Les systèmes bilinéaires jouent un rôle central dans la représentation des systèmes non-linéaires en tant qu'approximant des systèmes non-linéaires analytiques généraux. Une classe particulière de ces systèmes bilinéaires, dits homogènes, permet de représenter la fonctionnelle entrée-sortie comme une série de Volterra à horizon infini mais de degré fini. L'algorithme d'identification héréditaire jusqu'alors limité aux systèmes linéaires est ici étendu à l'identification de ces systèmes en utilisant une structure canonique de base pour l'approximant de degré deux (quadratique). Une forme NARX multidimensionnelle (Nonlinear AutoRegressive eXogenous input) est exploitée ici pour autoriser l'identification du système par la méthode héréditaire. On montre, sur un exemple académique quadratique, la supériorité de cette approche comparée aux algorithmes classiques.

Le travail présenté dans ce manuscrit a pour objet l’étude et le développement d’un banc de caractérisation généraliste appliqué à l’extraction du modèle comportemental d’amplificateur TPM-NIM (Two-Path Memory Nonlinear Integral). Ce modèle qui dispose d’une des architectures les plus abouties au laboratoire XLIM requiert une instrumentation microonde haut de gamme, très onéreuse, hors de portée de la majorité des concepteurs pour sa mise en œuvre expérimentale. L’objectif est donc de proposer des principes de mesure originaux permettant d’identifier le modèle TPM-NIM avec une instrumentation standard. Dans ces travaux, deux bancs sont présentés : tout d’abord, un banc de caractérisation développé autour d’une instrumentation de pointe disposant des meilleures propriétés pour extraire le modèle. Puis, un banc construit autour d’une instrumentation standard mais incluant des méthodes de traitement et de mesure novatrices. Ces deux bancs ont été utilisés avec plusieurs véhicules de tests et il ressort que le second permet de diminuer le bruit des mesures de phase tout en réduisant le coût total des équipements. Enfin, une dernière partie est consacrée à la comparaison du modèle TPM-NIM avec deux modèles comportementaux classiques mettant en avant sa polyvalence. / The work presented in this manuscript is devoted to the study and development of a general characterization bench applied to the extraction of the TPM-NIM (Two-Path Memory Nonlinear Integral) amplifier behavioral model. This model, has one of the most advanced architectures at the XLIM laboratory. It requires a high-end microwave instrumentation, overpriced and beyond reach for most of the designers for its experimental implementation. The aim is to propose some original measurements principles allowing the TPM-NIM model’s identification with a standard instrumentation. Two benches are presented in these works : firstly, a characterization bench, developed using a high performance instrumentation with the best properties to extract the model. Then, a bench, built with a standard instrumentation but through innovative processing and measurement methods. These two benches have been used with several test vehicles and it appears that the second one decreases the noise of phase measurements while reducing the equipment’s total cost. Finally, a last part is dedicated to the comparison of the TPM-NIM model with two classic behavioral models by emphasizing its versatility.

Le travail de recherche dans ce mémoire aborde les problèmes de l'identification des systèmes non linéaires et également de l'application de la théorie d'optimisation. Dans une première partie, nous proposons des méthodes efficaces et nouvelles afin d'identifier les systèmes linéaires dans le cas d'expérimentations multiples, les séries de Volterra à horizon infini et les systèmes quadratiques en l'état. Dans une seconde partie, nous appliquons la théorie d'identification à la modélisation de la locomotion humaine. Nous abordons ensuite l'optimisation des mouvements des robots humanoïdes, l'imitation des mouvements humains par un robot humanoïde et enfin le paramétrage temporel des chemins dans l'espace des configurations pour un robot humanoïde. Les résultats expérimentaux de nos méthodes sur la plate-forme HRP-2 ont révélé non seulement leur efficacité, mais aussi leurs bonnes performances qui dépassent largement celles des méthodes conventionnelles.

