Abstract Summary
We propose an approach to define alarm thresholds for vibration-based structural health monitoring (SHM) systems. The approach uses the frequencies of vibration, generally estimated from recorded accelerations, and it is based on the concept of Minimum Detectable Damage (MDD), namely the smallest damage size in each structural element associated with given probability of detection (POD) and false alarm (PFA). We here demonstrate the approach using pseudo-measured frequencies computed from finite element models of healthy and damaged structures. In particular, for each considered scenario (healthy or damaged), a dataset of modal frequencies is computed accounting for the variability introduced by temperature fluctuations and measurement noises. The approach considers first a baseline dataset of pseudo modal frequencies computed for a yearly thermal cycle on a healthy structure. The application of the Principal Component Analysis (PCA) on this dataset leads to (i) the projection of data on the maximal variance directions, (ii) the projection operator, and (iii) the residual between each sample (the frequencies for a given scenario) and its original one. For each sample, a Damage Index (DI) is computed as the Mahalanobis distance between the residual of sample and the residuals of the entire baseline samples. At this point, the threshold of the SHM system is defined as the DI value for a given PFA. Next, the approach considers dataset of pseudo frequencies computed for a yearly thermal cycle on damaged structures. For each sample of the dataset, the residual is computed using the projection operator of the baseline and its DI value by using the Mahalnobis distance having the covariance matrix based on the baseline data. Based on the DIs of the damaged structure, the POD is computed for the considered system threshold. This operation is repeated by increasing the level of damage. The MDD is thus defined as the level of damage associated to a desired value of POD. Finally, a probabilistic approach based on the binomial probability distribution is proposed to set the SHM alarm by distinguishing above threshold DIs between false alarms and true damages. The proposed idea is tested on a steel truss bridge, where the MDD for each element is estimated by considering PFA=2.5 % and POD=97.5 %.
