Nonparametric identification for hysteretic behavior modeled with a power series polynomial using EKF-WGI approach under limited acceleration and unknown mass

Identifying damage initiation and development in engineering structures non-parametrically in the form of a nonlinear restoring force (NRF) after strong dynamic loading is attractive. Due to the individuality of various engineering structures, it is quite challenging to assume, in advance, a general parametric model describing the nonlinear behavior. Although a traditional extended Kalman filter (EKF) is efficient in state vector estimation and structural parameter identification with partially available output measurements, a known structural mass is usually required. In this study, a simultaneous NRF and mass identification approach is developed for multi-degree-of-freedom (MDOF) structures using the EKF with weighted global iteration (EKF-WGI) based on limited available absolute acceleration response. The NRF is modeled in a nonparametric way with a power series polynomial model (PSPM) as a function of unknown structural displacement and velocity responses. Then, the performance of the new approach is numerically evaluated using multi-story structures equipped with magneto-rheological (MR) dampers having known applied excitations and partially available noise-contaminated acceleration measurements, but unknown mass. No parametric model for the NRF of the MR dampers is employed. The effect of different noise levels and different initial estimation errors of structural mass on both NRF and mass identification results and the convergence of the approach are investigated. Finally, a dynamic test on a four-story frame structure equipped with an MR damper is carried out and the algorithm is experimentally validated. Comparisons show that the identified NRF provided by the MR damper matches the measurement and that the identified mass is also accurate.