In this work, reconstruction of pressure time signal rising during a non-punctual impact occurring on an elastic structure has been achieved through using direct Bayesian approach. This was performed by means of posterior distribution of probabilities integrating the likelihood and prior random information. In the case of a noisy linear system for which the densities of probabilities associated to the prior information and noise could be assumed to be Gaussians and mutually independent, a new algorithm consisting of two steps was proposed. The first step works like a Wiener filter action and enables to determine the input pressure mean, while the second step yields evaluations of variability of the input pressure signal around that mean. It was found that the proposed method achieved perfect reconstruction of the original pressure taken at the input of the system.
Detection of cracks in mechanical components as early as possible enables monitoring structural health and scheduling efficiently the maintenance tasks such as replacing the critical parts just in time. Vibration analysis based techniques for crack detection have been largely considered in the framework of beam-like structures. This methodology relies essentially on the observed changes of beam frequencies and mode shapes induced by the presence of damage. In the present work, using an explicit analytical model assessing the effect of a crack on beam strain energy, the beam first resonance frequencies as they depend on a single crack defect characteristics were evaluated. The crack equations were obtained by means of fracture mechanics approach. Variations of the first beam frequencies and modes shapes were then related explicitly to the location and depth of the crack. Measuring the beam frequency changes and monitoring their variations can be used to perform identification of the crack defect parameters by solution of an inverse problem.