Application of Laplacian operators on noisy data to compute curvature with Proper Orthogonal Decomposition

Damage detection is a wide field of research and different approaches can be used to monitor structure integrity. Continuous monitoring of critical components is of vital importance to guarantee the safety of a structure. Variations in the dynamic response, in particular the curvature of mode shapes, are considered good indicators of the presence of possible defects. However noise, which often affects data, can lead to an erroneous calculation of the curvature, preventing the location of possible damage. The aim of this paper is to investigate the capability of the proper orthogonal decomposition (POD) to overcome noise, computing the curvature of proper orthogonal modes with a modified Laplacian operator. A numerical investigation on a cracked beam is compared to an analytical case present in literature. An extension of the mono-dimensional modified Laplacian scheme is introduced to study also plate-like structures. An experimental application on a vibrating composite plate will be presented in order to validate the numerical model.