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Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.18.2010.tde-23032010-092000
Document
Auteur
Nom complet
Wellison José de Santana Gomes
Adresse Mail
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2010
Directeur
Jury
Beck, André Teófilo (Président)
Trindade, Marcelo Areias
Vaz, Luiz Eloy
Titre en portugais
Estudo do efeito de incertezas na otimização estrutural
Mots-clés en portugais
Algoritmos híbridos
Estruturas-confiabilidade
Estruturas-otimização
Resumé en portugais
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.
Titre en anglais
On the effects of uncertainty on optimum structural design
Mots-clés en anglais
Hybrid algorithms
Structures-optimization
Structures-reliability
Resumé en anglais
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.
 
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Date de Publication
2010-04-08
 
AVERTISSEMENT: Le matériau se réfère à des documents provenant de cette thèse ou mémoire. Le contenu de ces documents est la responsabilité de l'auteur de la thèse ou mémoire.
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  • BECK, André Teófilo, and GOMES, Wellison José de Santana. A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty [doi:10.1016/j.probengmech.2011.08.007]. Probabilistic Engineering Mechanics [online], 2012, vol. 28, p. 18-29.
  • BECK, André Teófilo, and GOMES, Wellison José de Santana. On structural design optimization under uncertainty and risk [doi:10.1088/1757-899X/10/1/012193]. IOP Conference Series: Materials Science and Engineering [online], 2010, vol. 10, p. 012193.
  • Beck, Andre T., Gomes, W. J. S., e Bazan, F.A.V. ON THE ROBUSTNESS OF STRUCTURAL RISK OPTIMIZATION WITH RESPECT TO EPISTEMIC UNCERTAINTIES [doi:10.1615/Int.J.UncertaintyQuantification.v2.i1.20]. International Journal for Uncertainty Quantification [online], 2012, vol. 2, p. 1-20.
  • Beck, André Teófilo, and Gomes, W. J. S. A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty [doi:10.1016/j.probengmech.2011.08.007]. Probabilistic Engineering Mechanics [online], 2012, vol. 28, p. 18-29.
  • A. T., Beck, and W. J. S., Gomes. On the Effects of Uncertainty and Risk on Structural Design Optimization [doi:10.3850/978-981-08-7619-7_P007]. In Proceedings of the 6th International Conference on Computational Stochastic Mechanics(CSM-6) [online], 6, , 2010. Singapore : Research Publishing Services, 2011. p. 54-65.
  • BECK, A. T., Bazán, F.A.V., e Gomes, W.J.S. Robust Optimization of Structural Risks Under Epistemic Uncertainties. In 5th Asian-Pacific Symposium on Structural Reliability and its Applications, Singapura, 2012. Proc. of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications.Singapura : Research Publishing, 2012.
  • BECK, A. T., Bazán, F.A.V., e Gomes, W.J.S. Robust Optimization of Structural Risks Under Epistemic Uncertainties. In 5th Asian-Pacific Symposium on Structural Reliability and its Applications, Singapura, 2012. Proc. of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications.Singapura : Research Publishing, 2012. Resumo.
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  • BECK, A. T., e Gomes, W.J.S. A Comparison of Deterministic, Reliability-based and Risk-based Structural Optimization under Uncertainty. In MECSOL 2011 International Symposium on Solid Mechanics, Florianópolis, 2011. Solid Mechanics in Brazil 2011. : ABCM, 2011.
  • BECK, A. T., e Gomes, W.J.S. On the Effects of Uncertainty and Risk on Structural Design Optimization [doi:10.3850/978-981-08-7619-7_P007]. In 6th International Conference on Computational Stochastics Mechanics, Rodes, Grecia, 2010. Computational Stochastic Mechanics. : RESEARCH PUBLISHING, 2010.
  • BECK, A. T., e Gomes, W.J.S. On the Effects of Uncertainty and Risk on Structural Design Optimization [doi:10.3850/978-981-08-7619-7_P007]. In 6th International Conference on Computational Stochastics Mechanics, Rodes, Grecia, 2011. On the Effects of Uncertainty and Risk on Structural Design Optimization. : RESEARCH PUBLISHING, 2011.
  • BECK, A. T., e Gomes, W.J.S. On the Effects of Uncertainty on Optimum Structural Design. In 11th Pan-American Congress of Applied Mechanics - PACAM XI, Foz do Iguaçu, PR, 2010. Proceedings of the 11th Pan-American Congress of Applied Mechanics., 2010.
  • BECK, A. T., Gomes, W.J.S., e Bazán, F.A.V. Robust Optimization of Structural Risk: Coping with Epistemic Uncertainties. In Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering, Chania, Grecia, 2011. Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering.Stirlingshire, Scotland : Civil-Comp Press, 2011.
  • BECK, A. T., Gomes, W.J.S., e Bazán, F.A.V. Sensitivity of Structural Risk Optimization with respect to Epistemic Uncertainties. In XXXI Iberian Latin-American Congress on Computational Methods in Engineering - MECOM CILAMCE, Buenos Aires, 2010. Mecanica Computacional., 2010.
  • Beck, André Teófilo, e Gomes, W.J.S. On structural design optimization under uncertainty and risk [doi:10.1088/1757-899X/10/1/012193]. In 9th World Congress on Computational Mechanics, Sydney. IOP Conf. Series: Materials Science and Engineering. : IOP Publishing, 2010.
  • Gomes, W.J.S., e BECK, A. T. Hybrid Algorithms Based on Particle Swarm Optimization and the Powell Method for Global Optimization. In Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing, Chania, Grecia, 2011. Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing.Stirlingshire, Scotland : Civil-Comp Press, 2011.
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