Tidal Level Prediction Model Based on VMD-LSTM Neural Network
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Normalization
2.2. Variational Mode Decomposition
2.3. Long Short-Term Memory Neural Network
2.3.1. Basic Principles of RNN
2.3.2. Basic Principles of LSTM
2.4. VMD-LSTM Model
- (1)
- Preprocess the data using the Min-Max normalization algorithm.
- (2)
- Decompose the original tidal level data using variational mode decomposition (VMD) to obtain k intrinsic mode functions.
- (3)
- Utilize the long short-term memory (LSTM) neural network model to independently predict each IMF component (IMFi) and the residual (RES). Finally, the predicted results of each IMFi component are summed up with the residual RES to obtain the ultimate tidal level prediction.
3. Example Analysis
3.1. Data Source
3.2. VMD
3.3. Prediction Results and Analysis
4. Discussion
5. Conclusions
- Utilizing the VMD method, the tidal level data of Luchao Port is decomposed into four modal components (IMF), which reduces the complexity of the original tidal level data and makes the data series stable. LSTM neural network model is used to predict the IMFi obtained from VMD, respectively, and then these prediction results are superposed, effectively improving the prediction accuracy.
- After VMD, the prediction error of the LSTM model is reduced. Compared with the six prediction modes, the BP, SVM, LSTM, EMD-LSTM, VMD-LSTM, EEMD-LSTM, and CEEMDAN-LSTM models, the VMD-LSTM model has the smallest error, and the highest predictive accuracy, with a RMSE of 0.0385 m, MAE of 0.0267 mm, and R2 of 0.9991.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Li, L.B.; Wu, W.H.; Zhang, W.J.; Yin, J.C.; Zhu, Z.Y. Real-time Tide Level Prediction Model Based on Improved Nonlinear Auto Regressive Models Neural Network with Exogenous Inputs. Sci. Technol. Eng. 2022, 22, 9728–9735. [Google Scholar] [CrossRef]
- Meena, B.; Agrawal, J. Tidal Level Forecasting Using ANN. Procedia Eng. 2015, 116, 607–614. [Google Scholar] [CrossRef]
- Pan, M.; Zhou, H.; Cao, J.; Liu, Y.; Hao, J.; Li, S.; Chen, C.-H. Water Level Prediction Model Based on GRU and CNN. IEEE Access 2020, 8, 60090–60100. [Google Scholar] [CrossRef]
- Liu, C.; Yin, J.C. A high-accuracy short-term tide prediction model. J. Shanghai Marit. Univ. 2016, 37, 74–80. [Google Scholar] [CrossRef]
- Luo, J.M.; Jiang, Y.P.; Pang, L.; Feng, J.D. Numerical simulation of storm surge in the coast of Zhejiang based on parametric wind field model. Haiyang Xuebao 2022, 44, 20–34. [Google Scholar] [CrossRef]
- Yin, C.; Huang, H.; Wang, D.; Liu, Y.; Guo, Z. The Characteristics of Storm Wave Behavior and Its Effect on Cage Culture Using the ADCIRC plus SWAN Model in Houshui Bay, China. J. Ocean Univ. China (Ocean. Coast. Sea Res.) 2020, 19, 307–319. [Google Scholar] [CrossRef]
- Yang, H.; Wu, Q.; Li, G. A multi-stage forecasting system for daily ocean tidal energy based on secondary decomposition, optimized gate recurrent unit and error correction. J. Clean. Prod. 2024, 449, 141303. [Google Scholar] [CrossRef]
- Zhang, Z.; Zhang, L.; Yue, S.; Wu, J.; Guo, F. Correction of nonstationary tidal prediction using deep-learning neural network models in tidal estuaries and rivers. J. Hydrol. 2023, 622, 129686. [Google Scholar] [CrossRef]
