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.

本文介绍了一种新颖的贝叶斯滤波器，用于从一组振动测量中估计时域中的机械激励源。所提出的滤波器源自一个非常通用的贝叶斯公式，统一了过去十年开发的大多数最先进的递归滤波器，用于解决输入状态估计问题。更具体地说，所提出的贝叶斯滤波器允许通过假设预测输入向量是具有遵循广义高斯分布的独立且相同分布的分量的随机向量来提高估计输入向量的空间稀疏性。为了正确估计后一种概率分布的最可能参数，实施了嵌套贝叶斯优化。所提出的方法的有效性，称为稀疏自适应贝叶斯滤波器，在数值和实验上都进行了评估。特别是，与一些最先进的滤波器进行的比较表明，所提出的策略在输入估计精度方面优于现有滤波器，并避免了所谓的漂移效应。