A Novel Groundwater Burial Depth Prediction Model Based on Two-Stage Modal Decomposition and Deep Learning
Abstract
:1. Introduction
2. Models and Methods
2.1. CEEMDAN Model
2.2. VMD Model
2.3. CNN Principle Structure
2.4. Subsection
2.5. CEEMDAN-VMD-CNN-GRU Model
2.6. Evaluation Indicators
3. Case Studies
3.1. Data Sources
3.2. CEEMDAN Primary Modal Decomposition
3.3. VMD Secondary Modal Decomposition
3.4. CNN-GRU Model Prediction
3.5. Comparative Analysis
4. Discussion
- Prediction using CNN or GRU alone is less effective. The CEEMDAN-GRU model has 21.40% and 20.63% lower MAE and RMSE and 10.65% higher prediction accuracy than the single prediction model GRU. The “decomposition-prediction” model has significant advantages for dealing with uncertain, non-stationary and non-linear series data.
- S CNN-GRU can effectively extract the coupling relationship and temporal correlation implied by the time series and improve the prediction accuracy. the CEEMDAN-CNN-GRU model reduces the prediction result error indicators MAE and RMSE by 20.46% and 15.08% compared with the CEEMDAN-GRU model and improves the prediction accuracy by 4.55%.
- The CEEMDAN-VMD-CNN-GRU model has the lowest MAE and RMSE and 94% prediction accuracy compared to the other models, indicating that the model outperforms the other models in terms of prediction performance.
- The CEEMDAN-VMD-CNN-GRU model has the advantage of being computationally fast, with few input parameters and no need to consider the physical mechanisms of intermediate processes, requiring only the search for the best mapping relationship between input and output variables, offering more options for all types of hydrological forecasting.
- The model input data are the average groundwater depth of the People’s Victory Canal irrigation area, which does not take into account the spatial distribution of groundwater depth, which is a shortcoming and limitation of the model prediction and a direction for improvement in the future.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Layer | Parameter | Value |
---|---|---|
Input | Time step | 1 |
CEEMDAN | Noise standard deviation ratio | 0.2 |
Number of noise additions | 300 | |
Maximum number of allowed sieving iterations | 500 | |
VMD | Modal number | 4 |
Penalty Factor | 1500 | |
Convergence tolerances | 2 × 10−6 | |
CNN | Filters | 32 |
Kernel_size | 32 | |
Padding | same | |
Activation function | ReLU | |
GRU | Layers | 5 |
Number of neurons | {64, 64, 64, 64, 64} | |
Optimisation algorithms | Adam | |
Batch_size | 20 | |
Epochs | 80 | |
Error | MSE |
Evaluation Indicators | MAE (m) | RMSE (m) | NSE |
---|---|---|---|
VIMF1 | 0.1829 | 0.2371 | 0.0677 |
VIMF2 | 0.0023 | 0.0029 | 0.9993 |
VIMF3 | 0.0001 | 0.0001 | 0.9999 |
VIMF4 | 0.0001 | 0.0001 | 0.9994 |
IMF4 | 0.0176 | 0.0217 | 0.9935 |
IMF5 | 0.0026 | 0.0032 | 0.9998 |
IMF6 | 0.0005 | 0.0007 | 0.9999 |
IMF7 | 0.0003 | 0.0004 | 1.0000 |
Residual | 0.0005 | 0.0006 | 1.0000 |
Overall | 0.1824 | 0.2363 | 0.9429 |
Model | GRU | CEEMDAN-GRU | CEEMDAN-CNN-GRU | CEEMDAN-VMD-CNN-GRU |
---|---|---|---|---|
MAE | 0.3495 | 0.2747 | 0.2185 | 0.1824 |
RMSE | 0.4672 | 0.3708 | 0.3149 | 0.2363 |
NSE | 0.7768 | 0.8595 | 0.8986 | 0.9429 |
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Zhang, X.; Zheng, Z. A Novel Groundwater Burial Depth Prediction Model Based on Two-Stage Modal Decomposition and Deep Learning. Int. J. Environ. Res. Public Health 2023, 20, 345. https://doi.org/10.3390/ijerph20010345
Zhang X, Zheng Z. A Novel Groundwater Burial Depth Prediction Model Based on Two-Stage Modal Decomposition and Deep Learning. International Journal of Environmental Research and Public Health. 2023; 20(1):345. https://doi.org/10.3390/ijerph20010345
Chicago/Turabian StyleZhang, Xianqi, and Zhiwen Zheng. 2023. "A Novel Groundwater Burial Depth Prediction Model Based on Two-Stage Modal Decomposition and Deep Learning" International Journal of Environmental Research and Public Health 20, no. 1: 345. https://doi.org/10.3390/ijerph20010345