Clustering in Pareto Front: Application on an Aero Engine Rotor-Bearing System for Improved Design

In the aero engine rotor-bearing systems, a design modification to move the critical speed away from resonance zone and to improve the unbalance response is a practical problem for designers. The objective functions are selected as amplitude of vibration due to unbalance and second critical speed. The two selected objectives are found to be conflicting, and hence, multi-objective optimisation is used to solve this problem through numerical formulation. Diameters of the stepped shaft and stiffness of the two bearings are selected as design variables. Weight is set as a constraint, and additional constraints based on the initial design are introduced. Objectives resulting from multi-objective optimisation and corresponding design variables are clustered separately using k-means clustering algorithm. The novelty of the work is in empowering the designer to recognise the hugely diverse designs resulting in identical solutions and achieving manufacturing sovereignty in choice of design through clustering in objective and design space and their mapping.