Real-time Bayesian parameter, state and input estimation using output-only vibration measurements

Abstract

This paper presents a new sequential Bayesian method for the real-time estimation of state, input, parameters, and noise characteristics in dynamical systems using output-only measurements. It is an extension of the method developed by the authors for the joint input-state estimation in linear time-invariant systems [1], [2]. This method is built upon the Taylor series expansion of the state-space model and conjugate prior distributions, where the noise characteristics are described using Gaussian distributions and their covariance matrices are assumed to follow inverse Wishart distributions. When the Bayes rule is applied, explicit formulations for the posterior distributions are obtained, which allows efficient and real-time computations. The application of this method to a simple numerical example is demonstrated, which confirms its efficacy in handling this coupled estimation problem. It is observed that this method delivers accurate estimations for the state, input, model parameters, and noise covariance matrices when the results are compared with the actual values. Moreover, the proposed method has the potential to mitigate the low-frequency errors commonly produced in estimations of input forces and displacement responses when only acceleration responses are measured. © 2020 European Association for Structural Dynamics. All rights reserved.