The past 30 years have witnessed major developments in vibration based damage detection and identification, also collectively referred to as damage diagnosis. Moreover, the past 10 years have seen a rapid increase in the amount of research related to Structural Health Monitoring (SHM) as quantified by the significant escalation in papers published on this subject. Thus, the increased interest in this engineering field and its associated potential constitute the main motive for this thesis. The goal of the thesis is the development and introduction of novel advanced functional and sequential statistical time series methods for vibration based damage diagnosis and SHM. After the introduction of the first chapter, Chapter II provides an experimental assessment and comparison of vibration based statistical time series methods for Structural Health Monitoring (SHM) via their application on a lightweight aluminum truss structure and a laboratory scale aircraft skeleton structure. A concise overview of the main non-parametric and parametric methods is presented, including response-only and excitation-response schemes. Damage detection and identification are based on univariate (scalar) versions of the methods, while both scalar (univariate) and vector (multivariate) schemes are considered. The methods' effectiveness for both damage detection and identification is assessed via various test cases corresponding to different damage scenarios, multiple experiments and various sensor locations on the considered structures. The results of the chapter confirm the high potential and effectiveness of vibration based statistical time series methods for SHM. Chapter III investigates the identification of stochastic systems under multiple operating conditions via Vector-dependent Functionally Pooled (VFP) models. In many applications a system operates under a variety of operating conditions (for instance operating temperature, humidity, damage location, damage magnitude and so on) which affect its dynamics, with each condition kept constant for a single commission cycle. Typical examples include mechanical structures operating under different environmental conditions, aircrafts under different flight conditions (altitude, velocity etc.), structures under different structural health states (various damage locations and magnitudes). In this way, damage location and magnitude may be considered as parameters that affect the operating conditions and as a result the structural dynamics. This chapter's work is based on the novel Functional Pooling (FP) framework, which has been recently introduced by the Stochastic Mechanical Systems \& Automation (SMSA) group of the Mechanical Engineering and Aeronautics Department of University of Patras. The main characteristic of Functionally Pooled (FP) models is that their model parameters and innovations sequence depend functionally on the operating parameters, and are projected on appropriate functional subspaces spanned by mutually independent basis functions. Thus, the fourth chapter of the thesis addresses the problem of identifying a globally valid and parsimonious stochastic system model based on input-output data records obtained under a sample of operating conditions characterized by more than one parameters. Hence, models that include a vector characterization of the operating condition are postulated. The problem is tackled within the novel FP framework that postulates proper global discrete-time linear time series models of the ARX and ARMAX types, data pooling techniques, and statistical parameter estimation. Corresponding Vector-dependent Functionally Pooled (VFP) ARX and ARMAX models are postulated, and proper estimators of the Least Squares (LS), Maximum Likelihood (ML), and Prediction Error (PE) types are developed. Model structure estimation is achieved via customary criteria (Bayesian Information Criterion) and a novel Genetic Algorithm (GA) based procedure. The strong consistency of the VFP-ARX least squares and maximum likelihood estimators is established, while the effectiveness of the complete estimation and identification method is demonstrated via two Monte Carlo studies. Based on the postulated VFP parametrization a vibration based statistical time series method that is capable of effective damage detection, precise localization, and magnitude estimation within a unified stochastic framework is introduced in Chapter IV. The method constitutes an important generalization of the recently introduced Functional Model Based Method (FMBM) in that it allows, for the first time in the statistical time series methods context, for complete and precise damage localization on continuous structural topologies. More precisely, the proposed method can