Most parametric nonlinear behavior identification methods require an assumed mathematical model to describe the hysteretic behavior of structural members or substructures. Due to the individuality of various construction materials and structural systems, it is challenging to forecast the real nonlinear performance of a structure member or a substructure under dynamic loadings with a general parametric model in prior. In this paper, a nonparametric nonlinear restoring force (NRF) identification approach with limited output and unknown input is proposed by employing a double Chebyshev polynomial combined with an updated Extended Kalman filter (U-EKF) approach, where the observation equation is updated without using external excitation information. Moreover, data fusion is used to deal with the drift problem in dynamic response forecasting. The proposed approach is validated numerically with multi-degree-of-freedom (MDOF) structures equipped with various nonlinear members, including MR damper (damping-dominant) and SMA damper (stiffness-dominant) employed to mimic different structural nonlinear behavior. Moreover, a four-story shear frame model, including MR damper on the fourth floor, is employed to experimentally validate the approach. Identified results show that the proposed algorithm can identify structural nonlinear behavior in a nonparametric way without using excitation as an input, which is helpful for structural damage diagnosis where nonlinearity and loading profile should be considered.
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