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Decomposed intrinsic mode functions and deep learning algorithms for water quality index forecasting

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Abstract

The water quality index (WQI) serves as a global representation of river water quality (WQ). Existing studies related to the WQI have mainly focused on two aspects: (i) a WQI point estimation using multiple WQ inputs; and (ii) a one-step-ahead WQI forecasting with datasets of lower temporal resolution. These approaches, however, are limited in their ability to forecast future trends of the WQI for timely and prompt responses to pollution events. In this study, the deep learning algorithms, namely the long short-term memory (LSTM) and the gated recurrent unit (GRU), were selected for direct multi-step-ahead WQI forecasting. To enhance the capability of the models in capturing their temporal patterns, the input signal was pre-decomposed using the empirical mode decomposition (EMD) and variational mode decomposition (VMD) into several intrinsic mode functions (IMFs). The characteristics of these IMFs were then analyzed and used to ease model learning on capturing their temporal patterns. Our study shows that the selection of signal decomposition strategies significantly impact the model performance. Both deep learning algorithms offered comparable performances, with the VMD-LSTM exhibiting the lowest prediction errors (MAPE = 1.9237%) and the highest Kling–Gupta efficiency (KGE = 0.6761) over a two-month test period. To the best of our knowledge, this is the first paper that applies a direct forecast approach for the multi-step-ahead WQI forecasting, using the IMFs obtained from the EMD and VMD decompositions. The performance of the model was evaluated through a rolling forward setup to ensure its consistency across different test periods. The proposed modeling framework holds the potential to assist policymakers and stakeholders in decision-making, particularly in planning remedies and efficient water resource management.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

AN:

Ammoniacal nitrogen

ANN:

Artificial neural network

ARIMA:

Autoregressive integrated moving average

BOD:

Biochemical oxygen demand

CNN:

Convolutional neural network

COD:

Chemical oxygen demand

DL:

Deep learning

DO:

Dissolved oxygen

EMD:

Empirical mode decomposition

GRU:

Gated recurrent unit

IoT:

Internet of things

KGE:

Kling–Gupta efficiency

LSTM:

Long short-term memory

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

MBE:

Mean bias error

MIMO:

Multiple-input-multiple-output

MSE:

Mean-squared error

pH:

Potential for hydrogen

RMSE:

Root mean-squared error

RNN:

Recurrent neural network

SD:

Standard deviation

SS:

Suspended solids

VMD:

Variational mode decomposition

WQ:

Water quality

WQI:

Water quality index

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Acknowledgements

This research was funded by Universiti Tunku Abdul Rahman (UTAR), Malaysia through the Universiti Tunku Abdul Rahman Research Fund under project number IPSR/RMC/UTARRF/2020-C2/K03. The authors are very grateful and appreciate very much the financial support provided. We extend our appreciation to the Selangor State Government for generously providing the WQI dataset used in this research. Their contribution was instrumental in our study and greatly enriched our findings.

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Authors and Affiliations

  1. Department of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Sg. Long, Bandar Sg. Long, Cheras, 43000, Kajang, Selangor, Malaysia

    Kok Poh Wai, Chai Hoon Koo & Yuk Feng Huang

  2. Department of Chemical Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Jalan Sg. Long, Bandar Sg. Long, Cheras, 43000, Kajang, Selangor, Malaysia

    Woon Chan Chong

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Correspondence to Chai Hoon Koo.

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Wai, K.P., Koo, C.H., Huang, Y.F. et al. Decomposed intrinsic mode functions and deep learning algorithms for water quality index forecasting. Neural Comput & Applic (2024). https://doi.org/10.1007/s00521-024-09698-8

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