A Hybrid Intelligent Model and Computational Fluid Dynamics to Simulate Discharge Coefficient of Circular Side Orifices

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In this paper, a hybrid meta-heuristic artificial intelligence (AI) method, named “ANFIS–PSOGA,” is developed for modeling the discharge coefficient of circular side orifices for the first time. For this purpose, the adaptive neuro fuzzy inference system (ANFIS) network is optimized by means of two robust optimization algorithms: the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm. Furthermore, the Monte Carlo simulations are utilized to enhance the performance of the AI hybrid model. Besides, the k-fold cross-validation method is employed in order to verify the numerical results. Initially, the performance of three fuzzy inference system (FIS) generations of the ANFIS model including grid partitioning, subtractive clustering and fuzzy C-means clustering are evaluated. After that, using the parameters affecting the discharge coefficient, eleven ANFIS models are defined and then the best ANFIS model and the most influencing input parameters are identified through the conduction of a sensitivity analysis. For the superior ANFIS model, mean absolute percentage error, root-mean-square error and the correlation coefficient (R) are obtained 0.021, 0.020 and 0.871, respectively. Also, the Froude number (Fr) is detected as the most effective input parameter. Moreover, the discharge coefficient of the circular side orifices and the flow field within main channels along the side orifices are simulated through the adoption of a computational fluid dynamics (CFD) model. Additionally, the flow field at three different cross sections (beginning, middle and end of orifice) along the side weir is evaluated. For instance, by advancing the flow toward the side orifice, the Froude number is reduced. Besides, at each cross section, the maximum shear stress is estimated to occur in the vicinity of the crest of the circular side orifice. According to the CFD results, the maximum lateral velocity is estimated near the circular side orifice. In addition, the results yielded by the ANFIS, ANFIS–PSO, ANFIS–PSOGA and CFD models are compared and an uncertainty analysis is carried out for the models. Based on the comparison, ANFIS–PSOGA has the best performance in simulating the discharge coefficient. Ultimately, a simple and practical computer code for the best model (ANFIS–PSOGA) is proposed which can be easily used by scholars and engineers in practical usages.