Piecewise approximation based on nonparametric modeling algorithms

In this research the issue of inertialess processes modeling is under study. The main modeling algorithm is the nonparametric recovery algorithm of the regression function. The algorithm allows to build a process model under conditions of low a priori information. This feature may be particularly important in modeling processes of large dimensions prevailing in the space industry. One important feature of the algorithm for nonparametric estimation of the regression function is that the accuracy of modeling using this algorithm highly depends on the quality of the observations sample. Due to the fact that in processes with large dimensions of input and output variable vectors observation sampling elements are in most cases unevenly distributed, the development of modifications to improve the quality of modeling is relevant. The modification of the nonparametric dual algorithm based on piecewise approximations has been developed. According to the proposed modification, the process area is divided into sub-areas and a nonparametric estimate of the regression function for each of these sub-areas is recovered. The proposed modification reduces the impact of some observation sampling features, such as sparseness or voids in observation samples on the quality of the built model. The computational experiments were carried out, during which a comparison was made between the classical algorithm of nonparametric estimation of regression function and the developed modification. As the computational experiments have shown, with uniform distribution of the sample elements of observations, the developed modification does not lead to the improvement of the quality of modeling. With a substantial uneven distribution of the observations sample elements, the developed modification resulted in a 2-fold improvement in the quality of the simulation. The results suggest that the proposed modification can be used to model complex technological processes, including those in the space industry.