A demand-capacity approach to define failure thresholds in anomaly detection monitoring systems

This work proposes a procedure to establish the threshold for a structural anomaly detection system using a supervised computation of the demand-capacity ratio (DCR). A truss structure is analyzed with a large dataset of damage scenarios generated through Monte Carlo simulations, varying in types and intensities of damage. For each scenario, a structural model is subjected to ultimate loads to calculate the DCR for each element, as the ratio between the demand forces and the capacity of the element. Scenarios where the DCR of any element exceeds one, are identified as those potentially leading to failure. For these scenarios, a dataset of pseudo features sensitive to damage, such as modal frequencies, is created, incorporating environmental and operational variations, as well as noise. A damage index is then constructed for each damage scenario as the Mahalanobis distance between the damaged and the healthy modal frequencies datasets. The alarm threshold is finally set at the value exceeded by the damage indexes of all scenarios leading to failure. The method is demonstrated with a numerical example of a steel truss structure under a specific load, considering 100,000 damage scenarios. Results show that the proposed threshold is conservative, not easily derived from simple engineering intuition, and effectively minimizes false alarms in the detection scheme.