Optimization of result of the "Cut-Glue" approximation method of experimental data using a swarm algorithm
Abstract
Optimization of result of the "Cut-Glue" approximation method of experimental data using a swarm algorithm
Incoming article date: 20.09.2018The construction of mathematical models of objects of experimental or computer simulation is associated with the mathematical processing of experimental data. The point dependences of the output variables for the input variables obtained for them are essentially nonlinear, piecewise, sometimes discontinuous. Approximation of such dependencies using polynomial expansions or spline functions is both difficult and involves large errors. A fundamentally new solution to this problem was proposed in the article. This method, called the "Cut-Glue" approximation method, is based on the partitioning of the modeled dependence into sections, the approximation of each section by polynomial dependencies, the multiplicative "excision" from each dependence of the fragments along the boundaries of the plot and the additive "gluing" them together into a single function - the model of the approximated dependence . The analyticity property of the resulting function allows to study the model and use it in models of vehicle dynamics. One of the stages of the "Cut-Glue" method is the "Glue" process - the additive "gluing" of fragments into a single function. For this, an auxiliary multiplicative function is used. The function of this function includes the steepness of the pulse fronts. In this paper, a developed modification of the method of burrowing particles is used in the problem of research and suboptimization of this parameter. As a test bench of the developed algorithm developed a special software tool.
Keywords: optimization, approximation, mathematical model, experimental data, heuristic methods, the method of burrowing particles