Forecasting the discharge capacity of inflatable rubber dams using hybrid machine learning models

Inflatable dams are flexible hydraulic structures that are constructed on rivers and are inflated by fluids such as air or water. This research investigates the effects of influential dimensionless factors on estimating one of the critical hydraulic characteristics of inflatable dams, namely the discharge capacity. Various parameters such as the proportion of total upstream head to dam height (H ₁/D _h), the ratio of overflowing head to dam height (h/D _h), the ratio of discharge per unit width to its maximum value (q/q _max), the ratio of the internal pressure of the tube to its maximum value (p/p _max) and the ratio of the longitudinal coordinate placement of each element to x _max are used. A hybrid model based on  the Particle Swarm Optimization (PSO) and the Genetic Algorithm (GA), PSO-GA, is proposed to improve the accuracy of the estimation by combining the advantages of both algorithms. Moreover, the performance of the model is compared with available hybrid models, including the Artificial Neural Networks (ANNs) optimized by Stochastic Gradient Descent (SGD) model (ANN-SGD) and the ANN-PSO and ANN-GA models. Finally, the performance of the algorithms is evaluated using statistical indicators such as the coefficient of determination (R ²), root mean square error (RMSE), mean absolute percentage error (MAPE) and the scatter index (SI). The results show that the internal pressure plays a vital role with respect to forecasting the discharge coefficient, and omitting it degrades the accuracy by 2.12%. In comparison with other models, the proposed PSO-GA hybrid model provides the most accurate results (R ² = 0.999, MAPE = 0.04). Finally, comparing the results of the proposed PSO-GA with the benchmarked ANN-GA, ANN-PSO and ANN-SGD methods proves the superiority of the hybrid PSO-GA method.