A Slow Failure Particle Swarm Optimization Long Short-Term Memory for Significant Wave Height Prediction
Abstract
:1. Introduction
2. Materials and Methods
2.1. Long Short-Term Memory
2.2. Slow Failure Particle Swarm Optimization
2.3. SFPSO-LSTM
- Step 1: Normalize all the data within the range −1 to 1 by Equation (5). The normalization eliminates the influence of the scale between indicators and increases the speed of calculations.
- Step 2: In the SFPSO process, the mean square error (MSE) is set as the fitness function for SFPSO. All particles continuously update their velocity and position within the range and thus search for the optimal possible combination of parameters. The fitness function of the SFPSO is as follows:
- Step 3: The LSTM model is trained with the parameters searched by SFPSO.
- Step 4: The results are predicted using a trained SFPSO-LSTM.
3. Experiment and Results
3.1. Data Preparation
- P1, latidude and longitude: 42.0, 29.0, Date: 1 January 2023–31 May 2023, sampling method: hour, 3625 sets of data
- P2, latidude and longitude: 25.0, 165.0, Date: 1 January 2023–31 May 2023, sampling method: hour, 3625 sets of data
- P3, latidude and longitude: −31.0, 74.0, Date: 1 January 2023–31 May 2023, Sampling method: hour, 3625 sets of data
- P4, latidude and longitude: 74.5, 37.5, Date: 1 January 2023–31 May 2023, sampling method: hour, 3625 sets of data
- Diverse Environmental Conditions: The selected points offer a wide range of oceanic environments, from enclosed seas to open oceans, and from temperate to polar regions. This diversity ensures the model’s robustness and adaptability to various maritime conditions.
- Comprehensive Data Representation: By encompassing different latitudinal zones and oceanic conditions, the model can be trained on a comprehensive dataset, enhancing its predictive accuracy and generalizability.
- Enhanced Model Validation: The geographical diversity allows for extensive validation of the model across a range of conditions, ensuring that the model is not overfitted to a specific type of environment.
- Global Applicability: Training the model on data from these varied locations increases the likelihood that it can be effectively applied to wave height prediction in other parts of the world’s oceans, thereby enhancing its global utility.
3.2. Results
3.3. Analyses
3.4. Limitations and Future Recommendation
4. Conclusions
- Enhanced Predictive Accuracy: The integration of the slow failure particle swarm optimization (SFPSO) algorithm with the long short-term memory (LSTM) neural network significantly improves the accuracy of significant wave height (SWH) predictions compared to traditional methods.
- Adaptive Algorithm Efficiency: The SFPSO algorithm effectively addresses the limitations of traditional particle swarm optimization (PSO) by adaptively adjusting particle search ranges based on iteration count, reducing premature convergence and improving search precision.
- Robust Model Performance: The LSTM model, optimized with SFPSO, demonstrates robust performance across diverse marine environments, ensuring reliable predictions in various oceanic conditions, including enclosed seas, open oceans, temperate zones, and polar regions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | GRU | LSTM | PSO-LSTM | SFPSO-LSTM |
---|---|---|---|---|
Number of epochs | 500 | 500 | 500 | 500 |
Solver | Adam | Adam | Adam | Adam |
Dropout probability | 0.2 | 0.2 | 0.2 | 0.2 |
Batch size | 64 | 64 | [16, 128] | [16, 128] |
Number of hidden layer units | 60 | 60 | [10, 120] | [10, 120] |
Number of layers | 2 | 2 | [1, 5] | [1, 5] |
Initial learning rate | 0.001 | 0.001 | [0.0001, 0.005] | [0.0001, 0.005] |
Popularization | None | None | 5 | 5 |
Number of iterations | None | None | 20 | 20 |