La miniaturisation de circuits intégrés, les hautes fréquences de fonctionnement, la baisse des potentiels d'alimentation, les fortes densités d'intégration rendent les signaux numériques propagés sur les interconnexions très susceptibles à la dégradation voire à la corruption. En vue d’évaluer la compatibilité électromagnétique et l’intégrité du signal il est nécessaire de disposer dès les premières phases de développement de modèles précis de ces interconnexions pour les insérer dans les simulateurs temporels. Nos travaux s'inscrivent dans ce contexte et concernent plus particulièrement la modélisation comportementale des buffers et drivers de ligne de transmission. Ils ont abouti à une approche originale de modélisation notamment basée sur les séries de Volterra-Laguerre. Les modèles boites noires développés disposent d’une implémentation SPICE assez simple autorisant ainsi une très bonne portabilité. Ils sont faciles à identifier et disposent d’une complexité paramétrique permettant un gain important de temps de simulation vis-à-vis des modèles transistors des drivers. En outre les méthodes développées permettent une modélisation dynamique non linéaire plus précise du port de sortie, et une gestion plus générale des entrées autorisant notamment une très bonne prise en compte du régime de sur-cadencement ce que par exemple ne fait pas le standard IBIS. / Integrated circuits miniaturization, high operating frequencies, lower supply voltages, high-density integration make digital signals propagating on interconnects highly vulnerable to degradation. Assessing EMC and signal integrity in the early stages of the design flow requires accurate interconnect models allowing for efficient time-domain simulations. In this context, our work addressed the issue of behavioral modeling of transmission line buffers, and particularly that of drivers. The main result is an original modeling approach partially based on Volterra-Laguerre series. The black box models we developed have a fairly simple implementation in SPICE thus allowing a very good portability. They are easy to identify and have a parametric complexity allowing a large gain in simulation time with respect to transistor driver models. In addition, the developed methods allow a more accurate output port nonlinear dynamics modeling, and a more general management of inputs. A very good reproduction of driver behaviour in overclocking conditions provides a significant advantage over standard IBIS models.

Orientador: Samuel da Silva / Abstract: Structural Health Monitoring (SHM) methodologies aim to develop techniques able to detect, localize, quantify and predict the progress of damages in civil, aerospatial and mechanical structures. In the hierarchical process, the damage detection is the first and most important step. Despite the existence of numerous methods of damage detection based on vibration signals, two main problems can complicate the application of classical approaches: the nonlinear phenomena and the uncertainties. This thesis demonstrates the importance of the use of a stochastic nonlinear model in the damage detection problem considering the intrinsically nonlinear behavior of mechanical structures and the measured data variation. A new stochastic version of the Volterra series combined with random Kautz functions is proposed to predict the behavior of nonlinear systems, considering the presence of uncertainties. The stochastic model proposed is used in the damage detection process based on hypothesis tests. Firstly, the method is applied in a simulated study assuming a random Duffing oscillator exposed to the presence of a breathing crack modeled as a bilinear oscillator. Then, an experimental application considering a nonlinear beam subjected to the presence of damage with linear characteristics (loss of mass in a bolted connection) is performed, with the direct comparison between the results obtained using a deterministic and a stochastic model. Finally, an experimental application considering a n... (Complete abstract click electronic access below) / Resumo: As metodologias de Monitoramento da Integridade Estrutural (SHM) visam desenvolver técnicas capazes de detectar, localizar, quantificar e prever o progresso de danos em estruturas civis, aeroespaciais e mecânicas. Nesse processo hierárquico, a detecção de danos é o primeiro e mais importante passo. Apesar da existência de inúmeros métodos de detecção de danos baseados em sinais de vibração, dois problemas principais podem complicar a aplicação de abordagens clássicas: os fenômenos não lineares e as incertezas. Esta tese demonstra a importância do uso de um modelo não linear estocástico no problema de detecção de danos, considerando o comportamento intrinsecamente não linear de estruturas mecânicas e a variação dos dados medidos. Uma nova versão estocástica das séries de Volterra, combinada com funções aleatórias de Kautz, é proposta para prever o comportamento de sistemas não lineares, considerando a presença de incertezas. O modelo estocástico proposto é utilizado no processo de detecção de danos com base em testes de hipótese. Primeiramente, o método é aplicado em um estudo simulado, assumindo um oscilador Duffing aleatório exposto à presença de uma trinca respiratória modelada como um oscilador bilinear. Em seguida, uma aplicação experimental é realizada considerando uma viga não linear sujeita à presença de um dano com características lineares (perda de massa em uma conexão parafusada), com a comparação direta entre os resultados obtidos utilizando um modelo determinístic... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor

