engleski

Non-Linear Mathematical Models based on Analytical Multiplicative-Additive Transformations Approximating Experimental Data

The paper presents the creation of the mathematical models from experimental data, which are nonlinear and multidimensional. Such approach is required in many computer-based simulations for the variety of technical objects. It is well known that the modern mathematical methods are not able to define, at the same time, both: the needed numerical accuracy and the analytical properties. The presented approximation method for the non- linear experimental data is highly accurate mathematical model, which contains interesting analytical properties. The method correctness has been validated analytically and experimentally for 1-dimensional and 2- dimensional objects. The method accuracy is based on the data “piecewise” approximation, i.e. their local fragmentation. However, in contrast to the “piecewise” approximation, the numerical model fragments are combined by multiplicative-additive transformation, and not by fulfilling the coordinate-logical conditions. Therefore, such numerical model has analytical properties, which are used in the mathematical transformations, as multiplicative transformation of the created analytic functions, called “cut out” functions. These functions are locally approximating the data fragments and have analytical properties, which enable them to be added, when the combined analytical model is defined. The method implementation consists of the following successive and relatively independent stages: (1) splitting the data array into fragments, (2) their polynomial approximation, (3) the multiplicative transformation of fragments and (4) their additive combination into only one analytical function. The proposed method is appropriate for the experimental mathematical modeling of complex non-linear objects, in particular, for their use in the physical and technical simulation processes. The authors envisage that this proposed method would be especially useful for the mathematical modeling of the physics occurring in turbulent flows.

nonlinear multidimensional mathematical models ; experimental data approximation ; multiplicative analytical transformations

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