Effective Hybrid Algorithm of Taguchi Method, FEM, RSM, and Teaching Learning-Based Optimization for Multiobjective Optimization Design of a Compliant Rotary Positioning Stage for Nanoindentation Tester

This paper proposes an effective hybrid optimization algorithm for multiobjective optimization design of a compliant rotary positioning stage for indentation tester. The stage is created with respect to the Beetle’s profile. To meet practical demands of the stage, the geometric parameters are optimized so as to find the best performances. In the present work, the Taguchi method is employed to lay out the number of numerical experiments. Subsequently, the finite element method is built to retrieve the numerical data. The mathematical models are then established based on the response surface method. Before conducting the optimization implementation, the weight factor of each response is calculated exactly. Based on the well-established models, the multiple performances are simultaneously optimized utilizing the teaching learning-based optimization. The results found that the weight factors of safety factor and displacement are 0.5995 (59.95%) and 0.4005 (40.05%), respectively. The results revealed that the optimal safety factor is about 1.558 and the optimal displacement is 2.096 mm. The validations are in good agreement with the predicted results. Sensitivity analysis is carried out to identify the effects of variables on the responses. Using the Wilcoxon’s rank signed test and Friedman test, the effectiveness of the proposed hybrid approach is better than that of other evolutionary algorithms. It ensures a good effectiveness to solve a complex multiobjective optimization problem.