A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM

doi:10.1007/s11783-023-1688-y

Front. Environ. Sci. Eng.

2023, Vol. 17

Issue (7) : 88 https://doi.org/10.1007/s11783-023-1688-y

RESEARCH ARTICLE

A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM

Zhaocai Wang¹, Qingyu Wang¹, Tunhua Wu²(

)

¹. College of Information, Shanghai Ocean University, Shanghai 201306, China
². School of Information Engineering, Wenzhou Business College, Wenzhou 325035, China

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Abstract

● A novel VMD-IGOA-LSTM model has proposed for the prediction of water quality.

● Improved model quickly converges to the global optimal fitness and remains stable.

● The prediction accuracy of water quality parameters is significantly improved.

Water quality prediction is vital for solving water pollution and protecting the water environment. In terms of the characteristics of nonlinearity, instability, and randomness of water quality parameters, a short-term water quality prediction model was proposed based on variational mode decomposition (VMD) and improved grasshopper optimization algorithm (IGOA), so as to optimize long short-term memory neural network (LSTM). First, VMD was adopted to decompose the water quality data into a series of relatively stable components, with the aim to reduce the instability of the original data and increase the predictability, then each component was input into the IGOA-LSTM model for prediction. Finally, each component was added to obtain the predicted values. In this study, the monitoring data from Dayangzhou Station and Shengmi Station of the Ganjiang River was used for training and prediction. The experimental results showed that the prediction accuracy of the VMD-IGOA-LSTM model proposed was higher than that of the integrated model of Ensemble Empirical Mode Decomposition (EEMD), the integrated model of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Nonlinear Autoregressive Network with Exogenous Inputs (NARX), Recurrent Neural Network (RNN), as well as other models, showing better performance in short-term prediction. The current study will provide a reliable solution for water quality prediction studies in other areas.

Keywords Water quality prediction Grasshopper optimization algorithm Variational mode decomposition Long short-term memory neural network

Corresponding Author(s): Tunhua Wu

Issue Date: 13 February 2023

Cite this article:

Zhaocai Wang,Qingyu Wang,Tunhua Wu. A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM[J]. Front. Environ. Sci. Eng., 2023, 17(7): 88.

URL:

https://academic.hep.com.cn/fese/EN/10.1007/s11783-023-1688-y
https://academic.hep.com.cn/fese/EN/Y2023/V17/I7/88

Fig.1 LSTM network structure.

Fig.2 Reconstructed linear reduction factor

c

Fig.3 Convergence curves of two algorithms on different benchmark functions.

Fig.4 VMD-IGOA-LSTM model steps.

Fig.5 DO datasets of Dayangzhou Station.

Fig.6 Number of modes.

Fig.7 VMD decomposition results.

Fig.8 Observed and predicted values of each component.

Fig.9 Observed and predicted values of DO.

Fig.10 Predicted values of DO in each model for the Dayangzhou Station.

Model	MSE	RMSE	MAE	MAPE	$r 2$
VMD-IGOA-LSTM*	0.0032	0.0565	0.0436	0.4%	0.9877
EEMD-IGOA-LSTM	0.0285	0.1691	0.1031	0.96%	0.7780
CEEMDAN-IGOA-LSTM	0.0354	0.1881	0.1199	1.12%	0.8667
IGOA-LSTM	0.0829	0.2878	0.1565	1.47%	0.6450
LSTM	0.0899	0.2999	0.1754	1.64%	0.5955
NARX	0.1147	0.3388	0.2245	2.06%	0.5236
RNN	0.1297	0.3601	0.2577	2.36%	0.3361
BP	0.1159	0.3404	0.2378	2.15%	0.3898

Tab.1 Prediction error value of each model for the Dayangzhou Station

Fig.11 Error histogram of the prediction of each model for the Dayangzhou Station.

Model	MSE	RMSE	MAE	MAPE	$r 2$
VMD-IGOA-LSTM	0.0044	0.0661	0.0495	0.38%	0.9967
EEMD-IGOA-LSTM	0.0433	0.2081	0.1567	1.19%	0.9661
CEEMDAN-IGOA-LSTM	0.0499	0.2235	0.1758	1.33%	0.9608
IGOA-LSTM	0.2377	0.4875	0.3483	2.58%	0.8436
LSTM	0.2631	0.5130	0.3715	2.75%	0.7733
NARX	0.3403	0.5833	0.4578	3.45%	0.7134
RNN	0.3790	0.6156	0.3864	2.88%	0.6629
BP	0.4356	0.6599	0.4804	0.0359	0.6433

Tab.2 Error values of each model for the Shengmi Station

Fig.12 Predicted values of DO in each model for the Shengmi Station.

Fig.13 Error histogram of the prediction of each model for the Shengmi Station.

Tab.3 DM test results of each model in Dayangzhou Station

Tab.4 DM test results of each model in Shengmi Station

Fig.14 Correlation of various factors.

Model	MSE	RMSE	MAE	MAPE	$r 2$
VMD-IGOA-LSTM	0.0867	0.2944	0.1754	1.59%	0.5827
EEMD-IGOA-LSTM	0.1500	0.3873	0.2705	2.44%	0.2556
CEEMDAN-IGOA-LSTM	0.1377	0.3711	0.2577	2.33%	0.2544
LSTM	0.1195	0.3458	0.2200	2.00%	0.3684
NARX	0.2382	0.4881	0.3911	3.54%	0.1133
RNN	0.1315	0.3627	0.2312	2.01%	0.3318

Tab.5 Error values of each multi-factor model for the Dayangzhou Station

Fig.15 Predicted values of DO in multi-factor models in Dayangzhou Station.

Fig.16 Error histogram of the prediction in multi-factor models in the Dayangzhou Station.

Fig.17 Multi-step prediction results for each model.

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