Abstract

The problem of input identification using Bayesian estimation methods is considered. The forcing function is a time varying quantity hence it requires solution strategies that can account for the time variation, which is in contrast to methods for time invariant parameter identification. In the existing literature, in the absence of any prior information the forcing function is assumed to have a white noise model and the parameters associated with the model are taken such that the noise is uncorrelated to those associated with the response quantities. In the present work, the derivative of the force is assumed to be a white noise process and the noise parameters of this prior model and the system response quantities are taken to be correlated. The motivation to adopt this model is driven by the fact that the structure acts as a sensor in recording the load acting on it, which is available in the form of the measured structural responses. Furthermore, the estimation of the forcing function is governed by the updating of the predicted state at each time instant with respect to the measured system responses. Hence, a correlation between the force and response noise quantities may result in convergence in the estimation. The extended state vector approach, wherein the unknown force is introduced as an additional state to the system response quantities is adopted. The identification algorithm involves application of the Kalman filter and the sequential filters for the linear and nonlinear systems, respectively. The performance of the proposed algorithm will be illustrated on lower order linear and nonlinear dynamical systems.

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