Robust Regularized RVFLNs Modeling of Molten Iron Quality in Blast Furnace Ironmaking
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摘要: 高炉炼铁过程运行优化与控制依赖于可靠、稳定的难测铁水质量(Molten iron quality, MIQ)指标模型.针对现有MIQ建模方法的不足, 本文提出一种新型的数据驱动鲁棒正则化随机权神经网络(Random vector functional-link networks, RVFLNs)算法, 用于实现MIQ指标在线估计的鲁棒建模.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方法从众多变量中提取与MIQ相关性最强的变量作为建模输入变量; 其次, 由于传统RVFLNs网络的输出权值由最小二乘估计获得, 易受离群数据影响而鲁棒性差, 引入基于Gaussian分布加权的M估计技术, 提出新型鲁棒RVFLNs算法建立多元MIQ指标的鲁棒模型; 同时, 在鲁棒加权后的最小二乘损失函数基础上, 进一步引入${L_1}$和${L_2}$两个正则化项以构成优化目标函数的Elastic net, 用于稀疏化RVFLNs网络的输出权值矩阵, 解决RVFLNs网络多重共线性和过拟合的问题.最后, 基于某大型高炉工业数据, 进行充分数据实验, 结果表明所提方法具有更高的建模与估计精度以及较强的鲁棒性能.
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关键词:
- RVFLNs /
- 鲁棒建模 /
- Gaussian分布加权M估计 /
- 高炉炼铁 /
- 铁水质量
Abstract: Optimal operation and control of a practical blast furnace (BF) ironmaking process depend largely on a reliable model of molten iron quality (MIQ) indices that can not be measured online. Aiming at the shortcomings of the existing MIQ modeling methods, a new data-driven robust regularized random vector functional-link networks (RVFLNs) algorithm is proposed to realize robust modeling of MIQ indices. First, to improve modeling efficiency and reduce computational complexity, the data-driven canonical correlation analysis (CCA) is employed to identify the most influential components from multitudinous factors that affect the MIQ indices to serve as the input variables. Next, since the output weights of traditional RVFLNs are obtained by the least squares approach, the robustness may decrease when the training dataset is contaminated with outliers. To solve this problem, the robust RVFLNs model of MIQ using Gaussian distribution weighted M-estimation is established. Simultaneously, on the basis of the least-square loss function of the robustness, the ${L_1}$ regularization and ${L_2}$ regularization are introduced to achieve sparse output weight and prevent the overfitting and multicollinearity of the RVFLNs model by forming the Elastic net that optimizes the objective function. Finally, experiments using industrial data from a large balst furnace have demonstrated that the proposed method produces a higher modeling, estimating accuracy and stronger robustness than other modeling methods.-
Key words:
- Random vector functional-link networks (RVFLNs) /
- robust modeling /
- Gaussian distribution weighted M-estimator /
- blast furnace ironmaking /
- molten iron quality (MIQ)
1) 本文责任编委 贺威 -
图 2 建模误差RMSE与输入权值倍数和输入偏置倍数之间的关系
Fig. 2 The relationship between the modeling RMSE and the input weight multiple and the input bias multiple
图 3 建模误差RMSE与正则化系数之间的关系曲线
Fig. 3 The relation curve between the modeling RMSE and the regularization coefficient
图 4 不同离群点比例时铁水质量估计RMSE箱形图
Fig. 4 The box diagram of the Estimation RMSE of MIQ indices with different methods at each of the outlier contamination rates
图 5 不同离群幅值时铁水质量估计RMSE箱形图
Fig. 5 The box diagram of the Estimation RMSE of MIQ indices with different methods when the amplitudes of the outliers are increased
图 6 离群比例为20%和离群幅值步长$a$为2时, 不同RVFLNs建模方法铁水质量指标建模效果
Fig. 6 Modeling results of MIQ indices with different methods when outlier contamination rate is twenty percent and amplitude is two
图 7 离群比例为20%和离群幅值步长$a$为2时, 不同RVFLNs建模方法铁水质量指标估计效果
Fig. 7 Estimation results of MIQ indices with different methods when outlier contamination rates is twenty percent and amplitude is two
图 8 不同RVFLNs建模方法铁水质量估计误差PDF曲线
Fig. 8 PDF curve of MIQ estimation error with different methods
图 9 不同RVFLNs建模方法铁水质量估计时网络输出权值为0的数量曲线
Fig. 9 The curve of the number of output weights with '0' value of MIQ estimation error with different methods
表 1 典型相关系数的显著性检验
Table 1 Significance test of canonical correlation coefficient
典型变量 显著性检验指标 Wilk's Chi-SQ DF Sig. 1 0.337 299.701 72 0 2 0.527 176.485 51 0 3 0.754 77.786 32 0 4 0.958 11.678 15 0.703 
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表 2 高炉本体参数典型变量的标准化系数
Table 2 Standardized canonical coefficients of BF body variables
影响变量 典型变量 变量权值 1 2 3 4 冷风流量 14.821 2.609 $-3.502$ $-24.047$ 11.95769 送风比 $-0.669 $ 1.803 0.658 3.633 1.695912 热风压力 0.724 2.664 $-2.139$ -0.209 2.885878 压差 2.749 1.384 $ -0.527$ 2.382 2.655439 顶压富氧率 $-0.06$ $ -0.712$ 0.95 -0.022 0.865848 透气性 5.292 5.441 $-6.701$ 10.201 9.263463 阻力系数 0.801 0.268 $ -4.063$ 8.006 2.505639 热风温度 0.587 $-0.469$ $ -1.356$ $-0.268$ 1.23674 富氧流量 11.697 $ -4.429$ 0.07 1.748 9.493758 富氧率 -5.751 3.556 $ -4.229$ $-4.556$ 7.362393 设定喷煤量 $-0.931$ 3.284 4.027 $ -0.233$ 4.222921 鼓风湿度 0.533 0.805 1.932 $-0.465$ 1.654862 理论燃烧温度 $-3.408$ 2.774 5.055 1.685 5.906544 标准风速 $-2.222$ $ -0.705$ 2.385 6.454 2.824337 实际风速 $ -0.224 $ 0.023 0.55 $-0.767$ 0.401351 鼓风动能 $-1.85 $ $-1.067$ $-0.255$ $-0.002$ 1.815443 炉腹煤气量 $ -14.106 $ $-6.874$ 0.208 15.053 12.34763 炉腹煤气指数 0.292 0.651 $-0.006$ $ -0.198$ 0.535663
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