Este trabalho apresenta um estudo do efeito de incertezas na otimização estrutural. Tal efeito pode ser quantificado em termos de probabilidades de falha bem como do risco, ou custo esperado de falha. O estudo se baseia na comparação dos resultados obtidos através de três distintas formulações do problema de otimização estrutural: otimização determinística, otimização baseada em confiabilidade e otimização de risco estrutural. Para efeitos de comparação, informações sobre risco de falha estrutural (produto da probabilidade de falha pelo custo de falha) são incorporadas nas três formulações. A otimização determinística (DDO - Deterministic Design Optimization) permite encontrar uma configuração estrutural que é ótima em termos mecânicos, mas não considera explicitamente a incerteza dos parâmetros e seus efeitos na segurança estrutural. Em conseqüência, a segurança da estrutura ótima pode ser comprometida, em comparação à segurança da estrutura original. A otimização baseada em confiabilidade (RBDO - Reliability-Based Design Optimization) garante que a estrutura ótima mantenha um nível mínimo (e mensurável) de segurança. Entretanto, os resultados são dependentes da probabilidade de falha usada como restrição na análise. A otimização de risco estrutural (RBRO - Reliability-Based Risk Optimization) aumenta o escopo do problema, buscando um balanço entre economia e segurança, objetivos estes que de uma forma geral competem entre si. Isto é possível através da quantificação de custos associados à construção, operação e manutenção da estrutura, bem como das consequências monetárias de falha. A experiência mostra que problemas de otimização estudados, são utilizados neste trabalho dois métodos de otimização heurísticos: algoritmos genéticos e método do enxame de partículas. Tendo a eficiência como objetivo, dois métodos com fundamentação matemática também são estudados: os métodos de Powell e de Polak-Ribiere. Finalmente, buscando uma relação de compromisso entre confiabilidade (capacidade de encontrar o mínimo global em todos os problemas) e eficiência, quatro algoritmos híbridos são construídos, combinando os quatro métodos citados anteriormente. Efeitos de incertezas na otimização estrutural são estudados através da comparação de soluções obtidas via diferentes formulações do problema de otimização. São apresentados alguns estudos de caso, enfatizando as diferenças entre os projetos ótimos obtidos por cada formulação. O estudo mostra que, em geral, a estrutura ótima só é encontrada pela formulação mais abrangente: a otimização de risco ou RBRO. O estudo mostra que, para que a formulação DDO encontre a mesma configuração ótima da formulação RBRO, é necessário especificar um coeficiente de segurança ótimo para cada modo de falha. De maneira semelhante, o estudo mostra que quando os custos associados a diferentes modos de falha são distintos, a formulação RBDO somente resulta na estrutura ótima quando uma probabilidade de falha ótima é especificada como restrição para cada modo falha da estrutura. / In this study the effects of uncertainty on optimum structural design are investigated, by comparing three distinct formulations of a structural optimization problem. Such effects can be quantified in terms of failure probabilities and risk, or expected costs of failure. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation do not consider explicitly parameter uncertainty and its effects on structural safety. As a consequence, safety of the optimum structure can be compromised, in comparison to safety of the original structure. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probability used as constraint in the analysis. Risk optimization increases the scope of the problem, by addressing the compromising goals of economy and safety, and allowing one to find a proper point of balance between these goals. This is accomplished by quantifying the costs associated to construction, operation and maintenance of the structure, as well as the monetary consequences of failure. Experience shows that structural optimization problems can have multiple local minima. With the objective of finding the global minimum in all studied problems, two heuristic optimization methods are used in this study: genetic algorithms and particle swarm optimization. Aiming at efficiency, two methods with mathematical foundations are also considered: the methods of Powel and Polak-Ribiere. Finally, looking for a compromise between reliability (capacity to find the global minimum) and efficiency, four hybrid algorithms are constructed, combining the four methods just cited. The study investigates the effects of uncertainty on optimum structural design by comparing solutions obtained via the different formulations of the optimization problem. The paper presents some case studies, highlighting the differences in the optimum designs obtained with each formulation. The study leads to a better understanding of the limitations of each formulation in the solution of structural optimization problems. The investigation shows that, in general, the optimum structure can only be found by the most comprehensive formulation: risk optimization or RBRO. The study shows that DDO only leads to the optimum structure if an optimum safety coefficient is used as constraint for each individual failure mode. In a similar way, the investigation shows that when the costs associated to distinct failure modes are different, the RBDO formulation only leads to the optimum structural design if an optimum failure probability is specified as constraint for each failure mode of the structure.

