Robust optimization of engineering structures involving hybrid probabilistic and interval uncertainties
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RESEARCH PAPER
Robust optimization of engineering structures involving hybrid probabilistic and interval uncertainties Jin Cheng 1,2
&
Wei Lu 1,2 & Zhenyu Liu 1 & Di Wu 1 & Wei Gao 3 & Jianrong Tan 1
Received: 8 May 2020 / Revised: 28 August 2020 / Accepted: 7 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A novel, yet practically feasible, robust optimization approach is proposed in this study for engineering structures involving hybrid uncertainties. Both stochastic and interval uncertain system parameters are incorporated within a single analysis-design computational scheme. The generalized beta distribution is adopted to model the bounded stochastic system uncertainties, which offers the benefit of evaluating the performance of objective function and constraints of the robust optimization. A multi-layered refining Latin hypercube sampling–based Monte Carlo simulation approach is proposed to assess the robustness of the objective function. Furthermore, a new concept, namely, the interval angular vector, is presented to evaluate the robust feasibility of the constraints of the optimization problem. In order to systematically solve the robust optimization problem, a new genetic algorithm is presented in this study which utilizes the order preference by similarity to ideal solution technique so the feasible design vectors can be sorted according to their distances to the negative ideal solution. The effectiveness and applicability of the proposed computational approach are demonstrated by one numeral example and two realistic complex engineering structures including the bucket linkage mechanism of an excavator and the upper beam of a high-speed punching machine. Keywords Robustoptimization . Hybrid uncertainty . Multi-layered refiningLatin hypercube sampling(MRLHS) . Distancetothe negative ideal solution (DNIS) . Genetic algorithm (GA)
1 Introduction Robust optimization focuses on equilibrating the optimization of system performance and its sensitivity to uncertainties (Zaman et al. 2011). The engagement of robust optimization enables more practically available optimal solutions for problems across a wide range of engineering applications (Wei et al. 2018). The mathematical description of uncertainties Responsible Editor: Christian Gogu * Jin Cheng [email protected] 1
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
2
Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
3
School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
fundamentally affects the outcome of optimization. Generally, probabilistic and interval system uncertainties have been widely recognized. The probabilistic uncertainty modelling technique is constructed based on the availability of data of system parameter, which assumes that these uncertainties are following certain distributions. Conceivably, the system responses can be
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