Autoencoder and PCA Based RVFLNs Modeling for Multivariate Molten Iron Quality in Blast Furnace Ironmaking
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摘要: 针对随机权神经网络（Random vector functional-link networks，RVFLNs）建模存在的过拟合和泛化能力差的问题，集成自编码（Autoencoder）和主成分分析（Principal component analysis，PCA）技术，提出一种新型的改进RVFLNs算法，即AE-P-RVFLNs算法，用于建立高炉多元铁水质量在线估计的NARX（Nonlinear autoregressive exogenous）模型.首先，为了尽可能挖掘实际复杂工业数据中的有用信息和充分揭示输入数据之间的内在关系，采用Autoencoder前馈随机网络技术训练建模输入数据，并将训练得到的输出权值作为后续RVFLNs的输入权值；然后，引入PCA技术对RVFLNs的高维隐层输出矩阵进行降维，避免隐层输出矩阵多重共线性问题，从而解决由于隐层节点过多导致模型过拟合的问题；最后，基于所提AE-P-RVFLNs算法建立某大型高炉多元铁水质量在线估计的NARX模型.工业实验和比较分析表明：采用本文算法建立的多元铁水质量在线估计模型可有效提高运算效率和估计精度，尤其是避免常规RVFLNs建模存在的过拟合问题.Abstract: Aiming at the problems of overfitting and poor generalization capability of the conventional random vector functional-link networks (RVFLNs), this paper proposes a novel improved RVFLNs algorithm, named AE-P-RVFLNs, by combining hybrid techniques of autoencoder and principal component analysis (PCA), and applies it to nonlinear autoregressive exogenous (NARX) modeling of blast furnace ironmaking process for online estimation of multivariable molten iron quality indices. First, in order to find the useful information from the complex real industrial data and reveal the underlying relationship of input variables, autoencoder is introduced to train the input data and then calculate the output weights, which are treated as the input weights of the RVFLNs model. Then, PCA is used to reduce the dimension of hidden layer output matrix so as to avoid the multicollinearity problem in calculation and reduce the number of hidden nodes, which simplifies the network structure and gets rid of the overfitting problem caused by too many hidden nodes. Finally, the proposed AE-P-RVFLNs algorithm is used to establish the NARX model for online estimation of multivariable molten iron quality indices in blast furnace ironmaking. Industrial test and comparative analysis show that the developed model can not only effectively improve the operation efficiency and estimation accuracy, but also effectively solve the overfitting problem in conventional RVFLNs modeling.
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Key words:
- RVFLNs /
- AE-P-RVFLNs /
- autoencoder /
- principal component analysis (PCA) /
- NARX modeling /
- blast furnance /
- overfitting
1) 本文责任编委 贺威 -
图 5 基于AE-P-RVFLNs的多元铁水质量NARX模型建模结果
Fig. 5 Modeling results of multicomponent hot metal mass NARX model based on AE-P-RVFLNs
图 6 不同模型的多元铁水质量预测结果
Fig. 6 Comparison of multicomponent hot metal quality for difierent models
图 7 逐一增加隐层节点数时所提AE-P-RVFLNs训练集和测试集RMSE变化曲线
Fig. 7 The RMSE curve of the training set and test set of the proposed AE-P-RVFLNs when the number of hidden nodes is increased one by one
图 8 逐一增加隐层节点数时RVFLNs训练集和测试集RMSE变化曲线
Fig. 8 The RMSE curve of training set and test set of RVFLNs when the number of hidden nodes is increased one by one
图 9 逐一增加隐层节点数时AE-RVFLNs训练集和测试集RMSE变化曲线
Fig. 9 The RMSE curve of training set and test set of AE-RVFLNs when the number of hidden nodes is increased one by one
图 10 逐一增加隐层节点数时P-RVFLNs训练集和测试集RMSE变化曲线
Fig. 10 The RMSE curve of training set and test set of P-RVFLNs when the number of hidden nodes is increased one by one
表 1 PCA求取的各主成分特征值、方差贡献率以及累积方差贡献率
Table 1 PCA to obtain the principal component eigenvalues, variance contribution rate and cumulative variance contribution rate
主成分 特征值 方差贡献率(%) 累计方差贡献率(%) 1 7.467 46.666 46.666 2 4.205 26.279 72.945 3 1.951 12.196 85.141 4 1.130 7.063 92.204 5 0.683 4.268 96.472 6 0.360 2.251 98.723 7 0.140 0.874 99.597 8 0.034 0.211 99.809 9 0.020 0.126 99.935 10 0.004 0.024 99.959 11 0.003 0.021 99.980 12 0.001 0.009 99.989 13 0.001 0.006 99.995 14 0.001 0.004 99.999 15 0.000 0.001 100.000 16 0.000 0.000 100.000 
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表 2 因子载荷矩阵(由PCA提取的6个主成分)
Table 2 Factor load matrix (Six principal components extracted by PCA)
物理变量 主成分 1 2 3 4 5 6 冷风流量 0.816 -0.449 0.310 -0.180 0.004 0.032 送风比 0.813 -0.445 0.320 -0.179 0.007 0.041 热风压力(kPa) 0.186 0.250 0.897 0.133 0.159 -0.045 透气性 0.625 -0.318 -0.549 -0.347 -0.110 0.000 阻力系数 -0.786 0.226 0.526 0.071 0.133 -0.081 热风温度(℃) 0.161 0.958 -0.021 -0.177 0.141 -0.045 富氧流量 0.797 0.221 -0.175 0.525 -0.090 -0.036 富氧率 0.781 0.242 -0.188 0.534 -0.093 -0.037 设定喷煤量(m3/h) -0.049 0.868 0.040 0.067 -0.064 0.480 鼓风湿度(RH) 0.105 -0.512 -0.362 0.200 0.737 0.111 理论燃烧温度(℃) 0.747 0.580 -0.080 0.094 0.080 -0.286 炉顶压力(kPa) 0.813 -0.452 0.312 -0.181 0.003 0.033 实际风速 0.526 0.763 -0.119 -0.321 0.139 -0.028 鼓风动能 0.681 0.623 -0.049 -0.346 0.132 -0.018 炉腹煤气量(kg/t) 0.967 -0.138 0.158 0.105 -0.024 0.082 炉腹煤气指数 0.958 -0.129 0.162 0.100 -0.026 0.102
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表 3 不同算法相关统计指标比较
Table 3 Comparison of statistical indicators for difierent algorithms
算法 运算 RMSE MAPE (%) 时间 [Si] [P] [Si] MIT [Si] [P] [S] MIT RVFLNs 0.002269 0.1172 0.0080 0.0056 9.8078 5.1192 5.4152 4.5631 5.4759 P-RVFLNs 0.001457 0.1464 0.0087 0.0065 10.0500 4.8998 4.4591 5.9490 5.1976 AE-RVFLNs 0.002027 0.1307 0.0135 0.0064 11.4555 6.8174 6.0327 6.6126 7.4414 AE-P-RVFLNs 0.001358 0.1124 0.0071 0.0054 9.0443 4.5551 2.9175 3.0825 4.6068
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