Cette thèse porte sur l’identification de systèmes non linéaires représentables en séries de Volterra, et son application à des systèmes sonores. Les séries de Volterra, qui permettent de représenter une large classe de systèmes non linéaires, correspondent à un développement en série organisé par ordre d'homogénéité par rapport à l’entrée: chaque terme homogène est caractérisé par un noyau convolutif dont l’ensemble fournit une "signature complète" du système représenté. Les travaux présentés reposent sur le développement d’une étape préalable de séparation des termes de la série pour améliorer l’identification des noyaux de Volterra. Par rapport aux méthodes déjà existantes de séparation en ordres homogènes, basées sur des relations d’amplitudes entre signaux tests, l'approche adoptée dans cette thèse consiste à exploiter les relations de phase entre signaux afin d'obtenir une méthode robuste. Cela est tout d’abord obtenu de manière abstraite pour le cas de signaux d’excitations complexes. De cette idée, plusieurs méthodes adaptées au cas des signaux réels sont développées. Ceci amène à définir de nouvelles catégories de signaux pour décrire la sortie d’une série de Volterra, regroupant les contributions selon leurs propriétés de phase. Les méthodes de séparation proposées sont testées et appliquées à une pédale d’effet de guitare. Ensuite, des méthodes d’identification spécifiques aux nouveaux types de signaux sont présentées. Enfin, une méthode d’estimation des paramètres d’une représentation d’état à non-linéarités polynomiales est développée. Celle-ci est appliquée à un haut-parleur électrodynamique, dont les caractéristiques non linéaires sont étudiées. / This thesis addresses the identification of nonlinear systems that can be represented with Volterra series, and its application to audio systems. Volterra series give an input-output representation, approximated to within a given error, of any time-invariant continuous nonlinear system with fading memory. Technically, they correspond to a series expansion sorted by homogeneity order with respect to the input: each homogeneous term is characterized by a convolutive kernel whose set provides a "complete signature" of the modelled system. The works presented are based on the development of a preliminary step that consists in separating the series' terms to improve Volterra kernels' identification. Compared to existing homogeneous order separation methods, which are based on amplitude relationships between test signals, the approach chosen in this thesis is to exploit phase relationships between signals to obtain a robust method. This is first obtained in the theoretical case of complex excitation signals. From this idea, several methods suited to the use of real signals are developed. This leads to define new signals categories that describes the output of a Volterra series, sorting nonlinear contributions according to their phase properties. The proposed separation methods are applied and tested on a guitar pedal effect. Then, specific identification methods for the new types of signals are presented Finally, a method for estimating the parameters of a polynomial nonlinear state-space representation is developed. This is applied to an electrodynamic loudspeaker whose nonlinear characteristics are studied.

