This paper proposes system identification models of smart concrete structures equipped with magnetorheological (MR) dampers under a variety of high impact loads. The proposed model was used to predict and analyze the highly nonlinear behavior of integrated structure-control systems subjected to impact loading. Highly nonlinear behavior of the integrated structure-MR damper was represented by a wavelet-based time delayed adaptive neuro-fuzzy inference system (W-TANFIS). To generate sets of input and output data for training and validating the proposed W-TANFIS models, experimental studies were performed on a smart reinforced concrete beam under a variety of impact loads. The impact forces and current signals on an MR damper were used as input signals for training the W-TANFIS to predict the acceleration, deflection, and strain responses. As a benchmark, an adaptive neuro-fuzzy inference system (ANFIS) was used. It was demonstrated that the proposed W-TANFIS framework is effective in anticipating the structural responses of the reinforced concrete beam-MR damper system subjected to impact loading. In addition, the comparison of the W-TANFIS and ANFIS models demonstrated that the W-TANFIS model has better performance over the ANFIS model.