VIBRATION SOURCE CHARACTERIZATION USING FORCE ANALYSIS TECHNIQUE AND A BAYESIAN REGULARIZATION

The Force Analysis Technique (FAT) is a inverse method for the characterization of vibration sources applied on a structure, based on measurements of its displacement. From the knowledge of the local equation of motion of the structure, it allows both the localization and the quantifica-tion of sources, without the need of boundary conditions. As many inverse methods, the FAT is however highly sensitive to noise and includes traditionally a low pass filter to fix this instability. This work presents new strategies for the regularization step within the Bayesian framework. It introduces a priori probabilities which can lead to the Tikhonov regularization when Gaussian densities are used for both the source field and the noise, or to a sparse identification when using a Bernoulli-Gaussian a priori on sources. These two cases are performed by the Gibb's sampler, a particular Markov Chain Monte Carlo (MCMC) algorithm. It allows an unsupervised (or empirical) and automatic regularization besides confidence intervals on variables, especially on the source field.