An approach to define the minimum detectable damage and the alarm thresholds in vibration-based SHM systems

This paper proposes an approach to defining the alarm thresholds for vibration-based structural health monitoring (SHM). The approach uses natural frequencies identified from the acceleration response of the monitored structure and is based on the concept of Minimum Detectable Damage (MDD), namely the smallest damage size in each structural element associated with a given probability of detection (POD) and probability of false alarm (PFA). The approach is demonstrated using natural frequencies computed from finite element models of the healthy and damaged structure, also accounting for temperature fluctuations and measurement noise. The approach first builds a baseline dataset of modal frequencies for a yearly thermal cycle on the healthy structure. Then, different damage conditions are simulated. For each sample of natural frequencies, a Damage Index (DI) is computed as the Mahalanobis distance between the considered sample and the baseline distribution. The alarm threshold is defined as the DI value for a given PFA. Based on the DIs obtained for the damaged structure, the POD is computed for the considered system threshold. This operation is repeated by increasing the damage entity. The MDD is thus defined as the level of damage associated with a desired value of POD. The proposed idea is tested on a steel truss bridge, where the MDD for each element is estimated by considering PFA=5% and POD=95%.