Optimal sensors placement for damage detection of beam structures

This paper is dedicated to the identifiability of vibrating beam structures with uncertain damages. The probability of damage occurrence is computed assuming a Gaussian distributed random damage parameter. Then, we propose a technique for selecting an optimized solution of sensors placement based on the comparison among the probability of damage occurrence and the probability to detect the damage, where the latter is evaluated exploiting the closed-form asymptotic solution provided by a perturbation approach. This comparison must be intended as an investigation on the minimum number of sensors beyond which monitoring accuracy (estimated by an error function measuring the differences among the two probabilities) increases less than a ‘small’ predetermined threshold. The capabilities and efficiency of the technique are shown through a parametric analysis on a sample case study: a simply supported beam with a random parameter ruling the evolution of a non-localized damage. The relevant results are presented and discussed, showing which conditions (sensors network) properly characterizes the beam dynamics.