Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble

ZHOU Jinwei; LIN Mian; WU Jing; TANG Lili; CHEN Jianyu; DONG Hongyuan; CHEN Yan; LIU Yiqi

doi:10.11949/0438-1157.20260964

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Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble

更新时间：2026-08-26

- Semi-supervised soft sensor for wastewater treatment based on consistency constraints and entropy-weighted ensemble
- CIESC Journal (2026)
- 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：
- 基金信息：
- DOI：10.11949/0438-1157.20260964
  CLC： TP 277
- Received：16 July 2026，
  
  Revised：2026-08-26，
  
  Accepted：26 August 2026，
- 稿件说明：
移动端阅览
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：

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

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