A novel PINN algorithm for a bridge weigh in motion system without prior knowledge of axle location

Bridge Weigh-in-Motion (BWIM) is an effective method of using instrumented bridges to find the weights of passing vehicles. Traditional BWIM systems rely on axle detectors to determine axle locations/spacings, which are used to formulate the system of equations and calculate axle loads. However, commonly used Free of Axle Detector (FAD) systems exhibit reduced accuracy when vehicle speeds are high or when multiple vehicles cross the bridge simultaneously. Similarly, computer vision-based detectors are highly sensitive to environmental conditions (e.g. rain), which can degrade video quality and affect detection accuracy. Inaccurate axle location data introduces significant errors in vehicle load estimation. To address this challenge, this study proposes a novel BWIM system that does not require prior knowledge of vehicle locations. Since the relationship between vehicle axle information and bridge response is inherently non-linear, we introduce a Gaussian-based neural network layer as a function approximator to model this complex mapping. Furthermore, the physical principles governing time, location, axle spacing, axle loads, and bridge responses are embedded directly into the network structure, ensuring that the model predictions remain physically consistent. Once the network is trained, the error between theoretical and measured responses can be minimized to find axle loads from the neural network parameters, which correspond to the magnitudes of vehicle loads. Numerical results indicate that, for cases where two- and three-axle vehicles traverse different lanes simultaneously, the 99.9% confidence level error for GVW is 1.2%. Field test results further validate the approach, demonstrating that the 99.9% confidence interval error for GVW is 8.9%.