# Multiobjective Optimization Design for a MR Damper Based on EBFNN and MOPSO
## 1 Introduction  
Smart materials, especially magnetorheological (MR) fluids, have been attracting great attention in manufacturing research and development. MR fluids are widely used in various engineering applications such as MR intelligent devices [1, 2], transportation vehicles [3, 4], building suspensions [5, 6], and biomedical applications [7, 8]. As one of the typical application devices of MR fluid, the MR damper directly affects the damping effect of the vibration control system. The optimization design of the MR damper is an effective approach to improve damping performance. [PERSON] et al. [9] took the power consumption and damping force of the MR damper used for knee joints as the optimization objective. The optimal solution of the parameters was obtained by the multiobjective genetic algorithm. The experimental results show that after optimization, the damping force increased by 30% and the power consumption reduced by 43%. [PERSON] et al. [10] proposed a low-cost MR damper for washing machines regarding the height and width of the magnetic coil, radius of piston rod, and optimum fluid volume as the optimized parameters. The Generalized Reduction Gradient (GRG) and Grey Relation Analysis (GRA) were used to achieve low volume of the MR fluid (<2 mL), low power (~5 W) and high damping force (~55 N). [PERSON] et al. [11] optimized the maximum dynamic range and the minimum number of turns of the electromagnetic coil. The Nondominated Sorted Genetic Algorithm-II (NSGA-II) was used to optimize the structure of MR damper. After the optimization, the maximum damping force reached 1774 N and the dynamic range reached 10.8. [PERSON] et al. [12] considered the effects of the current and flow gap and particle volume fraction of MR fluid on the shear stress and damping force. By applying the PSO algorithm, results show that the particle volume fraction with the proportion of 33% gave an optimal damping force of 3718 N.  
Besides those mentioned above, other optimization methods such as the particle swarm optimization [13], response surface method, design of experiments [14], and genetic algorithm [15; 16; 17] are also used to optimize the MR damper structure. [PERSON] et al. [18] used the Bezier curve to optimize the piston shape of the MR damper. This method effectively solved the regional magnetic saturation in the transition areas of the piston, thus leading to a larger field-dependent force. Experimental results show that the optimized piston of the MR damper could maximize the field-dependent force by 52% and total damping force by 24% compared to the normal situation. [PERSON] et al. [19] applied the mathematical optimization and finite element analysis (FEA) methods on the optimal design for reducing the computational complexity. [PERSON] et al. [20] optimized the design of the magnetorheological damper geometry using the response surface method and considered the magnetic field strength and yield stress as the objective. Results show that the magnetic circuit geometric parameters representing the distance between piston rod and coil and pole length were more sensitive to the response of the MR damper. [PERSON] et al. [21] utilized the Box-Behnken design to optimize the hybrid MR damper. The optimized results show that the damping force increased from 1383 N at 0 A to 4141 N at 2.0 A. Compared to the model provided by [PERSON] et al. [22], the damping force in [15] was enhanced by more than 165%. Considering the compressibility of the MR fluid, [PERSON] et al. [23] applied a modified Bingham model to simulate the MR damper. In addition, a response surface method was used to optimize the performance of the MR damper. Results show the damping force was improved by 33% and the dynamically adjustable coefficient was improved by 17%. Generally speaking, the most critical point is that each optimization design method has its own advantages, and all have good optimization effects in practical engineering applications [24; 25; 26]. [PERSON] et al.