Orientador: Samuel da Silva / Resumo: Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat no... (Complete abstract click electronic access below) / Doutor

Submitted by OSCAR SCUSSEL null (oscar.scussel@gmail.com) on 2017-04-29T13:57:37Z No. of bitstreams: 1 PhDThesisScussel.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-05-03T16:39:39Z (GMT) No. of bitstreams: 1 scussel_o_dr_ilha.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) / Made available in DSpace on 2017-05-03T16:39:39Z (GMT). No. of bitstreams: 1 scussel_o_dr_ilha.pdf: 4308679 bytes, checksum: 08a1260ebbd5cc5320910fff695b1037 (MD5) Previous issue date: 2017-03-27 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Muitas aplicações da engenharia envolvem estruturas essencialmente não-lineares onde várias técnicas têm sido recentemente estudadas e investigadas por muitos pesquisadores. Dentre as várias abordagems, as que usam séries de Volterra têm apresentado propriedades úteis para fornecer um melhor entendimento para identificação e análise. Neste contexto, a presente tese propõem novas contribuições em como usar as séries de Volterra para caracterização, identificação e análise dinâmica de sistemas não-lineares usando sinais de entrada e saída e sinais somente de saída. Inicialmente, apresenta-se uma metodologia para análise de sistemas mecânicos não-lineares através das funções de resposta em frequência de alta-ordem (HOFRFs) e o conceito de HOFRFs estendidas com dados apenas de saída é introduzido e descrito em detalhes. Após isso, uma abordagem para identificação de sistemas não-lineares com base nas séries de Volterra através da expansão na base ortonormal de Kautz é proposta. Essa técnica permite identificar os seus núcleos mais facilmente e permite separar as contribuições dos termos lineares e não-lineares usando somente sinais de saída. Além disso, uma metodologia para análise modal de sistemas fracamente não-lineares sujeito a excitações com vários níveis de amplitude é também apresentada. A contribuição desse novo método reside no fato de que as HOFRFs são simplesmente estimadas como função das FRFs lineares. Basicamente, essa metodologia estende o conceito de métodos convencionais de analise modal experimental para caracterizar e tratar efeitos não-lineares. Os resultados via exemplos numéricos e experimentais apresentados ao longo da tese mostram as contribuições, benefícios e eficácia da proposta. / Most recent engineering applications involve structures essentially nonlinear where several techniques have been recently studied and investigated by many researchers. Among them, the methods based on Volterra series expansion have presented powerful properties to provide a better understanding for identification and analysis. In this context, the present thesis proposes new contributions in how to use Volterra series for characterization, identification and dynamical analysis of nonlinear systems based on input and output signals and output-only signals. Initially, a methodology for analysis of nonlinear mechanical systems through higher-order frequency response functions (HOFRFs) is presented and the concept of extended HOFRFs based on output-only is introduced and described in detail. Afterwards, an approach for identification of nonlinear systems based on Volterra series through the expansion onto orthonormal Kautz basis is proposed. This technique allows to identify the Volterra kernels easily and enable to split the contribution of the linear and nonlinear terms using input-output as well as output-only signals. Furthermore, a methodology for modal analysis of weakly nonlinear systems under multilevel excitation is also proposed. The contribution of this new approach lies in the fact that HOFRFs are simply computed as functions of the linear FRFs. Basically, it extends the conventional experimental modal analysis methods in order to characterize and treat nonlinear effects. The results based on numerical and experimental examples presented along the thesis show the contributions, benefits and effectiveness of the proposal. / FAPESP: 2012/09135-3 / CNPq: 47058/2012-0 / CNPq: 203610/2014-8

