Advanced aerospace materials, including fibre reinforced polymer and ceramic matrix composites, are increasingly being used in critical and demanding applications, challenging not only the current damage prediction, detection, and quantification methodologies, but also the residual life of the structure. The main objective of this work consists of developing theoretical and experimental studies about residual strength for composite structures, which are damaged by impact loading, aided by a SHM system, which combines different methods. For this, it is necessary: to identify, and to localize damage, as well as to calculate the severity of the damage and to predict the residual strength of the composite structure. To achieve these goals, the research methodology should consider three methods: (1) Vibration Based Method (VBM); (2) Shearography Speckle (SS) and (3) Flexural After Impact (FAI). Composite plates, made of epoxy resin reinforced by carbon or glass fibre, are evaluated. Firstly, VBM provide Frequency Response Functions to be analysed by suitable metrics (including a new metric), which are compared in terms of their capability for damage identification and global location. Afterwards, the extension of impact damage is determined by using shearography speckle. This technique has demonstrated great potential for damage detection in composite laminated structures. The identification of the damage from the measurements performed with the SS technique is based on the analysis of disturbances in the speed field caused because of the different properties of the material. These abnormal deformations can be verified as typical strains in damaged structures. SS is a laser interferometry method sensitive to displacement gradient in a surface direction out of the plane. Under the action of a smaller load, the structure is deformed and the presence of damage is shown through local peculiarities of surface deformation observed field. Finally, a flexure after impact (FAI) test is used to evaluate its limitations and potentialities as a damage tolerance technique. The residual flexural strength of damaged specimens is evaluated by quasi-static four-point bending test. A new criterion based on a relationship between damage metric from VBM and FAI analysis is presented and discussed. Thus, these results are normalized by using the maximum load and the metrics for damage analyses, i.e. if there is no damage in the structure, then the metric returns zero value. If the structure is partially damaged then the metric returns a number between one and zero. In addition, if the structure is totally damaged (i.e. residual strength is lower than specified in design), then the metric returns a value equal one. Finally, it is discussed the advantages and limitations of this combination into the context of SHM system (Structural Health Monitoring System). / Materiais compósitos estão cada vez mais sendo usados em aplicações críticas e exigentes, desafiando não apenas as metodologias atuais de previsão de dano, detecção, quantificação, mas também da vida residual da estrutura. O principal objetivo deste trabalho consiste no desenvolvimento de estudos teóricos e experimentais sobre a resistência residual de estruturas de compósito, que são danificadas pelo carregamento de impacto, auxiliado por um sistema SHM, que combina diferentes métodos. Para isso, é necessário: identificar, localizar danos, bem como determinar a severidade dos danos e estimar a resistência residual da estrutura. Para atingir esses objetivos, a metodologia de pesquisa considerou três métodos: (1) Método baseado em vibração; (2) Shearography Speckle (SS) e (3) Flexão após Impacto (FAI). Placas de compósito, fabricadas em resina epóxi reforçada por fibra de carbono ou de vidro, são avaliadas. Em primeiro lugar, o método baseado em vibração produz Funções de Resposta em Frequência, que são analisadas através de métricas adequadas (incluindo uma nova métrica), que são comparadas em termos de sua capacidade de identificação de danos e de localização global. Depois disso, a extensão de danos causados pelo impacto é determinada empregando SS. Esta técnica tem demonstrado grande potencial na detecção de dano em estruturas laminadas compósito. A identificação do dano a partir das medidas realizadas com a técnica SS tem por base a análise das perturbações no campo de curvaturas causada devido à heterogeneidade das propriedades do material. Estas deformações anormais podem ser verificadas como deformações típicas de estruturas danificadas. A SS é um método de interferometria laser sensível ao gradiente de deslocamento de uma superfície na direção fora do plano. Sob a ação de um pequeno carregamento, a estrutura é deformada e a presença de danos é revelada através de singularidades locais do campo de deformação observado na superfície. Finalmente, teste de flexão após o impacto (FAI) é usado para avaliar suas limitações e potencialidades como uma técnica de tolerância ao dano. A resistência à flexão das amostras intactas e danificadas é avaliada por ensaio de flexão em quatro-pontos quase-estático. Um novo critério baseado em uma relação entre a métrica de dano prevista pelos métodos de vibração e a análise via FAI é apresentado e discutido. Assim, estes resultados são normalizados utilizando a carga máxima e as métricas de dano, ou seja, se não houver nenhum dano na estrutura, a métrica retorna valor igual a zero. Se a estrutura é parcialmente danificada, a métrica retorna um valor entre um e zero. Além disso, se a estrutura está totalmente danificada (ou seja, a resistência residual está abaixo do especificado em projeto), a métrica retorna um valor igual a um. Por fim, discutem-se as vantagens e limitações desta combinação para o contexto de sistema SHM (Sistema de Monitoramento da Integridade Estrutural).

