“Cut-glue” Approximation based on evolutionary-genetic algorithm for essentially nonlinear parametric dependencies of mathematical models

Abstract

The paper presents the mathematical modeling of fragments by applying the polynomial regression to experimental data of arbitrary dimension. This approach aims to find out the minimal complexity polynomial structure defining the coefficients, which are optimized by the least squares criterion, enabling the error control when describing fragments. This mathematical formulation to approximate experimental data is essentially nonlinear as it uses piecewise approximation on small data fragments. The overall mathematical model requires maximum simplification when modeling each fragment, to ensure its small size and avoiding areas with high curvatures. The structural-parametric optimization for fragment models is implemented with a hybrid of classical regression analysis and a modified evolutionary-genetic algorithm, which varies and optimizes the polynomial structure describing the fragment. The specially developed software tool defines the optimal approximation for high-dimensional fragments, which usage in approximating fragments and the obtained results are demonstrated for real experimental data.