Paper:

# Research on Carbon-Monoxide Utilization Ratio in the Blast Furnace Based on Kolmogorov Entropy

## Dengfeng Xiao^{*}, Jianqi An^{**,†}, Min Wu^{**}, and Yong He^{**}

^{*}School of Information Science and Engineering, Central South University

Changsha 410083, China

^{**}School of Automation, China University of Geosciences

Wuhan 430074, China

^{†}Corresponding author

The accurate mastery of the Carbon-Monxide Utilization Ratio (CMUR) is a critical factor for reducing the energy consumption in the blast furnace (BF). Previous research of the CMUR focused on the mechanism model in which the CMUR is usually regarded as a random variable, and its analysis and prediction is seldom discussed. In this paper, a method for chaotic identifiability analysis by calculating Kolmogorov entropy is presented to study CMUR. The time series data of CMUR are selected from the two representative BFs as the example, and their Kolmogorov entropies are obtained based on the correlation integral algorithm. The results show that the value of the Kolmogorov entropy is finite and positive, which indicates the existence of chaos in the sample time series of the two BFs, and that the development process of the CMUR is corroborated to be a chaotic process. Furthermore, the predicted time scale of the CMUR development process is estimated by the obtained Kolmogorov entropy value.

- [1] Y. Kajiwara, T. Jimbo, T. Joko et al., “Investigation of bell-less charging based on full scale model experiments,” ISIJ Int., Vol.24, No.7, pp. 799-807, 1984.
- [2] W. H. Kim and D. J. Min, “A mass and energy estimation for the hydrogen utilization in the iron-making process,” Science China Technological Sciences, Vol.54, No.7, pp. 1655-1660, 2011.
- [3] S. R. Na, “Calculation and analysis of iron-making,” Beijing: Metallurgical Industry Press, 2010.
- [4] T. L. Guo, M. S. Chu, and Z. G. Liu, “Mathematical modeling and exergy analysis of blast furnace operation with natural gas injection,” J. of Iron and Steel Research Int., Vol.84, No.5, pp. 333-343, 2013.
- [5] J. Q. An, Y. F. Chen, and M. Wu, “A prediction method for carbon monoxide utilization ratio of blast furnace based on improved support vector regression,” J. of Chemical Industry and Engineering, Vol.66, No.1, pp. 206-214, 2015.
- [6] H. Helle, M. Helle, and H. Saxn, “Nonlinear optimization of steel production using traditional and novel blast furnace operation strategies,” Chemical Engineering Science, Vol.66, No.7, pp. 6470-6481, 2011.
- [7] H. Y. Wei, “The analysis and practice of gas utilization for blast furnace,” Efficiency of iron-making raw material and the practical seminar on new technology and new equipment, Annual Meeting, 2013.
- [8] C. H. Gao and J. X. Qian, “Time-dependent fractal characteristics on time series of silicon content in hot metal of blast furnace,” ISIJ Int., Vol.45, No.7, pp. 1269-1271, 2005.
- [9] C. H. Gao and Z. M. Zhou, “Chaotic analysis for blast furnace ironmaking process,” Acta Physica Sinica, Vol.54, No.4, pp. 1490-1493, 2005.
- [10] B. Yu, Y. H. Li, and P. Zhang, “Application of correlation dimension and kolmogorov entropy in aeroengine fault diagnosis,” J. of Aerospace Power, Vol.21, No.1, pp. 119-224, 2007.
- [11] G. B. Zhao and Y. F. Shi, “Computing fractal dimension and the kolmogorov Entropy from chaotic process,” Chinese J. of Computatioal Physics, Vol.16, No.3, pp. 309-315, 1999.
- [12] P. E. Rapp, “Filtered noised can mimicl low dimensional chaotic attractors,” Physical Review E, Vol.47, No.4, pp. 2289-2297, 1993.
- [13] A. Kraskov, H. Stogbauer, and P. Grassberger, “Estimating mutual information,” Physical Review E, Vol.69, No.5, pp. 6138-6146, 2004.
- [14] H. D. Navone and H. A. Ceceatto, “Forecasting chaos from small data sets: a comparison of different nonlinear algorithms,” J. of Physics A-Mathematical and General, Vol.28, No.12, pp. 3381-3388, 1995.
- [15] B. Sivakumar, “River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches,” J. of Hydrologic Engineering, Vol.66, No.8, pp. 225-245, 2002.
- [16] A. Ilhan, K. Mehmet, and A. Erhan, “An approach for automated fault diagnosis based on a fuzzy decision tree and boundary analysis of a reconstructed phase space,” ISA Trans., Vol.53, No.10, pp. 220-229, 2014.
- [17] F. Takens, “Detecting strange attractors in turbulence,” Lecture Notes in Mathematics, Vol.898, No.23, pp. 336-381, 1981.
- [18] Y. Fujimoto and T. Iokibe, “Determinism measurement in time series by chaotic approach and its applications,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.3, No.1, pp. 50-55, 1999.
- [19] H. L. Yang, H. Wang, and Y. Zhang, “Autocorrelation type, timescale and statistical property in financial time series,” Original Research Article. Physica A: Statistical Mechanics and its Applications, Vol.392, No.7, pp. 1681-1693, 2013.
- [20] Y. Yabuuchi and J. Watada, “Fuzzy autocorrelation model with confidence intervals of fuzzy random data,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.18, No.2, pp. 197-203, 2014.
- [21] A. M. Fraster, “Information and entropy in strange attrarcots,” IEEE Trans. on Information Theory, Vol.35, No.2, pp. 245-262, 1989.
- [22] A. Corana and C. Rolando, “An optimized direct algorithm to estimate the kolmogorov entropy from a time series,” Physics Letters A, Vol.207, No.1-2, pp. 77-82, 1995.
- [23] P. Grassberger and I. Procaccia, “Estimation of the kolmogorov entropy from a chaotic signa,” Physical Review E, Vol.28, No.4, pp. 2591-2593, 1983.