фрактальна розмірність

Localization of steel fractures based on the fractal model of their metallographic images

There are a number of tasks that require assessment of the condition of the material and its mechanical characteristics. Such tasks may arise at the production stage, when there’s a need to control the content of various components of the material, strength, hardness, etc. Also similar tasks arise during exploitation of materials, which is especially relevant today, when most of the responsible products and structures in the field of nuclear energy, chemical industry, machine-building industry are on the verge of wearing down.

Hurst exponent evaluated via calculated by box-counting method on short time series example fractal dimension

The three versions of box counting algorithm for determining the fractal dimension of a spreadsheet Ms Excel is implemented. Values of Hearst exponent have been obtained for ten short individual time series, by the designed algorithm, based on the equation D = 2-H. The values of Hearst exponent received by means of general methods are given. The research results prove that the exact value of the fractal dimension and Hearst exponent can be obtained using the third version of the algorithm.