Anomaly detection for bridges under moving loads with input-independent probabilistic feature distance measure and extreme value theory

Damage detection based on bridge responses under moving loads has garnered significant attention due to its ability to eliminate the need for costly excitation equipment. However, current methods in this field often require the measurement or identification of moving loads, adding complexity to the process. While the transmissibility function (TF) is promising for damage detection in properly handling the input, the understanding of TF properties under moving loads remains limited, impeding its full potential. To bridge the gap, this study proposes a novel approach that combines the physical properties of TF with the probabilistic feature extraction capabilities of the variational autoencoder (VAE) for bridge anomaly detection under moving loads. The finite element solution of TF under moving loads has been analytically derived, revealing that TF is independent of unknown input spectra and characterized by the frequency response functions of the beam and the Fourier transforms of elemental shape functions. Leveraging TF under moving loads as an effective damage indicator, a VAE model extracts low-dimensional probabilistic features from multiple TFs across a frequency band, facilitating a more efficient formulation of probabilistic distances as input-independent anomaly scores. The Kullback–Leibler divergence between the input-independent features under the baseline condition and those under potential damage scenarios, measuring the dissimilarity of probability distributions across different states, is computed as a damage index to detect the existence of structural damage. Furthermore, the application of extreme value theory aids in establishing a decision threshold for anomaly detection by harnessing the inherent advantages of modeling the tail behavior of extreme events more accurately, thereby improving the accuracy of damage detection while minimizing false positives. The effectiveness of this method is validated through numerical simulations on a simply supported beam and experimental studies on a two-span continuous beam, showcasing its potential for practical damage detection applications.