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

doi:10.16383/j.aas.c210035

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.c210035

崔琳琳^{1, 2,},
沈冰冰^{1, 2,},
葛志强^{1, 2,}

1.
浙江大学控制科学与工程学院工业控制研究所杭州 310027
2.
浙江大学工业控制技术国家重点实验室杭州 310027

基金项目: 国家自然科学基金(62103362, 92167106), 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

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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
- 刊出日期: 2022-02-18

A Mixture Variational Autoencoder Regression Model for Soft Sensor Application

CUI Lin-Lin^{1, 2
,},
SHEN Bing-Bing^{1, 2
,},
GE Zhi-Qiang^{1, 2
,}

1.
Institute of Industrial Process Control, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027
2.
State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027

Funds: Supported by National Natural Science Foundation of China (62103362, 92167106), 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

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.
- 软测量 /
- 变分自编码器 /
- 高斯混合模型 /
- 混合变分自编码器回归模型 /
- 多模态工业过程
Abstract: Recently, variational autoencoder (VAE) has caught much attention from academia and industry owing to its superiority in probabilistic data description and feature extraction, and has been introduced into industrial applications such as process monitoring, diagnosis and soft sensor modeling. However, traditional soft sensing methods based on VAE use the Gaussian distribution as the distribution of latent variables, which limits their ability to model complex industrial process data, especially multimode data. To tackle this issue, a mixture variational autoencoder regression (MVAER) model is proposed and applied to soft sensor modeling for complex multimode industrial processes in this paper. Specifically, the proposed model maps multimode data to the latent space by nonlinear mapping and uses the Gaussian mixture model to describe the distribution of latent variables. Thus, the latent variables under each mode are learned to obtain the effective feature representation of the original data. Meanwhile, a regression model between latent features and key quality variables is established for soft sensor application. Case studies including a numerical example and a real-world industrial process are carried out to assess the performance of the MVAER model, which demonstrate the effectiveness and superiority of the proposed approach.
- Soft sensor /
- variational autoencoder /
- Gaussian mixture model /
- mixture variational autoencoder regression model /
- multimode industrial process

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图 1 VAE模型结构图

Fig. 1 Model structure of VAE

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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

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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

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图 4 数值算例的数据模式

Fig. 4 Data pattern of the numerical example

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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

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图 6 预测结果散点图

Fig. 6 The predicted scatter points of different models

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图 7 一段炉工艺流程图

Fig. 7 Flowchart of the primary reformer

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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

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图 9 预测误差图

Fig. 9 The prediction errors of different models

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图 10 预测结果散点图

Fig. 10 The predicted scatter points of different models

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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
变量参数	$\pi$	$\mu$	$\Sigma $	$Y({y_1})$关系
$k = 1$	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]	$\left[ \begin{aligned}{8.2}\;\;{ - 2.5}\\{ - 2.5}\;\;\;{6.0}\;\;\end{aligned} \right]$	${y_1} = {x_1}{x_2}$

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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

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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

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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

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