Bayesian Inference Applied to Crack Detection in Beam-Like Structures

Abstract

In this work, a crack detection technique is presented by means of a bayesian inference approach. A simple non-linear model consisting of a slender beam subjected to transverse dynamic loads is considered. The nonlinearity is related to a breathing crack which is modelled as a bilinear spring. Given a certain crack configuration, the response of the system at specific locations is obtained (direct problem). These data are related to the crack configuration, depth and location. The aim of this work is the resolution of the inverse problem. That is, given a set of known responses (displacements) at specific points, the crack depth and location are sought i.e. level 3 of detection. For this purpose, the Bayesian Inference Method is used and the probability distributions of both the crack position and crack depth are obtained. As stated, this method is based on the Bayes Theorem which updates known statistical information (prior) giving place to a new statistics (posterior). This method was found to provide satisfying results, given limited available information.