Structure system estimation under seismic excitation with an adaptive extended kalman filter

Abstract

An adaptive extended Kalman filter (EKF) with two computation modes is proposed for system estimation of civil engineering structures under seismic excitations. The KF, in general, requires the process noise covariance matrix, which defines the uncertainty of the system model used in the filter, to be set appropriately. However, process noise is usually not known in practice, and tuning process noise in a trial-and-error manner can be time consuming and subjective; unsuccessful tuning can even result in divergence of the filter. In this study, the Robbins–Monro (RM) algorithm is combined with an EKF to adjust process noise automatically. Two computation modes, corresponding to time-invariant and time-varying parameter identification, are employed in the EKF-RM method. The RM algorithm makes the EKF-RM method robust and practical. In this study, the EKF-RM method is first numerically investigated with a simplified four-degrees-of-freedom (4-DOF) lumped mass model based on a real civil structure. In addition, the parameter variation tracking capability of the method is also studied by employing the 4-DOF lumped mass model. Further, the EKF-RM method is validated by two shaking table experiments from the E-defense database, including a full-scale four-story building experiment and a substructure experiment. Time-invariant system parameters are identified for the four-story building. Modal frequencies computed using the identified parameters are compared with the modal analysis results. Time-varying parameter identification is demonstrated by using the substructure experiment, which reveals strong nonlinearity.