Este trabalho apresenta um estudo do efeito de incertezas na otimização estrutural. Tal efeito pode ser quantificado em termos de probabilidades de falha bem como do risco, ou custo esperado de falha. O estudo se baseia na comparação dos resultados obtidos através de três distintas formulações do problema de otimização estrutural: otimização determinística, otimização baseada em confiabilidade e otimização de risco estrutural. Para efeitos de comparação, informações sobre risco de falha estrutural (produto da probabilidade de falha pelo custo de falha) são incorporadas nas três formulações. A otimização determinística (DDO - Deterministic Design Optimization) permite encontrar uma configuração estrutural que é ótima em termos mecânicos, mas não considera explicitamente a incerteza dos parâmetros e seus efeitos na segurança estrutural. Em conseqüência, a segurança da estrutura ótima pode ser comprometida, em comparação à segurança da estrutura original. A otimização baseada em confiabilidade (RBDO - Reliability-Based Design Optimization) garante que a estrutura ótima mantenha um nível mínimo (e mensurável) de segurança. Entretanto, os resultados são dependentes da probabilidade de falha usada como restrição na análise. A otimização de risco estrutural (RBRO - Reliability-Based Risk Optimization) aumenta o escopo do problema, buscando um balanço entre economia e segurança, objetivos estes que de uma forma geral competem entre si. Isto é possível através da quantificação de custos associados à construção, operação e manutenção da estrutura, bem como das consequências monetárias de falha. A experiência mostra que problemas de otimização estudados, são utilizados neste trabalho dois métodos de otimização heurísticos: algoritmos genéticos e método do enxame de partículas. Tendo a eficiência como objetivo, dois métodos com fundamentação matemática também são estudados: os métodos de Powell e de Polak-Ribiere. Finalmente, buscando uma relação de compromisso entre confiabilidade (capacidade de encontrar o mínimo global em todos os problemas) e eficiência, quatro algoritmos híbridos são construídos, combinando os quatro métodos citados anteriormente. Efeitos de incertezas na otimização estrutural são estudados através da comparação de soluções obtidas via diferentes formulações do problema de otimização. São apresentados alguns estudos de caso, enfatizando as diferenças entre os projetos ótimos obtidos por cada formulação. O estudo mostra que, em geral, a estrutura ótima só é encontrada pela formulação mais abrangente: a otimização de risco ou RBRO. O estudo mostra que, para que a formulação DDO encontre a mesma configuração ótima da formulação RBRO, é necessário especificar um coeficiente de segurança ótimo para cada modo de falha. De maneira semelhante, o estudo mostra que quando os custos associados a diferentes modos de falha são distintos, a formulação RBDO somente resulta na estrutura ótima quando uma probabilidade de falha ótima é especificada como restrição para cada modo falha da estrutura. / In this study the effects of uncertainty on optimum structural design are investigated, by comparing three distinct formulations of a structural optimization problem. Such effects can be quantified in terms of failure probabilities and risk, or expected costs of failure. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation do not consider explicitly parameter uncertainty and its effects on structural safety. As a consequence, safety of the optimum structure can be compromised, in comparison to safety of the original structure. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probability used as constraint in the analysis. Risk optimization increases the scope of the problem, by addressing the compromising goals of economy and safety, and allowing one to find a proper point of balance between these goals. This is accomplished by quantifying the costs associated to construction, operation and maintenance of the structure, as well as the monetary consequences of failure. Experience shows that structural optimization problems can have multiple local minima. With the objective of finding the global minimum in all studied problems, two heuristic optimization methods are used in this study: genetic algorithms and particle swarm optimization. Aiming at efficiency, two methods with mathematical foundations are also considered: the methods of Powel and Polak-Ribiere. Finally, looking for a compromise between reliability (capacity to find the global minimum) and efficiency, four hybrid algorithms are constructed, combining the four methods just cited. The study investigates the effects of uncertainty on optimum structural design by comparing solutions obtained via the different formulations of the optimization problem. The paper presents some case studies, highlighting the differences in the optimum designs obtained with each formulation. The study leads to a better understanding of the limitations of each formulation in the solution of structural optimization problems. The investigation shows that, in general, the optimum structure can only be found by the most comprehensive formulation: risk optimization or RBRO. The study shows that DDO only leads to the optimum structure if an optimum safety coefficient is used as constraint for each individual failure mode. In a similar way, the investigation shows that when the costs associated to distinct failure modes are different, the RBDO formulation only leads to the optimum structural design if an optimum failure probability is specified as constraint for each failure mode of the structure.