Advanced aerospace materials, including fibre reinforced polymer and ceramic matrix composites, are increasingly being used in critical and demanding applications, challenging not only the current damage prediction, detection, and quantification methodologies, but also the residual life of the structure. The main objective of this work consists of developing theoretical and experimental studies about residual strength for composite structures, which are damaged by impact loading, aided by a SHM system, which combines different methods. For this, it is necessary: to identify, and to localize damage, as well as to calculate the severity of the damage and to predict the residual strength of the composite structure. To achieve these goals, the research methodology should consider three methods: (1) Vibration Based Method (VBM); (2) Shearography Speckle (SS) and (3) Flexural After Impact (FAI). Composite plates, made of epoxy resin reinforced by carbon or glass fibre, are evaluated. Firstly, VBM provide Frequency Response Functions to be analysed by suitable metrics (including a new metric), which are compared in terms of their capability for damage identification and global location. Afterwards, the extension of impact damage is determined by using shearography speckle. This technique has demonstrated great potential for damage detection in composite laminated structures. The identification of the damage from the measurements performed with the SS technique is based on the analysis of disturbances in the speed field caused because of the different properties of the material. These abnormal deformations can be verified as typical strains in damaged structures. SS is a laser interferometry method sensitive to displacement gradient in a surface direction out of the plane. Under the action of a smaller load, the structure is deformed and the presence of damage is shown through local peculiarities of surface deformation observed field. Finally, a flexure after impact (FAI) test is used to evaluate its limitations and potentialities as a damage tolerance technique. The residual flexural strength of damaged specimens is evaluated by quasi-static four-point bending test. A new criterion based on a relationship between damage metric from VBM and FAI analysis is presented and discussed. Thus, these results are normalized by using the maximum load and the metrics for damage analyses, i.e. if there is no damage in the structure, then the metric returns zero value. If the structure is partially damaged then the metric returns a number between one and zero. In addition, if the structure is totally damaged (i.e. residual strength is lower than specified in design), then the metric returns a value equal one. Finally, it is discussed the advantages and limitations of this combination into the context of SHM system (Structural Health Monitoring System). / Materiais compósitos estão cada vez mais sendo usados em aplicações críticas e exigentes, desafiando não apenas as metodologias atuais de previsão de dano, detecção, quantificação, mas também da vida residual da estrutura. O principal objetivo deste trabalho consiste no desenvolvimento de estudos teóricos e experimentais sobre a resistência residual de estruturas de compósito, que são danificadas pelo carregamento de impacto, auxiliado por um sistema SHM, que combina diferentes métodos. Para isso, é necessário: identificar, localizar danos, bem como determinar a severidade dos danos e estimar a resistência residual da estrutura. Para atingir esses objetivos, a metodologia de pesquisa considerou três métodos: (1) Método baseado em vibração; (2) Shearography Speckle (SS) e (3) Flexão após Impacto (FAI). Placas de compósito, fabricadas em resina epóxi reforçada por fibra de carbono ou de vidro, são avaliadas. Em primeiro lugar, o método baseado em vibração produz Funções de Resposta em Frequência, que são analisadas através de métricas adequadas (incluindo uma nova métrica), que são comparadas em termos de sua capacidade de identificação de danos e de localização global. Depois disso, a extensão de danos causados pelo impacto é determinada empregando SS. Esta técnica tem demonstrado grande potencial na detecção de dano em estruturas laminadas compósito. A identificação do dano a partir das medidas realizadas com a técnica SS tem por base a análise das perturbações no campo de curvaturas causada devido à heterogeneidade das propriedades do material. Estas deformações anormais podem ser verificadas como deformações típicas de estruturas danificadas. A SS é um método de interferometria laser sensível ao gradiente de deslocamento de uma superfície na direção fora do plano. Sob a ação de um pequeno carregamento, a estrutura é deformada e a presença de danos é revelada através de singularidades locais do campo de deformação observado na superfície. Finalmente, teste de flexão após o impacto (FAI) é usado para avaliar suas limitações e potencialidades como uma técnica de tolerância ao dano. A resistência à flexão das amostras intactas e danificadas é avaliada por ensaio de flexão em quatro-pontos quase-estático. Um novo critério baseado em uma relação entre a métrica de dano prevista pelos métodos de vibração e a análise via FAI é apresentado e discutido. Assim, estes resultados são normalizados utilizando a carga máxima e as métricas de dano, ou seja, se não houver nenhum dano na estrutura, a métrica retorna valor igual a zero. Se a estrutura é parcialmente danificada, a métrica retorna um valor entre um e zero. Além disso, se a estrutura está totalmente danificada (ou seja, a resistência residual está abaixo do especificado em projeto), a métrica retorna um valor igual a um. Por fim, discutem-se as vantagens e limitações desta combinação para o contexto de sistema SHM (Sistema de Monitoramento da Integridade Estrutural).

The present document covers the studies over Structural Health Monitoring systems via vibration based methods. The topic is organized in two parallel studies. The first one analyzes the integrity of metal-composite single lap bonded joints. The second one approaches similar analyses for sandwich structures. The monitoring was made by investigating the dynamic response both computationally and experimentally to verify the reliability of applying vibration based SHM procedures, specifically with the objective of identifying the presence of debonding damage. The dynamic responses were obtained via accelerometers and piezoelectric sensors placed on top of the investigated structures (on the outward surface). The purpose for the accelerometers is to provide reference data for the analyses involving the piezoelectric sensors. Different metrics of damage identification were investigated, all working over a determined frequency range. They quantify the damage by analyzing either the magnitudes or phase angles of the dynamic responses among the undamaged and damage structures. This present work proposed modifications to some methodologies of damage quantification found in the literature and compared the results. The new metrics offered more reliable values for the damage quantification on several of the analyses. It was verified that the metrics are valid for the scenarios observed in the present study. The experimental analyses showed also the influence