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Due to high capacity and low energy consumption of Magneto-Rheological (MR) dampers, they are vastly being utilized to control seismic responses of structures. Presenting more precise methods for control algorithm, and including more realistic physical chara­­cteristics of MR dampers (e.g. nonlinearities, uncertainties and …) will help engineers to employ this kind of damper more efficiently. In order to achieve a controller that quickly and accurately determines the input voltages to the MR dampers, in this paper, a new strategy is proposed. The proposed strategy utilizes Adaptive Network based Fuzzy Inference System, (ANFIS) for optimal control of structures that are equipped with MR dampers. To obtain optimal time histories of demanded voltages, a new objective functional (J) that is a combination of some control criteria including reduction of relative drifts, absolute accelerations and absorbed energy is suggested. The optimization problem is such formulated that the set of equations of motions and equations representing the nonlinear model of MR dampers (here Bouc-Wen) are solved simultaneously. The optimization problem is solved by the enhanced method of steepest descend algorithm by Moharrami and Fayezi [3]. In this way, for a 15-storey building frame subjected to two deterministic earthquakes, the time histories of optimal input voltages of dampers are numerically computed. Next, the optimal voltages associated with the data on drifts, velocities and accelerations of stories are used as desired input- output data pairs to train the ANFIS as a quick and accurate controller. Three ANFISs were trained by different weights for drift (q₁) and absolute acceleration (q₂) data versus voltages. The weights of q₁ and q₂ controlling data were assumed to be (1,0), (0,1) and (1, 0.42) for ANFIS1, ANFIS2 and ANFIS3, respectively. Finally, to establish a context for assessment of the effectiveness of the proposed strategy in comparison with other conventional methods and to analyze the effects of weights in the objective functional, two numerical cases are presented. In the first case, the aforementioned 15-storey building frame is controlled against some earthquakes which were not applied for training process of ANFIS. Results show that ANFIS1 has decreased maximum and time-averaged relative drifts more than other control methods. In addition, this controller has somehow attenuated base shear similar to passive-on but has not been successful in reduction of absolute acceleration values. The ANFIS2 has controlled absolute accelerations better than other controllers whereas drifts have been reduced fairly well. By the ANFIS3, one can achieve reasonable decrease in all controlling criteria. Their values are between ANFIS1 and ANFIS2. It can be concluded that depending on the relative importance of control on drifts or accelerations of stories, one can chose proper weights for q₁ and q₂. In the second example, a benchmark six-storey building that is equipped with 2 dampers in the first, and 2 dampers in the second storey, has been controlled by the three proposed controllers. The results are compared with several conventional methods. The proposed strategy show more flexibility in reduction of the structural control criteria in comparison with some other conventional methods.  

Keywords: ANFIS, Optimal Control, MR damper, ANFIS, objective function, shear frame

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