Statistical extrapolation is required to predict extreme loads, associated with a target return period, for offshore wind turbines. In statistical extrapolation, “short-term" distributions of the load random variable(s) conditional on the environment are integrated with the joint probability distribution of environmental random variables (from wind, waves, current etc.) to obtain the so-called “long-term" distribution, from which long-term loads may be obtained for any return period. The accurate prediction of long-term extreme loads for offshore wind turbines, using efficient extrapolation procedures, is our main goal. While loads data, needed for extrapolation, are obtained by simulations in a design scenario, field data can be valuable for understanding the offshore environment and the resulting turbine response. We use limited field data from a 2MW turbine at the Blyth site in the United Kingdom, and study the influence of contrasting environmental (wind) regimes and associated waves at this site on long-term loads, derived using extrapolation. This study also highlights the need for efficient extrapolation procedures and for modeling nonlinear waves at sites with shallow water depths. An important first step in extrapolation is to establish robust short-term distributions of load extremes. Using data from simulations of a 5MW onshore turbine model, we compare empirical short-term load distributions when two alternative models for extremes--global and block maxima--are used. We develop a convergence criterion, based on controlling the uncertainty in rare load fractiles, which serves to assess whether or not an adequate number of simulations has been performed. To establish long-term loads for a 5MW offshore wind turbine, we employ an inverse reliability approach, which is shown to predict reasonably accurate long-term loads, compared to a more expensive direct integration approach. We show that blade pitching control actions can be a major source of response variability, due to which a large number of simulations may be required to obtain stable tails of short-term load distributions, and to predict accurate ultimate loads. We address model uncertainty as it pertains to wave models. We investigate the effect of using irregular nonlinear (second-order) waves, compared to irregular linear waves, on loads for an offshore wind turbine. We incorporate this nonlinear irregular wave model into a procedure for integrated wind-wave-response analysis of offshore wind turbines. We show that computed loads are generally somewhat larger with nonlinear waves and, hence, that modeling nonlinear waves is important is response simulations of offshore wind turbines and prediction of long-term loads. / text

Structural Reliability treats uncertainties in structural design systematically, evaluating the levels of safety and serviceability of structures. During the past decades, it has been established as a valuable design tool for the description of the performance of structures, and lately stands as a basis in the background of the most of the modern design standards, aiming to achieve a uniform behaviour within a class of structures. Several methods have been proposed for the estimation of structural reliability, both deterministic (FORM and SORM) and stochastic (Monte Carlo Simulation etc) in nature. Offshore structures should resist complicated and, in most cases, combined environmental phenomena of greatly uncertain magnitude (eg. wind, wave, current, operational loads etc). Failure mechanisms of structural systems and components are expressed through limit state functions, which distinguish a failure and a safe region of operation. For a jacket offshore structure, which comprises of multiple tubular members interconnected in a three dimensional truss configuration, the limit state function should link the actual load or load combination acting on it locally, to the response of each structural member. Cont/d.

The work reported in this thesis is in the area of computational modeling of reliability of engineering structures. The emphasis of the study is on developing methods that are suitable for analysis of large-scale structures such as aircraft structure components. This class of problems continues to offer challenges to an analyst with the most difficult aspect of the analysis being the treatment of nonlinearity in the structural behavior, non-Gaussian nature of uncertainties and quantification of low levels of probability of failure (of the order of 10-5 or less), requiring significant computational effort. The present study covers static/ dynamic behavior, Gaussian/ non-Gaussian models of uncertainties, and (or) linear/ nonlinear structures. The novel elements in the study consist of two components: • application of modeling tools that already exists in the area of design and analysis of computer experiments, and . • application of data based extreme value analysis procedures that are available in the statistics literature. The first component of the work provides opportunity to combine space filling sampling strategies (which have promise for reducing variance of estimation) with kriging based modeling in reliability studies-an opportunity that has not been explored in the existing literature. The second component of the work exploits the virtues of limiting behavior of extremes of sequence of random variables with Monte Carlo simulations of structural response-a strategy for reliability modeling that has not been explored in the existing literature. The hope here is that failure events with probabilities of the order of 10-5 or less could be investigated with relatively less number of Monte Carlo runs. The study also brings out the issues related to combining the above sources of existing knowledge with finite element modeling of engineering structures, thereby leading to newer tools for structural reliability analysis. The thesis is organized into four chapters. The first chapter provides a review of literature that covers methods of reliability analysis and also the background literature on design and analysis of computer experiments and extreme value analysis. The problem of reliability analysis of randomly