- Liu, Q.; Sun, X.Q. Harmonic analysis and forecast of tides in Qingdao Port. J. Mar. Meteorol. 2022, 42, 99–106. [Google Scholar] [CrossRef]
- Cai, S.; Liu, L.; Wang, G. Short-term tidal level prediction using normal time-frequency transform. Ocean Eng. 2018, 156, 489–499. [Google Scholar] [CrossRef]
- Monahan, T.; Tang, T.; Adcock, T.A. A hybrid model for online short-term tidal energy forecasting. Appl. Ocean Res. 2023, 137, 103596. [Google Scholar] [CrossRef]
- Wang, C.H. A model of the Harmonic analysis of tides. Mar. Forecast. 1995, 4, 71–76. [Google Scholar] [CrossRef]
- Yin, J.-C.; Wang, N.-N.; Hu, J.-Q. A hybrid real-time tidal prediction mechanism based on harmonic method and variable structure neural network. Eng. Appl. Artif. Intell. 2015, 41, 223–231. [Google Scholar] [CrossRef]
- Pan, Z.; Liu, H. Impact of human projects on storm surge in the Yangtze Estuary. Ocean Eng. 2020, 196, 106792. [Google Scholar] [CrossRef]
- Zhang, Z.G.; Yin, J.C.; Liu, C.H. Modular Real-Time level Prediction Based on Grey-GMDH. Period. Ocean. Univ. China 2018, 48, 140–146. [Google Scholar] [CrossRef]
- Kavousi-Fard, A. A Hybrid Accurate Model for Tidal Current Prediction. IEEE Trans. Geosci. Remote Sens. 2016, 55, 112–118. [Google Scholar] [CrossRef]
- Li, M.C.; Liang, S.X.; Sun, Z.C.; Zhang, G.Y. Tidal Level and Current Prediction on the Basis of Data-Driven Model. Trans. Beijing Inst. Technol. 2010, 30, 864–868. [Google Scholar] [CrossRef]
- Yan, Z.; Lu, X.; Wu, L. Exploring the Effect of Meteorological Factors on Predicting Hourly Water Levels Based on CEEMDAN and LSTM. Water 2023, 15, 3190. [Google Scholar] [CrossRef]
- Mandal, S.; Shanas, P.; Yuvaraj, S.; Joseph, D.; Aravind, P.; George, J.; Singh, J.; Kumar, V.S. Evaluating the estuarine tidal discharge through water stage component analysis and in-situ measurement—Case study Mandovi–Zuari estuary of Goa, India. Reg. Stud. Mar. Sci. 2023, 66, 103124. [Google Scholar] [CrossRef]
- He, F.; Wang, R.R.; Wang, J.Z. A kind of short-term height-prediction of tidal level of rivers based on BP neural network model. J. Yangze River Sci. Res. Inst. 2011, 28, 21–24. [Google Scholar] [CrossRef]
- Yao, S.Y.; Li, G.F.; Qian, R.Z.; Wang, Y.D.; Ma, F. Tidal level forecast of Yangtze River at the source of East Route of South-to-North Water Transfer Project. South-North Water Transf. Water Sci. Technol. 2021, 19, 1136–1146. [Google Scholar] [CrossRef]
- Di Nunno, F.; de Marinis, G.; Gargano, R.; Granata, F. Tide Prediction in the Venice Lagoon Using Nonlinear Autoregressive Exogenous (NARX) Neural Network. Water 2021, 13, 1173. [Google Scholar] [CrossRef]
- Li, C.; Gao, F.; Wang, H.Q. Improved Fruit Fly Optimization Algorithm for Optimizing Time Series Prediction Model of CIAO-LSTM Network. Comput. Eng. Appl. 2020, 56, 129–134. [Google Scholar] [CrossRef]
- Ye, S.; Jiang, J.G.; Li, J.J.; Liu, Y.L.; Zhou, Z.Z.; Liu, C. Fault diagnosis and tolerance control of five-level nested NPP converter using wavelet packet and LSTM. IEEE Trans. Power Electron. 2019, 35, 1907–1921. [Google Scholar] [CrossRef]
