17. Augmented Sequential Bayesian Filtering for Parameter and Modeling Error Estimation of Linear Dynamic Systems

In this paper an augmented sequential Bayesian filtering approach is proposed for parameter and modeling error estimation of linear dynamic systems of civil structures using time domain input-output data through a sequential maximum a posteriori (MAP) estimation approach, which is similar to Kalman filtering method. However, in the application of existing Kalman filters, the estimation of modeling errors is rarely considered. Unlike traditional Kalman filter which provides state estimation at every time step, the proposed filtering approach estimates the parameter and modeling error on a windowing basis, i.e., the input and output data are divided into windows for estimation which would save computation burden. The analytical derivation of the proposed augmented sequential Bayesian filtering method is first presented, and then the method is verified through a numerical case study of a 3-story building model. An earthquake excitation is used as the input and the acceleration time history response of the building model is simulated. The simulated response is then polluted with different levels of Gaussian white noise to account for the measurement noise. The simulated response is used as the measured data for calibrating another 3-story shear building model which is different from the original model for simulation. Modeling errors are introduced in this shear building model including the shear building assumption, grouping strategy and boundary conditions. The augmented sequential Bayesian filtering approach is applied to estimate the model parameters and modeling error. The performance of the proposed method is studied with respect to modeling errors, the number of sensors and the level of noise.