on the dynamic response due to the position of small elastomeric elements. In regards to the finite element analyses, the computational models showed similar results to the experimental data, the more accurate ones being the models for the bonded joints. For the computational models, improvements can be applied into the piezoelectric sensor (e.g. by using new finite element formulations), as well as the region of debonding (e.g. by using contact algorithms). It is important to highlight that the elastic properties of the skins for the sandwich structure were obtained by the literature, so the model can be improved in the future by applying properties obtained experimentally. / Esta dissertação aborda os estudos realizados no campo de Sistemas de Monitoramento da Integridade Estrutural por meio de métodos baseados em vibrações. O tópico abordado é organizado em dois estudos paralelos. O primeiro é relativo ao monitoramento da integridade de juntas coladas metal-compósito. O segundo versa sobre análises semelhantes em estruturas sanduíche. O monitoramento foi executado através das análises das assinaturas dinâmicas das estruturas, tanto computacionalmente quanto experimentalmente, visando avaliar a capacidade de metodologias vibracionais de SHM em detectar dano de descolamento. As respostas dinâmicas foram obtidas por meio de acelerômetros e sensores piezelétricos dispostos sobre a superfície das estruturas avaliadas. Os acelerômetros fornecem dados de referência para as análises realizadas com base nas respostas do sensor piezelétrico. Diferentes métricas de identificação de dano são abordadas, sendo que todas estão baseadas em análise no domínio da frequência, utilizando parâmetros de magnitude ou ângulo de fase das estruturas danificadas e intactas. O presente trabalho propôs alterações em algumas das metodologias encontradas na literatura e comparou os resultados das métricas originais com as modificadas. As métricas modificadas apresentaram resultados mais consistentes em vários cenários de análise. Constatou-se também que as métricas abordadas mostram-se válidas para os casos observados no presente estudo. As análises experimentais também evidenciaram a influência na assinatura dinâmica da estrutura sanduíche causada pelo posicionamento de pequenos elementos elastoméricos. Com relação às análises via elementos finitos, os modelos computacionais apresentaram resultados similares aos obtidos experimentalmente, sendo os da junta colada os mais precisos. Tais modelos computacionais podem ser melhorados no futuro por meio de uma modelagem mais detalhada dos elementos piezelétricos (por exemplo: por meio de novas formulações), como também da região de descolamento (por exemplo: por meio da implementação de algoritmos de contato). Deve-se ressaltar também que as propriedades elásticas das lâminas externas da estrutura sanduíche foram obtidas da literatura, assim sendo, o modelo poderá ser melhorado em estudos futuros por meio do emprego de propriedades obtidas experimentalmente.

Structural health monitoring (SHM) is concerned with the continuous, long-term assessment of structural integrity. One commonly investigated SHM technique uses guided ultrasonic waves, which travel through the structure and interact with damage. Measured signals are then analyzed in software for detection, estimation, and characterization of damage. One common configuration for such a system uses a spatially-distributed array of fixed piezoelectric transducers, which is inexpensive and can cover large areas. Typically, one or more sets of prerecorded baseline signals are measured when the structure is in a known state, with imaging methods operating on differences between follow-up measurements and these baselines. Presented here is a new class of SHM spatially-distributed array algorithms that rely on sparse reconstruction. For this problem, damage over a region of interest (ROI) is considered to be sparse. Two different techniques are demonstrated here. The first, which relies on sparse reconstruction, uses an a priori assumption of scattering behavior to generate a redundant dictionary where each column corresponds to a pixel in the ROI. The second method extends this concept by using multidimensional models for each pixel, with each pixel corresponding to a "block" in the dictionary matrix; this method does not require advance knowledge of scattering behavior. Analysis and experimental results presented demonstrate the validity of the sparsity assumption. Experiments show that images generated with sparse methods are superior to those created with delay-and-sum methods; the techniques here are shown to be tolerant of propagation model mismatch. The block-sparse method described here also allows the extraction of scattering patterns, which can be used for damage characterization.

Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-09-21Bitstream added on 2014-06-13T19:35:08Z : No. of bitstreams: 1 marqui_cr_me_ilha.pdf: 2038827 bytes, checksum: 471f672b818089216b3b9afc3b90a230 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Este trabalho apresenta o estudo e desenvolvimento de técnicas para o monitoramento da integridade estrutural em sistemas inteligentes com sensores e atuadores piezelétricos acoplados. Os índices de sensibilidade estudados e utilizados no monitoramento da estrutura são: índice de falha métrica, calculado diretamente do sinal de impedância elétrica dos sensores/atuadores piezelétricos; índices do sensor, calculados com as normas de sistemas ou com as matrizes grammiana de observabilidade e os índices de entrada, calculados com as matrizes grammianas de controlabilidade. Tais índices são utilizados para detectar e localizar as falhas em aplicações numéricas e experimentais. As normas de sistemas e as matrizes grammianas de controlabilidade e observabilidade são obtidas através de um modelo numérico, como por exemplo, Método dos Elementos Finitos; ou um modelo identificado experimentalmente, via o método de realização para autossistemas, mais conhecido como ERA (Eigensytem Realization Algorithm). Em uma segunda etapa do procedimento proposto, as falhas são quantificadas utilizando Redes Neurais Artificiais, que foram treinadas com as normas de sistemas e com as matrizes grammianas. / This work presents the study and development of Structural Health Monitoring techniques for application in intelligent systems with coupled piezoelectric sensors and actuators. The indices of sensitivity for structural monitoring are based on: root-means-square deviation index, directly calculated from electric impedance signal of the piezoelectric sensors/actuators; sensor indices, calculated from system norms or observability grammian matrix, and input index, calculated from controllability grammian matrix. Such indices are used for damage detection and location in numerical and experimental applications. System norms, controllability and observability grammian matrices are obtained through numerical model, as for instance, Finite Element Method; or by experimental identification technique, via Eigensytem Realization Algorithm (ERA). In the second stage of the proposed procedure, damages were quantified using Artificial Neural Networks, that were trained with systems norms and grammian matrices.

