Stacking Ensemble-Based Hybrid Algorithms for Discharge Computation in Sharp-Crested Labyrinth Weirs

Labyrinth weirs are utilized to increase the weir crest length to transport a greater discharge during floods in contrast to conventional weirs. Nevertheless, due to the increased geometric complexity of labyrinth weirs, determination of accurate discharge coefficients and accordingly, head-discharge ratings are quite essential issues in practical application. Hence, as a first step the present study proposes the following eight standalone algorithms: decision table (DT), Kstar, least median square (LMS), M5 prime (M5P), M5 rule (M5R), pace regression (PR), random forest (RF), and sequential minimal optimization (SMO). Then, applying the stacking (ST) algorithm, these stand-alone models were hybridized to develop ST-LMS, ST-PR, ST-SMO, ST-Kstar, ST-DT, ST-M5R, ST-M5P, and ST-RF to predict the discharge coefficient (C d ) for sharp-crested labyrinth weirs. Modeling resulted in 123 experimental data sets including consideration of vertex angle ( θ ), channel width ( B ), head over the crest of the weir ( h ), crest heights ( W ), crest length of the weir ( L ), C d , and flow discharge ( Q ). These effective variables were re-arranged in the form of several independent dimensionless parameters ( θ, h/W, L/B, L/h , Froude number ( Fr ), B/W and L/W ) to predict C d as an output. Datasets were randomly divided into two groups; 70% of data used for model training while 30% used for model validation. The accuracy of the developed models was examined in terms of different statistical error measurement criteria of visually-based (line graph, scatter plot, box plot) and quantitative-based [root mean square error (RMSE), mean absolute error (MAE), the Nash-Sutcliffe efficiency (NSE), and percentage of bias (PBIAS)]. Results illustrate that h/W and B/W parameters have the highest and lowest effect on the C d prediction, respectively. It was found that the most effective input combination included all input parameters except B/W. According to NSE, all developed algorithms provided accurate performances, while ST-Kstar has the highest prediction power (NSE=0.976, RMSE=0.011, MAE=0.008, PBIAS=0.027). Through incorporation of predicted C d into discharge equation, promising results are obtained for accurate discharge computation.