The article presents an approach for combining methods of recursive Bayesian estimation with models of dynamical systems with varying differentiation order. The work addresses the problem of explicit fractional order estimation and tracking by constructing an efficient Unscented Kalman filter, where the model order is directly estimated within an augmented state along with the variables of interest. The feasibility of the estimation method is assessed using a benchmark problem based on a simplified fractional neuron firing rate model and time-dependent differentiation order. The proposed technique is compared to an implicit method based on Interacting Multiple Model filtering and a computationally efficient method using a modification of the Ensemble Kalman filter. The performance with respect to different parameters and filter settings is analyzed and a corresponding discussion is provided.
Abstract
This paper deals with the estimation of forcing function, modal damping and mistuned modal stiffnesses in a bladed rotor. Previous research on parameter estimation in a mistuned bladed rotor relies on the knowledge of the forcing function as well as the vibration data. This paper presents two novel approaches. The first approach relies on knowledge of both the forcing and vibration data. The parameters are treated as states of the system and an augmented state space model is created. Unscented Kalman Filter is then used on the steady state data to estimate the parameters. The second approach eliminates the dependence on forcing data. Both the forcing and parameters are now treated as states of the system to construct an augmented state space model. Unscented Kalman Filter is then used on transient vibration data for estimation. Numerical results are presented for a simple model of a mistuned bladed rotor which considers a single mode of vibration per blade.
Application of the Scaled Unscented Kalman Filter with Augmented State in the Fiber Optic Gyroscope