The present document covers the studies over Structural Health Monitoring systems via vibration based methods. The topic is organized in two parallel studies. The first one analyzes the integrity of metal-composite single lap bonded joints. The second one approaches similar analyses for sandwich structures. The monitoring was made by investigating the dynamic response both computationally and experimentally to verify the reliability of applying vibration based SHM procedures, specifically with the objective of identifying the presence of debonding damage. The dynamic responses were obtained via accelerometers and piezoelectric sensors placed on top of the investigated structures (on the outward surface). The purpose for the accelerometers is to provide reference data for the analyses involving the piezoelectric sensors. Different metrics of damage identification were investigated, all working over a determined frequency range. They quantify the damage by analyzing either the magnitudes or phase angles of the dynamic responses among the undamaged and damage structures. This present work proposed modifications to some methodologies of damage quantification found in the literature and compared the results. The new metrics offered more reliable values for the damage quantification on several of the analyses. It was verified that the metrics are valid for the scenarios observed in the present study. The experimental analyses showed also the influence on the dynamic response due to the position of small elastomeric elements. In regards to the finite element analyses, the computational models showed similar results to the experimental data, the more accurate ones being the models for the bonded joints. For the computational models, improvements can be applied into the piezoelectric sensor (e.g. by using new finite element formulations), as well as the region of debonding (e.g. by using contact algorithms). It is important to highlight that the elastic properties of the skins for the sandwich structure were obtained by the literature, so the model can be improved in the future by applying properties obtained experimentally. / Esta dissertação aborda os estudos realizados no campo de Sistemas de Monitoramento da Integridade Estrutural por meio de métodos baseados em vibrações. O tópico abordado é organizado em dois estudos paralelos. O primeiro é relativo ao monitoramento da integridade de juntas coladas metal-compósito. O segundo versa sobre análises semelhantes em estruturas sanduíche. O monitoramento foi executado através das análises das assinaturas dinâmicas das estruturas, tanto computacionalmente quanto experimentalmente, visando avaliar a capacidade de metodologias vibracionais de SHM em detectar dano de descolamento. As respostas dinâmicas foram obtidas por meio de acelerômetros e sensores piezelétricos dispostos sobre a superfície das estruturas avaliadas. Os acelerômetros fornecem dados de referência para as análises realizadas com base nas respostas do sensor piezelétrico. Diferentes métricas de identificação de dano são abordadas, sendo que todas estão baseadas em análise no domínio da frequência, utilizando parâmetros de magnitude ou ângulo de fase das estruturas danificadas e intactas. O presente trabalho propôs alterações em algumas das metodologias encontradas na literatura e comparou os resultados das métricas originais com as modificadas. As métricas modificadas apresentaram resultados mais consistentes em vários cenários de análise. Constatou-se também que as métricas abordadas mostram-se válidas para os casos observados no presente estudo. As análises experimentais também evidenciaram a influência na assinatura dinâmica da estrutura sanduíche causada pelo posicionamento de pequenos elementos elastoméricos. Com relação às análises via elementos finitos, os modelos computacionais apresentaram resultados similares aos obtidos experimentalmente, sendo os da junta colada os mais precisos. Tais modelos computacionais podem ser melhorados no futuro por meio de uma modelagem mais detalhada dos elementos piezelétricos (por exemplo: por meio de novas formulações), como também da região de descolamento (por exemplo: por meio da implementação de algoritmos de contato). Deve-se ressaltar também que as propriedades elásticas das lâminas externas da estrutura sanduíche foram obtidas da literatura, assim sendo, o modelo poderá ser melhorado em estudos futuros por meio do emprego de propriedades obtidas experimentalmente.

Les structures intelligentes sont de plus en plus présentes dans différentes industries et notamment dans les domaines de l'aéronautique et du génie civil. Ces structures sont dotées de fonctions qui leur permettent d'interagir avec leur environnement, d'adapter leurs caractéristiques structurelles (raideur, amortissement, viscosité, etc.) selon les besoins ou de surveiller leur état de santé ou « SHM » (Structural Health Monitoring). Aujourd’hui, les performances des méthodes de contrôle actif peuvent être considérablement dégradées lors de l’apparition d’endommagement. Le contrôle actif tolérant aux dommages ou « DTAC » (Damage Tolerant Active Control) est un champ de recherche récent qui s'intéresse à l'élaboration d'approches intégrées pour réduire les vibrations tout en surveillant l'intégrité de la structure, en identifiant les éventuels dommages, et en reconfigurant la loi de commande.Cette thèse apporte une contribution au DTAC en proposant une approche originale basée sur la norme H∞ modale . Les méthodes proposées se focalisent principalement sur le cas où plusieurs actionneurs et capteurs piézoélectriques non-collocalisés sont utilisés pour atténuer les vibrations des structures endommagées. Le