Abstract
During their lifetime, structures are usually subjected to some mechanical shocks that generate high levels of vibration that can damage the structure itself as well as the embedded devices. However, the characteristics of these shocks (location, time history, maximum intensity, etc.) are often unknown due to the inaccessibility of the excitation region for direct force measurements or the inability to instrument the system. Therefore, inverse methods have been developed to quantify these complex excitations. Recently, a Bayesian formulation of the input-state estimation problem for linear systems has been proposed by the authors, which unifies most of the state-of-the-art filters. In this paper, we present two novel Bayesian filters derived from this framework - (a) the Correlated Dual Kalman Filter (CDKF), which is one of the filters that naturally follows from the unified Bayesian formulation, and (b) the Component Bayesian Filter (CBF), which promotes spatial sparsity of the input vector. Essentially, these filters differ in the prior distributions used to convey information about the spatial distribution of the input vector to be identified. The performance of these filters is evaluated through a numerical experiment and a real-world application aimed at reconstructing a sparse and transient excitation acting on a linear structure. A comparison of these original filters with other Bayesian filters proposed in the literature is also proposed. In particular, the numerical experiment allows to study the performance of the proposed filters in different scenarios, such as the number of sensors, the measurement noise level or the sensor configuration, while the real-world application allows to test them in operational conditions. More specifically, it is shown that filters promoting the spatial sparsity of the input vector, such as CBF, lead to a consistent identified excitation profile when acceleration measurements are the only available data.
Mathieu Aucejo
Associate Professor
My research interests include inverse problems, vibration control and vibro-acoustics.