The current study presents the problem of state and parameter estimation of flexible structures under a Kalman filtering framework. Inspired from a previous publication by the authors, the work presented here tackles the issue of practically acquiring the natural frequency of a flexible structure for structural health monitoring purposes. The Kalman filter theory is introduced where the linear Kalman filter and the unscnted Kalman filter algorithms are explained. An example of estimating the dynamics of a simply supported beam, modeled using the finite element method, is first discussed for the purpose of establishing the effectiveness of the Kalman filtering approach in dynamic structural systems. A more complicated system consisting of a flexible appendage attached at one end to a rotating hub is then introduced. The system dynamics are modeled using the finite element method, which is incorporated in a computer simulation where the Kalman filter is applied to estimate not only the appendage dynamics, but its parameters as well; specifically its natural frequency. The purpose of the work is to establish a practical method of acquiring the natural frequency for a flexible structure to accommodate a structural health monitoring system. Results show that the Kalman filter is a viable option for estimating the natural frequency of flexible structure.

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