Design optimization of hybrid uncertain structures with fuzzy-boundary interval variables
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Design optimization of hybrid uncertain structures with fuzzy-boundary interval variables Hui Lu¨ . Kun Yang . Xiaoting Huang . Hui Yin
Received: 13 May 2020 / Accepted: 3 September 2020 Springer Nature B.V. 2020
Abstract In some special engineering cases, the lower and upper bounds of uncertain parameters are appropriately quantified as fuzzy variables instead of deterministic values. To address such cases, a possibility-based robust design optimization (PBRDO) framework is suggested for the hybrid uncertain structures with fuzzy-boundary interval (FuBI) variables. Firstly, an optimization model with FuBI variables is established where FuBI uncertainties exist in both the objective and constraint functions. The socalled dual robust design is presented and it is adopted to create the optimization objective. The first robust design aims to handle fuzziness while the second one attends to tackle interval property. The failure possibility is employed to construct the optimization constraints in possibilitic context. Then, the fuzzy-
H. Lu¨ K. Yang H. Yin (&) School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China e-mail: [email protected] H. Lu¨ e-mail: [email protected] K. Yang e-mail: [email protected] X. Huang School of Automobile and Traffic Engineering, Guangzhou College of South China University of Technology, Guangzhou 510800, China e-mail: [email protected]
boundary interval Taylor series-central difference method (FITS-CDM) is derived to manage FuBI uncertainties and calculate the optimization objective efficiently. Next, the target performance approach (TPA) is employed to process the possibilistic constraints and the simplified constraints can be easily solved by FITS-CDM. The nested-loop PBRDO with FuBI variables can be simplified to a single-loop one based on FITS-CDM and TPA. Finally, the effectiveness of the proposed optimization approach on dealing with FuBI uncertainties is demonstrated by three examples. Keywords Fuzzy-boundary interval Design optimization Robust design Possibility Hybrid uncertainties
1 Introduction In engineering problems, the uncertainties in material properties, geometric dimensions and boundary conditions are always unavoidable (Cai et al. 2020a, b). In order to acquire more reliable designs, it is necessary to incorporate uncertainty into the design optimization of engineering problems. The most mature technology to address uncertainty is the probabilistic methods, in which uncertain properties are described with welldefined probability distributions (Stefanou 2009).
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However, uncertainty sometimes cannot be addressed appropriately by probabilistic methods, since it is difficult to build up the exact probability distributions with limited data or the randomness is not the main source of uncertainty (Shi and Lu 2019; Jiang et al. 2012). Therefore, the non-probabilistic methods, such as the interval analysis method and fuzzy analys
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