Quantifying the flow resistance in step-pool streams is of importance for studying the restoration of benthic animals and bedload transport. The Darcy–Weisbach friction factor of the total flow resistance is partitioned into components associated with grains, spills, and loose-packed particles. By extending the two-dimensional hydraulic radius, a new proposed rough ness height is applied to evaluate resistance components induced by spills and loose-packed particles. Three morphological patterns induced by different-magnitude foods can be classified to form different flow resistance components, depending on the morphological variation. The three components varying with hydraulic and geometric parameters by considering the closest-1 NSEI and smallest RMSE and MRE have been examined. It is found that the grain resistance factor component, in comparison with other factors, has a slight impact on hydraulic parameters. Hydraulic and geometric parameters have a significant influence on the spill resistance component, accounting for the main proportion of the total resistance. The resistance associated with loose-packed particles correlates with parameters due to the initial random movement of particles and abundant sources.
The optimum combination of blade angle of the runner and guide vane opening with Kaplan turbine can improve the hydroelectric generating the set operation efficiency and the suppression capability of oscillations. Due to time and cost limitations and the complex operation mechanism of the Kaplan turbine, the coordination test data is insufficient, making it challenging to obtain the whole curves at each head under the optimum coordination operation by field tests. The field test data is employed to propose a least-squares support vector machine (LSSVM)-based prediction model for Kaplan turbine coordination tests. Considering the small sample characteristics of the test data of Kaplan turbine coordination, the LSSVM parameters are optimized by an improved grey wolf optimization (IGWO) algorithm with mixed non-linear factors and static weights. The grey wolf optimization (GWO) algorithm has some deficiencies, such as the linear convergence factor, which inaccurately simulates the actual situation, and updating the position indeterminately reflects the absolute leadership of the leader wolf. The IGWO algorithm is employed to overcome the aforementioned problems. The prediction model is simulated to verify the effectiveness of the proposed IGWO-LSSVM. The results show high accuracy with small samples, a 2.59% relative error in coordination tests, and less than 1.85% relative error in non-coordination tests under different heads.
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