Improving Modelling of Discharge Coefficient of Triangular Labyrinth Lateral Weirs Using SVM, GMDH and MARS Techniques

Abstract

In this study the discharge coefficient (Cd) of labyrinth lateral weirs was modelled and predicted using artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS), support vector machine (SVM), group method of data handling (GMDH), and multivariate adaptive regression splines (MARS) techniques. To this end, a related data set was collected from the literature. Results indicated that the proposed ANN model includes two hidden layers with eight and five neurons in the first and second hidden layers, respectively. Testing transfer functions demonstrated that the radial basis function (RBF) has the best outcome. Evaluating the performance of the ANN model shows that this model with a coefficient of determination (R2 = 0.96) and root mean square error (RMSE =0.07) in the testing stage has suitable functionality. Reviewing the ANFIS model showed that this model with one hidden layer containing seven membership functions within the Gaussian function could achieve R2 = 0.94 and RMSE =0.136 for predicting the discharge coefficient. During preparation of SVM, it was found that this model with RBF as the best kernel function obtained R2 = 0.96 and RMSE =0.07. The structure of the MARS and GMDH models pointed out that the Froude number, grandiose index and ratio of upstream flow depth to the height of weir are the most effective parameters for predicting the discharge coefficient. Minimum R2 and RMSE achieved were equal to 0.93 and 0.08, respectively, in the testing stage for the MARS and GMDH models. Copyright © 2017 John Wiley & Sons, Ltd.

Prediction of Potential Evapotranspiration Using Temperature-Based Heuristic Approaches

“…GMDHNN is successfully applied in diverse engineering applications [31][32][33][34]. Within hydrology and water resources related research, Najafzadeh et al [35] developed the GMDHNN model for scour depth (SD) of pipelines estimation due to waves variability; the prediction of local SD at bridge abutments in coarse sediments with thinly armored beds was conducted by Najafzadeh et al [36]; simulation of flow discharge of straight compound channels was reported by Najafzadeh and Zahiri [37]; prediction of significant wave height was established by Shahabi et al [38]; prediction of turbidity considering daily rainfall and discharge data was determined by Tsai and Yen [39]; an improved modeling of the discharge coefficient for triangular labyrinth lateral weirs was described by Parsaie and Haghiabi [40]; an evaluation of treated water quality in a water treatment plant was carried out by Alitaleshi and Daghbandan [41]; a prediction of turbidity and the free residual aluminum of drinking water was tested by Daghbandan et al [42]. Based on the reported literature review, only one study reported the implementation of the GMDHNN ET 0 modeling developed by da Silva Carvalho and Delgado [43].…”

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

“…+ and − are Lagrange values determined by + and − . Verities of kernel functions are introduced in SVR; nonetheless, linear, polynomial, RBF, and Sigmoid kernel functions are more prevalent in solving general problems [21], [22]. Among the mentioned kernel functions, RBF, due to its higher efficiency, is more accomplished in complex problems [18], [34]; thus, the present study employs the RBF kernel function in SVR.…”

“…Parsaie and Haghiabi [21], through comparison of three popular ANNs (i.e., Multi-Layer Perceptron (MLP), SVR and RBFNN), found that in a triangular LW, SVR predicts C d more accurate than MLP and RBFNN. Nevertheless, in another study on triangular LW, which was conducted by the same scholars [22], MLP not only performed better than SVR but also was superior to ANFIS, Group Method of Data Handling (GMDH), and Multivariate Adaptive Regression Splines (MARS). Likewise, Norouzi et al [8] reported the superiority of MLP over SVR and RBFNN in estimating C d in a trapezoidal LW.…”

“…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.…”

Prediction of the sodium absorption ratio using data-driven models: a case study in Iran

“…Various researchers have been used various data mining and data-driven techniques in civil and environmental engineering applications (Mehdipour, Stevenson, Memarianfard, & Sihag, 2018;Nain, Sihag, & Parsaie, 2016;Parsaie, Azamathulla, & Haghiabi, 2018;Parsaie & Haghiabi, 2017, 2015Parsaie, Najafian, Omid, & Yonesi, 2017;Sihag, 2018;Sihag, Singh, Vand, & Mehdipour, 2018a;Sihag, Tiwari, & Ranjan, 2018bSingh, Sihag, & Singh, 2017;Singh, Sihag, Singh, & Kumar, 2018;Tiwari, Sihag, Kumar, & Ranjan, 2018;Vand, Sihag, Singh, & Zand, 2018). Asadollahfardi, Hemati, Moradinejad, and Asadollahfardi (2013) used ANN to predict the SAR in which Na, Mg, Ca, SO 4 , Cl, HCO − 3 , pH were input variables and SAR was output and found that ANN has the capability to predict the SAR accurately and precisely.…”