Probabilistic vehicle weight estimation using physics-constrained generative adversarial network

Traffic information plays an important role in the design and management of civil transportation infrastructure. Bridge weigh-in-motion (BWIM) provides an effective tool for traffic information gathering by estimating vehicle parameters including its weight through bridge responses. Most existing BWIM algorithms rarely consider the epistemic uncertainty of vehicle weight in terms of the probabilistic distribution of estimated axle weights (AWs) of the vehicle. This paper proposes a novel methodology for probabilistic vehicle weight estimation using a physics-constrained generative adversarial network (GAN). Generative models are introduced to describe the probabilistic distributions of estimated AWs and bridge responses. Physics constraints on the generative models are formulated and enforced by minimizing a physics-based loss function. The generative models are then learned by training a physics-constrained GAN using the observed bridge responses. Numerical study and field testing are conducted to demonstrate the proposed method using representative highway bridges and vehicles. The results show that the proposed method can successfully capture the uncertainty in the vehicle weight estimation and provide the probabilistic distributions of the estimated AWs for different vehicle types and loading conditions considered, which can enhance the application of BWIM for relevant tasks such as traffic data collection and truck overloading enforcement. Based on the results obtained from the numerical study and field testing, the maximum coefficient of variation obtained for the AWs and gross vehicle weight of the presented cases are 0.55 and 0.11, respectively.