Long-gauge strain wavelet transmissibility-guided uncertainty-aware distributed damage diagnosis under moving loads with disentangled representation learning

The Transmissibility Function (TF) is a widely used indicator for structural condition assessment, primarily for damage detection rather than diagnosis, due to the challenge of directly correlating it with local damage. This study presents an uncertainty-aware distributed damage diagnosis method for bridges subjected to moving loads by combining the advantages of the long-gauge strain wavelet transmissibility function (LSWTF) and disentangled representation learning. Defined as the ratio between the continuous wavelet transform of the long-gauge strain measurement from a target element and that from a reference element, LSWTF in the time-frequency domain has been demonstrated to be approximately independent of moving loads, relying solely on the intrinsic characteristics of the bridge. Moreover, LSWTF within the low-frequency band is associated with the bending stiffness of the reference and target elements, regardless of the stiffness of unmonitored elements. Leveraging these physical attributes, a distributed damage diagnosis framework is devised by decomposing the entire bridge damage diagnosis task into several decoupled sub-tasks at the element level. This framework introduces a parallel, disentangled representation learning approach for damage quantification. Each decoupled sub-task is based on a generative process where the LSWTF is connected with latent representations conditioned on the extent of damage. This setup allows a disentangled variational autoencoder-based regressor to predict the damage extent and provide uncertainty quantification concurrently. Through strategic decoupling and parallel training of disentangled learning in each sub-task, the proposed method concentrates on training the network with data from single-damage scenarios for each element, eliminating the necessity for a multi-damage scenario training dataset. This streamlined approach significantly improves the efficiency of network training and uncertainty quantification for damage assessment. Numerical applications to a three-span continuous bridge and experimental tests on a two-span continuous bridge are conducted to confirm the effectiveness of the proposed method.