Hysteresis and dynamic loading nonparametric identification for multi‐degree‐of‐freedom structures using an updated general extended Kalman filter and a Legendre polynomial model

In order to identify the hysteretic behavior in the form of nonlinear restoring force (NRF) and the unknown dynamic excitation when the acceleration measurement at the degree of freedom (DOF) of the excitation is unknown, and considering the fact that it is difficult to establish a general parametric mathematical model in advance to describe the real hysteretic behavior of an engineering structure, in this paper, a nonparametric identification approach for both NRF and dynamic loading is presented using an updated general extended Kalman filter with unknown input (UGEKF‐UI) algorithm with limited acceleration measurements excluding that at the DOF of the dynamic excitation. The NRF is expressed with a Legendre polynomial model, and no assumption on the parametric model of structure nonlinearity is required for the identification. Numerical studies on lumped mass multi‐DOFs numerical models equipped with different numbers of magnetorheological (MR) dampers modeled with different parametric mathematical models are carried out to verify the effectiveness of the proposed approach. Furthermore, experimental study is conducted on a four‐story shear frame structure with an MR damper under unknown external dynamic excitation. The unknown dynamic responses including the acceleration at the location where the excitation is applied, damping force provided by the MR damper, and the dynamic excitation are identified and compared with the test measurements. Both numerical and experimental results demonstrate the proposed approach is capable of identifying the NRF and the unknown dynamic excitation in a nonparametric way even the acceleration response at the DOF where the excitation is applied is unknown.