Bridge Moving Load Identification: A State-of-the-Art Review

Abstract

Bridge Moving Load Identification aims to reconstruct the spatiotemporal evolution of vehicle loads from measured structural dynamic responses, supporting load rating, fatigue assessment, and overload management in structural health monitoring. In bridge engineering practice, MFI is widely recognized as a severely ill-posed inverse problem. The system matrix derived from the vehicle–bridge dynamic model is typically ill-conditioned, leading to instability and non-uniqueness, so that small perturbations in measurements or modeling assumptions can produce large deviations in the identified loads. These difficulties are further aggravated by vehicle–bridge interaction effects, uncertain vehicle kinematics such as speed and axle configuration, limited sensor coverage, and operational and environmental variability. This review synthesizes recent progress along three complementary lines. First, classical time-domain and state-space identification frameworks are revisited, emphasizing regularization strategies and Krylov-subspace iterative solvers for stabilizing large ill-conditioned systems. Second, modern signal-processing approaches are summarized that exploit sparse sensing and sparse representations, including redundant dictionary modeling, non-convex and reweighted regularization to improve identification accuracy under noise and undersampling, and adaptive dictionary learning to mitigate representation mismatch. Third, deep-learning-based technologies are reviewed, covering data-driven inverse operator learning for near-real-time inference and physics-guided learning that embeds structural operators and governing equations, with particular attention to physics-informed neural networks for vehicle–bridge coupling and limited-label scenarios. Remaining challenges are discussed in real-time deployability, robustness to domain shift, uncertainty quantification, and data efficiency. Future directions point to physics–data dual-driven frameworks and digital-twin-enabled calibration for reliable load sensing in complex service environments.