A Sparse adaptive Bayesian filter for input estimation problems. (15th November 2022) - Ghibaudo, J.
Abstract: The present paper introduces a novel Bayesian filter for estimating mechanical excitation sources in the time domain from a set of vibration measurements. The proposed filter is derived from a very general Bayesian formulation, unifying most of the state-of-the-art recursive filters developed in the last decade for solving input-state estimation problems. More specifically, the proposed Bayesian filter allows promoting the spatial sparsity of the estimated input vector, by assuming that the predicted input vector is a random vector with independent and identically distributed components following a generalized Gaussian distribution. To properly estimate the most probable parameters of the latter probability distribution, a nested Bayesian optimization is implemented. The validity of the proposed approach, called Sparse adaptive Bayesian Filter, is assessed both numerically and experimentally. In particular, the comparisons performed with some state-of-the-art filters show that the proposed strategy outperforms the existing filters in terms of input estimation accuracy and avoids the so-called drift effect. Highlights: Bayesian formulations of joint and sequential input-state estimation problems are proposed. State of the art methods are derived from the proposed Bayesian framework. A new method promoting the sparsity of the excitation field is developed. Numerical and experimental validations are performed and comparisons with standard methods are proposed. The proposed method avoids the drift effect and is robust to sensors' density and measurement noise.