FRACTAL ANALYSIS OF REAL DATA ON THE CHEMICAL COMPOSITION OF CAST IRON AT THE OUTPUT OF A BLAST FURNACE

Abstract

The characteristic features of blast furnace production include: – the random nature of changes over time in the physical and chemical properties of the charge materials; – a large number of factors (especially uncontrolled ones) that affect the final result of blast furnace melting. The goal of the work. The specified features make it necessary to conduct studies of the properties of time series, which present the results of the chemical analysis of cast iron at the release. Such studies are necessary for the development of recommendations for the creation of methods for forecasting the chemical composition of cast iron under the conditions of current production, adequate to the nature of the predicted process. Methodology. As a rule, time series are random changes in values that allow us to consistently visualize the evolution of complex systems based on the received data (Boffetta, Cencini, Falconi, Vulpiani, 2002). Such an analysis comes to the calculation of correlation functions of state vectors - time sequences of values characterizing the system. The most common methods use correlation and spectral analyses, data smoothing and filtering, autoregression and forecasting models ( Tiuryn, Makarov, 1998; Kornienko, Gerasina, Gusev, 2013). Statistical analysis is very often based on the assumption that the studied system is random, the causal process, that created the time series and has many constituent parts or degrees of freedom. The interaction of these components is so complex that a deterministic explanation is impossible. At the same time, the object of research is a class of models that correspond to the class of a random Gaussian process. However, many real time series are characterized by invariance of scale transformations (property of self-similarity), due to which standard Gaussian statistics are untenable and the problem of studying time series comes to the analysis of stochastic self-similar processes that can be described by fractal sets (Mandelbrot, 2002; Feder, 1991). Scientific novelty. This research involves substantiating the hypothesis about the fractal nature of time series, which present the results of chemical analysis of cast iron at the output of a blast furnace.