Explicit data-driven models for prediction of pressure fluctuations occur during turbulent flows on sloping channels
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ORIGINAL PAPER
Explicit data-driven models for prediction of pressure fluctuations occur during turbulent flows on sloping channels Mehrshad Samadi1 • Hamed Sarkardeh2 • Ebrahim Jabbari1
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Pressure fluctuations are among the favorite topics for hydraulic engineers due to their critical role in the design and safe operation of hydraulic structures. In this study, three explicit data-driven models, including Classification and Regression Trees (CART), Gene Expression Programming (GEP), and Multivariate Adaptive Regression Splines (MARS), are used. 0 These methods are applied to predict the pressure fluctuation intensity ðCP Þ, which occurs beneath a hydraulic jump on sloping channels using reliable experimental observations. The main features of the suggested data-driven models are their 0 capability to provide practical formulas for prediction of CP based on the dimensionless form of the effective parameters. The application of these models leads to the extraction of knowledge from data in the form of predictive formulas. In addition, to evaluate the accuracy and performance of the proposed models, some statistical indices and several validation 0 criteria are employed. The obtained results confirm that MARS predicts CP better than CART and GEP. Based on the 0 effective independent variables, MARS presents a simple predictive formula for the computation of CP . GEP-based equations use mathematical trigonometric functions that cause a more complicated and time-consuming process to predict 0 0 CP . However, the application of simple rules generated by CART enables hydraulic engineers to predict CP , easily and quickly. Keywords Multivariate adaptive regression splines Gene expression programming Decision trees Pressure fluctuation Hydraulic structures Turbulent flow
1 Introduction Turbulent flows are among the most challenging problems for hydraulic engineers due to their direct influences on the stability of hydraulic structures and their environmental
& Ebrahim Jabbari [email protected] Mehrshad Samadi [email protected]; [email protected] Hamed Sarkardeh [email protected] 1
School of Civil Engineering, Iran University of Science and Technology (IUST), P.O. Box 16765-163, Narmak, Tehran, Iran
2
Department of Civil Engineering, Hakim Sabzevari University, P.O. Box 961797648, Sabzevar, Iran
impacts (Sarkar et al. 2015; Esfahani and Keshavarzi 2013). A hydraulic jump is a common type of fully turbulent flow that may occur below spillways, weirs, control gates, and inside stilling basins. This process is accompanied by entrainment of air in the stream, large-scale turbulence, fluctuations of velocity and pressure, and formation of surface waves (Chanson 2015). The significance of pressure fluctuations is due to the occurrence probability of uplift, cavitation, the fatigue of material, and structural vibration (Sobani 2014). Historical severe damages of pressure fluctuations have been reported in Karnafuli, Mal
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