Recursive Bayesian Estimation of Partially Observed Dynamic Systems

In the current Chapter, recursive Bayesian inference of partially observed dynamical systems is reviewed. As a tool for structural system identification, nonlinear Bayesian filters are applied to dual estimation problem of linear and nonlinear dynamical systems. In so doing, dual estimation of state and parameters of structural state space models is considered; EKF, SPKF, PF and EK-PF are used for parameter identification and state estimation. Dealing with a SDOF structure, it is shown that the hybrid EK-PF filter is able to furnish a reasonable estimation of parameters of nonlinear constitutive models. Assessment of SDOF systems is followed by identification of multi storey buildings. In this regard, performances of the EK-PF and EKF algorithms are compared, and it is concluded that they are nearly the same, and by an increase in the number of storeys of the building, both of the algorithms fail to provide an unbiased estimate of the parameters (stiffness of the storeys). Therefore, they are not reliable tools to monitor state and parameters of multi storey systems.

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