基于最近邻与神经网络融合模型的软测量建模方法

doi:10.11949/0438-1157.20200401

摘要/Abstract

摘要：

软测量建模能够有效地解决生产过程中在线分析仪表测量滞后大、价格昂贵、维护保养复杂等问题。目前，基于数据驱动的神经网络是软测量建模的主要工具之一。而在建模数据的采集过程中，主导变量的采集相对辅助变量要困难得多，由此产生了大量缺失标签的数据。但传统的软测量建模方法却忽视了这些无标签数据，只利用少量的有标签数据建模，从而影响了模型的预测精度。为了解决标签缺失的问题，采用最近邻算法对无标签数据进行伪标记，同时设计了由卷积操作与门限循环单元神经网络（GRU）结合的网络结构来进一步利用无标签数据，提取不同时刻数据中的动态特征，提高神经网络的预测精度。最后将该方法应用于丙烯精馏塔塔顶丙烷浓度的预测，实验结果表明该模型能有效处理非线性动态系统的标签缺失问题，具有更高的预测精度。

关键词: 软测量, 动态建模, 过程系统, 最近邻算法, 门限循环单元神经网络

Abstract:

Soft-sensing modeling can effectively solve the problems of large measurement lag, high price, and complex maintenance of online analytical instruments in the production process. At present, neural network based on data-driven is one of the main tools of soft sensor. In the process of modeling data collection, the collection of dominant variables is much more difficult than that of auxiliary variables, resulting in a large amount of unlabeled data. However, traditional soft sensor modeling methods ignore these unlabeled data and only use a small amount of labeled data for modeling, which has negative effect on the prediction accuracy of the model. To solve the problem of label missing, the nearest neighbor algorithm is used to pseudo label the unlabeled data. At the same time, a network structure is designed by combining convolution operation and gated recurrent unit neural network (GRU) to further utilize the unlabeled data, extract the dynamic feature from data at different time, and improve the prediction accuracy of the neural network. Finally, the method is applied to the prediction of propane concentration on the top of propylene distillation column. The results show that the model can solve the problem of label missing in the nonlinear dynamic system and has higher prediction accuracy.

Key words: soft sensor, dynamic modeling, process systems, nearest neighbor algorithm, gated recurrent unit neural network

中图分类号:

TP 273

杨逸俊,王振雷,王昕. 基于最近邻与神经网络融合模型的软测量建模方法[J]. 化工学报, 2020, 71(12): 5696-5705.

YANG Yijun,WANG Zhenlei,WANG Xin. Soft sensor modeling method based on hybrid model of nearest neighbor and neural network[J]. CIESC Journal, 2020, 71(12): 5696-5705.

图/表 14

图1 HNN结构图

Fig.1 Structure of HNN

表1 KNN的伪代码

Table 1 Pseudocode of KNN

算法：KNN伪标记及组成新样本

输入：有标签数据集 $D l = x i, y i i = 1 l$ ；需要伪标记的无标签数据集

$D u = x j j = 1 u$ ；

KNN算法中的参数K；

1. for j = 1 : u

2. for i = 1 : l

3. 计算{x_j}与{x_i}间的欧几里德距离S_ji

4. end

5. 根据距离S_ji的大小对有标签数据集D_l进行升序排列

6. 选取前K个有标签数据，记录其距离与标签信息

{s₁,y₁},…,{s_K,y_K}

7. for k = 1 : K

8. $w k = e x p (- s k 2 / 2)$

9. end

10. $y j = ∑ k = 1 K w k y k ∑ k = 1 K w k$

11. end

12. 得到伪标记数据集 $D p = x j, y j j = 1 u$

输出：新数据集 $D K N N = D l ? D p$

表1 KNN的伪代码

Table 1 Pseudocode of KNN

算法：KNN伪标记及组成新样本

输入：有标签数据集 $D l = x i, y i i = 1 l$ ；需要伪标记的无标签数据集

$D u = x j j = 1 u$ ；

KNN算法中的参数K；

1. for j = 1 : u

2. for i = 1 : l

3. 计算{x_j}与{x_i}间的欧几里德距离S_ji

4. end

5. 根据距离S_ji的大小对有标签数据集D_l进行升序排列

6. 选取前K个有标签数据，记录其距离与标签信息

{s₁,y₁},…,{s_K,y_K}

7. for k = 1 : K

8. $w k = e x p (- s k 2 / 2)$

9. end

10. $y j = ∑ k = 1 K w k y k ∑ k = 1 K w k$

11. end

12. 得到伪标记数据集 $D p = x j, y j j = 1 u$

输出：新数据集 $D K N N = D l ? D p$

图2 GRU结构图

Fig.2 Structure of GRU

图3 卷积操作示意图

Fig.3 Schematic diagram of convolution operation

图4 HNN的建模流程图

Fig.4 Modeling flow chart of HNN

图5 HNN的在线预测示意图

Fig.5 Schematic diagram of HNN online prediction

图6 四种模型的预测效果比较

Fig.6 Comparison of prediction effects of four models

表2 四种模型的性能评估

Table 2 Performance evaluation of four models

Model	MSE	MAE	MAPE
NARX	3.1788	1.4757	219.5918
SVM	0.6522	0.7681	133.9137
GRU	0.0197	0.1083	15.0631
HNN	0.0026	0.0396	6.4383

图7 丙烯精馏塔示意图

Fig.7 Schematic diagram of propylene rectification tower

图8 NARX对丙烷浓度的预测结果

Fig.8 Prediction of propane concentration by NARX

图9 SVM对丙烷浓度的预测结果

Fig.9 Prediction of propane concentration by SVM

图10 GRU对丙烷浓度的预测结果

Fig.10 Prediction of propane concentration by GRU

表3 四种模型对丙烷浓度预测的性能评估

Table 3 Performance evaluation of four models for propane concentration prediction

Model	MSE	MAE	MAPE
NARX	7.1124 $×$ 10^-5	7.0758 $×$ 10^-3	2.4195
SVM	4.8657 $×$ 10^-5	4.7382 $×$ 10^-3	1.4910
GRU	3.6935 $×$ 10^-5	4.6781 $×$ 10^-3	1.5813
HNN	7.9529 $×$ 10^-6	1.9485 $×$ 10^-3	0.6479

表3 四种模型对丙烷浓度预测的性能评估

Table 3 Performance evaluation of four models for propane concentration prediction

Model	MSE	MAE	MAPE
NARX	7.1124 $×$ 10^-5	7.0758 $×$ 10^-3	2.4195
SVM	4.8657 $×$ 10^-5	4.7382 $×$ 10^-3	1.4910
GRU	3.6935 $×$ 10^-5	4.6781 $×$ 10^-3	1.5813
HNN	7.9529 $×$ 10^-6	1.9485 $×$ 10^-3	0.6479

图11 HNN对丙烷浓度的预测结果

Fig.11 Prediction of propane concentration by HNN

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