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-04-21T15:01:16Z No. of bitstreams: 1 MOISÉS TAVARES DA SILVA - DISSERTAÇÃO PPGEE 2014..pdf: 2264297 bytes, checksum: 0373ed53c40783016694166232616bf6 (MD5) / Made available in DSpace on 2018-04-21T15:01:16Z (GMT). No. of bitstreams: 1 MOISÉS TAVARES DA SILVA - DISSERTAÇÃO PPGEE 2014..pdf: 2264297 bytes, checksum: 0373ed53c40783016694166232616bf6 (MD5) Previous issue date: 2014-09 / Neste trabalho utiliza-se um método do Relé sob condições de não-linearidade e perturbação estática para identificação de modelos não-lineares do tipo Hammstein e Wiener. Este método do relé modificado garante uma saída simétrica do relé quando um estado estacionário cíclico é obtido, independente da perturbação estática, enquanto o método do relé original mostra uma saída assimétrica para processos não-lineares. Para modelos do tipo Wiener, é proposto um sinal de excitação que incorpora as vantagens do método do relé modificado e além disso, obtém as características da baixa frequência da excitação a partir da utilização de um pulso retangular. Para identificação de modelos do tipo Hammterin, inicialmente, o método do relé modificado é aplicado e assim os dados da resposta em frequência do subsistema dinâmico linear são obtidos. em seguida, um sinal triangular é utilizado para identificar a função estática não-linear da entrada. A principal dificuldade na identificação de modelos Hammstein e Wiener é a indisponibilidade do sinal intermediário. Dessa forma, são apresentados procedimentos para obtenção do sinal intermediário a partir do método do relé sob condições de não-linearidade. As técnicas de identificação apresentadas ao longo da dissertação são avaliadas em casos simulados e experimentais para verificar o desempenho de cada uma. / In this work is used a method of the relay feedback under conditions of non-linearity and static disturbance for identification of Hammerstein and Wiener-type nonlinear process. The relay feedback approach used guarantees a symmetrical output relay when a cyclic steady state is obtained, regardless of static disturbance, while the original method shows an asymmetric output relay in such conditions. For Wiener-type process is proposed an exitation signal that incorporates the advantages of the modified method relay feedback and in addition, characteristics of the obtained low frequency excitation from the use of a rectangular pulse. for identification of Hummerstein-type process, initially the method of modified relay is applied and so the data of frequency response of the linear dynamic subsystem are obtained. Then, a triangular signal is used to identify the static nonlinear function. The principal difficulty in the identification of Hammerstein and Wiener process is the unavailability of intermediate signal. Therefore, procedures for obtaining intermediate signal are presented from the relay feedback under conditions of non-linearity. The identification techniques presented throughout in this work are evaluated simulated and experimental cases to verify the performance of each

Cette thèse porte sur la caractérisation de structures mécaniques, au travers de leurs paramètres structuraux, à partir d'observations perturbées par des bruits de mesure, supposés additifs blancs gaussiens et centrés. Pour cela, nous proposons d'utiliser des modèles à temps discret à parties linéaire et non-linéaire séparables. La première permet de retrouver les paramètres recherchés tandis que la seconde renseigne sur la non-linéarité présente. Dans le cadre d'une modélisation non-récursive par des séries de Volterra, nous présentons une approche à erreurs-dans-les-variables lorsque les variances des bruits ne sont pas connues ainsi qu'un algorithme adaptatif du type LMS nécessitant la connaissance de la variance du bruit d'entrée. Dans le cadre d'une modélisation par un modèle récursif polynomial, nous proposons deux méthodes à partir d'algorithmes évolutionnaires. La première inclut un protocole d'arrêt tenant compte de la variance du bruit de sortie. Dans la seconde, les fonctions fitness sont fondées sur des fonctions de corrélation dans lesquelles l'influence du bruit est supprimée ou compensée. / This PhD deals with the caracterisation of mechanical structures, by its structural parameters, when only noisy observations disturbed by additive measurement noises, assumed to be zero-mean white and Gaussian, are available. For this purpose, we suggest using discrete-time models with distinct linear and nonlinear parts. The first one allows the structural parameters to be retrieved whereas the second one gives information on the nonlinearity. When dealing with non-recursive Volterra series, we propose an errors-in-variables (EIV) method to jointly estimate the noise variances and the Volterra kernels. We also suggest a modified unbiased LMS algorithm to estimate the model parameters provided that the input-noise variance is known. When dealing with recursive polynomial model, we propose two methods using evolutionary algorithms. The first includes a stop protocol that takes into account the output-noise variance. In the second one, the fitness functions are based on correlation criteria in which the noise influence is removed or compensated.