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基于数据驱动多输出ARMAX建模的高炉十字测温中心温度在线估计

周平 刘记平

周平, 刘记平. 基于数据驱动多输出ARMAX建模的高炉十字测温中心温度在线估计. 自动化学报, 2018, 44(3): 552-561. doi: 10.16383/j.aas.2018.c160840
引用本文: 周平, 刘记平. 基于数据驱动多输出ARMAX建模的高炉十字测温中心温度在线估计. 自动化学报, 2018, 44(3): 552-561. doi: 10.16383/j.aas.2018.c160840
ZHOU Ping, LIU Ji-Ping. Data-driven Multi-output ARMAX Modeling for Online Estimation of Central Temperatures for Cross Temperature Measuring in Blast Furnace Ironmaking. ACTA AUTOMATICA SINICA, 2018, 44(3): 552-561. doi: 10.16383/j.aas.2018.c160840
Citation: ZHOU Ping, LIU Ji-Ping. Data-driven Multi-output ARMAX Modeling for Online Estimation of Central Temperatures for Cross Temperature Measuring in Blast Furnace Ironmaking. ACTA AUTOMATICA SINICA, 2018, 44(3): 552-561. doi: 10.16383/j.aas.2018.c160840

基于数据驱动多输出ARMAX建模的高炉十字测温中心温度在线估计

doi: 10.16383/j.aas.2018.c160840
基金项目: 

中央高校基本科研业务费项目 N160805001

矿冶过程自动控制技术国家(北京市)重点实验室开放课题资助 BGRIMM-KZSKL-2017-04

国家自然科学基金 61333007

国家自然科学基金 61473064

国家自然科学基金 61290323

详细信息
    作者简介:

    刘记平  东北大学硕士研究生.2015年获得河南科技大学学士学位.主要研究方向为数据驱动建模与控制, 机器学习算法.E-mail:m18842388402@163.com

    通讯作者:

    周平  东北大学教授.分别于2003年、2006年和2013年获得东北大学学士、硕士和博士学位.主要研究方向为工业过程运行反馈控制, 数据驱动建模与控制.本文通信作者.E-mail:zhouping@mail.neu.edu.cn

Data-driven Multi-output ARMAX Modeling for Online Estimation of Central Temperatures for Cross Temperature Measuring in Blast Furnace Ironmaking

Funds: 

the Fundamental Research Funds for the Central Universities N160805001

the State (Beijing) Key Laboratory of Process Automation in Mining and Metallurgy BGRIMM-KZSKL-2017-04

National Natural Science Foundation of China 61333007

National Natural Science Foundation of China 61473064

National Natural Science Foundation of China 61290323

More Information
    Author Bio:

     Master student at Northeastern University. She received her bachelor degree from Henan University of Science and Technology in 2015. Her research interest covers data-driven modeling and control and machine learning algorithm

    Corresponding author: ZHOU Ping  Professor at Northeastern University. He received his bachelor, master and Ph. D. degrees from Northeastern University in 2003, 2006, and 2013, respectively. His research interest covers operation feedback control of industrial process, data-driven modeling and control. Corresponding author of this paper
  • 摘要: 高炉(Blast furnace,BF)炼铁中,十字测温作为炉顶温度和煤气流分布监测的最主要手段,对高炉的安全、稳定和高效运行起着重要作用.然而,由于高炉炉顶中心部位温度较高,造成十字测温装置中心位置传感器极易损坏,并且更换周期长,因而无法及时判断炉顶煤气流分布.针对这一实际工程问题,本文基于时间序列建模思想,集成采用多输出自回归移动平均(Multi-output autoregressive moving average,M-ARMAX)建模、因子分析、Pearson相关分析、基于赤池信息准则(Akaike information criterion,AIC)与模型拟合优度联合定阶等混合技术,提出一种模型结构简单、精度较高且易于工程实现的十字测温中心温度在线估计方法.首先,提出利用因子分析与Pearson相关分析相结合的稳健特征选择方法选取多输出建模输入变量.然后,采用样本均值消去法预处理采集的高炉样本数据,使其成为离散随机数.基于离散随机数,建立算法简单、易于工程实现的M-ARMAX温度模型:为了克服传统基于AIC阶数确定造成模型阶次高、结构复杂的问题,提出在AIC准则基础上进一步引入模型拟合优度来选取模型最小阶,可保证模型估计精度的同时降低模型阶次;同时,采用可快速收敛的递推最小二乘算法辨识M-ARMAX模型参数,并用残差分析方法检验模型.工业试验和比较分析表明:建立的M-ARMAX模型能够根据实时数据同时对十字测温装置多个中心温度点进行准确和稳定估计,且模型估计误差符合高斯白噪声特性.
    1)  本文责任编委 谢永芳
  • 图  1  高炉炼铁过程与十字测温装置

