基于一致性约束与熵加权集成的污水处理半监督软测量方法

周金卫; 林勉; 吴菁; 唐莉丽; 陈建育; 董宏远; 陈妍; 刘乙奇

doi:10.11949/0438-1157.20260964

您当前的位置：

首页 >

文章列表页 >

基于一致性约束与熵加权集成的污水处理半监督软测量方法

智能过程工程 | 更新时间：2026-08-26

- 基于一致性约束与熵加权集成的污水处理半监督软测量方法
- Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble
- 化工学报 2026年
- 作者机构：
  
  1.贵州民族大学数据科学与信息工程学院，贵州贵阳 550025
  2.华南理工大学自动化科学与工程学院，广东广州 510641
- 作者简介：
  
  周金卫（2000—），男，硕士研究生，20240714001020@stu.gzmu.edu.cn
  吴菁（1988—），女，博士，副教授，ipicq@gzmu.edu.cn
- 基金信息：
  
  国家自然科学基金项目(12461077;62273151;62073145);贵州省教育厅自然科学研究项目([2023]012;[2023]061);贵州省教育厅自然科学基金项目(QJJ2022047);贵州省科技支撑计划项目(黔科合支撑[2026]一般 237,一般 184);贵州省高层次创新型人才项目(GCC[2023]027);贵州民族大学博士科研启动项目(GZMUZK[2024]QD11);海南省自然科学基金项目(623QN256);贵州省数据科学与计算智能科技创新人才团队项目(黔科合人才CXTD[2025]038);贵州省应用数学与算力算法全省重点实验室项目(黔科合平台ZSYS[2025]039)
- DOI：10.11949/0438-1157.20260964
  中图分类号： TP 277
- 收稿：2026-07-16，
  
  修回：2026-08-26，
  
  录用：2026-08-26，
- 稿件说明：
移动端阅览
周金卫, 林勉, 吴菁, 等. 基于一致性约束与熵加权集成的污水处理半监督软测量方法[J/OL]. 化工学报, 2026.

ZHOU Jinwei, LIN Mian, WU Jing, et al. Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble[J/OL]. CIESC Journal, 2026.
周金卫, 林勉, 吴菁, 等. 基于一致性约束与熵加权集成的污水处理半监督软测量方法[J/OL]. 化工学报, 2026. DOI： 10.11949/0438-1157.20260964.

ZHOU Jinwei, LIN Mian, WU Jing, et al. Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble[J/OL]. CIESC Journal, 2026. DOI： 10.11949/0438-1157.20260964.

摘要

针对污水处理过程中总氮(total nitrogen

TN)和五日生化需氧量(five-day biochemical oxygen demand

BOD

)等关键水质指标存在实验室检测滞后、标注样本稀缺以及过程噪声强等问题。提出一种基于一致性约束与熵加权集成的半监督软测量方法。按时间顺序划分外部训练集和测试集，在训练阶段采用指数移动平均和标准化预处理，以MiniRocket-Ridge构建多尺度动态基学习器；随后由双学习器交叉生成伪标签，利用内部真实标签验证集对增强候选模型进行结构保真度门控，接纳或回退候选模型，并依据各输出预测信息熵进行自适应融合，最终聚合多轮扰动结果完成预测。与最优全监督基线相比，TN和BOD

的均方根误差在模拟数据集上分别降低72.43%和79.44%，在真实污水处理厂数据上分别降低37.67%和32.46%。半监督策略比较和消融实验表明，MiniRocket和EWC-SS对性能提升贡献较大，熵加权与结构保真度门控进一步降低联合误差；SHapley 加性解释(SHapley Additive exPlanations

SHAP)分析显示主要变量贡献与污水处理过程机理一致。研究为标签获取代价高、过程动态复杂的污水处理软测量提供了一种准确、轻量且可解释的实现路径。

Abstract

To address issues such as delays in laboratory testing

a scarcity of labeled samples

and high process noise for key water quality indicators

including total nitrogen (TN) and five-day biochemical oxygen demand (BOD

)

in the wastewater treatment process

this study proposes a semi-supervised soft-measurement method based on consistency constraints and entropy-weighted integration. The external training and test sets are divided chronologically. During the training phase

exponential moving average and standardization are applied for preprocessing

and a multiscale dynamic basis learner is constructed using MiniRocket-Ridge; Subsequently

pseudo-labels are generated through cross-validation between the two learners

and the internal true-label validation set is used to perform structural fidelity gating on the enhanced candidate models to accept or reject them. The models are then adaptively fused based on the entropy values of their respective output predictions

and the prediction is finalized by agg

regating the results from multiple rounds of perturbation. Compared to the optimal fully supervised baseline

the RMSE for TN and BOD5 on the BSM2 dataset was reduced by 72.43% and 79.44%

respectively

and by 37.67% and 32.46% on real wastewater treatment plant data. Comparisons of semi-supervised strategies and ablation experiments indicate that MiniRocket and EWC-SS contribute significantly to performance improvements

while entropy weighting and structural fidelity gating further reduce the combined error; SHapley Additive Explanations (SHAP) analysis shows that the contributions of key variables are consistent with the mechanisms of the wastewater treatment process. This study provides an accurate

lightweight

and interpretable implementation approach for soft metrics in wastewater treatment

where label acquisition costs are high and process dynamics are complex.

