| With silicon content time series obtained from No.1 BF at Laiwu Steel, No.6 BF atLinfen Steel and No.7 BF at Hansteel as sample space, the single fractal andmulti-fractal characteristics of silicon content fluctuation are studied in detail. Theidentification information is used to fit, predict and control the silicon content series,and the simulation results are in good agreement with real data.To begin with-we provide a brief introduction to the development of iron-makingtechnique, BF expert system and predictive models of silicon content. This will befollowed by a description of theory and methods on research of fractal characteristicsin complex nonlinear systems.The next section gives some statistical tests on the silicon content series, includingD test without direction, skewness test and kurtosis test. The tests show that the [Si]series doesn't follow normal distribution. Further test like Q test has confirmed theexistence of strong linear correlation. Using an AR model to filter the linearcorrelation we get the residuals. A BDS test show there is strong nonlinear correlationin the residual series. Thus the silicon content series is proved to be a group ofcomplex "mixed signals".To further explore the nonlinear relation in the silicon content series, a robust Hurstindex computation is implemented for data from the above 3 blast furnaces. The Hurstindex for the 3 blast furnaces are 0.121 for No.7 BF at Hansteel, 0.257 for No.1 BF atLaiwu Steel and 0.224 for No.6 BF at Linfen Steel respectively. For the first time wehave proved that blast furnace is a kind of anti-continuous system, or a"mean-reverse'" system. It is also proved the silicon content series is a fractal serieswith negative long range correlation. Then the fractal dimension of silicon content Dis computed and it satisfies "D=2-H". This further confirms the existence of fractalcharacteristics in silicon content series. Thus we come to a conclusion that previousmodels based on the hypothesis of normal distribution have interior shortcomings.Section 5 introduces the MF-DFA method proposed by Kantelhardt to identify themulti-fractal structure of silicon content, so that the numerical constraints on timeseries of previous methods are discarded. The generalized Hurst index, scale functionand multi-fractal spectrum are then computed by MF-DFA. The results show blastfurnace silicon content is time variant and obvious multi-fractal characteristics existfor the fluctuation of silicon content at different time points and different range. Toexplain we study the blast furnace from the aspect of energy consumption and chemical reaction dynamics. The nonlinearity of energy consumption, the disunity ofiteration function for carbon reduction with its mathematical form and different timelags of control measures are among the reasons for the existence of fractalcharacteristics.On the basis of identification of fractal characteristics, section 6 proposes a fittingand predictive model. Techniques like improved iteration function system (IFS), localpiecewise iteration function system (LIFS) and vertical definite proportion factor areapplied to fitting the silicon content series. Take the historical data as fractal elementswe then expand the fitting model to construct the fractal predictive model. Simulationresults on data from NO. 7 blast furnace at Han Steel and No. 1 blast furnace at LaiwuSteel show the hit rates of silicon content are 86% and 82% on the range of[Si]±0.1%. The algorithm has fast convergence speed and it is valuable both fortheoretical research and practical application.Section 7 constructs the hybrid control partial differential function and give a"coarse solution" for the function after analysis of several main parameters in theprocess of iron-making like speed of materials LS, permeability FF, wind blasted FQand coal injected PM. It is proved that this method is worth further research. Section 8gives the conclusion and classifies the creative issues in this paper, also future workare discussed.
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