Pareto Optimization Based Tradeoff Between the Controllable Damping Force and the Relative Displacement Sensing of a Self-Sensing Magnetorheological Damper

The theoretical analysis and the prototype testing of the integrated relative displacement self-sensing magnetorheological damper (IRDSMRD) indicate that the controllable damping performance and the relative displacement sensing performance influence each other. For the IRDSMRD with a constrained volume, in order to make the best compromise between the damping force and the IRDS performance (the linearity), a Pareto optimization principle based method, which optimizes the key structural parameters taking the linearity of the IRDS and the controllable damping performance of the IRDSMRD as the objective functions, is proposed and realized. The mathematical models that relate the linearity of the IRDS and the controllable damping performance of the developed IRDSMRD to the magnetomotive force and the key structural parameters are established by modeling and analyzing the magnetic circuit of the IRDSMRD. The key structure in the primary flux path of the IRDSMRD is analyzed and optimized using the finite element method with the software package Maxwell 2D. On these bases, the Pareto optimal curve, i.e. the Pareto front, representing the balance of the controllable damping and the linearity of the IRDS of the IRDSMRD is obtained by considering that the maximum input magnetomotive force is constant. The IRDSMRD with the optimized structural geometry is tested on the experimental setup based on the MTS 849 shock absorber test system and the real time simulation system. According to the research results, every point on the Pareto front is an optimal solution of the damping force and the linearity of the IRDS of the IRDSMRD. The optimal damping force of the IRDSMRD with a certain linearity of the IRDS can be determined on the Pareto front, and vice versa, for a specific application. The feasibility of the Pareto optimization principle based method is validated by the experimental results and the research results have a universal significance for making the tradeoff between the sensing performance and the actuation performance of the self-sensing actuators based on smart materials.