融合即时学习的深层扩展VAE软测量建模方法

doi:10.11949/0438-1157.20250798

摘要/Abstract

摘要：

传统基于深度学习的软测量建模方法缺乏在线更新机制，且随着网络层数增加易产生信息冗余，从而限制了模型预测性能的提升。针对上述问题，提出一种融合即时学习的深层扩展变分自编码器（deep extended variational autoencoder with just-in-time learning，JITL-DE-VAE），包括离线训练和在线更新两个阶段。首先，针对离线阶段多层VAE重构误差累积，以及特征提取中无效信息过多导致预测性能不佳的问题，引入基于关键变量指导的特征约束机制，构建扩展变分自编码器（extended variational autoencoder，E-VAE）提高特征提取的准确性。其次，在E-VAE基础上提出深层扩展变分自编码器（deep extended variational autoencoder，DE-VAE），将前一层的输入和隐藏特征共同作为下一层的输入，通过跨层信息整合策略显著增强特征利用效率。此外，在线更新阶段引入即时学习思想，基于最大互信息系数计算加权欧氏距离从历史数据库中检索相似样本，并根据样本相似度对损失函数进行动态加权以更新模型，从而提高模型对时变过程的自适应能力。最后，基于工业脱丁烷塔和硫回收过程数据开展了消融实验和对比实验，结果验证了所提方法的有效性和优越性。

关键词: 动态建模, 神经网络, 预测, 软测量, 变分自编码器, 即时学习, 模型更新

Abstract:

Traditional deep learning-based soft sensor modeling methods lack online updating mechanisms, and are susceptible to information redundancy as the network depth increases, thereby limiting further improvement in model prediction performance. To address these issues, a deep extended variational autoencoder with just-in-time learning (JITL-DE-VAE) is proposed, which consists of an offline training stage and an online updating stage. First, to mitigate the accumulation of reconstruction errors in multi-layer VAEs during the offline phase and impaired prediction performance caused by excessive invalid information in feature extraction, a key variable-guided feature constraint mechanism is introduced and an extended variational autoencoder (E-VAE) is constructed to improve feature extraction accuracy. Second, a deep extended variational autoencoder (DE-VAE) is proposed on the basis of E-VAE, which utilizes both the input and hidden features from the previous layer as inputs to the next layer, significantly enhancing the feature utilization efficiency through cross-layer information integration strategy. Moreover, a just-in-time learning strategy is introduced during the online updating stage to enhance model adaptability to time-varying processes, which calculates the weighted Euclidean distance metric based on the maximum information coefficient to retrieve similar samples from the historical database, and updates the model via a dynamically weighted loss function according to sample similarity. Finally, ablation experiments and comparative experiments were conducted using data from an industrial butane removal tower and sulfur recovery process. The results validate the effectiveness and superiority of the proposed method.

Key words: dynamic modeling, neural networks, prediction, soft sensor, variational autoencoder, just-in-time learning, model adaptation

中图分类号:

TP 273

熊晟杰, 谢莉, 徐梁, 曹余庆, 杨慧中. 融合即时学习的深层扩展VAE软测量建模方法[J]. 化工学报, 2025, 76(12): 6486-6496.

Shengjie XIONG, Li XIE, Liang XU, Yuqing CAO, Huizhong YANG. Soft sensor development based on deep extended variational autoencoder with just-in-time learning[J]. CIESC Journal, 2025, 76(12): 6486-6496.

图/表 15

图1 VAE结构图

Fig.1 Diagram of VAE structure

图2 E-VAE结构图

Fig.2 Diagram of E-VAE structure

图3 DE-VAE结构图

Fig.3 Diagram of DE-VAE structure

图4 脱丁烷塔流程图[33]

Fig.4 Schematic of the debutanizer process [33]

表1 脱丁烷塔工艺变量

Table 1 Process variables of the debutanizer column

输入变量	变量描述
u₁	顶部温度/℃
u₂	顶部压力/(kg/cm²)
u₃	塔顶回流量/(m³/h)
u₄	塔顶出料量/(m³/h)
u₅	塔板6温度/℃
u₆	塔底温度1/℃
u₇	塔底温度2/℃

表2 脱丁烷塔消融实验五种模型的评价指标

Table 2 Evaluation metrics of the five models for the debutanizer column ablation study

方法	RMSE	R²
VAE	0.0432	0.9537
E-VAE	0.0297	0.9759
DE-VAE	0.0121	0.9961
JITL-DE-VAE(ed)	0.0112	0.9972
JITL-DE-VAE	0.0093	0.9984

图5 脱丁烷塔消融实验输出误差箱形图

Fig. 5 Boxplot of output errors for the debutanizer column ablation study

表3 脱丁烷塔对比实验五种模型的评价指标

Table 3 Evaluation metrics of the five models for the debutanizer column comparative experiment

方法	RMSE	R²	RMSE降低幅度
SAE	0.0456	0.9342	79.6%
SQAE	0.0428	0.9456	78.3%
SVAE	0.0302	0.9720	69.2%
H-NPLVR	0.0289	0.9775	67.8%
JITL-DE-VAE	0.0093	0.9984	—

图6 丁烷浓度预测结果

Fig.6 The prediction results of butane concentration

图7 脱丁烷塔对比实验输出误差箱形图

Fig.7 Boxplot of output errors for the debutanizer column comparative experiment

图8 硫回收流程图[34]

Fig.8 Schematic of the sulfur recovery process [34]

表4 硫回收过程变量

Table 4 Process variables of the sulfur recovery

变量	描述	单位
u₁	MEA气体流	m³/s
u₂	初级空气流	m³/s
u₃	二级空气流	m³/s
u₄	SWS区域气体流	m³/s
u₅	SWS区域空气流	m³/s
y	SO₂浓度	mol/m³

表5 硫回收对比实验五种模型的评价指标

Table 5 Evaluation metrics of the five models for the sulfur recovery comparative experiment

方法	RMSE	R²	R²提升幅度
KPLS	0.0227	0.7041	19.7%
VWSAE	0.0232	0.7963	5.9%
H-NPLVR	0.0234	0.7832	7.6%
DE-VAE	0.0227	0.8285	1.8%
JITL-DE-VAE	0.0222	0.8438	—

图9 SO2浓度预测结果散点图

Fig.9 Scatter diagram of SO2 concentration prediction results

图10 SO2浓度测试集输出误差箱形图

Fig.10 Boxplot of output errors for SO2 concentration test set

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