Soft sensor development based on deep extended variational autoencoder with just-in-time learning

doi:10.11949/0438-1157.20250798

Abstract

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

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

CLC Number:

TP 273

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.

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.

Figures/Tables 15

Fig.1 Diagram of VAE structure

Fig.2 Diagram of E-VAE structure

Fig.3 Diagram of DE-VAE structure

Fig.4 Schematic of the debutanizer process [33]

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/℃

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

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

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	—

Fig.6 The prediction results of butane concentration

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

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

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

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	—

Fig.9 Scatter diagram of SO2 concentration prediction results

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

References 34

[1]	Jia M W, Yang C, Pan Z X, et al. Adversarial relationship graph learning soft sensor via negative information exclusion[J]. Journal of Process Control, 2025, 145: 103354.
[2]	闫琳琦, 王振雷. 基于STA-BiLSTM-LightGBM组合模型的多步预测软测量建模[J]. 化工学报, 2023, 74(8): 3407-3418.
	Yan L Q, Wang Z L. Multi-step predictive soft sensor modeling based on STA-BiLSTM-LightGBM combined model[J]. CIESC Journal, 2023, 74(8): 3407-3418.
[3]	Liu Y, Jia M W, Xu D Y, et al. Physics-guided graph learning soft sensor for chemical processes[J]. Chemometrics and Intelligent Laboratory Systems, 2024, 249: 105131.
[4]	Sun Q Q, Ge Z Q. A survey on deep learning for data-driven soft sensors[J]. IEEE Transactions on Industrial Informatics, 2021, 17(9): 5853-5866.
[5]	Jia M W, Jiang L W, Guo B, et al. Physical-anchored graph learning for process key indicator prediction[J]. Control Engineering Practice, 2025, 154: 106167.
[6]	黎宏陶, 王振雷, 王昕. 基于即时学习的改进条件高斯回归软测量[J]. 化工学报, 2024, 75(6): 2299-2312.
	Li H T, Wang Z L, Wang X. Improved conditional Gaussian regression soft sensor based on just-in-time learning[J]. CIESC Journal, 2024, 75(6): 2299-2312.
[7]	Jia M W, Xu D Y, Yang T, et al. Graph convolutional network soft sensor for process quality prediction[J]. Journal of Process Control, 2023, 123: 12-25.
[8]	Hasnen S H, Shahid M, Zabiri H, et al. Semi-supervised adaptive PLS soft-sensor with PCA-based drift correction method for online valuation of NO _x emission in industrial water-tube boiler[J]. Process Safety and Environmental Protection, 2023, 172: 787-801.
[9]	王春鹏, 于佐军, 孟凡强. 折息移动窗递推PLS算法及其在聚丙烯生产过程中的应用[J]. 化工学报, 2013, 64(12): 4592-4598.
	Wang C P, Yu Z J, Meng F Q. Discount moving window recursive PLS algorithm and its application to process of polypropylene production[J]. CIESC Journal, 2013, 64(12): 4592-4598.
[10]	赵超, 戴坤成, 王贵评, 等. 基于AWLS-SVM的污水处理过程软测量建模[J]. 仪器仪表学报, 2015, 36(8): 1792-1800.
	Zhao C, Dai K C, Wang G P, et al. Soft sensor modeling for wastewater treatment process based on adaptive weighted least squares support vector machines[J]. Chinese Journal of Scientific Instrument, 2015, 36(8): 1792-1800.
[11]	He Y L, Li X Y, Ma J H, et al. Attribute-relevant distributed variational autoencoder integrated with LSTM for dynamic industrial soft sensing[J]. Engineering Applications of Artificial Intelligence, 2023, 119: 105737.
[12]	赵武灵, 满奕. 基于变分编码器的纳米纤维素分子结构预测模型框架研究[J]. 化工学报, 2024, 75(9): 3221-3230.
	Zhao W L, Man Y. Research on framework of nanocellulose molecular structure prediction model based on variational encoder[J]. CIESC Journal, 2024, 75(9): 3221-3230.
[13]	Hinton G E, Osindero S, Teh Y W. A fast learning algorithm for deep belief nets[J]. Neural Computation, 2006, 18(7): 1527-1554.
