Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams

The beam is among the most important structural elements, and it can fail by different causes. In many cases it is important to access the loading acting on them. The determination of loading on beams is important, for example, for model calibration purposes and or to estimate remaining fatigue life. In this article we first prove that identification of the loading is theoretically possible from the observation of the displacement of small portion of it for an arbitrary small interval of time and then propose a method to infer the spatial distribution of forces acting upon a beam from the measurement of the displacement of one of its points. The Bayesian method is used to combine measurements taken from different points at different times. This method enables an effective way of reducing the practical amount of time for obtaining meaningful loading estimates.