An optimal Bayesian regularization for force reconstruction problems

In a paper, recently published in Mechanical Systems and Signal Processing, we have proposed a full Bayesian inference for reconstructing mechanical sources acting on a linear and time invariant structure. The main interest of this approach is to propose an estimation of all the parameters of the model and quantify the posterior uncertainty associated to each parameter. Since all the necessary information about the problem is available, statistical measures, such as the mean, the median and the mode of the solution, can be easily estimated. In many practical situations, however, one only wants to determine the most probable parameters given the available data. Consequently, it is not relevant to implement a full Bayesian inference to only extract a point estimate. To overcome this potential issue, this paper introduces an optimal Bayesian regularization aiming at computing the Maximum a Posteriori estimate of the Bayesian formulation previously introduced by the authors. In doing so, the most probable parameters are obtained without heavy computations. The validity of the proposed method is assessed numerically and experimentally. In particular, obtained results highlight the ability of the proposed regularization strategy in computing solutions with a minimal amount of prior information on the sources to identify. (C) 2019 Elsevier Ltd. All rights reserved.