les ressources requises par les applications ainsi que leur utilisation. Pour faire correspondre les exigences de l’application à une infrastructure de capteurs cible, nous considérons les déclarations de conception à différents stades du cycle de vie des applications. Le passage à l’échelle de cette approche est évaluée dans une expérience qui montre comment les cadres de programmation générés s’appuyant sur le modèle de programmation MapReduce sont utilisés pour le traitement efficace de grands ensembles de données de relevés des capteurs. Nous examinons l’efficacité de l’approche proposée pour relever les principaux défis du génie logiciel dans ce domaine en mettant en oeuvre des scénarios d’application qui nous sont fournis par des partenaires industriels. Nous avons sollicité des programmeurs professionnels pour évaluer l’utilisabilité de notre approche et présenter des données quantitatives et qualitatives de l’expérience. / Our environment is increasingly populated with large amounts of smart objects. Some monitor free parking spaces, others analyze material conditions in buildings or detect unsafe pollution levels in cities. The massive amounts of sensing and actuation devices constitute large-scale infrastructures that span over entire parking lots, campuses of buildings or agricultural fields. Despite being successfully deployed in a number of domains, the development of applications for such infrastructures remains challenging. Considerable knowledge about the hardware/network specificities of the sensor infrastructure is required on the part of the developer. To address this problem, software development methodologies and tools raising the level of abstraction need to be introduced to allow non-expert developers program applications. This dissertation presents a design-driven methodology for the development of applications orchestrating massive amounts of networked objects. The methodology is based on a domain-specific design language, named DiaSwarm that provides high-level, declarative constructs allowing developers to deal with masses of objects at design time, prior to programming the application. Generative programming is used to produce design-specific programming frameworks to guide and support the development of applications in this domain. The methodology integrates the parallel processing of large-amounts of data collected from masses of sensors. We introduce specific language declarations resulting in the generation of programming frameworks based on the MapReduce programming model. We furthermore investigate how design can be used to make explicit the resources required by applications as well as their usage. To match the application requirements to a target sensor infrastructure, we consider design declarations at different stages of the application lifecycle. The scalability of this approach is evaluated in an experiment, which shows how the generated programming frameworks relying on the MapReduce programming model are used for the efficient processing of large datasets of sensor readings. We examine the effectiveness of the proposed approach in dealing with key software engineering challenges in this domain by implementing application scenarios provided to us by industrial partners. We solicited professional programmers to evaluate the usability of our approach and present quantitative and qualitative data from the experiment.

La transition laminaire-turbulent au sein de la couche limite qui se développesur les parois des aéronefs augmente fortement la traînée de frottement. Ainsi, afin derépondre à une problématique à la fois environnementale et économique, une piste envisagéepour réduire la consommation en carburant des aéronefs du futur est de diminuerla trainée en reculant cette transition le plus en aval possible. Dans ce cadre, l’objectifde cette thèse est de caractériser expérimentalement et numériquement l’effet d’actionneursà plasma de type Décharge à Barrière Diélectrique sur la transition. Alimentés parune haute tension alternative, ces actionneurs actifs produisent une force volumique pulséequi permet, sous certaines conditions, de modifier les profils de vitesse moyenne dansla couche limite et de reculer la transition. Sous d’autres conditions, le caractère instationnairede cette force volumique peut entrainer une amplification des instabilités modalesnaturellement présentes dans la couche limite (ondes de Tollmien-Schlichting) et ainsiconduire à une transition prématurée. Une première expérience a permis de mettre enévidence cette compétition entre l’effet moyen stabilisant et l’effet instationnaire déstabilisanten mesurant respectivement un recul et une avancée de la transition. Parallèlementà ces activités expérimentales, une étude numérique, basée sur des analyses destabilité linéaire, a montré que l’effet moyen de la force volumique permettait d’atténuerune large gamme de fréquences d’ondes TS dans la couche limite et d’expliquer le reculde transition observé expérimentalement. En se concentrant sur l’effet moyen, une secondeexpérience a permis d’étudier l’influence de la position de l’actionneur ainsi quel’effet cumulatif de plusieurs actionneurs sur le recul de transition. / The boundary layer transition from a laminar to a turbulent state increases thewall friction drag. Particularly on future aircrafts, one way of reducing fuel consumption,and answering both an environmental and economic issue, consists in delaying the transitionfarther downstream. In this context, the aim of this work is to characterize the impactof Dielectric Barrier discharge (DBD) plasma actuators on the boundary layer transition.When powered with an alternative high voltage, these active actuators produce apulsed body force which is tangential to the wall and, under some conditions, enablesto modify the boundary layer mean velocity profiles to delay the transition. Under otherconditions, the unsteady body force amplifies modal instabilities (Tollmien-Schlichtingwaves) may destabilize the boundary layers, leading to a promoted transition. A first experimentenabled to highlight this competition between the stabilizing mean effect andthe destabilizing unsteady effect by measuring respectively a transition delay and a transitionpromotion. A numerical study based on local stability analyses wass conducted inparallel and showed that a wide frequency range of TS waves is damped by the mean bodyforce, which explains the transition delay. A second experiment, focusing on the mean effect,enabled to show the influence of the actuator position and the cumulative effect ofseveral actuators on the transition delay.

