Simulation of energy dissipation downstream of labyrinth weirs by applying support vector regression integrated with meta-heuristic algorithms

In this study, multi-tracker optimization algorithm (MTOA), particle swarm optimization (PSO), and differential evolution (DE) algorithms were integrated with support vector regression (SVR) to predict energy dissipation downstream of labyrinth weirs (ΔE). In order to evaluate the performance of these methods, the results are compared with corresponding outcome obtained by applying two other methods, namely, multilayer perceptron neural network (MLPNN) and multiple linear regressions methods (MLR). The input parameters comprise the discharge, the upstream flow depth, the crest length of a single cycle of the labyrinth weir, the width of a single cycle of the labyrinth weir, the apex width, the number of labyrinth weir cycles, the sidewall angle, and the height of weir. The results indicate that the meta-heuristic algorithms substantially improve the performance of SVR. The results show that the integrative methods, SVR-MTOA, SVR-PSO, and SVR-DE, are more accurate than the MLPNN and the MLR. In average, the integrative methods provide 39.63% more accurate results than the MLPNN and 79.34% more accurate results than the MLR. The average RMSE and R² for the integrative methods are 0.0054 m and 0.977, respectively. Among all integrative methods, the SVR-MTOA yields the best results, with RMSE = 0.0044 m and R² = 0.986.