高炉冶炼过程的分形特征辨识及其应用研究
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摘要
本文以河北邯钢7号高炉、山东莱钢1号高炉和山西新临钢6号高炉在线采集的铁水含硅量[Si]序列为样本，对高炉炉温波动的内在非线性单分形特征、多重分形特征进行了细致的辨识研究，并将辨识信息用于对铁水[Si]序列的拟合、预报和控制，有一定的理论价值和应用价值。
论文首先对高炉冶炼技术发展、高炉专家系统以及炉温预测模型发展的历史和现状做了概述。然后给出了研究复杂非线性系统内在分形特征的相关分形基础理论和方法。
论文第4章对铁水含硅量[Si]时间序列进行无方向的D检验，有方向的偏度、峰度检验，检验计算结果表明铁水[Si]不满足正态分布。通过Q检验证明高炉[Si]序列存在较强的线性自相关，通过AR模型“过滤”线性自相关后得到的残差序列并非无关，BDS检验证明残差序列存在较强的非线性相关，这说明铁水硅[Si]序列是一组复杂的“混合信号”。
为了进一步研究铁水[Si]序列的非线性关系，对3座不同容积的高炉数据进行了稳健的Hurst指数计算，得到邯钢7#、莱钢1#、新临钢6#高炉的Hurst指数分别为H=0.121、0.257、0.224。首次从理论上证明高炉是一类反持续性的系统，也常被称为“均值回复”，同时也说明铁水[Si]是一类长程负相关的分形时间序列。随后进一步测定了[Si]序列的轨迹分形维数D，并且发现它和前面的Hurst指数H基本满足关系式：D=2—H，两者均反映出铁水[Si]序列是具有很强的反持续性的分形时间序列。说明以往把铁水[Si]序列看成满足正态(或近似正态)分布的相关模型存在“先天性”缺陷。
论文第5章中引入Kantelhardt等人提出的MF-DFA方法来改进多重分形结构辨识方法，克服了原来方法对序列的诸多限制条件。随后分别计算了序列的广义Hurst指数、尺度函数、多重分形谱。三者的计算结果均表现出明显的时变特征，证明高炉炉温波动在不同时刻、不同幅度的波动部分具有明显多重分形结构特征。为什么高炉炉温的波动会表现出如此显著的分形特征?本章还对高炉炉温波动出现非线性分形特征的原因进行了深入探索，从冶炼过程能耗的非线性、碳元素的迭代反应形式与数学上的迭代函数系统的形式一致性、不同炉温调控手段到达时效的不一致性等多方面阐述了分形产生的原因。
在对分形特征详细辨识的基础上，第六章将辨识获取的量化信息引入分形拟合、预报模型。通过改进迭代函数系统(IFS)以及局部分段迭代函数系统(LIFS)的构造方法、垂直定比因子等关键参数的确定算法，进行铁水[Si]序列的拟合。再以历史数据为分形元，利用外推IFS构造分形预报模型，对邯钢7#高炉和莱钢1#高炉各50炉数据进行了仿真计算，得出两座高炉的铁水含硅量[Si]的命中率在[Si]±0.1％的范围内分别为86％和82％，命中率较高且该预报方法不存在收敛速度问题，计算速度快，有较高的理论价值和一定的应用价值。
在分析了高炉冶炼过程中状态变量：料速指数LS、透气指数FF以及控制变量：风量指数FQ、喷煤指数PM与高炉铁水含硅量[Si]的强相关性的基础上，论文第7章建立了基于混合动力学机理的混合控制偏微分方程并给出了混合控制方程的“粗糙求解”方法。半在线仿真研究取得了较好的控制效果，值得继续深入研究控制方程的更精确求解方法。第8章对全文的研究内容以及创新点做了归纳，并对本课题的后续研究做了展望。
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.
论文首先对高炉冶炼技术发展、高炉专家系统以及炉温预测模型发展的历史和现状做了概述。然后给出了研究复杂非线性系统内在分形特征的相关分形基础理论和方法。
论文第4章对铁水含硅量[Si]时间序列进行无方向的D检验，有方向的偏度、峰度检验，检验计算结果表明铁水[Si]不满足正态分布。通过Q检验证明高炉[Si]序列存在较强的线性自相关，通过AR模型“过滤”线性自相关后得到的残差序列并非无关，BDS检验证明残差序列存在较强的非线性相关，这说明铁水硅[Si]序列是一组复杂的“混合信号”。
为了进一步研究铁水[Si]序列的非线性关系，对3座不同容积的高炉数据进行了稳健的Hurst指数计算，得到邯钢7#、莱钢1#、新临钢6#高炉的Hurst指数分别为H=0.121、0.257、0.224。首次从理论上证明高炉是一类反持续性的系统，也常被称为“均值回复”，同时也说明铁水[Si]是一类长程负相关的分形时间序列。随后进一步测定了[Si]序列的轨迹分形维数D，并且发现它和前面的Hurst指数H基本满足关系式：D=2—H，两者均反映出铁水[Si]序列是具有很强的反持续性的分形时间序列。说明以往把铁水[Si]序列看成满足正态(或近似正态)分布的相关模型存在“先天性”缺陷。
论文第5章中引入Kantelhardt等人提出的MF-DFA方法来改进多重分形结构辨识方法，克服了原来方法对序列的诸多限制条件。随后分别计算了序列的广义Hurst指数、尺度函数、多重分形谱。三者的计算结果均表现出明显的时变特征，证明高炉炉温波动在不同时刻、不同幅度的波动部分具有明显多重分形结构特征。为什么高炉炉温的波动会表现出如此显著的分形特征?本章还对高炉炉温波动出现非线性分形特征的原因进行了深入探索，从冶炼过程能耗的非线性、碳元素的迭代反应形式与数学上的迭代函数系统的形式一致性、不同炉温调控手段到达时效的不一致性等多方面阐述了分形产生的原因。
在对分形特征详细辨识的基础上，第六章将辨识获取的量化信息引入分形拟合、预报模型。通过改进迭代函数系统(IFS)以及局部分段迭代函数系统(LIFS)的构造方法、垂直定比因子等关键参数的确定算法，进行铁水[Si]序列的拟合。再以历史数据为分形元，利用外推IFS构造分形预报模型，对邯钢7#高炉和莱钢1#高炉各50炉数据进行了仿真计算，得出两座高炉的铁水含硅量[Si]的命中率在[Si]±0.1％的范围内分别为86％和82％，命中率较高且该预报方法不存在收敛速度问题，计算速度快，有较高的理论价值和一定的应用价值。
在分析了高炉冶炼过程中状态变量：料速指数LS、透气指数FF以及控制变量：风量指数FQ、喷煤指数PM与高炉铁水含硅量[Si]的强相关性的基础上，论文第7章建立了基于混合动力学机理的混合控制偏微分方程并给出了混合控制方程的“粗糙求解”方法。半在线仿真研究取得了较好的控制效果，值得继续深入研究控制方程的更精确求解方法。第8章对全文的研究内容以及创新点做了归纳，并对本课题的后续研究做了展望。
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.
引文
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