Substructure-level damage identification based on the spectrum-probability space of the transmissibility function

In structural health monitoring (SHM), the measured data is insufficient to accurately identify the potential damages when the measurements are contaminated by noise. In this study, a spectrumprobability space-based methodology is developed to manage the uncertainty in damage detection, integrated with the substructure division strategy to localize damage. The transmissibility function (TF), that is an output-only quantity and sensitive to changes in structural stiffness, is used to detect an anomaly. The variation of the probability-spectrum space of a TF is used as the damage indicator, and it is measured by a novel damage indicator, the spectrum-weighted Kullback-Leibler divergence. This indicator jointly considers the changes in spectrum density and statistics of a TF due to damage. The damaged sub-domain of a structure is subsequently identified out from all monitored sub-domains. Numerical and experimental models are tested to verify the approach in the ambient and impulse load conditions. The results demonstrate that the developed method can correctly detect anomalies and localize the damaged substructure with high sensitivity and robustness, and it is convenient to implement in practice.