accurately localize damage anywhere on properly defined continuous topologies on the structure, instead of pre-defined specific locations. Estimator uncertainties are taken into account, and uncertainty ellipsoids are provided for the damage location and magnitude. To achieve its goal, the method is based on the extended class of Vector-dependent Functionally Pooled (VFP) models, which are characterized by parameters that depend on both damage magnitude and location, as well as on proper statistical estimation and decision making schemes. The method is validated and its effectiveness is experimentally assessed via its application to damage detection, precise localization, and magnitude estimation on a prototype GARTEUR-type laboratory scale aircraft skeleton structure. The damage scenarios considered consist of varying size small masses attached to various continuous topologies on the structure. The method is shown to achieve effective damage detection, precise localization, and magnitude estimation based on even a single pair of measured excitation-response signals. Chapter V presents the introduction and experimental assessment of a sequential statistical time series method for vibration based SHM capable of achieving effective, robust and early damage detection, identification and quantification under uncertainties. The method is based on a combination of binary and multihypothesis versions of the statistically optimal Sequential Probability Ratio Test (SPRT), which employs the residual sequences obtained through a stochastic time series model of the healthy structure. In this work the full list of properties and capabilities of the SPRT are for the first time presented and explored in the context of vibration based damage detection, identification and quantification. The method is shown to achieve effective and robust damage detection, identification and quantification based on predetermined statistical hypothesis sampling plans, which are both analytically and experimentally compared and assessed. The method's performance is determined a priori via the use of the analytical expressions of the Operating Characteristic (OC) and Average Sample Number (ASN) functions in combination with baseline data records, while it requires on average a minimum number of samples in order to reach a decision compared to most powerful Fixed Sample Size (FSS) tests. The effectiveness of the proposed method is validated and experimentally assessed via its application on a lightweight aluminum truss structure, while the obtained results for three distinct vibration measurement positions prove the method's ability to operate based even on a single pair of measured excitation-response signals. Finally, Chapter VI contains the concluding remarks and future perspectives of the thesis. / Κατά τη διάρκεια των τελευταίων 30 ετών έχει σημειωθεί σημαντική ανάπτυξη στο πεδίο της ανίχνευσης και αναγνώρισης βλαβών, το οποίο αναφέρεται συνολικά και σαν διάγνωση βλαβών. Επίσης, κατά την τελευταία δεκαετία έχει σημειωθεί σημαντική πρόοδος στον τομέα της παρακολούθησης της υγείας (δομικής ακεραιότητας) κατασκευών. Στόχος αυτής της διατριβής είναι η ανάπτυξη εξελιγμένων συναρτησιακών και επαναληπτικών μεθόδων χρονοσειρών για τη διάγνωση βλαβών και την παρακολούθηση της υγείας κατασκευών υπό ταλάντωση. Αρχικά γίνεται η πειραματική αποτίμηση και κριτική σύγκριση των σημαντικότερων στατιστικών μεθόδων χρονοσειρών επί τη βάσει της εφαρμογής τους σε πρότυπες εργαστηριακές κατασκευές. Εφαρμόζονται μη-παραμετρικές και παραμετρικές μέθοδοι που βασίζονται σε ταλαντωτικά σήματα διέγερσης και απόκρισης των κατασκευών. Στη συνέχεια αναπτύσσονται στοχαστικά συναρτησιακά μοντέλα για την στοχαστική αναγνώριση κατασκευών υπό πολλαπλές συνθήκες λειτουργίας. Τα μοντέλα αυτά χρησιμοποιούνται για την αναπαράσταση κατασκευών σε διάφορες καταστάσεις βλάβης (θέση και μέγεθος βλάβης), ώστε να είναι δυνατή η συνολική μοντελοποίσή τους για όλες τις συνθήκες λειτουργίας. Τα μοντέλα αυτά αποτελούν τη βάση στην οποία αναπτύσσεται μια συναρτησιακή μέθοδος η οποία είναι ικανή να αντιμετωπίσει συνολικά και ενιαία το πρόβλημα της ανίχνευσης, εντοπισμού και εκτίμησης βλαβών σε κατασκευές. Η πειραματική αποτίμηση της μεθόδου γίνεται με πολλαπλά πειράματα σε εργαστηριακό σκελετό αεροσκάφους. Στο τελευταίο κεφάλαιο της διατριβής προτείνεται μια καινοτόμος στατιστική επαναληπτική μέθοδο για την παρακολούθηση της υγείας κατασκευών. Η μέθοδος κρίνεται αποτελεσματική υπό καθεστώς λειτουργικών αβεβαιοτήτων, καθώς χρησιμοποιεί επαναληπτικά και στατιστικά τεστ πολλαπλών υποθέσεων. Η αποτίμηση της μεθόδου γίνεται με πολλαπλά εργαστηριακά πειράματα, ενώ η μέθοδος κρίνεται ικανή να λειτουργήσει με τη χρήση ενός ζεύγους ταλαντωτικών σημάτων διέγερσης-απόκρισης.