关键词

Keywords

references

Venkatasubramanian V , Rengaswamy R , Yin K W , et al . A review of process fault detection and diagnosis Part I: Quantitative model-based methods [J ] . Computers & Chemical Engineering , 2003 , 27 ( 3 ): 293 - 311 .

Qin S J . Survey on data-driven industrial process monitoring and diagnosis [J ] . Annual Reviews in Control , 2012 , 36 ( 2 ): 220 - 234 .

Perera Y S , Ratnaweera D A A C , Dasanayaka C H , et al . The role of artificial intelligence-driven soft sensors in advanced sustainable process industries: a critical review [J ] . Engineering Applications of Artificial Intelligence , 2023 , 121 : 105988 .

Luttmann R , Bracewell D G , Cornelissen G , et al . Soft sensors in bioprocessing: a status report and recommendations [J ] . Biotechnology Journal , 2012 , 7 ( 8 ): 1040 - 1048 .

Mowbray M , Vallerio M , Perez-Galvan C , et al . Industrial data science–a review of machine learning applications for chemical and process industries [J ] . Reaction Chemistry & Engineering , 2022 , 7 ( 7 ): 1471 - 1509 .

Kadlec P , Gabrys B , Strandt S . Data-driven soft sensors in the process industry [J ] . Computers & Chemical Engineering , 2009 , 33 ( 4 ): 795 - 814 .

Kadlec P , Grbić R , Gabrys B . Review of adaptation mechanisms for data-driven soft sensors [J ] . Computers & Chemical Engineering , 2011 , 35 ( 1 ): 1 - 24 .

Haimi H , Mulas M , Corona F , et al . Data-derived soft-sensors for biological wastewater treatment plants: an overview [J ] . Environmental Modelling & Software , 2013 , 47 : 88 - 107 .

Ching P M L , So R H Y , Morck T . Advances in soft sensors for wastewater treatment plants: a systematic review [J ] . Journal of Water Process Engineering , 2021 , 44 : 102367 .

Bahramian M , Dereli R K , Zhao W Q , et al . Data to intelligence: the role of data-driven models in wastewater treatment [J ] . Expert Systems with Applications , 2023 , 217 : 119453 .

Ching P M L , Zou X , Wu D , et al . Development of a wide-range soft sensor for predicting wastewater BOD5 using an eXtreme gradient boosting (XGBoost) machine [J ] . Environmental Research , 2022 , 210 : 112953 .

Pisa I , Santín I , Vicario J L , et al . ANN-based soft sensor to predict effluent violations in wastewater treatment plants [J ] . Sensors , 2019 , 19 ( 6 ): 1280 .

Teh H Y , Kempa-Liehr A W , Wang K I . Sensor data quality: a systematic review [J ] . Journal of Big Data , 2020 , 7 ( 1 ): 11 .

Wang X Y , Wei W G , Yoo C , et al . Data-driven fault detection and diagnosis methods in wastewater treatment systems: a comprehensive review [J ] . Environmental Research , 2025 , 268 : 120822 .

Wu J , Tang L L , Jin S Q , et al . Modeling an adaptive hybrid soft sensor with co-training learning toward applications in wastewater treatment [J ] . Industrial & Engineering Chemistry Research , 2023 , 62 ( 41 ): 16841 - 16853 .

Li T Z , Gao S W , Dong X H . Semi-supervised soft sensor modeling based on reward mechanism [J ] . Measurement , 2025 , 247 : 116761 .

Li Y W , Jin H P , Dong S L , et al . Pseudo-labeling optimization based ensemble semi-supervised soft sensor in the process industry [J ] . Sensors , 2021 , 21 ( 24 ): 8471 .

Jin H P , Rao F H , Yu W Y , et al . Pseudo label estimation based on label distribution optimization for industrial semi-supervised soft sensor [J ] . Measurement , 2023 , 217 : 113036 .

Wang Y C , Jin H P , Chen X G , et al . Online-dynamic-clustering-based soft sensor for industrial semi-supervised data streams [J ] . Sensors , 2023 , 23 ( 3 ): 1520 .

Jin H P , Liu G K , Qian B , et al . Semi-supervised soft sensor development based on dynamic dimensionality reduction-assisted large-scale pseudo label optimization and sample-weighted quality-relevant deep learning [J ] . Chemical Engineering Science , 2024 , 298 : 120387 .