[14]	Jia M W, Zhou L, Liu Y, et al. Global dependency graph network for soft sensing in process industry[J]. IEEE Sensors Journal, 2024, 24(16): 26290-26300.
[15]	LeCun Y, Bengio Y, Hinton G. Deep learning[J]. Nature, 2015, 521(7553): 436-444.
[16]	Shang C, Yang F, Huang D X, et al. Data-driven soft sensor development based on deep learning technique[J]. Journal of Process Control, 2014, 24(3): 223-233.
[17]	Yao L, Ge Z Q. Deep learning of semisupervised process data with hierarchical extreme learning machine and soft sensor application[J]. IEEE Transactions on Industrial Electronics, 2018, 65(2): 1490-1498.
[18]	Jia M W, Yao Y, Liu Y. Review on graph neural networks for process soft sensor development, fault diagnosis, and process monitoring[J]. Industrial & Engineering Chemistry Research, 2025, 64(17): 8543-8564.
[19]	Yuan X F, Huang B, Wang Y L, et al. Deep learning-based feature representation and its application for soft sensor modeling with variable-wise weighted SAE[J]. IEEE Transactions on Industrial Informatics, 2018, 14(7): 3235-3243.
[20]	Yuan X F, Zhou J, Huang B, et al. Hierarchical quality-relevant feature representation for soft sensor modeling: a novel deep learning strategy[J]. IEEE Transactions on Industrial Informatics, 2020, 16(6): 3721-3730.
[21]	Tian Y, Zhu Q X, He Y L. Novel deep layers-extended autoencoder with correlation and its industrial soft sensing[J]. IEEE Transactions on Industrial Informatics, 2024, 20(1): 596-604.
[22]	Kingma D P, Welling M. Autoencoding variational bayes[J]. arXiv:.
[23]	Shen B B, Yao L, Ge Z Q. Nonlinear probabilistic latent variable regression models for soft sensor application: fom shallow to deep structure[J]. Control Engineering Practice, 2020, 94: 104198.
[24]	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[J]. 自动化学报, 2022, 48(2): 398-407.
	Cui L L, Shen B B, Ge Z Q. A mixture variational autoencoder regression model for soft sensor application[J]. Acta Automatica Sinica, 2022, 48(2): 398-407.
[25]	Wang C Z, Li Y G, Huang K K, et al. VAE4RSS: a VAE-based neural network approach for robust soft sensor with application to zinc roasting process[J]. Engineering Applications of Artificial Intelligence, 2022, 114: 105180.
[26]	Xu L, Xie L, Sun L, et al. A novel soft sensor modeling method based on gated stacked target-supervised VAE with variable weights[J]. Control Engineering Practice, 2025, 155: 106181.
[27]	Pan B, Jin H P, Wang L, et al. Just-in-time learning based soft sensor with variable selection and weighting optimized by evolutionary optimization for quality prediction of nonlinear processes[J]. Chemical Engineering Research and Design, 2019, 144: 285-299.
[28]	Jia M W, Liu Q, Jiang L W, et al. Just-in-time process soft sensor with spatiotemporal graph decoupled learning[J]. Chemometrics and Intelligent Laboratory Systems, 2025, 261: 105367.
[29]	Liu Q, Yin R D, Guo X W, et al. Locally spatiotemporal soft sensor for key indicator prediction in cement production process[J]. Chemical Engineering Science, 2025, 307: 121386.
[30]	Wu Y J, Liu D J, Yuan X F, et al. A just-in-time fine-tuning framework for deep learning of SAE in adaptive data-driven modeling of time-varying industrial processes[J]. IEEE Sensors Journal, 2021, 21(3): 3497-3505.
[31]	Pu Y C, Gan Z, Henao R, et al. Variational autoencoder for deep learning of images, labels and captions[C]//Proceedings of the 30th International Conference on Neural Information Processing Systems. ACM, 2016: 2360-2368.
[32]	Rani A, Singh V, Gupta J R P. Development of soft sensor for neural network based control of distillation column[J]. ISA Transactions, 2013, 52(3): 438-449.
[33]	Fortuna L, Graziani S, Rizzo A, et al. Soft Sensors for Monitoring and Control of Industrial Processes[M]. London: Springer London, 2007.
[34]	Fortuna L, Rizzo A, Sinatra M, et al. Soft analyzers for a sulfur recovery unit[J]. Control Engineering Practice, 2003, 11(12): 1491-1500.