Problem of identification of materials structures based on fractal representations

Abstract

The research work is devoted to the control of materials structures described on the basis of fractal representations. The formation of fractal structures of materials is carried out due to positive feedback. The article describes the first stage of the work – statements of the problem of identification of materials structures based on fractal representations. Many recent studies indicate the fractal nature of material structures, while the mechanisms of positive feedbacks are based on the generation of fractal structures. At the present stage, the fundamental physicochemical laws governing the emergence and transformation of material structures are developed and presented in such a way that it is difficult to use them for the synthesis of structure control algorithms. In other words, they do not meet the requirements of control models – they do not reflect the dependence of the output actions on external factors. Therefore, it seems useful to go along the path of creating fractal models of structures that are identification structures of materials and then development of control actions, in particular on the parameters of positive feedback for predicting and changing the material structure in the required direction. This corresponds to the method of control algorithms synthesis with an assessment of the control object state and choice of controller gain coefficient. In this work, the statements of the problem of identification images of natural materials structures are formulated. Firstly, fractal models are built using well-known (standard) fractals, and secondly, fractal models are generated using the fractal structure formation mechanism. In the future, these statements of the problem will be used to develop methods and algorithms for materials structuresidentification in various industries, including mining and metallurgical industries.