Cerâmicas piezelétricas possibilitam posicionamento e sensoriamento de precisão ou captação de energia mecânica valendo-se do efeito piezelétrico, capaz de converter energia mecânica em elétrica ou o contrário. Para aprimorar ou estender as aplicações dessas cerâmicas, mecanismos flexíveis podem ser acoplados a elas, formando um Dispositivo Piezelétrico Flextensional (DPF). No projeto desse tipo de estrutura, o conceito de Material com Gradação Funcional (MGF) é interessante, já que esses materiais apresentam variações graduais de suas propriedades efetivas, permitindo a alternância entre um material mais flexível e um mais rígido de acordo com a intensidade de deslocamento desejada em cada região da estrutura. Assim, neste trabalho, implementa-se o Método de Otimização Topológica (MOT) no projeto de estruturas gradadas com o intuito de identificar as vantagens e desvantagens da utilização do conceito de MGF em DPF. Esse método combina algoritmos de otimização e o Métodos dos Elementos Finitos (MEF) para distribuir material dentro de um domínio fixo através de um modelo de material, que no presente caso é o de Material Isotrópico Sólido com Penalização (MISP) adaptado a MGF. Na fabricação desses dispositivos otimizados, utiliza-se a Sinterização por Jato de Plasma (SJP) para a obtenção de tarugos gradados que são submetidos a processos de eletro-erosão e de corte a laser. Por fim, para a verificação dos resultados numéricos, utiliza-se um vibrômetro para aferir os deslocamentos dos protótipos de atuadores fabricados. / Piezoelectric devices enable precision positioning and sensing or mechanical energy harvesting based on the piezoelectric effect. In flextensional piezoelectric devices, flexible coupling structures are attached to ceramics to improve or extend the application possibilities. On the design of this kind of structure, the concept of Functionally Graded Materials (FGM) can be interesting, since it allows gradual variations of its effective properties along some direction by mixing two or more materials. Thus, in order to identify the advantages and disadvantages of using FGM, graded flexible coupling structures that maximize the performance of piezoelectric devices are obtained by implementing the Topology Optimization Method (TOM). This method combines optimization algorithms and the Finite Element Method (FEM) to distribute material inside a fixed domain. In this work, the formulation is based on the Solid Isotropic Material with Penalization (SIMP) material model adapted for the FGM concept, which can represent continuous change in material properties along the domain. Resulting optimal graded topologies of coupling structures are presented and compared with homogeneous structures. Finally, graded devices are manufactured through Spark Plasma Sintering (SPS) technique in order to be characterized, validating numerical results. The numerical results demonstrate the TOM efficacy in designing functionally graded piezoelectric devices and show, by its implementation, significant gains in graded mechanisms performance when compared with analogous homogeneous. Furthermore, the feasibility of proposed manufacturing process is confirmed, allowing the fabrication of prototypes with expected behavior.

