Physically Guided Estimation of Vehicle Loading-Induced Low-Frequency Bridge Responses with BP-ANN

The intersectional relationship in bridge health monitoring refers to the mapping function that correlates bridge responses across different locations. This relationship is pivotal for estimating structural responses, which are then instrumental in assessing a bridge’s service status and identifying potential damage. The current research landscape is heavily focused on high-frequency responses, especially those associated with single-mode vibration. When it comes to low-frequency responses triggered by multi-mode vehicle loading, a prevalent strategy is to regard these low-frequency responses as “quasi-static” and subsequently apply time-series prediction techniques to simulate the intersectional relationship. However, these methods are contingent upon data regarding external loading, such as traffic conditions and air temperatures. This necessitates the collection of long-term monitoring data to account for fluctuations in traffic and temperature, a task that can be quite daunting in real-world engineering contexts. To address this challenge, our study shifts the analytical perspective from a static analysis to a dynamic analysis. By delving into the physical features of bridge responses of the vehicle–bridge interaction (VBI) system, we identify that the intersectional relationship should be inherently time-independent. The perceived time lag in quasi-static responses is, in essence, a result of low-frequency vibrations that are aligned with driving force modes. We specifically derive the intersectional relationship for low-frequency bridge responses within the VBI system and determine it to be a time-invariant transfer matrix associated with multiple mode shapes. Drawing on these physical insights, we adopt a time-independent machine learning method, the backpropagation–artificial neural network (BP-ANN), to simulate the intersectional relationship. To train the network, monitoring data from various cross-sections were input, with the responses at a particular section designated as the output. The trained network is now capable of estimating responses even in scenarios where time-related traffic conditions and temperatures deviate from those present in the training data set. To substantiate the time-independent nature of the derived intersectional relationship, finite element models were developed. The proposed method was further validated through the in-field monitoring of a continuous highway bridge. We anticipate that this method will be highly effective in estimating low-frequency responses under a variety of unknown traffic and air temperature conditions, offering significant convenience for practical engineering applications.