parametered, linear (or) nonlinear structures subjected to static and (or) dynamic loads is considered in Chapter 2. A deterministic finite element model for the structure to analyze sample realization of the structure is assumed to be available. The reliability analysis is carried out within the framework of response surface methods, which involves the construction of surrogate models for performance functions to be employed in reliability calculations. These surrogate models serve as models of models, and hence termed as meta-models, for structural behavior in the neighborhood of design point. This construction, in the present study, has involved combining space filling optimal Latin hypercube sampling and kriging models. Illustrative examples on numerical prediction of reliability of a ten-bay truss and a W-seal in an aircraft structure are presented. Limited Monte Carlo simulations are used to validate the approximate procedures developed. The reliability of nonlinear vibrating systems under stochastic excitations is investigated in Chapter 3 using a two-stage Monte Carlo simulation strategy. Systems subjected to Gaussian random excitation are considered for the study. It is assumed that the probability distribution of the maximum response in the steady state belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of an objective selection of the form of the extreme value distribution based on hypothesis tests, and the next involves the estimation of parameters of the relevant extreme value distribution. Both these steps are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear single-degree and multi-degree of freedom systems driven by random excitations. The predictions from the proposed method are compared with results from large-scale Monte Carlo simulations and also with classical analytical results, when available, from theory of out-crossing statistics. The method is further extended to cover reliability analysis of nonlinear dynamical systems with randomly varying system parameters. Here the methods of meta-modeling developed in Chapter 2 are extended to develop response surface models for parameters of underlying extreme value distributions. Numerical examples presented cover a host of low-dimensional dynamical systems and also the analysis of a wind turbine structure subjected to turbulent wind loads and undergoing large amplitude oscillations. A summary of contributions made along with a few suggestions for further research is presented in Chapter 4.

This work aims to evaluate the reliability levels associated to a probabilistic approach of mechanical strength models of casing tubes on oil and gas wells. A comparative study between different reliability evaluation methods commonly applied is also carried out. On the oil and gas well design, casing tubes must bear the mechanical loadings in the subsurface, such as the ones from formations, from drilling and completion fluids, from production fluid over the well lifetime, from the self-weight of casing column and from weight of other components. Reliability-based analysis applied to a structural design allows the assessment of the probability of violation for a given limit state of the structure, so that it can be predicted with adequate value since the design stage. This kind of analysis is useful to obtain adequate safety levels in design and to discuss the quality control level in the manufacturer production process. In this work, the failure probability is evaluated by the following reliability methods: failure domain numericintegration,MonteCarlosimulationandthetransformationmethods:FirstOrder eliabilityMethod(FORM)andSecondOrderReliabilityMethod(SORM).Thelimitstatesv rified are established by using casing strength models found in the literature, based on mechanics of materials theory and rupture test data.Statistical data are based on technical reports from casing manufacturers found in open-access literature. The achieved results contributes to well casing structural assessment taking into account the influence of design uncertainties, motivating the adoption of reliability-based analysis in decision-making process on OCTG design. / FUNDEPES - Fundação Universitária de Desenvolvimento de Extensão e Pesquisa / Estetrabalho visa avaliar os níveis de confiabilidade associados a uma abordagem probabilística das resistências mecânicas de tubos de revestimento em poços de petróleo. Além disso, durante as análises realizadas, objetiva-se comparar os diferentes métodos de confiabilidade comumente encontrados na literatura com a finalidade de identificar o método mais vantajoso para a aplicação proposta. Em projetos de poços de petróleo e gás natural, os revestimentos exercem o papel de resistir mecanicamente aos esforços existentes na subsuperfície, como as solicitações impostas pela formação, pelo fluido de perfuração, pelos fluidos produzidos ao longo da vida útil do poço e pelos pesos da própria coluna de revestimento e de outros equipamentos. Já a análise de confiabilidade, aplicada a um projeto estrutural, permite a avaliação da probabilidade de violação de um determinado estado limite da estrutura, de forma que esta pode ser prevista, com valor adequado, ainda na fase de projeto.Esse tipo de análise é útil não obtenção da margem de segurança adequada do projeto e na discussão do nível de controle no processo de produção de elementos estruturais. Neste trabalho, o cálculo da probabilidade de falha é realizado através dos seguintes métodos: integração numérica sobre o domínio de falha, simulação de Monte Carlo e dos métodos de transformação: First Order Reliability Method (FORM) e Second Order Reliability Method (SORM). Os estados limites dos tubos são estimados por modelos de resistência encontrados na literatura, baseados em teorias da mecânica dos materiais e em dados de ensaios de ruptura. Os dados estatísticos utilizados são baseados em relatórios técnicos de produção disponíveis na literatura sob domínio público. Os resultados obtidos contribuem para a avaliação estrutural de revestimentos de poços de petróleo sob a influência de incertezas de projeto, motivando a incorporação da análise de confiabilidade no processo de tomada de decisão do projetista.