Spatiotemporal modeling of vehicle loads on bridges using importance and decoupling-aware rectified flow

Spatiotemporal modeling of vehicle loads plays a crucial role in the accurate evaluation of the safety and durability of bridges. Although existing methods consider the temporal variability of vehicle loads and differences in lane distribution to some extent, it remains challenging to jointly model variable-length sequences and mixed axle weights of traffic flows within a unified generative framework. This study proposes the importance and decoupling-aware rectified flow (ID-RF), in which two innovative strategies are conducive to the spatiotemporal modeling of vehicle loads. Initially, the importance-aware strategy conducts sequence attenuation on Gaussian noise, concentrating on effective vehicle loads in variable-length traffic flows while disregarding zero padding. Subsequently, the decoupling-aware strategy decomposes multi-lane time headways and mixed axle weights based on parity of the number of axles, facilitating the learning of different vehicle types. The rectified flow is founded on ordinary differential equations and learns the distribution transformation between random noise and decoupled vehicle loads via the U-Net. Applying this method to vehicle loads monitored by weigh-in-motion systems, the accuracy and interpretability of the ID-RF are verified by comparing the similarity between monitored and generated values.