A static model for a magneto-rheological (MR) damper based on artificial neural networks (ANNs) is proposed, and an intensive and experimental study is presented for designing the ANN structure. The ANN model does not require time delays in the input vector. Besides the electric current signal, only one additional sensor is used to achieve a reliable MR damper structure. The model is experimentally validated with two commercial MR dampers of different characteristics: MR _1 damper with continuous actuation and MR _2 damper with two levels of actuation. The error to signal ratio (ESR) index is used to measure the model accuracy; for both MR dampers, an average value of 6.03% of total error is obtained from different experiments, which are designed to explore the nonlinearities of the MR phenomenon at different frequencies by including the impact of the electric current fluctuations. The proposed ANN model is compared with other well known parametric models; the qualitative and quantitative comparison among the models highlights the advantages of the ANN for representing a commercial MR damper. The ESR index was reduced by the ANN-based model by up to 29% with respect to the parametric models for the MR _1 damper and up to 40% for the MR _2 damper. The force-velocity diagram is used to compare the modeling properties of each approach: (1) the Bingham model cannot describe the hysteresis of both MR dampers and the distribution function of the modeled force varies from the experimental data, (2) the algebraic models have complications in representing the nonlinear behavior of the asymmetric damper (MR _2) and, (3) the ANN-based MR damper can model the nonlinearities of both MR dampers and presents good scalability; the accuracy of the results supports the use of this model for the validation of semi-active suspension control systems for a vehicle, by using nonlinear simulations.
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