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Non-linear hysteresis is a complicated phenomenon associated with magnetorheological (MR) fluid dampers. A new model for MR dampers is proposed in this paper. For this, computationally-tractable algebraic expressions are suggested here in contrast to the commonly-used Bouc–Wen model, which involves internal dynamics represented by a non-linear differential equation. In addition, the model parameters can be explicitly related to the hysteretic phenomenon. To identify the model parameters, a particle swarm optimization (PSO) algorithm is employed using experimental force–velocity data obtained from various operating conditions. In our algorithm, it is possible to relax the need for a priori knowledge on the parameters and to reduce the algorithmic complexity. Here, the PSO algorithm is enhanced by introducing a termination criterion, based on the statistical hypothesis testing to guarantee a user …