Otimização multi-objetivo de sistemas de engenharia na presença de incerteza

• Autor(a) principal: Libotte, Gustavo Barbosa
• Data de Publicação: 2020
• Outros Autores: [e-mail]
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/16820
• topic: Multi-objective optimization; Robust optimization; Otimização matemática; Algoritmo numérico; Análise matemática; Otimização multi-objetivo; Otimização robusta; Otimização baseada em confiabilidade; Análise de confiabilidade inversa; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

Mathematical models are applied to simulate various events under different conditions, enabling an early overview of the system to be implemented in practice,with reduced waste of resource sand in less time. In project optimization, these models play a fundamental role, as they allow obtaining parameters and attributes capable of enhancing product performance, reducing costs and operating time. These possibilities are subject to several factors,including a most accurate computational modeling of the inherent characteristics of the system. In general, computational models capable of describing physical phenomena with satisfactory accuracy consider possible uncertainties in their mathematical formulations. The inclusion of uncertainties in the computational model also affects the feasibility of the results and their practical implementation. In this work, two different approaches capable of quantifying uncertainties during the optimization of mathematical models are considered: in the first, robust optimization, the sensitivity of decision variables in relation to perturbations caused by external factors is assessed. Robust solutions reduce the possibility of deviation from possible system changes. The purpose of the second approach, reliability-based optimization, is to measure the probability of failure of a system and to obtain model parameters that can ensure an established level of reliability. In this context, the fundamental objective is to formulate a multi-objective optimization problem capable of considering together robust optimization and reliability-based optimization, to obtain solutions that are least sensitive to external noise and that satisfy prescribed reliability levels. In this work, it is also proposed an algorithm for inverse reliability analysis, suitable to be employed during the reliability-based optimization procedure. The algorithm adopts an adaptive second order step length calculation concept, which enables a remarkable reduction in the use of computational resources to obtain reliable solutions.