An innovative approach to predicting vessel traffic flow and visualizing traffic density in multiple-bridge inland waterways

Multi-bridge inland waterways constitute some of the most constrained and high-risk navigation environments. The dense spacing of bridges and the resulting fragmentation of navigable channels create complex spatiotemporal variability that existing prediction models struggle to capture, which limits their applicability in such areas. This study proposes a spatiotemporal variational model, Spatio-Temporal Variational Autoencoder (ST-VAE), for multi-step vessel traffic and density prediction in multi-bridge inland waterways. The framework integrates an embedded graph-enhanced Long Short-Term Memory (LSTM) encoder, which exploits bridge-to-bridge connectivity, with a variational latent space and a distributed sampling network to represent uncertainty in traffic evolution. Using Automatic Identification System (AIS) data from 13 consecutive bridge areas in Wuhan, two datasets are constructed for high-flow (V-high) and low-flow (V-low) seasons, and 12∼48-hour prediction tasks are evaluated against ten baseline models. On the V-high dataset with a 24-hour horizon, ST-VAE achieves a mean absolute error (MAE) of 2.57 and a mean absolute percentage error (MAPE) of 3.83%, which are 24% and 61% lower than the best baseline, respectively, and reaches a Pearson correlation coefficient (PCC) of 98.0%. For 48-hour forecasts, MAE and MAPE are reduced by 34% and 50% compared with the strongest competitor. One-week rolling experiments further show that ST-VAE maintains a PCC above 90% while achieving approximately 38% lower MAE than the best ablation model. Finally, K-means clustering is applied to convert predicted flows into three density levels, revealing persistent bottlenecks near key bridges and providing actionable support for congestion monitoring and traffic management in bridge-dense inland waterways.