Nonlinear Subspace Modeling of Multivariate Molten Iron Quality in Blast Furnace Ironmaking and Its Application
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摘要: 高炉炼铁是一个物理化学反应复杂、多相多场耦合的大滞后、非线性动态系统，其关键工艺指标——铁水质量参数的检测、建模和控制一直是冶金工程和自动控制领域的难题.本文提出一种面向控制的数据驱动高炉炼铁多元铁水质量非线性子空间建模方法.首先，为了提高建模效率和降低计算复杂度，采用数据驱动典型相关性分析与相关性分析相结合的方法提取与铁水质量相关性最强的关键可控变量作为建模的输入变量；同时，为了更好地反映高炉非线性动态特性，将相关输入输出变量的时序和时滞关系在建模过程进行考虑；最后，采用基于最小二乘支持向量机（Least square support vector machine，LS-SVM）的非线性Hammerstein系统子空间辨识方法建立数据驱动的多元铁水质量非线性状态空间模型.同时，将核函数表示的模型非线性特性用多项式函数拟合，在仅损失很小模型精度的前提下大大降低模型的计算复杂度.基于实际数据的工业试验验证了所提建模方法的准确性、有效性和先进性.Abstract: Blast furnace ironmaking is a nonlinear dynamic process containing complex physical-chemical reaction, multi-phase multi-field coupling and large time delay. Measuring, modeling and control of the key process indices of ironmaking process, molten iron quality (MIQ) parameters, have always been treated as a difficult problem in metallurgic engineering and automation field. This paper presents a control oriented data-driven nonlinear subspace modeling method for multivariate prediction of MIQ. First, to improve modeling efficiency, data driven canonical correlation analysis (CCA) and correlation analysis (CA) are combined to pick out the most influential controllable variables from multitudinous factors to serve as the input variables of modeling. Second, to better reflect the nonlinear dynamic characteristics of blast furnace ironmaking process, the time series and time delays of the relevant input and output variables are taken into account. Finally, a data-driven nonlinear state-space model of MIQ is built using least square support vector machine (LS-SVM) based nonlinear subspace identification method for Hammerstein system. With polynomial fitting method, the nonlinear parts expressed by kernel functions in the obtained Hammerstein model are simplified, so as to greatly reduce the computational complexity of the model on the premise of only a small loss of accuracy. Industrial experiments based on real data verifies the accuracy, effectiveness and advancement of the proposed method.
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图 2 多元铁水质量参数非线性子空间建模策略
Fig. 2 Strategy diagram of multivariable nonlinear dynamic modeling for molten iron quality
图 4 基于非线性子空间辨识的多元铁水质量模型在多项式拟合非线性特性前后的建模结果
Fig. 4 Modeling results of molten iron quality prediction with and without polynomial ¯tting
图 5 模型在多项式拟合非线性特性前后对多元铁水质量参数的实际估计效果
Fig. 5 Estimation results of molten iron quality prediction with and without polynomial ¯tting
图 6 不同建模方法对多元铁水质量的实际估计效果对比
Fig. 6 Estimation results of molten iron quality prediction with di®erent models
图 7 不同模型估计误差自相关函数
Fig. 7 Autocorrelation function of estimating error of di®erent models
图 8 不同建模方法的估计值与实际值散点图
Fig. 8 Scatter diagram of estimated and actual value by di®erent models
图 10 多元铁水质量预测控制控制量曲线
Fig. 10 Control input curves of predictive control of molten iron quality parameters
表 1 典型相关分析结果
Table 1 The results of canonical correlation analysis
0.563[Si]-0.453[P]- 0.638[Si]+0.899[P]- -0.857[Si]-0.368[P]- 0.447[S]+0.287MIT 0.986[S]-0.518MIT 0.801[S]-0.398MIT 送风比 -1.103 -3.254 0.716 热风压力 0.587 -1.109 -1.493 顶压0 .974 -0.911 -0.320 压差 0.495 -7.118 2.506 顶压风量 -0.948 -0.794 3.185 透气性- 2.687 -4.104 -2.782 阻力系数 -2.702 6.501 -5.392 热风温度 -5.375 14.185 4.230 富氧流量 4.914 -4.014 -0.054 富氧率 -7.284 8.123 -0.377 设定喷煤量 0.998 -7.335 -3.443 鼓风湿度 0.096 0.208 -0.071 理论燃烧温度 3.789 -12.762 -5.639 标准风速 -0.439 -3.953 -0.717 实际风速 1.816 2.624 3.444 鼓风动能 -0.438 -4.662 -2.728 炉腹煤气量 -1.306 14.932 4.029 炉腹煤气指数 -0.176 -1.503 -0.335 
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表 2 两种模型对各个铁水质量指标估计的均方根误差和计算时间比较
Table 2 Comparison between two models in RMSE for molten iron quality prediction and computation time
RMSE Time (s) [Si] (%) [P] (%) [S] (%) MIT (±C) Kernel 0.0633 0.0032 0.0021 6.2388 0.01123 Polynomial 0.0664 0.0031 0.0022 6.6907 0.00061
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表 3 多元铁水质量估计值均方根误差比较
Table 3 RMSE for molten iron quality prediction
RMSE [Si] (%) [P] (%) [S] (%) MIT (±C) N-SM 0.0664 0.0031 0.0022 6.6907 L-SM 0.1584 0.0107 0.0073 8.4801 M-LS-SVR 0.0811 0.0058 0.0051 8.0037 RLS-ARMA 0.0721 0.0060 0.0044 7.2992
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