Modeling the Discharge Coefficient of Labyrinth Weirs Using Artificial Intelligence Techniques

In this research, an evolutionary based Neuro-fuzzy technique was utilized to estimate the discharge coefficient of labyrinth weirs. In order to optimize the parameters of the adaptive Neuro-fuzzy inference system (ANFIS), the Firefly Algorithm (FFA) was implemented. In modeling the ANFIS-FFA and ANFIS methods, the Monte Carlo simulation was used to evaluate uncertainty of the model. Furthermore, several models with significant flexibility and generalizability were provided using the k-fold cross validation method. First, the input dimensionless parameters including the Froude number (Fr), ratio of the head above the weir to the weir height (HT/p < /em>), cycle sidewall angle (α), ratio of length of the weir crest to the channel width (Lc/W), ratio of length of the apex geometry to the width of a single cycle (A/w) and the ratio of width of a single cycle to weir height (w/p < /em>) were defined. After that, seven different models were introduced for ANFIS and ANFIS-FFA. Then, using a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) were identified. In addition, the error distribution results showed that about 70% of the superior model (ANFIS-FFA 5) results had an error less than 5%. In other words, the superior model had a high statistical significance. Ultimately, the uncertainty analysis for the superior models was carried out.