Toward the accurate estimation of elliptical side orifice discharge coefficient applying two rigorous kernel-based data-intelligence paradigms

Masoud Karbasi,Iman Ahmadianfar,Amin Asadi,Mehdi Jamei

doi:10.1038/s41598-021-99166-3

Masoud Karbasi, Iman Ahmadianfar + Show 2 more

Open Access

https://doi.org/10.1038/s41598-021-99166-3

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Abstract

In the present study, two kernel-based data-intelligence paradigms, namely, Gaussian Process Regression (GPR) and Kernel Extreme Learning Machine (KELM) along with Generalized Regression Neural Network (GRNN) and Response Surface Methodology (RSM), as the validated schemes, employed to precisely estimate the elliptical side orifice discharge coefficient in rectangular channels. A total of 588 laboratory data in various geometric and hydraulic conditions were used to develop the models. The discharge coefficient was considered as a function of five dimensionless hydraulically and geometrical variables. The results showed that the machine learning models used in this study had shown good performance compared to the regression-based relationships. Comparison between machine learning models showed that GPR (RMSE = 0.0081, R = 0.958, MAPE = 1.3242) and KELM (RMSE = 0.0082, R = 0.9564, MAPE = 1.3499) models provide higher accuracy. Base on the RSM model, a new practical equation was developed to predict the discharge coefficient. Also, the sensitivity analysis of the input parameters showed that the main channel width to orifice height ratio (B/b) has the most significant effect on determining the discharge coefficient. The leveraged approach was applied to identify outlier data and applicability domain.

Highlights

In the present study, two kernel-based data-intelligence paradigms, namely, Gaussian Process Regression (GPR) and Kernel Extreme Learning Machine (KELM) along with Generalized Regression Neural Network (GRNN) and Response Surface Methodology (RSM), as the validated schemes, employed to precisely estimate the elliptical side orifice discharge coefficient in rectangular channels
This section discusses and evaluates the results obtained from Gaussian process regression (GPR), KELM, GRNN, and RSM models and regression-based models
The results obtained from the statistical parameters of the test dataset showed that all four machine learning models had performed well in estimating the elliptical side orifice discharge coefficient, and the R-value varies between 0.9580 for the GPR model to 0.9291 for the GRNN model

Summary

Introduction

Two kernel-based data-intelligence paradigms, namely, Gaussian Process Regression (GPR) and Kernel Extreme Learning Machine (KELM) along with Generalized Regression Neural Network (GRNN) and Response Surface Methodology (RSM), as the validated schemes, employed to precisely estimate the elliptical side orifice discharge coefficient in rectangular channels. Hussain et al.[22] reported an analytical and laboratory study on the hydraulic characteristics of flow-through side square orifices in rectangular open channels They provided a new discharge coefficient relationship based on the approach flow Froude number and ratio of orifice and channel width. Hussain et al.[23] conducted extensive laboratory and theoretical research on the performance of sharp-crested rectangular side orifice under the free-flow condition compared to square and circular side orifice. They found that the circular orifice is more efficient to divert flow than square side orifice by the same opening area. They developed their research in the aim of modifying the concept used by R amamurthy[15] in the derivation of discharge coefficient relationship for flow through lateral side rectangular orifice

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