Comparison of the performance of nonlinear Kalman filter based algorithms for state-parameter identification of base isolated structures

In this paper, different variants of Kalman filter based algorithms extended Kalman filter (EKF), two-stage EKF, and unscented Kalman filter (UKF) are used to estimate and compare the performance of these algorithms in identifying the state and parameters of nonlinear hysteretic model, simulating unbonded fibre reinforced elastomeric isolator (U-FREI). A two-story masonry building supported on U-FREI is utilized for the present study. The model is excited on a shake table using recorded excitations and measured responses are considered for the identification study. Since the hysteretic behavior of U-FREI is different from that of conventional steel reinforced elastomeric isolator, U-FREI is modeled using extended Bouc-Wen model. The considered model comprises of mainly six parameters and the identified parameters as obtained from various considered algorithms as well for different input excitations are observed to be different. In view of this, percentage error index (PEI) has been introduced to compare the performance of these algorithms. PEI is evaluated using the parameter weights obtained from parameter sensitivity analysis in the form of spider diagram. The state and parameters of the U-FREI are also identified using noise corrupted responses from a numerically simulated model of the same considered two-story masonry building. The responses are contaminated with varying level of artificially added Gaussian white noise. It is observed that the performances of these algorithms are quite stable and are unaffected due to artificially added noise. Further, studies have also been carried out for proper selection of measurement noise covariance and a significant influence on the performance of these algorithms are observed.