manuscrit comprend quatre parties principales. Le chapitre 2 présente des rappels sur la commande H∞ et sur sa solution sous optimale obtenue par une approche par inégalité matricielle ou « LMI » (Linear Matrix Inequality), sur lesquels s’appuient les développements proposés dans ce travail. Le chapitre 3 décrit la norme H∞ modale introduite pour le contrôle actif des vibrations. Cette commande présente une sélectivité modale élevée, permettant ainsi de se concentrer sur les effets du dommage tout en bénéficiant des propriétés de robustesse qu'offre la commande H∞ vis-à-vis du spillover et des variations de paramètres. Une nouvelle stratégie de rejet des vibrations est proposée au chapitre 4. C'est une approche dite préventive où une prise en compte lors de l'élaboration de la commande H∞ modale, des zones fortement contraintes de la structure, où le risque d’endommagement est élevé est réalisée. Un algorithme SHM est proposé afin d'évaluer la sévérité du dommage pour chaque mode. Le chapitre 5 propose une nouvelle approche modale à double boucle de commande pour faire face à des endommagements imprévisibles. Un premier correcteur est conçu dans ce but pour satisfaire les contraintes de performance et de robustesse sur la structure saine, tandis que le second a pour objectif de conserver un contrôle satisfaisant quand un dommage survient. La loi de commande s'appuie sur un observateur d’état et d'un algorithme SHM pour reconfigurer en ligne le correcteur. Toutes les approches DTAC proposées sont testées en utilisant des simulations (analytiques et éléments finis) et/ou des expérimentations sur des structures intelligentes. / Smart structures have increasingly become present in different industry applications and particularly in the fields of aeronautics and civil engineering. These structures have features that allow interactions with the environment, adapting their characteristics according to the needs (stiffness, damping, viscosity, etc.), monitoring their health or controlling their vibrations. Today smart structure active control methods do not respond appropriately to damage, despite the capacity of external disturbances good rejection. Damage-tolerant active control (DTAC) is a recent research area that aims to develop integrated approaches to reduce the vibrations while monitoring the integrity of the structure, identifying damage occurrence and reconfiguring the control law of the adopted active vibration control method.This thesis contributes to DTAC area, proposing a novel modal control framework and some applying strategies. Developed methods focus in non-collocated flexible structures, where multiples piezoelectric sensors and actuators are used to attenuate damaged structure vibration. The chapters present four main topics and the conclusions. Chapter 2 reviews the regular suboptimal H∞ problem and its respective solution based on the linear matrix inequality (LMI) approach, which is a fundamental tool for the development of subsequent topics. Chapter 3 introduces the modal H∞-norm based method for vibration control, which reveals high modal selectivity, allowing control energy concentration on damage effects and presenting robustness to spillover and parameter variation. A new control strategy is developed in Chapter 4, taking into account existing knowledge about the structure stressed regions with high probability of damage occurrence, leading to specific requirements in the modal H∞ controller design. A structural health monitoring (SHM) technique assesses each damaged mode behavior, which is used to design a preventive controller. Chapter 5 presents a novel modal double-loop control methodology to deal with the unpredictability of damage, nevertheless ensuring a good compromise between robustness and performance to both healthy and damaged structures. For this purpose, the first loop modal controller is designed to comply with regular requirements for the healthy structure behavior, and the second loop controller is reconfigured aiming to ensure satisfactory performance and robustness when and if damage occurs, based on a state-tracking observer and an SHM technique to adapt the controller online. In all these chapters, simulated (analytical and finite elements based) and/or experimental aluminum structures are used to examine the proposed methodology under the respective control strategies. The last chapter subsumes the achieved results for each different approach described in the previous chapters.

Problems in the control and identification of structural dynamic systems can lead to multimodal optimization problems, which are difficult to solve using classical gradient based methods. In this work, optimization problems pertaining to the vibration control of smart structures and the exploration of isospectral systems are addressed. Isospectral vibrating systems have identical natural frequencies, and existence of the isospectral systems proves non-uniqueness in system identification. For the smart structure problem, the optimal location(s) of collocated actuator(s)/sensor(s) and the optimal feedback gain matrix are obtained by maximizing the energy dissipated by the feedback control system. For the isospectral system problem, both discrete and continuous systems are considered. An error function is designed to calculate the error between the spectra of two distinct structural dynamic systems. For the discrete system, the Jacobi matrix, derived from the given system, is modified and the problem is posed as an optimization problem where the objective is to minimize the non-negative error function. Isospectral spring-mass systems are obtained. For the continuous system, finite element modeling is used and an error function is designed to calculate the error between the spectra of the uniform beam and the non-uniform beam. Non-uniform cantilever beams which are isospectral to a given uniform cantilever beam are obtained by minimizing the non-negative error function. Numerical studies reveal several isospectral systems, and optimal gain matrices and sensor/actuator locations for the smart structure. New evolutionary algorithms, which do not need genetic operators such as crossover and mutation, are used for the optimization. These algorithms are: Artificial bee colony (ABC) algorithm, Glowworm swarm optimization (GSO) algorithm, Firefly algorithm (FA) and Electromagnetism inspired optimization (EIO) algorithm.

