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

Soft Computing Techniques (SCT) are extensively used to estimate Labyrinth Weir's (LW) flow-rate. Due to the multiplicity of these techniques, identifying the most competent SCT is indispensable. This study aims to estimate the flow-rate of a sharp-crest triangular LW as a function of its side leg angle α and total head ratio (H/P) through several SCTs such as Adaptive Neuro-Fuzzy Inference System (ANFIS), Multi-Layer Perceptron (MLP), Support Vector Regression, and Radial Basis Function Neural Network. Additionally, these SCTs' potential combinations with Firefly Optimization Algorithm (FA) and Particle Swarm Optimization (PSO) are also investigated and used for estimation. The conducted experimental studies on LW examined a wide range of H/P in some limited α values. Correspondingly, all the proposed models and techniques are incapable of estimating the flow rate for intermediate α values without interpolation. Therefore, SCT's Interpolation accuracy is of the utmost importance. Besides the standard evaluation in the testing stage, a novel approach is utilized to evaluate the SCT's accuracy in the interpolation task. The SCTs are evaluated based on several statistical criteria, the Taylor diagram, Kruskal-Wallis, and Mann-Whitney tests. It is concluded that the competence of an SCT in the testing stage cannot guarantee its accuracy in the interpolation task. Subsequently, ANFIS-PSO and MLP-FA show the highest accuracy in the testing stage and interpolation task, respectively. Eventually, according to a systematic investigation in the implemented diagnostic test results, two rankings are presented for the applied SCTs based on their performance in the testing stage and their interpolation accuracy.