Kernel function based regression approaches for estimating the oxygen transfer performance of plunging hollow jet aerator

Purpose: To evaluate the capability of various kernels employed with support vector regression (SVR) and Gaussian process regression (GPR) techniques in estimating the volumetric oxygen transfer coefficient of plunging hollow jets. Design/methodology/approach: In this study, a data set of 81 observations is acquired from laboratory experiments of hollow jets plunging on the surface of water in the tank. The jet variables: jet velocity, jet thickness, jet length, and water depth are varied accordingly and the values of volumetric oxygen transfer coefficient is computed. An empirical relationship expressing the oxygenation performance of plunging hollow jet aerator in terms of jet variables is formulated using multiple nonlinear regression. The performance of this nonlinear relationship is compared with various kernel function based SVR and GPR models. Models developed with the training data set (51 observations) are checked on testing data set (24 observations) for performance comparison. Sensitivity analysis is carried out to examine the influence of jet variables in effecting the oxygen transfer capabilities of plunging hollow jet aerator. Findings: The overall comparison of kernels yielded good estimation performance of Radial Basis Function kernel (RBF) and Pearson VII Function kernel (PUK) using the SVR technique which is followed by nonlinear regression, and other kernel function based regression models. Research limitations/implications: The results of the study pertaining to the performance of kernels are based on the current experimental conditions and the estimation potential of the regression models may fluctuate beyond the selection of current data range due to datadependant learning of the soft computing models. Practical implications: Volumetric oxygen transfer coefficient of plunging hollow jets can be predicted precisely using SVR model by employing RBF as kernel function as compared to empirical correlation and other kernel function based regression models. Originality/value: The comparative analysis of kernel functions is conducted in this study. In previous studies, the predictive modelling approaches are implemented in simulating the aeration properties of cylindrical solid jets only, while this paper simulates the volumetric oxygen transfer coefficient of diverging hollow jets with the jet variables by utilizing polynomial, normalized polynomial, PUK, and RBF kernels in SVR and GPR.