No description available.

This thesis addresses the identification of stochastic systems operating under different conditions, based on data records corresponding to a sample of such operating conditions. This topic is very important, as systems operating under different, though constant conditions at different occasions (time intervals) are often encountered in practice. Typical examples include mechanical, aerospace or civil structures that operate under different environmental conditions (temperature or humidity, for instance) on different occasions (period of day, and so on). Such different operating conditions may affect the system characteristics, and therefore its dynamics. Given a set of data records corresponding to distinct operating conditions, it is most desirable to establish a single global model capable of describing the system throughout the entire range of admissible operating conditions. In the present thesis this problem is treated via a novel stochastic Functional Pooling (FP) identification framework which introduces functional dependencies (in terms of the operating condition) in the postulated model structure. The FP framework offers significant advantages over other methods providing global models by interpolating a set of conventional models (one for each operating condition), as it: (i) treats data records corresponding to different operating conditions simultaneously, and fully takes cross-dependencies into account thus yielding models with optimal statistical accuracy, (ii) uses a highly parsimonious representation which provides precise information about the system dynamics at any specified operating condition without resorting to customary interpolation schemes, (iii) allows for the determination of modeling uncertainty at any specified operating condition via formal interval estimates. To date, all research efforts on the FP framework have concentrated in identifying univariate (single excitation-single response) stochastic models. The present thesis aims at (i) properly formulating and extending the FP framework to the case of multivariate stochastic systems operating under multiple operating conditions, and (ii) introducing an approach based on multivariate FP modeling and statistical hypothesis testing for damage detection under different operating conditions. The case of multivariate modeling is more challenging compared to its univariate counterpart as the couplings between the corresponding signals lead to more complicated model structures, whereas their nontrivial parametrization raises issues on model identifiability. The main focus of this thesis is on models of the Functionally Pooled Vector AutoRegressive with eXogenous excitation (FP-VARX) form, and Vector AutoRegressive Moving Average (FP-VARMA) form. These models may be thought of as generalizations of their conventional VARX/VARMA counterparts with the important distinction being that the model parameters are explicit functions of the operating condition. Initially, the identification of FP-VARX models is addressed. Least Squares (LS) and conditional Maximum Likelihood (ML) type estimators are formulated, and their consistency along with their asymptotic normality is established. Conditions ensuring FP-VARX identifiability are postulated, whereas model structure specification is based upon proper forms of information criteria. The performance characteristics of the identification approach are assessed via Monte Carlo studies, which also demonstrate the effectiveness of the proposed framework and its advantages over conventional identification approaches based on VARX modeling. Subsequently, an experimental study aiming at identifying the temperature effects on the dynamics of a smart composite beam via conventional model and novel global model approaches is presented. The conventional model approaches are based on non-parametric and parametric VARX representations, whereas the global model approaches are based on parametric Constant Coefficient Pooled (CCP) and Functionally Pooled (FP) VARX representations. Although the obtained conventional model and global representations are in rough overall agreement, the latter simultaneously use all available data records and offer improved accuracy and compactness. The CCP-VARX representations provide an ``averaged'' description of the structural dynamics over temperature, whereas their FP-VARX counterparts allow for the explicit, analytical modeling of temperature dependence, and attain improved estimation accuracy. In addition, the identification of FP-VARMA models is addressed. Two-Stage Least Squares (2SLS) and conditional ML type estimators are formulated, and their consistency and asymptotic normality are established. Furthermore, an effective method for 2SLS model estimation featuring a simplified procedure for obtaining residuals in the first stage is introduced. Conditions ensuring FP-VARMA model identifiability are also postulated. Model structure specification