    Fig.  1  Blast furnace ironmaking process and cross temperature measuring device

    图  2  碎石图

    Fig.  2  Scree plot

    图  3  所有输入与主因子的Pearson相关系数

    Fig.  3  Pearson correlation coefficients between all inputs and the main factor

    图  4  不同阶次所对应的模型AIC值

    Fig.  4  The AIC value corresponding to different order

    图  5  参数收敛曲线

    Fig.  5  Parameter convergence curves

    图  6  所提方法十字测温中心温度建模效果

    Fig.  6  Modeling results of center temperature estimation model for cross temperature measuring

    图  7  建模散点图(左)及建模误差自相关函数(中)和PDF曲线(右)

    Fig.  7  Scatter diagram of modeling and autocorrelation function and PDF curve of modeling error

    图  8  不同建模方法下的十字测温中心温度估计效果对比

    Fig.  8  Estimation results of center temperature estimation model for cross temperature measuring with different method

    图  9  不同建模方法温度估计值与实际值散点图

    Fig.  9  Scatter diagram of estimated temperature and actual temperature by different models

    图  10  不同建模方法温度估计误差PDF曲线

    Fig.  10  PDF curve of temperature estimation error by different models

    表  1  KMO和Bartlett分析结果

    Table  1  The results of KMO and Bartlett analysis

    取样足够度的KMO度量 Bartlett的球形度检验
    近似卡方 df Sig.
    0.778 10 051.361 10 0
    下载: 导出CSV

    表  2  因子载荷矩阵

    Table  2  Factor loading matrix

    测温点 $T$5 $T$6 $T$15 $T$16 $T$17
    因子载荷 0.756 0.418 0.850 0.889 0.560
    下载: 导出CSV

    表  3  输入输出变量的Pearson相关系数

    Table  3  Pearson correlation coefficients between inputs and outputs

    温度点 $T$5 $T$6 $T$15 $T$16 $T$17
    $T$3 0.676** 0.131** 0.498** 0.299** 0.556**
    $T$4 0.860** 0.026 0.538** 0.296** 0.648**
    $T$8 0.631** 0.246** 0.462** 0.242** 0.591**
    $T$10 0.677** 0.141** 0.462** 0.325** 0.580**
    $T$20 0.487** 0.023 0.243** -0.021 0.411**
    顶温东南 0.684** 0.634** 0.656** 0.617** 0.467**
    顶温西北 0.786** 0.434** 0.734** 0.579** 0.691**
    顶温东北 0.616** 0.702** 0.612** 0.545** 0.545**
    顶温西南 0.788** 0.569** 0.737** 0.741** 0.620**
    **相关性在0.01显著. $T$1, $T$2, $\cdots, $ $T$21分别表示测温点1, 2, $\cdots$, 21.
    下载: 导出CSV

    表  4  不同阶次对应的模型拟合优度

    Table  4  The goodness of model fit value corresponding to different order

    模型阶次组合 (1, 1) (2, 1) (2, 2) (3, 3)
    模型拟合优度函数值 91.03 95.42 96.27 96.7
    模型阶次组合 (4, 1) (5, 1) (4, 4) (5, 5)
    模型拟合优度函数值 95.32 95.89 96.29 94.61
    下载: 导出CSV
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  • 收稿日期:  2016-12-26
  • 录用日期:  2017-05-06
  • 刊出日期:  2018-03-20

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