Bridge Weigh-in-motion System Based on Maximum Entropy Regularization

Overloaded vehicles can cause irreversible damage to a bridge structure, reduce its service life, and even lead to collapse. Generally, the primary method for weighing the vehicles crossing a bridge is the commercial bridge weigh-in-motion (BWIM) system. However, the core algorithm employed by this method (Moses' algorithm) produces ill-conditioned equations for axle load recognition, leading to overfitting problems when the axle spacing is close and the road surface is rough. Moreover, the axle load recognition process does not differentiate among the contributions of individual axle loads, resulting in less accurate single axle load recognition. To address this issue, this study proposed a novel BWIM algorithm based on maximum entropy regularization. In this algorithm, entropy regularization terms and weight coefficients related to axle load distribution are first employed to establish an error function. Next, the gradient of the error function is calculated and input into the iterative formula of the nonlinear conjugate gradient method to obtain the axle load corresponding to each regularization parameter. Finally, each axle load corresponding to the regularization parameter is input into Regihska's formula to calculate the parameter, draw the curve, and obtain the axle load corresponding to the minimum value of this curve, which is the desired axle load value. The accuracy and robustness of the maximum entropy algorithm's recognition results were verified through numerical simulation and field tests. The results show that the axle load recognition accuracy of the proposed maximum entropy algorithm is superior to that of Moses' algorithm. The field test results indicate that the average error of the front axle load obtained using the maximum entropy algorithm is 27. 1 %, significantly less than the 36. 3% error obtained using Moses' algorithm. Collectively, these results illustrate that by employing the entropy regularization terms and weight coefficients, the proposed algorithm can suppress the overfitting of equations to an considerable extent, eliminate the influence of select measurement errors, and improve the accuracy of single axle load recognition results, making it more suitable for practical bridge vehicle load monitoring than Moses' method. © 2024 Chang'an University. All rights reserved.