Les dispositifs de stimulation tactile sont des systèmes destinés à fournir un retour sensoriel à leurs utilisateurs. Ils enrichissent les interfaces homme-machine dans les applications de réalité virtuelle ou augmentée. Ce mémoire traite de l’apport des microsystèmes électromécaniques (MEMS) actionnés magnétiquement à la réalisation d’interfaces de stimulation tactile facilement intégrables.Un état de l’art des solutions d’actionnement mises en œuvre dans les dispositifs existants est proposé, ainsi qu'une définition des besoins pour les applications visées. Les solutions retenues sont basées sur l’actionnement magnétostatique.Les premiers prototypes d’interfaces de stimulation tactile se présentent sous la forme d'un réseau de 4x4 actionneurs élastomériques hybrides avec un pas de 2 mm, combinant microfabrication et techniques de fabrication conventionnelles. La conception et l’élaboration de ces micro-actionneurs est présentée en détail. L'actionnement impulsionnel permet d'atteindre des amplitudes de vibration importantes (jusqu'à 200 µm) et des forces élevées (32mN par actionneur). Des tests sensoriels confirment enfin leur efficacité. Des micro-bobines ont aussi été développées afin de répondre aux besoins des micro-actionneurs magnétiques, ainsi qu'au cahier des charges des interfaces de stimulation tactile. Diverses configurations de micro-bobines adaptées à l'actionnement de puissance sont proposées et réalisées par électrodéposition. Des micro-actionneurs basés sur ces bobines intégrées ont alors été réalisés, puis caractérisés. L'utilité des bobines pour les micro-actionneurs de puissance est alors discutée face aux solutions d’actionnement hybride / Tactile display devices are systems bound to provide a tactile feedback to their users. They improve human-machine interfaces in the fields of virtual or augmented reality. This report deals with the contribution of magnetically actuated micro-electro-mechanical systems (MEMS) to the elaboration of easily integrable tactile display devices.A state of the art of actuation techniques used in existing devices is proposed, along with a requirements analysis for tactile applications. Magnetostatic actuation was considered for these needs.First tactile display device prototypes are designed as a network of 4x4 hybrid elastomeric micro-actuators with a 2 mm pitch, and combined microfabrication and conventional fabrication techniques.The conception and elaboration of these micro-actuators is detailed. High vibration amplitudes can be reached using pulse actuation (up to 200 µm), with instantaneous forces of 32 mN per actuator. Sensitive tests were also achieved in order to confirm their efficiency.Micro-coils were also developed in order to fulfill the magnetic micro-actuators needs, and meet the requirements for tactile display devices. Various micro-coil configurations suitable for power actuation are proposed and elaborated by electrodeposition. Micro-actuators based on elastomeric membranes were fabricated and characterized. The contribution of these micro-coils for micro-actuation is discussed face with hybrid approaches

Dans l’environnement concurrentiel d’aujourd’hui, la mondialisation des marchés et les enjeux socio-écologiques du développement durable représentent des défis majeurs pour l’industrie automobile. Afin de relever ces défis, les entreprises doivent investir dans des outils de développent plus performants. Pour améliorer la performance d’un moteur thermique en termes de consommation et d’émissions une compréhension enrichie de la boucle d’air autour du moteur et de l’interaction entre ses composants est indispensable Cette thèse suit deux axes de recherche dans ce contexte. Dans un premier temps, les problèmes liés à la modélisation d’une boucle d’air globale sont traités. En particulier, sont modélisés le débit d’air entre les différents sous-systèmes, la combustion en fonction du degré vilebrequin, la pulsation du débit et de la pression et l’estimation de la force aérodynamique sur les vannes des turbocompresseurs à géométrie variable (TGV). Cette étude de modélisation détaillée à été utilisée pour mettre en place un simulateur de la boucle d’air, qui prend en compte ces interactions et qui peut prédire l’influence des sous-systèmes sur la boucle globale. En suite, l’effort de notre recherche a été consacré à la modélisation des actionneurs mécatroniques de la boucle d’air et de leur comportement non linéaire dû au frottement, aux variations de la température, etc. Un modèle dynamique non linéaire à été développé et intégré dans le simulateur. Ce modèle peut être adapté aux plusieurs types d’actionneurs commerciaux. Le simulateur complet à été implémenté sous AMESim pour les modèles du moteur et de la boucle d’air, et sous Simulink pour le contrôle. Les modèles ont été paramétrées selon les spécifications d’un moteur commercial et le simulateur à été validé expérimentalement. Finalement, des lois de commande robustes ont été étudiées pour le contrôle en position (contrôle locale) des actionneurs. Un contrôleur adaptatif à été développé pour garantir la performance des actionneurs malgré des changements dans le frottement, ainsi que dans la charge externe. La performance de toutes les méthodes étudiées, a été validée expérimentalement. / Today’s globally competitive market and its associated environmental and social issues of sustainable development are major challenges for the automobile industry. To meet them, the industry needs to invest in high performance development tools. For improving engine performance in terms of consumption and emission, the interactions between the subsystems of the engine air-path need to be understood. This thesis followed two major axes of research in this context. First, the problems related to the modeling of the global air-path system were studied, which include the airflow characteristics between the different subsystems of the air-path, high frequency combustion modeling and pulsating airflow, and estimation of the exhaust aerodynamic force on the vanes of variable geometry turbochargers (VGT). The detailed modeling study was used for developing an engine air-path simulator, which takes into account these interactions and predicts the influence of subsystems on the global air-path. The second axis of research was focused on modeling of mechatronic actuators of the air-path, taking into account their nonlinear behavior due to friction and changes in operating conditions. A generic nonlinear dynamic model was developed and included in the simulator. This model can be adapted to most commercial actuators. The complete simulator has been implemented using AMESim for engine and air-path modeling, and Simulink for control. It has been parameterized according to the specifications of a commercial diesel engine and validated against experimental data. Finally, robust local controllers were studied for actuator position control, aimed at guaranteeing the performance of the actuators under parametric uncertainty and external disturbances. An advanced controller was developed, which adapts to changes in friction characteristics of the actuator and external load changes. The performance of all controllers has been demonstrated experimentally.

