A novel approach using CFD and neuro-fuzzy-firefly algorithm in predicting labyrinth weir discharge coefficient

Abstract

In this paper, for the first time, to model the discharge coefficient of labyrinth weirs, the evolutionary firefly algorithm (FFA) is used for optimizing the membership functions of the adaptive neuro-fuzzy inference system (ANFIS). Also, to enhance the performance of the ANFIS and ANFIS-FFA models, the Monte Carlo simulations (MCs) are employed. Additionally, the k-fold cross-validation is utilized for training and testing the methods. Next, some input dimensionless parameters including the Froude number (Fr), the ratio of the head above the weir to the weir height (H T /P), cycle sidewall angle (α), the ratio of length of the weir crest to the channel width (L c /W), the ratio of length of apex geometry to the width of a single cycle (A/w) and the ratio of the width of a single cycle to the weir height (w/P) are determined. After that, seven different models are developed for ANFIS and ANFIS-FFA. Then, by conducting a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) are identified. Moreover, the error distribution results exhibit that about 70% of the superior model results have errors less than 5%. Subsequently, the discharge coefficient is simulated by means of a computational fluid dynamics (CFD) model. Furthermore, a comparison of the CFD model with the ANFIS and ANFIS-FFA models reveals that the ANFIS-FFA model is significantly more accurate. Also, an uncertainty analysis is performed for the CFD, ANFIS and ANFIS-FFA models. Finally, a very simple code calculating the discharge coefficient of labyrinth wires is presented. This code can be easily employed without any knowledge on ANFIS, FFA and prior information about MATLAB.

Interpolation Accuracy of Hybrid Soft Computing Techniques in Estimating Discharge Capacity of Triangular Labyrinth Weir

“…According to the reported results in Table I, it is evident that employing meta-heuristic algorithms for training SCTs has improved their estimation accuracy, which is in agreement with previously published results [18]- [20], [23] In the case of ANFIS structure, ANFIS-FA has the best performance in the training stage, and ANFIS-PSO reports better performance in the testing stage, while in both training and testing stages, ANFIS-PSO and ANFIS-FA estimated q with higher confidence than ANFIS-BP&LS. Nevertheless, regardless of the employed training algorithm, the ANFIS structure reports a feeble performance in the interpolation task.…”

“…Karimi et al [19] showed that SVR-FA not only has a better performance compared to the classic SVR but also is superior to the Response Surface Methodology (RSM) and Principal Component Analysis (PCA). In a study in 2020, Shafiei et al [20] employed ANFIS-FA to estimate the C d in both Triangular and Trapezoidal LW. They found that the reported results by ANFIS-FA are more accurate than a simulated LW in Computational Fluid Dynamic (CFD).…”

“…In the previous studies, the applied techniques have been evaluated by a random testing dataset extracted from the experimental data [14][15][16][17][18][19][20][21][22][23]. Consequently, this testing approach provides no clarification on the SCT's capability for estimating the intermediate values, which are not similar to either testing or training data.…”

Using soft computing and machine learning algorithms to predict the discharge coefficient of curved labyrinth overflows

“…They found that the LSSVM and ELM methods were the top performers. Shafiei et al (2020) used the evolutionary firefly algorithm (FFA) algorithm to optimize the membership functions of the adaptive neural-fuzzy inference system (ANFIS) model and observed that the ANFIS-FFA model was significantly more accurate than the ANFIS model in estimating the discharge coefficient of labyrinth overflows. Mahmoud et al (2021a) utilized a hybrid MLP-firefly algorithm (MLP-FFA) to estimate the discharge coefficient of labyrinth spillways.…”

Energy Dissipation and Hydraulics of Flow over Trapezoidal–Triangular Labyrinth Weirs

“…The results showed that CFD models are able to provide very good evaluations of the discharge on free and submerged labyrinth weirs for a large sidewall angle. Norouzi et al [28] and Shafiei et al [29] investigated the discharge coefficient of labyrinth weirs using support vector machines and adaptive neuro-fuzzy interface system (ANFIS) as well as a hybrid model called "firefly algorithm" via the CFD approach. The firefly algorithm has the ability to find optimized values for non-linear problems with high convergence speed.…”