Sequential Bayesian estimation of state and input in dynamical systems using output-only measurements

Abstract

The problem of joint estimation of the state and input in linear time-invariant dynamical systems is revisited proposing novel sequential Bayesian formulations. An appealing feature of the proposed method is the promise it delivers for updating the covariance matrices of the process and measurement noise in a real-time fashion using asymptotic approximations. The proposed method avoids the direct transmission of the input into predictions of the state using a zero-mean Gaussian distribution for the input. This prior distribution aims to eliminate low-frequency drifts from estimations of the state and input. Moreover, the method is outlined in a computational algorithm offering real-time estimations of the state and input forces. Numerical and experimental examples are used to examine and demonstrate the efficacy of the method. It is observed that the proposed method achieves decent accuracy for estimating the state, input forces, and noise covariance matrices when compared to the actual values. Contrary to the present methods that produce significant low-frequency drifts while using noisy acceleration response-only measurements, the proposed method offers drift-free perfect predictions. This Bayesian filtering-technique proposed for the reconstruction of the state and input forces can next be employed in the emerging fatigue prognosis frameworks. © 2019 Elsevier Ltd