Ramírez-Sanz J M , Maestro-Prieto J A , Arnaiz-González Á , et al . Semi-supervised learning for industrial fault detection and diagnosis: a systemic review [J ] . ISA Transactions , 2023 , 143 : 255 - 270 .

Wu J , Zhou J W , Tang L L , et al . Tackling data scarcity in wastewater treatment resulting from time-delay: a semi-supervised collaborative MTN-MRR framework with batch consistency confidence [J ] . Water Research , 2026 , 292 : 125249 .

Blum A , Mitchell T . Combining labeled and unlabeled data with co-training [C ] // Proceedings of the Eleventh Annual Conference on Computational Learning Theory . Madison Wisconsin USA . ACM , 1998 : 92 - 100 .

Laine S , Aila T . Temporal ensembling for semi-supervised learning [EB/OL ] . 2016 : arXiv : 1610 . 02242 . https://arxiv.org/abs/1610.02242 https://arxiv.org/abs/1610.02242

Hochreiter S , Schmidhuber J . Long short-term memory [J ] . Neural Computation , 1997 , 9 ( 8 ): 1735 - 1780 .

Cho K , van Merriënboer B , Gulcehre C , et al . Learning phrase representations using RNN encoder–decoder for statistical machine translation [C ] // Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP) . Doha, QatarAssociation for Computational Linguistics , 2014 : 1724 - 1734 .

Bai S J , Kolter J Z , Koltun V . An empirical evaluation of generic convolutional and recurrent networks for sequence modeling [EB/OL ] . 2018 : arXiv : 1803 . 01271 . https://arxiv.org/abs/1803.01271 https://arxiv.org/abs/1803.01271

Vaswani A , Shazeer N , Parmar N , et al . Attention is all you need [J ] . Advances in Neural Information Processing Systems , 2017 , 30 : 5998 - 6008 .

Zhou H Y , Zhang S H , Peng J Q , et al . Informer: beyond efficient transformer for long sequence time-series forecasting [J ] . Proceedings of the AAAI Conference on Artificial Intelligence , 2021 , 35 ( 12 ): 11106 - 11115 .

Wu H X , Xu J H , Wang J M , et al . Autoformer: decomposition transformers with auto-correlation for long-term series forecasting [C ] // Neural Information Processing Systems ., 2021

Nie Y Q , Nguyen N H , Sinthong P , et al . A time series is worth 64 words: long-term forecasting with transformers [EB/OL ] . 2022 : arXiv : 2211 . 14730 . https://arxiv.org/abs/2211.14730 https://arxiv.org/abs/2211.14730

Hoerl A E , Kennard R W . Ridge regression: biased estimation for nonorthogonal problems [J ] . Technometrics , 1970 , 12 ( 1 ): 55 - 67 .

Jeppsson U , Pons M N , Nopens I , et al . Benchmark simulation model no 2: general protocol and exploratory case studies [J ] . Water Science and Technology , 2007 , 56 ( 8 ): 67 - 78 .

Nopens I , Benedetti L , Jeppsson U , et al . Benchmark Simulation Model No2: finalisation of plant layout and default control strategy [J ] . Water Science and Technology , 2010 , 62 ( 9 ): 1967 - 1974 .

Gernaey . Benchmarking of Control Strategies for Wastewater Treatment Plants [M ] . IWA Publishing , 2014 .

Jeppsson U , Alex J , Batstone D J , et al . Benchmark simulation models, quo vadis? [J ] . Water Science and Technology , 2013 , 68 ( 1 ): 1 - 15 .

Benedetti L , De Baets B , Nopens I , et al . Multi-criteria analysis of wastewater treatment plant design and control scenarios under uncertainty [J ] . Environmental Modelling & Software , 2010 , 25 ( 5 ): 616 - 621 .

Lundberg S M , Lee S I . A unified approach to interpreting model predictions [C ] // Neural Information Processing Systems ., 2017

Marco Tulio Ribeiro , Sameer Singh , Carlos Guestrin . " Why Should I Trust You "[C ] . Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 2016 : 1135 - 1144 .

Gupta R , Zhang L , Hou J Y , et al . Review of explainable machine learning for anaerobic digestion [J ] . Bioresource Technology , 2023 , 369 : 128468 .

Duarte M S , Martins G , Oliveira P , et al . A review of computational modeling in wastewater treatment processes [J ] . ACS ES&T Water , 2024 , 4 ( 3 ): 784 - 804 .

Alprol A E , Mansour A T , Ibrahim M E E , et al . Artificial intelligence technologies revolutionizing wastewater treatment: current trends and future prospective [J ] . Water , 2024 , 16 ( 2 ): 314 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于动态多核相关向量机的软测量建模研究

基于二次分解和优化TCN-BiGRU的污水处理出水TP/TN预测

基于数据分块策略的双流多采样率GRU软测量建模

基于XGBoost的多尺度时空特征融合软测量模型

融合即时学习的深层扩展VAE软测量建模方法