Abstract
Prediction of dynamic pressure distribution (\( P^{*} \)) is a subject of great importance in the design and operation of the hydraulic structures. Flip buckets, using as hydraulic structures for dissipation of the excess energy outflow, are usually constructed at the end of the chute of the spillways. In this research, based on experimental studies of large hydraulic models, five well-known soft computing methods including artificial neural networks (ANN), gene expression programming (GEP), classification and regression trees (CART), M5 model tree (M5MT), and multivariate adaptive regression splines (MARS) approaches are examined. Mathematical expressions are obtained by these methods to predict \( P^{*} \) in flip buckets. Compared to ANN and GEP expressions, explicit formulas derived by CART, M5MT, and MARS demonstrated more straightforward calculations. In addition, linear and nonlinear equations are generated for better comparison with the outcomes of the proposed soft computing methods. The obtained results showed the high performance of the suggested soft computing methods for the prediction of \( P^{*} \) in flip buckets. It is found that the GEP approach culminated in more accurate results than other proposed soft computing methods and conventional linear and nonlinear regression techniques. Error measures in the testing stage showed that the formula provided by GEP with root mean square error (RMSE = 0.095), scatter index (SI = 13%), and mean absolute error (MAE = 0.073) has the best accuracy among the other predictive equations.
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Acknowledgments
The first author is very grateful for Ms. Touran Amini for her support. Also, the first author would like to express his sincere gratitude to Mr. Mohammad Mojallal for his helpful comments during this research. The project is supported by Iran National Science Foundation (INSF) (No. 97014783).
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Samadi, M., Sarkardeh, H. & Jabbari, E. Prediction of the dynamic pressure distribution in hydraulic structures using soft computing methods. Soft Comput 25, 3873–3888 (2021). https://doi.org/10.1007/s00500-020-05413-6
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DOI: https://doi.org/10.1007/s00500-020-05413-6