is based upon a novel two-step approach using Canonical Correlation Analysis (CCA) and proper forms of information criteria, thus avoiding the use of exhaustive search procedures. The performance characteristics of the identification approach are assessed via a Monte Carlo study, which also demonstrates the effectiveness of the proposed framework over conventional identification approaches based on VARMA modeling. An approach based on the novel FP models and statistical hypothesis testing for damage detection under different operating conditions is also proposed. It includes two versions: the first version is based upon the obtained modal parameters, whereas the second version is based upon the discrete-time model parameters. In an effort to streamline damage detection, procedures for compressing the information carried by the modal or the discrete-time model parameters via Principal Component Analysis (PCA) are also employed. The effectiveness of the proposed damage detection approach is assessed on a smart composite beam with hundreds of experiments corresponding to different temperatures. In its present form, the approach relies upon response (output-only) vibration data, although excitation-response data may be also used. FP-VAR modeling is used identify the temperature dependent structural dynamics, whereas a new scheme for model structure selection is introduced which avoids the use of exhaustive search procedures. The experimental results verify the capability of both versions of the approach to infer reliable damage detection under different temperatures. Furthermore, alternative methods attempting removal of the temperature effects from the damage sensitive features are also employed, allowing for a detailed and concise comparison. Finally, some special topics on global VARX modeling are treated. The focus is on the identification of the Pooled (P) and Constant Coefficient Pooled (CCP) VARX model classes. Although both model classes are of limited scope, they are useful tools for global model identification. In analogy to the FP-VARX/VARMA model case, the LS and conditional ML type estimators are studied for both model classes, whereas conditions ensuring model identifiability are also postulated. The relationships interconnecting the P-VARX and CCP-VARX models to the FP-VARX models in terms of compactness and achievable accuracy are studied, whereas their association to the conventional VARX models is also addressed. The effectiveness and performance characteristics of the novel global modeling approaches are finally assessed via Monte Carlo studies. / Η παρούσα διατριβή πραγματεύεται την αναγνώριση πολυμεταβλητών στοχαστικών συστημάτων που παρουσιάζουν πολλαπλές συνθήκες λειτουργίας, βασιζόμενοι σε δεδομένα που αντιστοιχούν σε ένα δείγμα ενδεικτικών συνθηκών λειτουργίας. Η σπουδαιότητα του προβλήματος είναι μεγάλη, καθώς στην πράξη συναντώνται πολύ συχνά συστήματα όπου οι επιμέρους συνθήκες λειτουργίας παραμένουν σταθερές ανά χρονικά διαστήματα. Τυπικά παραδείγματα περιλαμβάνουν μηχανολογικές, αεροναυτικές και δομικές κατασκευές που λειτουργούν κάτω από διαφορετικές συνθήκες (π.χ. θερμοκρασίας και/ή υγρασίας) σε διαφορετικές συνθήκες (π.χ. περίοδος της ημέρας). Οι διαφορετικές συνθήκες λειτουργίας ενδέχεται να επηρεάσουν ένα σύστημα και ως εκ τούτου τα δυναμικά χαρακτηριστικά του. Λαμβάνοντας υπόψη ένα σύνολο δεδομένων που αντιστοιχούν σε διαφορετικές συνθήκες λειτουργίας, είναι επιθυμητή η εύρεση ενός "γενικευμένου" μοντέλου ικανού να περιγράψει το σύστημα σε όλο το φάσμα των αποδεκτών συνθηκών λειτουργίας. Στην παρούσα διατριβή το πρόβλημα αυτό αντιμετωπίζεται μέσω ενός καινοτόμου πλαισίου αναγνώρισης στοχαστικών μοντέλων Συναρτησιακής Σώρευσης (stochastic Functional Pooling Framework), το οποίο εισάγει συναρτησιακές εξαρτήσεις (αναφορικά με την κατάσταση λειτουργίας) στην δομή του μοντέλου. Το συγκεκριμένο πλαίσιο Συναρτησιακής Σώρευσης προσφέρει σημαντικά πλεονεκτήματα σε σχέση με άλλες μεθόδους εύρεσης γενικευμένων μοντέλων που χρησιμοποιούν μεθόδους παρεμβολής (interpolation) σε ένα σύνολο συμβατικών μοντέλων (ένα για κάθε συνθήκη λειτουργίας), όπως: (i) Η ταυτόχρονη διαχείριση δεδομένων που αντιστοιχούν σε διαφορετικές συνθήκες λειτουργίας, καθώς και η διευθέτηση των αλληλοεξαρτήσεων μεταξύ δεδομένων που ανήκουν σε διαφορετικές συνθήκες λειτουργίας παρέχοντας με τον τρόπο αυτό μοντέλα με βέλτιστη στατιστική ακρίβεια, (ii) η χρήση συμπτυγμένων μοντέλων τα οποία περιγράφουν με ακρίβεια τα δυναμικά χαρακτηριστικά του συστήματος σε κάθε κατάσταση λειτουργίας, αποφεύγοντας έτσι την χρήση συμβατικών μεθόδων παρεμβολής, (iii) ο προσδιορισμός των αβεβαιοτήτων στη μοντελοποίηση κάθε κατάστασης λειτουργίας μέσω εκτίμησης κατάλληλων διαστημάτων εμπιστοσύνης. Μέχρι στιγμής, η έρευνα πάνω στο πλαίσιο Συναρτησιακής Σώρευσης έχει επικεντρωθεί στα βαθμωτά στοχαστικά μοντέλα. Η παρούσα διατριβή σαν στόχο έχει (i) την κατάλληλη διαμόρφωση και επέκταση του πλαισίου Συναρτησιακής Σώρευσης για την περίπτωση πολυμεταβλητών στοχαστικών συστημάτων που λειτουργούν με πολλαπλές συνθήκες λειτουργίας , και (ii) την εισαγωγή μιας καινοτόμου μεθοδολογίας ανίχνευσης βλαβών για συστήματα που παρουσιάζουν πολλαπλές συνθήκες λειτουργίας βασιζόμενη σε πολυμεταβλητά μοντέλα Συναρτησιακής Σώρευσης και στον στατιστικό έλεγχο υποθέσεων. Η περίπτωση των πολυμεταβλητών μοντέλων παρουσιάζει τεχνικές δυσκολίες που δεν συναντώνται στα βαθμωτά μοντέλα, καθώς η δομή των μοντέλων είναι πιο περίπλοκη ενώ η παραμετροποίησή τους είναι μη-τετριμμένη θέτοντας έτσι ζητήματα αναγνωρισιμότητας (model identifiability). Η παρούσα διατριβή εστιάζει σε Συναρτησιακά Σωρευμένα Διανυσματικά μοντέλα ΑυτοΠαλινδρόμησης με εΞωγενή είσοδο (Functionally Pooled Vector