Understanding of air entrainment process in the sewage drop structure using physically-based symbolic intelligence models

The vortex drop structure is employed to transport water through subterranean channels in urban sewer and drainage networks. As the water descends, it incorporates a significant amount of air, which is subsequently discharged from the drop shaft further downstream. Quantifying the volume of entrained air is generally a challenging task. A physical prototype was built as part of this study to comprehend the process of air movement within a vortex structure. The researchers conducted experiments to examine the effects of different variables on the air circulation. The outcomes of the dimensional analysis revealed that certain effective factors, such as the approach flow Froude number (Fr), the ratio of the total drop height to the diameter of the shaft (L/D), and the ratio of the sump depth to the diameter of the shaft (H_s/D), had a substantial impact on the relative air discharge (β). In order to understand effects of independent variables on the relative air discharge (β), 144 experimental observations were used to develop four robust symbolic intelligence models (i.e., Model Tree [MT], Evolutionary Polynomial Regression [EPR], Multivariate Adaptive Regression Spline [MARS], and Gene-Expression Programming [GEP]) in order to provide with mathematical expressions for evaluation of vortex structures under operation. The performance of symbolic intelligence models were evaluated by using various setting parameters of the intelligent models. In addition, the results demonstrated MT (Index of Agreement [IOA] = 0.9713, Root Mean Square Error [RMSE] = 0.0160, and Scatter Index [SI] = 0.1094) provided the most accurate prediction of the relative air discharge and followed by MARS (IOA = 0.9561, RMSE = 0.0199, and SI = 0.1357), EPR (IOA = 0.9455, RMSE = 0.0221, and SI = 0.1513), and GEP (IOA = 0.9145, RMSE = 0.0277, and SI = 0.1885). Moreover, the performance of empirical equation, given by Central Composite Face-entered Design (RSM-CCFD) methodology, demonstrated the minimum level of precision (IOA = 0.8931, RMSE = 0.0310, and SI = 2016) in comparison with all symbolic intelligence models. Furthermore, as found in the experimental observations, the performance of mathematical expressions proved that β ratio displayed an upward trend as both Fr and L/D ratio increased.