A procedure to estimate the Minimum Observable Damage in truss structures using vibration-based Structural Health Monitoring systems

In this work, we propose a procedure to estimate the Minimum Observable Damage (MOD) by a vibration -based Structural Health Monitoring (SHM) system. The MOD is defined as the smallest damage size that can be detected by an SHM system with given Probability of Detection (POD) and Probability of False Alarm (PFA). To this purpose, the MOD is computed by exploiting the Receiver Operating Characteristic (ROC) analysis, once a damage index (DI) built on monitoring data/features is defined. In particular, the MOD is defined as the damage intensity corresponding to an area under the ROC curve of 95%. The proposed idea is discussed by utilizing pseudo-experimental data generated via numerical simulations for undamaged and damaged structures. In the developed simulations, environmental uncertainties and measurement noises are considered. As case studies, we consider truss structures and use modal data, namely frequencies of vibrations and mode shapes, to build the DIs. Using the dataset of DIs, the ROC methodology is exploited to establish the probability of detecting certain damage over the probability of false alarms. For a given DI, results are provided in terms of MOD for each structural element of the truss structure considering one damaged element at a time. By establishing a relation between modal data, damage size, and POD/PFA, the proposed approach can assess the quality of the adopted DI, thus supporting the initial design of an SHM system.