A robust bridge weigh-in-motion algorithm based on regularized total least squares with axle constraints

The identification of traffic loads, including the axle weight (AW) and the gross vehicle weight (GVW) of vehicles, plays an important role in bridge design refinement, safety evaluation, and maintenance strategies. Bridge weigh in motion (BWIM) is a promising technique to weigh vehicles passing through bridges. Though the state-of-the-art BWIM can accurately identify the GVW, unacceptable weighing errors are reported when identifying the AW of vehicles, particularly for those with closely spaced axles. To address the axle weighing problem, this paper aims to improve the performance of BWIM in weighing individual axle loads apart from the gross vehicle weight. The work first theoretically analyzes the possible sources of errors of existing BWIM algorithms, which are observational errors residing in the BWIM equation, no constraint imposed on individual axle loads, and ill-conditioned nature. Accordingly, three measures are taken to establish a novel robust BWIM algorithm, which is based on regularized total least squares, as well as imposing constraints on the relationship between axles. To validate the proposed algorithm, a series of weighing experiments are carried out on a high-fidelity vehicle-bridge scale model. The corresponding results indicate that the proposed BWIM algorithm significantly outperforms other existing BWIM algorithms in terms of the accuracy and robustness of identifying individual axle weight, while retaining satisfactory identification of the gross vehicle weight as well.