Fig. 5: Model-based water flow monitoring and PSD analysis.

a–d Model-based water flow monitoring and recognition at four distinct time points: 13:00, 14:30, 16:00, and 17:19. Each panel combines a strip heatmap and a line graph to depict flow state distribution along the aqueduct’s length. The strip heatmap employs a color gradient to represent transitions between flow states: “dispersed bubble flow,” “plug flow,” “stratified wavy flow,” “stratified smooth flow,” and “dry.” The vertical axis of the line graph indicates the model-predicted probability of water presence, with the gray curve showing raw predictions and the orange curve presenting a smoothed version obtained by averaging adjacent predictions. A probability threshold of 50% (dashed line) delineates regions of active water flow, with the estimated water head position marked by a red circle; e–h Corresponding PSD cloud diagrams illustrating the spatial variation in signal energy as the aqueduct fills with water; i Model-estimated water head migration path (blue line) and velocity (read line) throughout the monitoring period.