Design of Computational Models for Hydroturbine Units Based on a Nonparametric Regression Approach with Adaptation by Evolutionary Algorithms

This article deals with the problem of designing regression models for evaluating the parameters of the operation of complex technological equipment—hydroturbine units. A promising approach to the construction of regression models based on nonparametric Nadaraya–Watson kernel estimates is considered. A known problem in applying this approach is to determine the effective values of kernel-smoothing coefficients. Kernel-smoothing factors significantly impact the accuracy of the regression model, especially under conditions of variability of noise and parameters of samples in the input space of models. This fully corresponds to the characteristics of the problem of estimating the parameters of hydraulic turbines. We propose to use the evolutionary genetic algorithm with an addition in the form of a local-search stage to adjust the smoothing coefficients. This ensures the local convergence of the tuning procedure, which is important given the high sensitivity of the quality criterion of the nonparametric model. On a set of test problems, the results were obtained showing a reduction in the modeling error by 20% and 28% for the methods of adjusting the coefficients by the standard and hybrid genetic algorithms, respectively, in comparison with the case of an arbitrary choice of the values of such coefficients. For the task of estimating the parameters of the operation of a hydroturbine unit, a number of promising approaches to constructing regression models based on artificial neural networks, multidimensional adaptive splines, and an evolutionary method of genetic programming were included in the research. The proposed nonparametric approach with a hybrid smoothing coefficient tuning scheme was found to be most effective with a reduction in modeling error of about 5% compared with the best of the alternative approaches considered in the study, which, according to the results of numerical experiments, was the method of multivariate adaptive regression splines.