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基于混合变分自编码器回归模型的软测量建模方法

崔琳琳 沈冰冰 葛志强

崔琳琳, 沈冰冰, 葛志强. 基于混合变分自编码器回归模型的软测量建模方法. 自动化学报, 2021, 45(x): 1−10 doi: 10.16383/j.aas.c200256
引用本文: 崔琳琳, 沈冰冰, 葛志强. 基于混合变分自编码器回归模型的软测量建模方法. 自动化学报, 2021, 45(x): 1−10 doi: 10.16383/j.aas.c200256
Cui Lin-Lin, Shen Bing-Bing, Ge Zhi-Qiang. A mixture variational autoencoder regression model for soft sensor application. Acta Automatica Sinica, 2021, 45(x): 1−10 doi: 10.16383/j.aas.c200256
Citation: Cui Lin-Lin, Shen Bing-Bing, Ge Zhi-Qiang. A mixture variational autoencoder regression model for soft sensor application. Acta Automatica Sinica, 2021, 45(x): 1−10 doi: 10.16383/j.aas.c200256

基于混合变分自编码器回归模型的软测量建模方法

doi: 10.16383/j.aas.c200256
基金项目: 国家自然科学基金(61833014), 浙江省自然科学基金(LR18F030001)资助
详细信息
    作者简介:

    崔琳琳:浙江大学控制科学与工程学院硕士研究生. 主要研究方向为工业软测量. E-mail: linlincui@zju.edu.cn

    沈冰冰:浙江大学控制科学与工程学院博士研究生. 主要研究方向为数据驱动建模, 过程数据分析和软测量应用. E-mail: shenbingbing@zju.edu.cn

    葛志强:浙江大学教授、博导. 主要研究方向为工业大数据、过程监测与故障诊断、软测量技术、智能系统与知识自动化. 本文通信作者. E-mail: gezhiqiang@zju.edu.cn

A Mixture Variational Autoencoder Regression Model for Soft Sensor Application

Funds: Supported by National Natural Science Foundation of China (61833014), the Natural Science Foundation of Zhejiang Province (LR18F030001)
More Information
    Author Bio:

    CUI Lin-Lin Master student at the Department of Control Science and Engineering, Zhejiang University. Her research interest covers industrial soft sensor

    Shen Bing-Bing Ph.D. candidate at the Department of Control Science and Engineering, Zhejiang University. Her research interest covers data-driven modeling, process data analysis and soft sensor applications

    GE Zhi-Qiang Professor and doctoral supervisor at Zhejiang University. His research interest covers industrial big data, process monitoring and fault diagnosis, soft sensor, intelligent system and knowledge automation. Corresponding author of this paper

  • 摘要: 近年来, 变分自编码器(Variational auto-encoder, VAE)模型由于在概率数据描述和特征提取能力等方面的优越性, 受到了学术界和工业界的广泛关注, 并被引入到工业过程监测、诊断和软测量建模等应用中. 然而, 传统基于VAE的软测量方法使用高斯分布作为潜在变量的分布, 限制了其对复杂工业过程数据, 尤其是多模态数据的建模能力. 为了解决这一问题, 本论文提出了一种混合变分自编码器回归模型(Mixture variational autoencoder regression, MVAER), 并将其应用于复杂多模态工业过程的软测量建模. 具体来说, 该方法采用高斯混合模型来描述VAE的潜在变量分布, 通过非线性映射将复杂多模态数据映射到潜在空间, 学习各模态下的潜在变量, 获取原始数据的有效特征表示. 同时, 建立潜在特征表示与关键质量变量之间的回归模型, 实现软测量应用. 通过一个数值例子和一个实际工业案例, 对所提模型的性能进行了评估, 验证了该模型的有效性和优越性.
  • 图  1  VAE模型结构图

    Fig.  1  Model structure of VAE

    图  2  混合变分自编码器回归模型结构图

    Fig.  2  Model structure of the MVAER model

    图  3  基于MVAER的软测量建模流程图

    Fig.  3  Flowchart for soft sensor modeling based on the MVAER model

    图  4  数值算例的数据模式

    Fig.  4  Data pattern of the numerical example

    图  5  PLS、GMR、AE、VAE和MVAER模型的预测结果图

    Fig.  5  Predicted results of PLS, GMR, AE, VAE and MVAER models

    图  6  预测结果散点图

    Fig.  6  The predicted scatter points of different models

    图  7  一段炉工艺流程图

    Fig.  7  Flowchart of the primary reformer

    图  8  PLS、GMR、VAE和MVAER模型的预测结果图

    Fig.  8  Predicted results of PLS, GMR, VAE and MVAER models

    图  9  预测误差图

    Fig.  9  The prediction errors of different models

    图  10  预测结果散点图

    Fig.  10  The predicted scatter points of different models

    表  1  数值算例的配置

    Table  1  Configuration of the numerical example

    变量参数$X({x_1},{x_2})$$Y({y_1})$关系
    $\pi$$\mu$$\Sigma $
    $k = 1$0.3[18 12]$\left[ \begin{aligned} \;\;{7.5}\;\; - 2.5\\{ - 2.5}\;\;\;{4.5}\;\;\end{aligned} \right]$${y_1} = 5{x_1}\sin {x_2}$
    $k = 2$0.4[1 10]$\left[ \begin{aligned} {4.5}\;\;{1.6}\\{1.6}\;\;{6.6}\end{aligned} \right]$${y_1} = {x_1} + x_2^2$
    $k = 3$0.4[12 5]$\left[ \begin{aligned}{8.2}\;\;{ - 2.5}\\{ - 2.5}\;\;\;{6.0}\;\;\end{aligned} \right]$${y_1} = {x_1}{x_2}$
    下载: 导出CSV

    表  2  PLS、GMR、AE、VAE和MVAER模型的性能评价指标

    Table  2  Performance evaluation indices of PLS, GMR, AE, VAE and MVAER models

    模型 PLS GMR AE VAE MVAER
    RMSE 33.2076 9.2463 25.0299 25.3014 6.1914
    R2 0.3964 0.9532 0.6571 0.6496 0.9797
    下载: 导出CSV

    表  3  一段炉过程变量描述

    Table  3  The description of the process instruments in the primary reformer

    标签 名称
    U1 燃料天然气流量
    U2 燃料尾气流量
    U3 E3出口燃料天然气压力
    U4 PR出口炉膛烟气压力
    U5 E3出口燃料尾气温度
    U6 PH出口燃料天然气温度
    U7 PR入口工艺气温度
    U8 PR顶部左侧炉膛烟气温度
    U9 PR顶部右侧炉膛烟气温度
    U10 PR顶部混合炉膛烟气温度
    U11 PR出口转换气温度
    U12 PR右侧出口转换气温度
    U13 PR出口转换气温度
    Y 炉内顶部氧气含量
    下载: 导出CSV

    表  4  PLS、GMR、VAE和MVAER模型的性能评价指标

    Table  4  Performance evaluation indices of PLS, GMR, VAE and MVAER models

    模型 PLS GMR VAE MVAER
    RMSE 1.7329 1.0844 1.1379 0.8940
    R2 0.6129 0.8484 0.8331 0.8970
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-13
  • 录用日期:  2021-04-16
  • 网络出版日期:  2021-05-30

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