A mechatronic chewing robot of 6-DOF mechanism which consists mainly of the skull, six crank actuators, end effector and motion control system has been designed and is required to simulate human chewing behaviours while the chewed food properties are evaluated. The robotic mechanism is proposed and its kinematic parameters are defined according to the biomechanical findings and measurements of the human masticatory system. This thesis is concerned with the design and implementation of trajectory tracking control for robotic jaw actuators via Galil motion controller. The aim of this project is to simulate the dynamics behaviour and force-motion control of the robot, and to quantitatively assess food texture changes during chewing. A control system based Galil motion control card has been formed to achieve the motion of simulated human mastication. Some real human mastication motion have been tracked and used as targeted trajectories for the robot to reproduce. Several experiments have been executed to measure the jaw movements and chewing forces. To reduce the vibration of the actuators and protect sensitive linkage part of the robot, the traditional PID control and some advanced control theories were implemented to achieve most effective efforts. A mathematical model was also designed at the first stage when a test actuator powered by brushless motor was formed; however, it is finally proven not well controlled in either mechanical and control ways. Major features of the built robot including the motion control system are presented and tested. Experimental results including free chewing, soft-food and hard-food chewing are given where the foods are simulated by foam and hard objects. Also the joint actuations and driving torques required are compared for the chewing of different foods. In conclusion, tracking motion control has been attempted on the physical robot and a solution to the trajectory control has been developed.

The application of static shape control was investigated in this thesis particularly for a composite plate configuration using piezoelectric actuators. A new electro-mechanically coupled mathematical model was developed for the analysis and is based on a third order displacement field coupled with a layerwise electric potential concept. This formulation, TODL, is then implemented into a finite element program. The mathematical model represents an improvement over existing formulations used to model intelligent structures using piezoelectric materials as actuators and sensors. The reason is TODL does not only account for the electro-mechanical coupling within the adaptive material, it also accounts for the full structural coupling in the entire structure due to the piezoelectric material being attached to the host structure. The other significant improvement of TODL is that it is applicable to structures which are relatively thick whereas existing models are based on thin beam / plate theories. Consequently, transverse shearing effects are automatically accounted for in TODL and unlike first order shear deformation theories, shear correction factors are not required. The second major section of this thesis uses the TODL formulation in static shape control. Shape control is defined here as the determination of shape control parameters, including actuation voltage and actuator orientation configuration, such that the structure that is activated using these parameters will conform as close as possible to the desired shape. Several shape control strategies and consequently algorithms were developed here. Initial investigations in shape control has revealed many interesting issues which have been used in later investigations to improve shape controllability and also led to the development of improved algorithms. For instance, the use of discrete actuator patches has led to greater shape controllability and the use of slopes and curvatures as additional control criteria have resulted in significant reduction in internal stresses. The significance of optimizing actuator orientation and its relation to piezoelectric anisotropy in improving shape controllability has also been presented. Thus the major facets of shape control has been brought together and the algorithms developed here represent a comprehensive strategy to perform static shape control.

The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.