- Wu, J.; Hu, K.; Cheng, Y.; Zhu, H.; Shao, X.; Wang, Y. Data-driven remaining useful life prediction via multiple sensor signals and deep long short-term memory neural network. ISA Trans. 2019, 97, 241–250. [Google Scholar] [CrossRef]
- Yang, X.K.; Tang, G.; Li, D.G. Tidal level prediction and analysis based on LSTM neural network. Port Sci. Technol. 2022, 5, 39–46. [Google Scholar] [CrossRef]
- Liu, Y.Y.; Zhang, L.; Li, L.; Liu, Y.S.; Chen, B.W.; Zhang, H.W. Storm surge nowcasting based on multivariable LSTM neural network model. Mar. Sci. Bull. 2020, 39, 689–694. [Google Scholar]
- Xu, X.W.; Chen, Y.P.; Gan, M.; Liu, C.; Zhou, H.J. Hybrid model for short-term prediction of tide level in estuary based on LSTM and non-stationary harmonic analysis. Mar. Sci. Bull. 2022, 41, 401–410. [Google Scholar] [CrossRef]
- Giaremis, S.; Nader, N.; Dawson, C.; Kaiser, C.; Nikidis, E.; Kaiser, H. Storm surge modeling in the AI era: Using LSTM-based machine learning for enhancing forecasting accuracy. Coast. Eng. 2024, 191, 104532. [Google Scholar] [CrossRef]
- Ian, V.-K.; Tang, S.-K.; Pau, G. Assessing the Risk of Extreme Storm Surges from Tropical Cyclones under Climate Change Using Bidirectional Attention-Based LSTM for Improved Prediction. Atmosphere 2023, 14, 1749. [Google Scholar] [CrossRef]
- Liu, J.; Shi, G.Y.; Zhu, K.G.; Zhang, J.W.; Li, S.H.; Chen, Z.H.; Wang, W. A combined tide prediction model based on harmonic analysis and ARIMA-SCR. J. Shanghai Marit. Univ. 2019, 40, 93–99. [Google Scholar] [CrossRef]
- Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.-C.; Tung, C.C.; Liu, H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 1998, 454, 903–995. [Google Scholar] [CrossRef]
- Wu, L.L.; Yin, L.L.; Ren, Q.L. A Short-Term Traffic Flow Forecasting Method Based on EMD and DE-BPNN Combined Optimization. J. Chongqing Univ. Technol. (Nat. Sci.) 2021, 35, 155–163. [Google Scholar] [CrossRef]
- Ren, Z.; Hou, J.; Wang, P.; Wang, Y. Tsunami resonance and standing waves in Hangzhou Bay. Phys. Fluids 2021, 33, 081702. [Google Scholar] [CrossRef]
- Wang, R.M.; Xie, N.; Yu, H.Y.; Yu, J.; Jiang, L.; Yang, H.Y. Short-term Load Forecasting Method Based on EMD-LSTM Model. Res. Explor. Lab. 2022, 41, 62–66. [Google Scholar] [CrossRef]
- Yin, J.; Wang, H.; Wang, N.; Wang, X. An adaptive real-time modular tidal level prediction mechanism based on EMD and Lipschitz quotients method. Ocean Eng. 2023, 289, 116297. [Google Scholar] [CrossRef]
- Lv, T.; Tao, A.; Zhang, Z.; Qin, S.; Wang, G. Significant wave height prediction based on the local-EMD-WaveNet model. Ocean Eng. 2023, 287, 115900. [Google Scholar] [CrossRef]
- Wang, Z.; Wang, Q.; Wu, T. A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM. Front. Environ. Sci. Eng. 2023, 17, 88. [Google Scholar] [CrossRef]
- Zhang, J.; Xin, X.; Shang, Y.; Wang, Y.; Zhang, L. Nonstationary significant wave height forecasting with a hybrid VMD-CNN model. Ocean Eng. 2023, 285, 115338. [Google Scholar] [CrossRef]
- Wang, J.; Bethel, B.J.; Xie, W.; Dong, C. A hybrid model for significant wave height prediction based on an improved empirical wavelet transform decomposition and long-short term memory network. Ocean Model. 2024, 189, 102367. [Google Scholar] [CrossRef]
