Parameter Estimation of Stochastic Fractional Dynamic Systems Using Nonlinear Bayesian Filtering System Identification Methods

This paper presents the application of nonlinear Bayesian filtering-based system identification (SI) methods when employed to estimate the parameters of stochastic fractional dynamic systems. The objective is to demonstrate the capabilities and limitations of time-domain stochastic filtering-based SI for systems endowed with fractional derivative elements when the estimation is performed under different operating conditions. The conditions include measured forcing inputs (input-output identification), stochastic/unmeasured forcing inputs (output-only identification), and different types of measurements and levels of measurement noise, in the context of both linear and hysteretic fractional oscillators. The accuracy and estimation error of three methods was studied, namely, the unscented Kalman filter, the ensemble Kalman filter, and the particle filter. Baseline results that can be applied to the modeling, identification, and control of fractional structural and mechanical systems are provided. It is shown that nonlinear Bayesian filtering methods have the capability to accurately estimate the response and parameters of fractional oscillators, and that the coefficient and order of fractional elements are observable/identifiable from output response measurements.