This article develops an optimal design method with multiple stages for a flexure mechanism. This mechanism can be employed as a rotary joint or a torsional spring. The developed method is a hybridization of density-based topology, multilayer perceptron, and water cycle-moth flame algorithm. Firstly, the topology design for flexure mechanism is conducted to create a draft shape of flexure mechanism, and it is redesigned to seek a proper structure. Secondly, datasets of finite element simulations are collected. These data are then normalized, and the feed-forward multilayer perceptron (FMLP) is utilized to formulate the regression models for all performances. In order to determine the best suitable parameters of each FMLP model, their architectures are optimized by the Taguchi technique. By evaluating the measurement indexes such as correlation coefficient, mean square error, and root mean square error, the developed FMLP models show a superiority as compared to the multiple linear regression. Then, the sensitivity of design parameters is investigated. Thirdly, based on the well-established FMLP models, the size optimization is conducted by the water cycle-moth flame algorithm. Finally, in comparison with the FMLP-based differential evolution, FMLP-based firefly algorithm, FMLP-based particle swarm optimization, and FMLP-based teaching-learning based optimization, the present method has a better efficiency through the Friedman and Wilcoxon tests.

本文开发了一种用于弯曲机构的多阶段优化设计方法。该机构可用作旋转接头或扭转弹簧。所开发的方法是基于密度的拓扑、多层感知器和水循环-飞蛾火焰算法的混合。首先对挠性机构进行拓扑设计，形成挠性机构的草图，并对其进行重新设计，寻找合适的结构。其次，收集有限元模拟数据集。然后将这些数据归一化，并利用前馈多层感知器 (FMLP) 为所有性能制定回归模型。为了确定每个 FMLP 模型的最佳参数，它们的架构通过田口技术进行了优化。通过评估相关系数、均方误差和均方根误差等测量指标，开发的 FMLP 模型与多元线性回归相比显示出优越性。然后，研究了设计参数的敏感性。第三，在已建立的FMLP模型的基础上，通过水循环-飞蛾火焰算法进行尺寸优化。最后，与基于FMLP的差分进化、基于FMLP的萤火虫算法、基于FMLP的粒子群优化和基于FMLP的教学优化相比，本方法通过Friedman和Wilcoxon测试具有更好的效率。研究了设计参数的敏感性。第三，在已建立的FMLP模型的基础上，通过水循环-飞蛾火焰算法进行尺寸优化。最后，与基于FMLP的差分进化、基于FMLP的萤火虫算法、基于FMLP的粒子群优化、基于FMLP的教学优化相比，通过Friedman和Wilcoxon检验，本方法具有更好的效率。研究了设计参数的敏感性。第三，在已建立的FMLP模型的基础上，通过水循环-飞蛾火焰算法进行尺寸优化。最后，与基于FMLP的差分进化、基于FMLP的萤火虫算法、基于FMLP的粒子群优化和基于FMLP的教学优化相比，本方法通过Friedman和Wilcoxon测试具有更好的效率。