- Ban, W.; Shen, L.; Lu, F.; Liu, X.; Pan, Y. Research on Long-Term Tidal-Height-Prediction-Based Decomposition Algorithms and Machine Learning Models. Remote Sens. 2023, 15, 3045. [Google Scholar] [CrossRef]
- Chen, H.; Huang, S.; Xu, Y.; Teegavarapu, R.S.V.; Guo, Y.; Nie, H.; Xie, H. Using Baseflow Ensembles for Hydrologic Hysteresis Characterization in Humid Basins of Southeastern China. Water Resour. Res. 2024, 60, e2023WR036195. [Google Scholar] [CrossRef]
- Meng, Z.; Wang, Y.; Zheng, S.; Wang, X.; Liu, D.; Zhang, J.; Shao, Y. Abnormal Monitoring Data Detection Based on Matrix Manipulation and the Cuckoo Search Algorithm. Mathematics 2024, 12, 1345. [Google Scholar] [CrossRef]
- Yang, H.Y.; Zhao, X.Y.; Wang, L. Review of Data Normalization Methods. Comput. Eng. Appl. 2023, 59, 13–22. [Google Scholar] [CrossRef]
- Li, Q.; Luo, Y.; Zhang, M.L. LoRaWAN water quality adaptive monitoring system based on LSTM energy prediction. Internet Things Technol. 2023, 13, 8–12. [Google Scholar] [CrossRef]
- Zhao, J.; Xie, Z.X.; Liu, S.X. Tide prediction accuracy improvement method research based on VMD optimal decomposition of energy and GRU recurrent neural network. Chin. J. Sci. Instrum. 2023, 44, 79–87. [Google Scholar] [CrossRef]
- Jiange, J.; Liqin, Z.; Senjun, H.; Qianqian, M. Water quality prediction based on IGRA-ISSA-LSTM model. Water Air Soil Pollut. 2023, 234, 172. [Google Scholar] [CrossRef]
Sliding Window | RMSE | MAE | MAPE | R2 |
---|---|---|---|---|
2 | 0.1602 | 0.1424 | 12.545 | 0.9511 |
3 | 0.1554 | 0.1324 | 12.002 | 0.9547 |
4 | 0.1385 | 0.1217 | 11.754 | 0.9583 |
5 | 0.1404 | 0.1235 | 11.781 | 0.9571 |
6 | 0.1322 | 0.1054 | 10.855 | 0.9642 |
7 | 0.1275 | 0.1022 | 10.843 | 0.9663 |
8 | 0.1281 | 0.1014 | 10.837 | 0.9666 |
9 | 0.1180 | 0.0945 | 10.115 | 0.9734 |
10 | 0.1103 | 0.0912 | 9.854 | 0.9773 |
11 | 0.1012 | 0.0905 | 9.801 | 0.9814 |
12 | 0.0965 | 0.0844 | 9.527 | 0.9889 |
13 | 0.0982 | 0.0895 | 9.912 | 0.9809 |
14 | 0.1194 | 0.1025 | 10.154 | 0.9701 |
15 | 0.1162 | 0.1011 | 10.038 | 0.9720 |
16 | 0.1245 | 0.1067 | 10.845 | 0.9653 |
Evaluation Index | Prediction Model | Improvement Ratio | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
BP | SVM | LSTM | EMD-LSTM | EEMD-LSTM | CEEMDAN-LSTM | VMD-LSTM | I1 | I2 | I3 | |
RSME (m) | 0.1871 | 0.1496 | 0.114 | 0.0943 | 0.0537 | 0.093 | 0.0385 | 59.2% | 28.3% | 58.6% |
MAE (m) | 0.1594 | 0.1193 | 0.1003 | 0.0805 | 0.0425 | 0.076 | 0.0267 | 66.8% | 37.2% | 64.9% |
MAPE/% | 16.551 | 14.354 | 11.412 | 9.136 | 8.585 | 8.862 | 5.8327 | 36.2% | 32.1% | 34.2% |
R2 | 0.8968 | 0.9363 | 0.9702 | 0.9905 | 0.9963 | 0.9949 | 0.9991 | −0.9% | −0.3% | −0.4% |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Huang, S.; Nie, H.; Jiao, J.; Chen, H.; Xie, Z. Tidal Level Prediction Model Based on VMD-LSTM Neural Network. Water 2024, 16, 2452. https://doi.org/10.3390/w16172452
Huang S, Nie H, Jiao J, Chen H, Xie Z. Tidal Level Prediction Model Based on VMD-LSTM Neural Network. Water. 2024; 16(17):2452. https://doi.org/10.3390/w16172452
Chicago/Turabian StyleHuang, Saihua, Hui Nie, Jiange Jiao, Hao Chen, and Ziheng Xie. 2024. "Tidal Level Prediction Model Based on VMD-LSTM Neural Network" Water 16, no. 17: 2452. https://doi.org/10.3390/w16172452