Force identification by comparing likelihood function using Bayesian filtering methods Radhika, B.
The paper addresses the problem of force identification in randomly excited dynamical systems using Bayesian filtering methods. These are recursive algorithms comprising of the prediction and updating steps operating on specified models for the dynamical system and measurements. The Bayes‘ theorem is adopted in the updating step where the updated estimate is obtained as a product of normalization constant, likelihood function and the estimate in the prediction step. It is assumed that a model for the dynamical system is specified either in the form of a governing equation or a finite element model and measurements of system response to the unknown input are also available. In the proposed method the force to be identified is modeled as a white noise process with an unknown standard deviation. A procedure based on comparing the likelihood function in the updating step is proposed to select the noise parameter adaptively. This adaptive choice is proposed to identify forces which are realizations of a nonstationary random process model. The same will be demonstrated using illustrations on linear and nonlinear dynamical systems.
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