A reliable and accurate monitoring of traffic load is of significance for the operational management and safety assessment of bridges. Traditional weight-in-motion techniques are capable of identifying moving vehicles with satisfactory accuracy and stability, whereas the cost and construction induced issues are inevitable. A recently proposed traffic sensing methodology, combining computer vision techniques and traditional strain based instrumentation, achieves obvious overall improvement for simple traffic scenarios with less passing vehicles, but are enfaced with obstacles in complicated traffic scenarios. Therefore, a traffic monitoring methodology is proposed in this paper with extra focus on complicated traffic scenarios. Rather than a single sensor, a network of strain sensors of a pre-installed bridge structural health monitoring system is used to collect redundant information and hence improve accuracy of identification results. Field tests were performed on a concrete box-girder bridge to investigate the reliability and accuracy of the method in practice. Key parameters such as vehicle weight, velocity, quantity, type and trajectory are effectively identified according to the test results, in spite of the presence of one-by-one and side-by-side vehicles. The proposed methodology is infrastructure safety oriented and preferable for traffic load monitoring of short and medium span bridges with respect to accuracy and cost-effectiveness.

Collecting the information of traffic load, especially heavy trucks, is crucial for bridge statistical analysis, safety evaluation, and maintenance strategies. This paper presents a traffic sensing methodology that combines a deep learning based computer vision technique with the influence line theory. Theoretical background and derivations are introduced from both aspects of structural analysis and computer vision techniques. In addition, to evaluate the effectiveness and accuracy of the proposed traffic sensing method through field tests, a systematic analysis is performed on a continuous box-girder bridge. The obtained results show that the proposed method can automatically identify the vehicle load and speed with promising efficiency and accuracy and most importantly cost-effectiveness. All these features make the proposed methodology a desirable bridge weigh-in-motion system, especially for bridges already equipped with structural health monitoring system.

The dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems, which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this article proposes a framework—termed neural modal ordinary differential equations (Neural Modal ODEs)—to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via Pi-Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigenanalysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to out perform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, that is, the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.