Position | Predicted Time | Indicators | GRU | LSTM | PSO-LSTM | SFPSO-LSTM |
---|---|---|---|---|---|---|
P1 | 1 h | MAE | 0.074 | 0.050 | 0.043 | 0.035 |
RMSE | 0.100 | 0.072 | 0.057 | 0.043 | ||
MAPE | 18.447% | 14.888% | 9.246% | 7.610% | ||
R2 | 0.936 | 0.966 | 0.979 | 0.988 | ||
3 h | MAE | 0.119 | 0.119 | 0.142 | 0.104 | |
RMSE | 0.168 | 0.024 | 0.182 | 0.130 | ||
MAPE | 19.587% | 22.905% | 22.721% | 16.496% | ||
R2 | 0.817 | 0.845 | 0.787 | 0.891 | ||
6 h | MAE | 0.197 | 0.210 | 0.168 | 0.131 | |
RMSE | 0.254 | 0.257 | 0.248 | 0.175 | ||
MAPE | 25.807% | 28.565% | 20.758% | 20.472% | ||
R2 | 0.583 | 0.575 | 0.604 | 0.802 | ||
12 h | MAE | 0.279 | 0.255 | 0.248 | 0.206 | |
RMSE | 0.345 | 0.335 | 0.322 | 0.277 | ||
MAPE | 43.992% | 41.964% | 33.521% | 30.268% | ||
R2 | 0.229 | 0.274 | 0.330 | 0.503 | ||
P2 | 1 h | MAE | 0.047 | 0.034 | 0.028 | 0.019 |
RMSE | 0.053 | 0.049 | 0.034 | 0.023 | ||
MAPE | 2.701% | 1.973% | 1.574% | 1.060% | ||
R2 | 0.958 | 0.964 | 0.983 | 0.992 | ||
3 h | MAE | 0.075 | 0.116 | 0.064 | 0.061 | |
RMSE | 0.096 | 0.156 | 0.076 | 0.087 | ||
MAPE | 4.337% | 6.815% | 3.602% | 3.273% | ||
R2 | 0.861 | 0.636 | 0.914 | 0.888 | ||
6 h | MAE | 0.129 | 0.121 | 0.123 | 0.105 | |
RMSE | 0.161 | 0.154 | 0.155 | 0.130 | ||
MAPE | 7.687% | 7.232% | 7.081% | 5.661% | ||
R2 | 0.611 | 0.644 | 0.639 | 0.746 | ||
12 h | MAE | 0.204 | 0.165 | 0.150 | 0.131 | |
RMSE | 0.256 | 0.211 | 0.194 | 0.165 | ||
MAPE | 12.058% | 9.449% | 8.615% | 7.399% | ||
R2 | 0.022 | 0.335 | 0.434 | 0.593 |
Position | Predicted Time | Indicators | GRU | LSTM | PSO-LSTM | SFPSO-LSTM |
---|---|---|---|---|---|---|
P3 | 1 h | MAE | 0.062 | 0.063 | 0.059 | 0.054 |
RMSE | 0.122 | 0.107 | 0.091 | 0.090 | ||
MAPE | 1.956% | 2.073% | 1.994% | 1.782% | ||
R2 | 0.963 | 0.972 | 0.979 | 0.980 | ||
3 h | MAE | 0.200 | 0.180 | 0.170 | 0.138 | |
RMSE | 0.330 | 0.256 | 0.244 | 0.226 | ||
MAPE | 6.778% | 6.259% | 5.944% | 4.741% | ||
R2 | 0.731 | 0.838 | 0.853 | 0.874 | ||
6 h | MAE | 0.274 | 0.285 | 0.266 | 0.252 | |
RMSE | 0.381 | 0.404 | 0.376 | 0.343 | ||
MAPE | 9.853% | 10.163% | 9.657% | 9.079% | ||
R2 | 0.641 | 0.597 | 0.651 | 0.709 | ||
12 h | MAE | 0.374 | 0.376 | 0.365 | 0.318 | |
RMSE | 0.519 | 0.533 | 0.485 | 0.487 | ||
MAPE | 13.601% | 13.973% | 13.535% | 10.609% | ||
R2 | 0.334 | 0.299 | 0.418 | 0.414 | ||
P4 | 1 h | MAE | 0.055 | 0.060 | 0.054 | 0.045 |
RMSE | 0.069 | 0.071 | 0.068 | 0.059 | ||
MAPE | 3.142% | 3.409% | 2.929% | 2.591% | ||
R2 | 0.988 | 0.987 | 0.988 | 0.991 | ||
3 h | MAE | 0.264 | 0.330 | 0.285 | 0.260 | |
RMSE | 0.330 | 0.416 | 0.361 | 0.327 | ||
MAPE | 15.007% | 18.993% | 16.686% | 14.560% | ||
R2 | 0.716 | 0.548 | 0.659 | 0.721 | ||
6 h | MAE | 0.463 | 0.472 | 0.440 | 0.449 | |
RMSE | 0.565 | 0.568 | 0.553 | 0.540 | ||
MAPE | 27.143% | 27.897% | 26.549% | 26.256% | ||
R2 | 0.168 | 0.158 | 0.200 | 0.240 | ||
12 h | MAE | 0.506 | 0.497 | 0.465 | 0.429 | |
RMSE | 0.600 | 0.586 | 0.577 | 0.575 | ||
MAPE | 30.405% | 30.264% | 28.325% | 24.086% | ||
R2 | 0.060 | 0.103 | 0.132 | 0.136 |
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Guo, J.; Yan, Z.; Shi, B.; Sato, Y. A Slow Failure Particle Swarm Optimization Long Short-Term Memory for Significant Wave Height Prediction. J. Mar. Sci. Eng. 2024, 12, 1359. https://doi.org/10.3390/jmse12081359
Guo J, Yan Z, Shi B, Sato Y. A Slow Failure Particle Swarm Optimization Long Short-Term Memory for Significant Wave Height Prediction. Journal of Marine Science and Engineering. 2024; 12(8):1359. https://doi.org/10.3390/jmse12081359
Chicago/Turabian StyleGuo, Jia, Zhou Yan, Binghua Shi, and Yuji Sato. 2024. "A Slow Failure Particle Swarm Optimization Long Short-Term Memory for Significant Wave Height Prediction" Journal of Marine Science and Engineering 12, no. 8: 1359. https://doi.org/10.3390/jmse12081359