By the definition of the metric object identification

Abstract

Formulation of the problem. As the studies found in basic and applied sciences, they can be interpreted as a search space metric state identification object (SSOI). In carrying out this research, increasing the complexity of its perception. This leads to the appearance of problems of identification, for which the existing methods, for example mathematical programming, are unsuitable, since they use mathematical causes serious difficulties. To overcome these difficulties, usually injected a single metric, which is completely arbitrary choice, which often leads to serious losses in the accuracy of identification, as "... some forces in nature follow one other of its special geometry" [1]. Results and discussion. Nonconservation SSOI measures, leads to the definition of its nonergodicity. The latter initiates the modification of "mathematical space", ie the construction of new, abstract schemes. Out of this situation, some researchers have found in the application of fractal geometry to identify the language. For greater reliability of the results may be that the sensitivity of the fractal dimension is determined in several randomly selected points SSOI. If the difference is obtained at these points exceeds the error indications, with which it is determined, the identifiable structure - fractal. Determine the sensitivity of micro-hardness of ferrite grains St3ps steel (0,16 % C) to their fractal dimension. Despite the fact that the steel structure of the entire cross section of the section of ferrite-pearlite properties, calculated in the three fiducial points, differ from each other, as evidenced by the change of the fractal dimension of its components. Sensitivity values 1,333...2,500 an order of magnitude higher than the values of error in determining the fractal dimension 0,1...0,3, which indicates the possibility of applying fractal theory to register qualitative transformation of the metal. Conclusions. This example confirms the fact that the structure is a steel St3ps fractal under consideration and may increase when reaching the threshold of sensitivity serve as an indicator of quality characteristics of the metal.