Detection and localisation of structural damage based on the error in the constitutive relations in dynamics

In the present work the authors revisit the problem of detecting and localising errors in the finite element modelling of structures subjected to dynamic loading, with the objective of adapting it to the development of a reliable tool that may be used to indicate zones that may be damaged, when applied to structural heath monitoring. It can also be applied in the context of an updating process and in that case the aim is to obtain important information on zones that are not sufficiently well modelled, leading to the improvement of the numerical model. The problem is formulated by establishing an indicator based upon an error function focused on the constitutive relations of the material and on the discrepancy between the healthy and damaged states of a structure. In both cases the experimental results are introduced in the form of frequency response functions (FRFs), which are supposed to be known at just a few locations along the structure, as it happens in real applications. The developed indicator accommodates possible errors in the stiffness, mass and (proportional) damping properties. Numerical examples simulating the measured FRFs are given to assess the capability of the proposed indicator when applied to the damage detection and localisation problem.