Application of hybrid neural network in discharge coefficient prediction of triangular labyrinth weir

Discharge coefficient (C_d) is an important parameter of triangular labyrinth weir. It is of great significance to predict the discharge coefficient accurately. In this research, in order to more accurately predict the C_d, in view of the traditional BP neural network is easy to fall into the local minimum in the training process, genetic algorithm (GA) and particle swarm optimization (PSO) are employed to optimize the traditional BP neural network's initial weights and thresholds. Nonlinear regression analysis (NLR) is also added to compare with these intelligent methods and four discharge coefficient prediction models are built, namely the NLR, the BPNN, the GA-BPNN and the PSO-BPNN. After the completion of the model construction, in order to objectively evaluate the performance of these models, the prediction results of these models are compared with the experiment results, and the determination coefficient (R²), the mean absolute error (MAE) and the root mean square error (RMSE) are introduced as the performance indicators to quantify the model performance. The results show that the accuracy and stability of the NLR are much worse than that of the intelligent models. The prediction results of the GA-BPNN and the PSO-BPNN are quite accurate with a higher decision coefficient than the BPNN. Moreover, the MAEs and the RMSEs of the GA-BPNN and the PSO-BPNN were significantly reduced by 25 and 40% compared with BPNN, respectively, and the maximum prediction errors were 4.4% and 2.6%, severally. Meanwhile, the width of error uncertainty band of GA-BPNN and PSO-BPNN is narrower than BPNN. By comparing GA-BPNN and PSO-BPNN with the discharge coefficient prediction models of triangular labyrinth weir in previous literatures, it is found that the mean absolute percentage error (MAPE) values of GA-BPNN and PSO-BPNN are 1.504% and 1.225% respectively, which are lower than other existing models. At the same time, the other performance indexes are better than most existing models, indicating that the genetic algorithm and PSO algorithm are more effective than the traditional BP algorithm in adjusting BP neural network parameters, easier to find the global optimal value, and improve the prediction accuracy and applicability of the model.