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Multiresponse Optimization for a Novel Compliant Z-Stage by a Hybridization of Response Surface Method and Whale Optimization Algorithm


Minh Phung Dang, Hieu Giang Le, Ngoc N. Trung Le, Ngoc Le Chau, Thanh-Phong Dao*

Source title: 
Mathematical Problems in Engineering, 2021: 9974230, 2021 (ISI)
Academic year of acceptance: 

A novel compliant z-stage is applied for positioning and indenting a specimen in nano/microindentation testing system. For an excellent operation, the proposed z-stage can concurrently satisfy multicriteria comprising high safety factor, small parasitic motion, and large output displacement. The key aims of this article are to present a novel design of the compliant z-stage as well as an effective integration methodology of Taguchi method, response surface method, weight factor calculation based on signal to noise, and the whale optimization algorithm to resolve a design optimal problem so as to enrich the quality performances of the proposed stage. Primarily, the z-stage is designed based on four-lever amplifier, compliant hinge shifted arrangement mechanism, zigzag-based flexure spring guiding mechanism, and symmetric six leaf hinges-based parallel guiding mechanism. Secondly, the number experiment data are achieved by the Taguchi method and finite element analysis. Subsequently, the regression functions among input variables and quality characteristics are formed by exploiting response surface method. In addition, the weight factors for every characteristic are defined. Additionally, the sensitivity analysis is accomplished for determining influences of input variables on quality responses. Ultimately, based on regression equations, the whale optimization algorithm is executed to define the optimal factors. The consequences indicated that the output deformation is about 454.55 μm and the safety factor is around 2.38. Furthermore, the errors among the optimal consequences and the confirmations for the safety factor and output deformation are 7.12% and 4.25%, correspondingly. By using Wilcoxon and Friedman methods, the results revealed that the proposed algorithm is better than the cuckoo search algorithm. Based on the quality convergence characteristics of hybrid approach, the proposed method is proficient for resolving complicated multiobjective optimization.