Practical Design of Stepped Spillways Using Machine Learning Methods and Fuzzy Inference System

Energy-dissipating pools or flip bucket structures reduce the energy of downstream flow in conventional spillways. Recently, stepped spillways have been widely used to dissipate the flow of energy downstream. Flows on the stepped spillways are complex and advanced techniques such as Fuzzy Logic (FL), Adaptive Neuro-Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN), Genetic Programming (GP), Deep Learning, and Tree-Based models are required to calculate energy dissipation ratios. Fuzzy Logic has the advantage of considering physical processes when examining problems using rule bases. In this study, energy dissipation over stepped spillways is calculated using machine learning methods and the Fuzzy Inference System in Python programming language. Experimental data by different researchers are used to model stepped spillways. Two new parameters, such as an approach channel and step-top geometric ratios, are used in addition to the literature to obtain energy dissipation ratios on stepped spillways. Artificial Neural Network Regressor (ANN) from machine learning methods gives minimum percentages and absolute errors (-0.117% and 1.398) and maximum R^2 values (0.976) for the testing dataset. Although the accuracy of the ANN method changes with hidden layer sizes and ratios between training and testing data, the Fuzzy Logic (FL) is independent to training data. The FL method represents good results with low Mean Percentages Error (MPE) and Mean Absolute Errors (MAE) (-1.688% and 2.000) and an R^2 value (0.951), and the produced Python function using the fuzzy inference system can be applied easily to different flow conditions and stepped spillways.