AutoRegressive with eXogenous excitation; FP-VARX), και σε Διανυσματικά μοντέλα ΑυτοΠαλινδρόμησης με Κινητό Μέσο Όρο (Functionally Pooled AutoRegressive with Moving Average; FP-VARMA). Τα μοντέλα αυτά μπορεί να θεωρηθούν ως γενικεύσεις των συμβατικών μοντέλων VARX/VARMA με την σημαντική διαφοροποίηση ότι οι παράμετροι του μοντέλου είναι συναρτήσεις της συνθήκης λειτουργίας. Το πρώτο κεφάλαιο της διατριβής επικεντρώνεται στην αναγνώριση μοντέλων FP-VARX. Αναπτύσσονται εκτιμήτριες βασισμένες στις μεθόδους των Ελαχίστων Τετραγώνων (Least Squares; LS) και της Μέγιστης Πιθανοφάνειας (Maximum Likelihood; ML), ενώ στη συνέχεια μελετώνται η συνέπεια (consistency) και η ασυμπτωτική κατανομή (asymptotic distribution)τους. Επιπλέον, καθορίζονται συνθήκες που εξασφαλίζουν την αναγνωρισιμότητα (identifiability) των FP-VARX μοντέλων, ενώ ο προσδιορισμός της δομής τους βασίζεται σε κατάλληλα τροποποιημένα κριτήρια πληροφορίας (information criteria). Η αποτίμηση της μοντελοποίησης με FP-VARX, καθώς επίσης και η αποτελεσματικότητά τους έναντι των συμβατικών μοντέλων VARX εξακριβώνεται μέσω προσομοιώσεων Monte Carlo. Στο δεύτερο κεφάλαιο διερευνάται η αναγνώριση των θερμοκρασιακών επιρροών στα δυναμικά χαρακτηριστικά μιας ευφυούς δοκού από σύνθετο υλικό. Το πρόβλημα μελετάται χρησιμοποιώντας συμβατικά μοντέλα καθώς και "γενικευμένα" μοντέλα. Η συμβατική μοντελοποίηση περιλαμβάνει μη-παραμετρικές παραστάσεις που βασίζονται στην μέθοδο Welch (ανάλυση στο πεδίο συχνοτήτων), καθώς και παραμετρικές παραστάσεις βασισμένες στα μοντέλα VARX (ανάλυση στο πεδίο χρόνου). H "γενικευμένη" μοντελοποίηση περιλαμβάνει παραστάσεις Σώρευσης με Σταθερές Παραμέτρους (Constant Coefficient Pooled VARX; CCP-VARX), καθώς και VARX παραστάσεις Συναρτησιακής Σώρευσης (Functionally Pooled VARX; FP-VARX). Η ανάλυση υποδεικνύει ότι τα χαρακτηριστικά των "γενικευμένων" και των συμβατικών μοντέλων βρίσκονται σε γενική συμφωνία μεταξύ τους. Ωστόσο, τα "γενικευμένα" μοντέλα περιγράφουν τα δυναμικά χαρακτηριστικά του συστήματος με μικρότερο αριθμό παραμέτρων, γεγονός που προσδίδει μεγαλύτερη ακρίβεια στην εκτίμησή τους. Το μοντέλο CCP-VARX τείνει να σταθμίσει τα δυναμικά χαρακτηριστικά του συστήματος σε κάποιον "μέσο όρο" με σχετική ακρίβεια. Απεναντίας το μοντέλο FP-VARX υπερέχει σε ακρίβεια, καθώς επιδεικνύει μια εξομαλυμένη καθοριστική εξάρτηση των δυναμικών χαρακτηριστικών του συστήματος με την θερμοκρασία, γεγονός που είναι συμβατό με την φυσική του προβλήματος. Το τρίτο κεφάλαιο επικεντρώνεται στην αναγνώριση μοντέλων FP-VARMA. Αναπτύσσονται εκτιμήτριες βασισμένες στις μεθόδους των Ελαχίστων Τετραγώνων Δύο Σταδίων (Two Stage Least Squares; 2SLS) και της Μέγιστης Πιθανοφάνειας (Maximum Likelihood; ML), ενώ στην συνέχεια μελετώνται η συνέπεια και η ασυμπτωτική κατανομή τους. Επιπλέον, εισάγεται μια νέα μέθοδος για την εκτίμηση 2SLS που απλοποιεί σημαντικά την διαδικασία εξαγωγής υπολοίπων (residuals) από το πρώτο στάδιο. Επίσης, καθορίζονται οι συνθήκες που εξασφαλίζουν αναγνωρισιμότητα στα μοντέλα FP-VARMA. Ο προσδιορισμός της δομής των μοντέλων FP-VARMA πραγματοποιείται χάρη σε μια μεθοδολογία δύο σταδίων που βασίζεται στην Ανάλυση Κανονικοποιημένων Συσχετίσεων (Canonical Correlation Analysis; CCA) και κριτηρίων πληροφορίας, αποφεύγοντας έτσι την εκτεταμένη χρήση αλγορίθμων αναζήτησης. Η αποτίμηση της μοντελοποίησης με FP-VARMA, καθώς επίσης και η αποτελεσματικότητά τους έναντι των συμβατικών VARMA εξακριβώνεται μέσω προσομοιώσεων Monte Carlo. Το τέταρτο κεφάλαιο πραγματεύεται την ανίχνευση βλαβών σε συστήματα που παρουσιάζουν πολλαπλές συνθήκες λειτουργίας. Προτείνεται μια νέα μεθοδολογία που βασίζεται σε καινοτόμα μοντέλα Συναρτησιακής Σώρευσης και στον στατιστικό έλεγχο υποθέσεων. Παρουσιάζονται δυο εκδόσεις της μεθοδολογίας: η πρώτη βασίζεται στα μορφικά χαρακτηριστικά του μοντέλου ενώ η δεύτερη στις παραμέτρους του μοντέλου. Επιπλέον, χρησιμοποιούνται μέθοδοι συμπίεσης της πληροφορίας που περιέχουν τα μορφικά χαρακτηριστικά ή οι παράμετροι του μοντέλου μέσω της Ανάλυσης Κύριων Συνιστωσών (Principal Component Analysis; PCA) σε μια προσπάθεια απλοποίησης της διαδικασίας ανίχνευσης βλαβών. Η αποτελεσματικότητα της μεθοδολογίας επαληθεύεται πειραματικά σε μια "ευφυή" δοκό από σύνθετο υλικό, η οποία ταλαντώνεται σε διαφορετικές θερμοκρασίες. Στην παρούσα μορφή της η μεθοδολογία χρησιμοποιεί δεδομένα απόκρισης ταλάντωσης, ωστόσο δεδομένα διέγερσης-απόκρισης μπορούν να χρησιμοποιηθούν εφόσον κριθεί σκόπιμο. Η εξάρτηση των δυναμικών χαρακτηριστικών της δοκού με την θερμοκρασία περιγράφεται με τη χρήση μοντέλων FP-VAR, ενώ εισάγεται μια νέα μέθοδος καθορισμού της δομής του μοντέλου που αποφεύγει την χρήση αλγορίθμων αναζήτησης. Πλήθος πειραμάτων που καλύπτουν ένα ευρύ θερμοκρασιακό πεδίο, καθώς και συγκρίσεις με άλλες μεθοδολογίες ανίχνευσης βλαβών, πιστοποιούν την ικανότητα της προτεινόμενης μεθοδολογίας να διαγνώσει την κατάσταση της δοκού σε διάφορες θερμοκρασίες. Το πέμπτο κεφάλαιο ασχολείται με ειδικά θέματα μοντελοποίησης των "γενικευμένων" VARX . Ιδιαίτερη προσοχή δίνεται στην μελέτη Σωρευμένων VARX (P-VARX) και CCP-VARX μοντέλων. Σε αντιστοιχία με τα μοντέλα FP, αναπτύσσονται εκτιμήτριες LS και ML, ενώ στην συνέχεια μελετώνται οι ιδιότητές τους. Επιπλέον, καθορίζονται οι συνθήκες που εξασφαλίζουν την αναγνωρισιμότητα των μοντέλων P-VARX και CCP-VARX. Μελετώνται επίσης και οι σχέσεις που συνδέουν τις δομές των μοντέλων P-VARX και CCP-VARX με τα FP-VARX ως προς την παραμετροποίησή τους και την ακρίβεια που επιτυγχάνουν. Επιπλέον, μελετάται και η σχέση των παραπάνω μοντέλων με τα συμβατικά VARX. Η αποτίμηση των γενικευμένων μοντέλων VARX αναφορικά με το πλήθος των εκτιμώμενων παραμέτρων και την ακρίβεια που επιτυγχάνουν εξακριβώνεται μέσω προσομοιώσεων Monte Carlo.