Submerged characteristics of radial gate using machine learning and global sensitivity

Quantitative performance indicators of irrigation water management are required the measurement of flow rates at key locations in a conveyance and distribution system. Radial gates have been widely used for the agricultural water management in the irrigation areas, due to the small lifting forces and significant economic benefits. However, the inaccurate calibration is often found in the submerged flow, where the error is as high as 50%. Therefore, it is of great significance for the accurate determination of discharge capacity. This study aims to achieve the accurate water measurement and determination of discharge coefficient in the irrigation areas. The discharge capacity of submerged flow pattern was predicted using support vector machine (SVM), generalized regression neural network (GRNN), extreme learning machine (ELM), and kernel extreme learning machine (KELM). The performance of the models was comprehensively evaluated by evaluation indexes, objective function (OBJ) criteria and uncertainty analysis. At the same time, the Sobol's method was used to quantify the dimensionless parameters using the performance of the optimal model. A systematic evaluation was implemented to obtain the importance of each parameter (the discharge coefficient (C_d)) and the interaction of the parameters. In addition, there was the great variation between important parameters and C_d, according to the discharge characteristics of radial gate. The model evaluation results show that the better performance was found in the KELM with the determination coefficient R²=0.972, the mean absolute percentage error K_MAPE=5.038%, the root mean square error K_RMSE=0.020, the Willmott’s agreement index K_WIA=0.993, and objective function K_OBJ=0.0127. The uncertainty analysis show that the average error of KELM was the lowest (S_e=0.00015), the width of confidence band was the narrowest (BD=0.04942), and the range of 95% confidence interval was the smallest (−0.04927-0.04956), indicating the highly consistent data and the high reliability of the sample. Therefore, the KELM shared the higher accuracy and robustness, compared with the SVM, GRNN, and ELM models. An efficient and high-precision model was achieved for the flow calibration of the radial gate. The Sobol’s sensitivity analysis showed that the main influencing factors were the ratio of trunnion pin height to upstream water depth (h/Y₀), the ratio of gate radius to upstream water depth (R/Y₀), and the ratio of gate width to upstream water depth (B/Y₀). Furthermore, these parameters (h/Y₀, R/Y₀, B/Y₀) should be considered emphatically in the design of radial gates in practice. The first-order sensitivity coefficient and global sensitivity coefficient to C_d were ranked in the descending order of 0.1162, 0.0754, 0.0752, and 0.5311, 0.4966, 0.4959, respectively. Therefore, the global sensitivity coefficient was much higher than the first-order sensitivity, indicating that the interaction of parameters increased the influence of each parameter on the discharge coefficient. The variation between important parameters and discharge coefficient C_d showed that the C_d increased linearly with the increase of h/Y₀, R/Y₀ and B/Y₀. In addition, the smaller the gate opening W was, the larger the increase of the discharge coefficient C_d was. This finding can further improve and enrich the hydraulic mechanism of the radial gate under submerged flow conditions. A strong reference can be offered for the calibration of submerged radial gates during the engineering design in irrigation areas.