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Protecting civil engineering structures from severe impacts like strong earthquakes has demanded intensive research in the past two decades. One of the most promising devices proposed for structural protection is the magnetorheological (MR) fluid dampers. To fully explore their potentials in the real-time feedback control implementations, accurate and robust modeling of the devices is a prerequisite. This paper first proposes a general nonlinear blackbox structure to model the MR damping behavior on the displacement-velocity phase plane. Two constructive parameter estimation algorithms are subsequently developed which are based on the recent mathematical advances in wavelets and ridgelets analysis. Compared with the traditional physical modeling, this research aims at improving model numerical stability and model structure generality. The achievement of these objectives is evaluated in the modeling of an experimental MR-damper in a base-isolation structural control system.