# Multiobjective Optimization Design for a MR Damper Based on EBFNN and MOPSO
## 1 Introduction
[27] proposed a multiobjective helical dynamic optimization algorithm (MOSDA), which introduced the nondominated sorting (NS) method from the NSGA-II into SDA, and developed its multiobjective (MO) algorithm. Meanwhile, the MO algorithm was tested with various benchmark functions, and its test results show that MOSDA has better performance in finding Pareto Front and de-spreading when tested with benchmark functions compared to NSGA-II. [PERSON] et al. [28] proposed an improved particle swarm optimization (PSO) for multimodal MO problems. Meanwhile, a learning strategy based on dynamic neighborhood was introduced to replace the global learning strategy, and 11 multimodal MO optimization functions were used to verify the feasibility of the method. The experimental results and statistical analysis show that the proposed algorithm has better performance than the five existing multimodal MO algorithms. In addition, various MO optimization methods are also widely used in vibration-reduction engineering applications. [PERSON] et al. [29] optimized the structural dimensions of the MR damper for a prosthetic knee joint based on the PSO algorithm, with the objective of minimizing the total energy consumption of one gait cycle and the weight of the MR damper. The experimental results verified that for the optimized MR damper, the energy consumption was reduced to 1.34 J with a weight of 0.74 kg. [PERSON] et al. [30] developed a cosimulation optimal platform by using ISIGHT, MATLAB, and ANSYS software, and the NSGA-II was used to carry out MO optimization design of the suspension magnetic circuit with the target of improving the quality of vehicle noise, vibration, and harshness. Based on this, scholars at home and abroad had conducted a lot of research on the optimization design of MR dampers, and put forward a variety of different ideas and optimization algorithms. Among them, the optimization design based on parametric programming and design of experiments are two commonly used methods at present, which have achieved good practical results in improving the dynamic performance of dampers. However, the optimization algorithm of parametric programming still has defects, such as few constraint variables and a single optimization method. In addition, the noisy nature of the finite element results can lead to errors if higher-order methodsare used. On the other hand, for the general optimization algorithm based on design of experiments, a large number of mathematical models need to be established to characterize the objective function of the optimization process. Moreover, due to the limited sampling level and sample points, this method cannot efficiently and accurately optimize the structure size of the damper. Thus, in order to make the optimization process more efficient, on the premise of ensuring the simulation accuracy, the appropriate approximate model is selected in the comprehensive comparison to replace the simulation results based on the finite element method. Meanwhile, the optimization algorithm proposed in this paper avoids the disadvantages of large amounts of calculation and long search time in the optimization solution, and has enough sample points to greatly improve the efficiency of global optimization. To increase the damping force and dynamic range, here a design optimization methodology of the novel MR damper with bended magnetic circuit and folded flow gap was developed based on the optimal Latin hypercube design (Opt LHD), the ellipsoidal basis function neural network (EBFNN), and the MOPSO. The Opt LHD method was used to generate samples, and the prediction model was developed based on the EBFNN method. The MOPSO was employed to optimize design objectives, and the optimal MR damper was investigated and validated via the FEA simulation and experiment.