Developing an uncertainty-informed model-free plate-like weight-in-motion system with strain-transmissibility-like metric

Weigh-in-Motion (WIM) systems play a critical role in traffic management and overload control, where accurate identification of wheel loads is essential. However, conventional mechanics-based plate-like WIM approaches typically depend on structural influence lines or finite element models of the weighing plate, which are difficult to obtain accurately. Moreover, wheel loads are often inferred from peak features in vehicle-induced responses, and such peak-based detection is highly sensitive to measurement noise and peak blurring under realistic operating conditions. To address these limitations, this study proposes an uncertainty-informed model-free plate-like WIM system that enables the identification of wheel loads using a strain-transmissibility-like metric, defined as the ratio of frequency-domain responses at the same location for two different wheel loads. The zero-frequency component of this metric is analytically proven to equal the ratio of the corresponding wheel loads, thereby eliminating the need for structural influence line construction. By leveraging the response of a reference vehicle with known axle configuration, the wheel loads of an unknown vehicle can be reliably inferred through this equivalence. A Bayesian inference framework is further developed to fuse multiple measurements and accommodate uncertainties from noise and modeling discrepancies. Closed-form expressions for the likelihood function, its gradients, and the posterior covariance are derived to ensure efficient optimization and uncertainty quantification. Numerical simulations and laboratory experiments demonstrate that the proposed method achieves accurate and robust identification under diverse operating conditions, without requiring influence line estimation.