[pt] Nos últimos anos, observa-se crescente penetração da energia eólica na matriz energética mundial e brasileira. Em 2015, ela já representava (seis por cento) da capacidade total de geração de energia do país, colocando-o na (décima) posição entre os países com capacidade eólica instalada. A crescente penetração dessa fonte de energia e suas características de intermitência e forte sazonalidade, passaram a demandar modelos de otimização capazes de auxiliar tanto a gestão dos sistemas elétricos com geração intermitente de energia eólica, quanto a comercialização dessa energia. Avançaram, assim, os estudos de previsões de médias a cada (dez) minutos, horárias e diárias de geração eólica, para atender a sua inserção na programação dos sistemas elétricos e a sua comercialização em mercados diários e horários. Contudo, poucos estudos deram atenção à previsão e simulação de médias mensais de geração eólica, imprescindíveis para gestão e otimização da comercialização dessa energia no Brasil, visto que esta ocorre essencialmente em base mensal. Neste contexto, insere-se esta tese, que busca avaliar a otimização comercial de um parque eólico no mercado livre de energia brasileiro, considerando diferentes modelos de simulação da incerteza de geração eólica e níveis de aversão ao risco do gestor. Para representar diferentes níveis de aversão ao risco do gestor, desenvolveu-se uma nova função de preferência, capaz de modelar a variação do nível de aversão ao risco de um mesmo gestor, para diferentes faixas de preferência, definidas a partir de percentis αs de VaRα. A função de preferência desenvolvida é uma ponderação entre o valor esperado e níveis de CVaR dos resultados. De certo modo, ela altera as probabilidades dos resultados, de acordo as preferências do gestor, similar ao efeito dos pesos de decisão na Teoria do Prospecto. Para simulação da geração eólica são adotados modelos autorregressivos com sazonalidade representada por dummies mensais (ARX-11) e periódicos (PAR). Considera-se, ainda, a inclusão de variáveis climáticas exógenas no modelo ARX-11, com ganho de capacidade preditiva. Observou-se que, para um gestor neutro ao risco, as diferentes simulações de geração eólica não alteraram a decisão ótima. O mesmo não é válido para um gestor avesso ao risco, especialmente ao ser considerado o modelo de simulação com variáveis climáticas exógenas. Portanto, é importante a definição de um único modelo de simulação a ser considerado pelo gestor avesso ao risco ou, a adoção de alguma técnica multicritério para ponderação de diferentes modelos. O perfil de risco também altera as decisões ótimas do gestor, observando-se redução do desvio-padrão e da média da distribuição dos resultados e, aumento dos CVaRs e prêmio de risco, à medida que aumenta a aversão ao risco. Assim, é importante a especificação de uma única função de preferência, que represente adequadamente o perfil de risco do gestor ou da empresa, para otimização da comercialização. A flexibilidade da função de preferência desenvolvida, ao permitir a definição de diferentes níveis de aversão ao risco do gestor, para diferentes faixas de preferência, contribui para essa especificação. / [en] In recent years, we have seen an increased penetration of wind power in the Brazilian energy matrix and also worldwide. In 2015, wind power already accounted for (six percent) of the Brazilian total power capacity and the country was the (tenth) in the world raking of wind power installed capacity. Due to the growing penetration of the source, its intermittency and strong seasonality, optimization models able to deal with the management of wind power, both in electrical systems operation and in trading environment, are necessary. Thus, we see the growth in the number of studies concerned about wind power forecasts for every (10) minutes, hours and days, meeting the electrical systems and international trading schedules. However, few studies have given attention to the forecasting and simulation of wind power monthly averages, which are essential for the management and optimization of energy trading in Brazil, since its occurs essentially on a monthly basis. In this context, we introduce this thesis, which seeks to assess the commercial optimization of a wind farm in the Brazilian energy free market, considering different simulation models for the wind power production uncertainty and different levels of manager s risk aversion. In order to represent the manager s different levels of risk aversion, we developed a new preference function, which is able to model the variation of risk aversion level of the same manager, for different preference groups. These groups are defined by α s percentiles of VaRα. The developed preference function is a weighted average between expected value of results and CVaR levels. In a way, it changes the odds of the results, according to the manager s preference, similar to the effect of the decision weights on Prospect Theory. We adopted autoregressive models to simulate wind power generation, with seasonality represented by monthly dummies (ARX -11) or periodic model (PAR). Furthermore, we consider