基于改进PatchTST的多步水质预测模型

doi:10.16088/j.issn.1001-6600.2025041802

摘要/Abstract

摘要： 随着城镇化和工业化进程的持续推进,水资源污染问题愈发凸显,提高水质预测模型的精度对有效管理水资源和保护生态环境至关重要。针对水质时间序列多步预测面临的复杂非线性关系建模与计算效率问题,本文提出一种改进PatchTST模型。该模型通过3个关键模块优化:1)设计轻量级CMixer编码器替代传统Transformer编码器,通过一维卷积和残差连接高效提取时序特征,降低计算负担;2)引入自适应中频能量优化器(AMEO),增强时序中频谱信息,提高对水质参数周期性变化的感知能力;3)设计基于切比雪夫多项式与Kolmogorov-Arnold表示定理的CKAHead预测头,增强对复杂非线性关系的建模能力。在长江流域宜宾市石门子断面溶解氧预测中,改进模型的MSE较PatchTST降低12.9%,较iTransformer降低14.0%,同时计算效率与资源消耗也得到平衡。此外,在5个不同监测断面的泛化验证中,48 h预见期任务上MSE较次优模型平均降低约10%。实验结果表明,改进模型有效提高了水质多步预测的精度与计算效率,对环境时间序列分析与水质预测研究有一定的参考价值。

关键词: 水质预测, 时序预测, PatchTST, 深度学习, 水质监测

Abstract: Water pollution issues in China are becoming increasingly prominent, making improvements in the accuracy of water quality prediction models crucial for effective water resource management and ecological protection. This study addresses the challenges of complex nonlinear relationship modeling and computational efficiency in multi-step water quality time series prediction by proposing an improved PatchTST model. The model incorporates three key module optimizations: 1) a lightweight CMixer encoder replacing the traditional Transformer encoder, which efficiently extracts temporal features through one-dimensional convolution and residual connections while reducing computational burden; 2) an Adaptive Mid-Frequency Energy Optimizer (AMEO) that enhances mid-frequency spectral information, improving the model’s ability to detect periodic changes in water quality parameters; and 3) a CKAHead prediction module based on Chebyshev polynomials and the Kolmogorov-Arnold representation theorem, strengthening the modeling of complex nonlinear relationships. In dissolved oxygen prediction at the Shimenzi section, the improved model achieves an MSE reduction of 12.9% compared with PatchTST and 14.0% compared with iTransformer, while maintaining a balance between computational efficiency and resource consumption. Furthermore, in generalization tests across five different monitoring sections, the model reduces MSE by approximately 10% compared with the next-best model for 48-hour forecasting tasks. Experimental results demonstrate that the improved model effectively enhances the accuracy and computational efficiency of multi-step water quality prediction, offering reference value for environmental time series analysis and water quality prediction research.

Key words: water quality prediction, time series forecasting, PatchTST, deep learning, water quality monitoring

中图分类号: X832; X52; TP391

罗缘, 朱文忠, 王文, 吴宇浩. 基于改进PatchTST的多步水质预测模型[J]. 广西师范大学学报（自然科学版）, 2026, 44(2): 115-131.

LUO Yuan, ZHU Wenzhong, WANG Wen, WU Yuhao. A Multi-step Water Quality Prediction Model Based on Improved PatchTST[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(2): 115-131.

