Development of a computational efficient tool for robust structural optimization

Abstract

Purpose – Optimization under a deterministic approach generally leads to a final design in which the performance may degrade significantly and/or constraints can be violated because of perturbations arising from uncertainties. The purpose of this paper is to obtain a better strategy that would obtain an optimum design which is less sensitive to changes in uncertain parameters. The process of finding these optima is referred to as robust design optimization (RDO), in which improvement of the performance and reduction of its variability are sought, while maintaining the feasibility of the solution. This overall process is very time consuming, requiring a robust tool to conduct this optimum search efficiently. Design/methodology/approach – In this paper, the authors propose an integrated tool to efficiently obtain RDO solutions. The tool encompasses suitable multiobjective optimization (MO) techniques (encompassing: Normal-Boundary Intersection, Normalized Normal-Constraint, weighted sum method and min-max methods), a surrogate model using reduced order method for cheap function evaluations and adequate procedure for uncertainties quantification (Probabilistic Collocation Method). Findings – To illustrate the application of the proposed tool, 2D structural problems are considered. The integrated tool prove to be very effective reducing the computational time by up to five orders of magnitude, when compared to the solutions obtained via classical standard approaches. Originality/value – The proposed combination of methodologies described in the paper, leads to a very powerful tool for structural optimum designs, considering uncertainty parameters, that can be extended to deal with other class of applications.

A surrogate based multi-fidelity approach for robust design optimization

“…This is because, the optimum design variables reported in [48] violates the stress constraint in member 13. Similar observation has also been stated in [50].…”

“…Next, in order to allow the solutions obtained by Doltsinis and kang [48] to be valid, s max = 12, 5000 has been considered [50]. The solutions obtained with this setup are reported in Table 7.…”

Escolha de Franquias Considerando Decisão Multicritério e Avaliação de Rentabilidade-Risco

“…Shukur, Mansson e Sjolander (2014), complementam dizendo que, usando a simulação de Monte Carlo, pode-se avaliar a robustez de modelos variando o tamanho de amostras e a distribuição de erros. No método de Monte Carlo, o uso de uma técnica eficiente de amostragem é aconselhável, como aquela que, em geral, fornece melhores distribuições de pontos amostrais, com uma consequente melhora na taxa de convergência (Motta;Afonso;Lyra & Willmersdorf, 2014). Vose apud Pinto, Golini e Lagorio (2016), citam que a simulação de Monte Carlo consiste na produção de milhares de cenários de amostragem (também chamados de iterações) obtidos a partir de distribuições de probabilidade dos eventos que podem ocorrer.…”

Uncertainty quantification/propagation in nonlinear models

“…Mohammadali and Ahmadian (2014) associated a linearized ROM over localized nonlinear regions to the HBM to solve nonlinear systems with localized nonlinearities under periodic motion. MO techniques are combined, by Motta et al (2015), with a metamodel coupling of the PCM and a reduced basis method (RBM) whose efficiency is evaluated through a posteriori error estimators and an effective off-line/on-line computational strategy.…”