the inclusion of climate exogenous variables in the ARX-11 model and obtain predictive gain. We observed that for a risk neutral manager, different simulations of wind power production do not change the optimal decision. However, this does not apply for risk averse managers, especially when we consider the simulation model with climate exogenous variables. Therefore, it is important that the risk averse manager establishes a single simulation model to consider or adopts some multi-criteria technique for weighting different models. The risk profile also changes the manager optimal decision. We observed that increasing risk aversion, the standard deviation and mean of the results distribution decrease, while risk premium and CVaRs increase. Therefore, to proceed the optimization, it is important to specify a single preference function, which represents adequately the manager or company risk profile. The flexibility of the developed preference function, allowing the definition of different manager s risk aversion levels for different preference groups, contributes to this specification.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In the present scenario rotating machines have been widely used in industry because of its relative simplicity, constructive robustness and low price. In this context, adequately characterize engine behavior in nominal operating conditions, as this mathematical modeling of these machines becomes interesting and can contribute to the implementation of a predictive control real-time, moreover, there fault detection possibility to, since the engine behavior change will be felt by the identified model. One way to get this mathematical structure is through their experimental data input and output, in order to identify systems is a good option as it studies ways to model and analyze systems, through its information input and output, with the aim of discovering knowledge standards. In this context, the work is to develop a mathematical model using system identification techniques in three phase induction machines through the experimental data with the objective to implement a model apt to behavior anticipate the three-phase induction motor application control for prediction. Moreover, it presents the importance of modeling the rotating machine, moreover, is demonstrated using the method of modeling identification system and a brief justification about ARX and ARMAX models. Also there was performed parametric estimation and then we performed a test to show the performance of the identification of the three-phase induction motor. / No cenário atual as máquinas rotativas têm sido bastante utilizadas nas indústrias, devido a sua relativa simplicidade, robustez construtiva e baixo preço. Neste contexto, caracterizar adequadamente o comportamento do motor operando em condições nominais diários, visto isto a modelagem matemática destas máquinas se torna interessante podendo contribuir para a implementação de um controle preditivo em tempo real, além disso, existe a possibilidade de detecção de falhas, visto que a mudança de comportamento do motor será sentida pelo modelo identificado. Essas falhas se desencadeiam com o envelhecimento e com condições adversas as quais os motores são submetidos ao longo de suas vidas úteis. Uma forma de obter essa estrutura matemática é por meio de seus dados experimentais de entrada e saída, neste intuito a identificação de sistemas é uma boa opção visto que estuda formas de se modelar e analisar sistemas, por meio de suas informações de entrada e saída, com o objetivo de descobrir padrões de comportamento. Neste contexto, o trabalho consiste em elaborar uma modelagem matemática utilizando as técnicas de identificação de sistema em máquinas de indução trifásicas por intermédio dos dados experimentais com o objetivo de implementar um modelo apto a antecipar o comportamento do motor de indução trifásico com aplicação em controle por predição. Além disso, apresenta a importância de se modelar a máquina rotativa, além disso, é demonstrada a metodologia da modelagem utilizando identificação de sistema e uma breve fundamentação sobre os modelos ARX e ARMAX. Também realizou-se a estimação paramétrica e em seguida efetuou-se um teste para mostrar o desempenho da identificação do motor de indução trifásico. / Mestre em Ciências

The goal of this thesis was to create a mathematical model of a steam turbine based on the data acquired by measurement, and to verify its behaviour. The first part contains research, which is supposed to introduce basic principles of the steam turbine and description of important construction parts and the possibilities of control. The second part describes the experimental identification method of least squares, used for the calculation of an ARX model of the steam turbine. Finally, the last part focuses on the program environment used for creation of the mathematical model and explanation of measured data analysis process. Furthermore this segment describes the created simulation program as well as a visualisation of the dynamic processes in the steam turbine, including the design of control.