参考文献

[1] YAN X, XIA Y Q, TI C P, et al.Thirty years of experience in water pollution control in Taihu Lake:a review[J].Science of the Total Environment, 2024, 914:169821.DOI:10.1016/j.scitotenv.2023.169821.
[2] 程浩淼, 杨富康, 张健, 等.基于机器学习的河湖水质评估的研究进展[J].环境科学, 2025, 46(6):3349-3360.DOI:10.13227/j.hjkx.202406089.
[3] 国家环境保护总局,国家质量监督检验检疫总局.地表水环境质量标准:GB 3838—2002[S].北京:中国环境科学出版社, 2002.
[4] XU C, LUO P C, WU P, et al.Detection of periodicity, aperiodicity, and corresponding driving factors of river dissolved oxygen based on high-frequency measurements[J].Journal of Hydrology, 2022, 609:127711.DOI:10.1016/j.jhydrol.2022.127711.
[5] 许泽婷, 余香英, 徐闯, 等.广东省7大流域地表水溶解氧分布特征及影响因素[J].水生态学杂志, 2025, 46(2):52-61.DOI:10.15928/j.1674-3075.202404030110.
[6] ANMALA J, TURUGANTI V.Comparison of the performance of decision tree (DT) algorithms and extreme learning machine (ELM) model in the prediction of water quality of the Upper Green River watershed[J].Water Environment Research, 2021, 93(11):2360-2373.DOI:10.1002/wer.1642.
[7] LU H F, MA X.Hybrid decision tree-based machine learning models for short-term water quality prediction[J].Chemosphere, 2020, 249:126169.DOI:10.1016/j.chemosphere.2020.126169.
[8] LI L, RONG S M, WANG R, et al.Recent advances in artificial intelligence and machine learning for nonlinear relationship analysis and process control in drinking water treatment:a review[J].Chemical Engineering Journal, 2021, 405:126673.DOI:10.1016/j.cej.2020.126673.
[9] LIANG W Z, LIU T C, WANG Y T, et al.Spatiotemporal-aware machine learning approaches for dissolved oxygen prediction in coastal waters[J].Science of the Total Environment, 2023, 905:167138.DOI:10.1016/j.scitotenv.2023.167138.
[10] 张建奇, 冯乐源, 李东鹤, 等.采用堆叠长短期记忆神经网络的水质连续预测方法[J].西安交通大学学报, 2025, 59(6):93-102.DOI:10.7652/xjtuxb202506010.
[11] 张海霞, 李瑞, 王霞, 等.基于VMD和GA-BiLSTM组合模型的河流水质预测[J].环境工程技术学报, 2025, 15(4):1181-1188.
[12] LIN Y Z, QIAO J F, BI J, et al.Transformer-based water quality forecasting with dual patch and trend decomposition[J].IEEE Internet of Things Journal, 2025, 12(8):10987-10997.DOI:10.1109/JIOT.2024.3514133.
[13] HUANG X Y, TANG J, SHEN Y M.Long time series of ocean wave prediction based on PatchTST model[J].Ocean Engineering, 2024, 301:117572.DOI:10.1016/j.oceaneng.2024.117572.
[14] YU G, LI Y, WANG J, et al.ReFocus:reinforcing mid-frequency and key-frequency modeling for multivariate time series forecasting[EB/OL].(2025-03-03)[2025-06-10].https://arxiv.org/abs/2502.16890.
[15] DONG C, ZHENG L W, CHEN W T.Kolmogorov-arnold networks (KAN) for time series classification and robust analysis[C]//Advanced Data Mining and Applications.Cham:Springer, 2025:342-355.DOI:10.1007/978-981-96-0840-9_24.
[16] CORDES D, LATIFI S, MORRISON G M.Systematic literature review of the performance characteristics of Chebyshev polynomials in machine learning applications for economic forecasting in low-income communities in sub-Saharan Africa[J].SN Business & Economics, 2022, 2(12):184.DOI:10.1007/s43546-022-00328-w.
[17] BHATT S, MISHRA A P, CHANDRA N, et al.Characterizing seasonal, environmental and human-induced factors influencing the dynamics of Rispana River’s water quality:Implications for sustainable river management[J].Results in Engineering, 2024, 22:102007.DOI:10.1016/j.rineng.2024.102007.
[18] LIU Y, WU H, WANG J, et al.Non-stationary transformers:exploring the stationarity in time series forecasting[J].Advances in neural information processing systems, 2022, 35:9881-9893.
[19] 杨信廷, 郭向阳, 韩佳伟, 等.基于TiDE-PatchTST模型的柑橘冷藏效率时序预测模型优化[J].农业机械学报, 2024, 55(7):396-404.DOI:10.6041/j.issn.1000-1298.2024.07.039.
[20] 王舒雨, 李豪, 马刚, 等.基于TCN和DLinear的光伏发电功率多步预测模型[J].电力建设, 2025, 46(4):173-184.DOI:10.12204/j.issn.1000-7229.2025.04.015.
[21] ZOU Y J, CHEN Y B, XU Y J, et al.Short-term freeway traffic speed multistep prediction using an iTransformer model[J].Physica A:Statistical Mechanics and Its Applications, 2024, 655:130185.DOI:10.1016/j.physa.2024.130185.
[22] 刘智锋, 王继民.可解释机器学习在信息资源管理领域的应用研究综述[J].数据分析与知识发现, 2024, 8(1):16-29.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed