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ARIMA-Based Forecasting of Wastewater Flow Across Short to Long Time Horizons

Author

Listed:
  • Jiawen Ye

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Xulai Meng

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Haiying Wang

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Qingdao Zhou

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Siwei An

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Tong An

    (School of Science, China University of Geosciences (Beijing), Beijing 100083, China)

  • Pooria Ghorbani Bam

    (Department of Civil & Environmental Engineering, University of California, Irvine, CA 92697-2175, USA)

  • Diego Rosso

    (Department of Civil & Environmental Engineering, University of California, Irvine, CA 92697-2175, USA
    Water-Energy Nexus Center, University of California, Irvine, CA 92697-2175, USA)

Abstract

Improving urban wastewater treatment efficiency and quality is urgent for most cities. The accurate wastewater flowrate forecast of a wastewater treatment plant (WWTP) is crucial for cutting energy use and reducing pollution. In this study, two hybrid models are proposed: ARIMA–Markov and ARIMA–LSTM–Transformer. Using 5 min-interval inlet flowrate data from a WWTP in 2024, the two models were verified and compared. Forecasts for 1 day, 7 days, and 2 months ahead were made, and model accuracies were compared. Ten repetitions with the same dataset assess stability, and ARIMA–LSTM–Transformer, with better performance, were selected. Then, the Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO) algorithm, and Sparrow Search Algorithm (SSA) were used for optimization, with the WOA excelling in accuracy and stability. Experimental results show that compared to the single model Transformer, WOA–ARIMA–LSTM–Transformer did better in forecasting wastewater flowrate. The combined model enables efficient and accurate wastewater flowrate forecasting, highlighting the combined model’s application potential.

Suggested Citation

  • Jiawen Ye & Xulai Meng & Haiying Wang & Qingdao Zhou & Siwei An & Tong An & Pooria Ghorbani Bam & Diego Rosso, 2025. "ARIMA-Based Forecasting of Wastewater Flow Across Short to Long Time Horizons," Mathematics, MDPI, vol. 13(13), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2098-:d:1688063
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    References listed on IDEAS

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    1. Cui, Xuyang & Zhu, Junda & Jia, Lifu & Wang, Jiahui & Wu, Yusen, 2024. "A novel heat load prediction model of district heating system based on hybrid whale optimization algorithm (WOA) and CNN-LSTM with attention mechanism," Energy, Elsevier, vol. 312(C).
    2. Xu Chen & Kai Zhang & Zhenning Ji & Xiaoli Shen & Piyang Liu & Liming Zhang & Jian Wang & Jun Yao, 2023. "Progress and Challenges of Integrated Machine Learning and Traditional Numerical Algorithms: Taking Reservoir Numerical Simulation as an Example," Mathematics, MDPI, vol. 11(21), pages 1-44, October.
    3. Jiachen Wang & Zuojing Zhang & Shihong Yue, 2025. "A Validity Index for Clustering Evaluation by Grid Structures," Mathematics, MDPI, vol. 13(6), pages 1-13, March.
    4. Ji-Hee Yu & Yoon-Ju Choi & Seung-Hwan Seo & Seong-Gyun Choi & Hye-Yoon Jeong & Ja-Eun Kim & Myung-Sun Baek & Young-Hwan You & Hyoung-Kyu Song, 2025. "Improved Connected-Mode Discontinuous Reception (C-DRX) Power Saving and Delay Reduction Using Ensemble-Based Traffic Prediction," Mathematics, MDPI, vol. 13(6), pages 1-18, March.
    5. Zizhen Yang & Wei Li & Fang Yuan & Haifeng Zhi & Min Guo & Bo Xin & Zhilong Gao, 2025. "Hybrid CNN-BiLSTM-MHSA Model for Accurate Fault Diagnosis of Rotor Motor Bearings," Mathematics, MDPI, vol. 13(3), pages 1-28, January.
    6. Salam Rabindrajit Luwang & Anish Rai & Md. Nurujjaman & Om Prakash & Chittaranjan Hens, 2024. "High-Frequency Stock Market Order Transitions during the US-China Trade War 2018: A Discrete-Time Markov Chain Analysis," Papers 2405.05634, arXiv.org.
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