Design optimization of hybrid uncertain structures with fuzzy-boundary interval variables

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 so-called 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-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.