Water wave height prediction using a novel hybrid deep learning model with output uncertainty quantification

نوع مقاله : Special Issue: New Approaches to Water and Soil Management and Modeling

نویسندگان

1 Associate Professor, Department of the Water Engineering, Faculty of Agriculture, Shahrekord University, Shahrekord, Iran

2 Ph.D. Department of Hydraulic Structures, Semnan University, Semnan, Iran

چکیده

Accurate significant wave height (SWH) prediction is essential for improving the safety and efficiency of maritime operations. Thus, our study develops the Gaussian data augment (GDA) technique- Meerkat optimization algorithm (MOA)- variational mode decomposition (VMD)- complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)- bidirectional long short-term memory neural network model (BILSTM)- attention mechanism (AT)- gated recurrent unit (GRU) model to accurately predict SWH and overcome the limitations of the GRU model. First, the GDA method addresses the problem of data scarcity by providing new data points. Next, MOA is used to adjust the parameters of the components of the hybrid model. The VMD method then reduces the intricacy of the time series by converting them into subseries with lower complexity named intrinsic mode functions (IMFs). However, as the first IMF retains the complex characteristics of the original time series, the CEEMDAN method is applied to decompose it into secondary IMFs with reduced complexity. Subsequently, the BILSTM model extracts forward and backward temporal features from the secondary IMFs and the initial remaining IMFs. An attention mechanism is then applied to assign the attention weights to the extracted features. Each attention weight indicates the importance of a feature, enabling the GRU model to identify the most important time series features for predicting SWH. Finally, the weighted features are fed into the GRU model to predict SWH accurately. Our study also couples the kernel density estimation method with the GDA- MOA-VMD-CEEMDAN-BILSTM- attention mechanism-GRU (GMVCBAG) model to quantify the uncertainty of the model outputs. The new model is benchmarked against multiple predictive models. Our study also uses various performance metrics to evaluate the accuracy of predictions. Our findings indicate that Nash–Sutcliffe efficiency (NSE), mean absolute error (MAE), standard deviation of the relative error (STDRE), and explained variance of the GMVCBAG model are 0.973, 0.245, 1.245, and 0.899, respectively. Results indicate that GMVCBAG provides reliable SWH predictions. Moreover, the outputs of the new model have a lower uncertainty than those of the other predictive models. Thus, GMVCBAG is a suitable model for predicting SWH in the different regions of the world.  

کلیدواژه‌ها

موضوعات

مراجع

Abbas, M., Min, Z., Liu, Z., & Zhang, D. (2024). Unravelling oceanic wave patterns: A comparative study of machine learning approaches for predicting significant wave height. Applied Ocean Research, 145, 103919. doi: 10.1016/j.apor.2024.103919
Adnan, R. M., Sadeghifar, T., Alizamir, M., Azad, M. T., Makarynskyy, O., Kisi, O., Barati, R., & Ahmed, K. O. (2023). Short-term probabilistic prediction of significant wave height using bayesian model averaging: Case study of chabahar port, Iran. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.113887
Alizadeh, M. J., & Nourani, V. (2024). Multivariate GRU and LSTM models for wave forecasting and hindcasting in the southern Caspian Sea. Ocean Engineering. doi: 10.1016/j.oceaneng.2024.117193
Altunkaynak, A., Çelik, A., & Mandev, M. B. (2023). Hourly significant wave height prediction via singular spectrum analysis and wavelet transform based models. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.114771
Aung, N. N., Pang, J., Chua, M. C. H., & Tan, H. X. (2023). A novel bidirectional LSTM deep learning approach for COVID-19 forecasting. Scientific Reports. doi: 10.1038/s41598-023-44924-8
Ban, W., Shen, L., Chen, J., & Yang, B. (2023). Short-term prediction of wave height based on a deep learning autoregressive integrated moving average model. Earth Science Informatics, 16(3), 2251-2259. doi: 10.1007/s12145-023-01023-6
Cao, L., Zhang, H., Meng, Z., & Wang, X. (2023). A parallel GRU with dual-stage attention mechanism model integrating uncertainty quantification for probabilistic RUL prediction of wind turbine bearings. Reliability Engineering and System Safety. doi: 10.1016/j.ress.2023.109197
Chen, H., Wu, H., Kan, T., Zhang, J., & Li, H. (2023). Low-carbon economic dispatch of integrated energy system containing electric hydrogen production based on VMD-GRU short-term wind power prediction. International Journal of Electrical Power and Energy Systems. doi: 10.1016/j.ijepes.2023.109420
Chen, Y., Xia, R., Yang, K., & Zou, K. (2024). DNNAM: Image inpainting algorithm via deep neural networks and attention mechanism. Applied Soft Computing. doi: 10.1016/j.asoc.2024.111392
Chen, Y., Zhang, D., Li, X., Peng, Y., Wu, C., Pu, H., Zhou, D., Cao, Y., & Zhang, J. (2023). Significant wave height prediction through artificial intelligent mode decomposition for wave energy management. Energy and AI. doi: 10.1016/j.egyai.2023.100257
Cui, S., Lyu, S., Ma, Y., & Wang, K. (2024). Improved informer PV power short-term prediction model based on weather typing and AHA-VMD-MPE. Energy, 307, 132766. doi: 10.1016/j.energy.2024.132766
Ding, L., Bai, Y., Liu, M. De, Fan, M. H., & Yang, J. (2022). Predicting short wind speed with a hybrid model based on a piecewise error correction method and Elman neural network. Energy. doi: 10.1016/j.energy.2021.122630
Ding, T., Wu, D. A., Li, Y., Shen, L., & Zhang, X. (2024). A hybrid CEEMDAN-VMD-TimesNet model for significant wave height prediction in the South Sea of China. Frontiers in Marine Science, 11, 1375631. doi: 10.3389/fmars.2024.1375631
Ehteram, M., Ahmed, A. N., Khozani, Z. S., & El-Shafie, A. (2023). Graph convolutional network–Long short term memory neural network-multi layer perceptron-Gaussian progress regression model: A new deep learning model for predicting ozone concertation. Atmospheric Pollution Research, 14(6), 101766. doi: 10.1016/j.apr.2023.101766
Ehteram, M., Barzegari Banadkooki, F., & Afshari Nia, M. (2024). Gaussian mutation-alpine skiing optimization algorithm-recurrent attention unit-gated recurrent unit-extreme learning machine model: an advanced predictive model for predicting evaporation. Stochastic Environmental Research and Risk Assessment. doi: 10.1007/s00477-023-02657-0
Farhan, H. R., Kod, M. S., Taqi, A., & Ghazi, S. A. (2024). Ovarian Cancer Detection Based on Elman Recurrent Neural Network. Periodica Polytechnica Electrical Engineering and Computer Science. doi: 10.3311/PPee.23081
Fu, Y., Ying, F., Huang, L., & Liu, Y. (2023). Multi-step-ahead significant wave height prediction using a hybrid model based on an innovative two-layer decomposition framework and LSTM. Renewable Energy. doi: 10.1016/j.renene.2022.12.079
Ghanbari-Adivi, E. A new machine learning model for predicting the water quality index. Model. Earth Syst. Environ. 10, 5635–5667 (2024). doi: 10.1007/s40808-024-02083-3
Ghanbari-Adivi, E., Ehteram, M. CEEMDAN-BILSTM-ANN and SVM Models: Two Robust Predictive Models for Predicting River flow. Water Resour Manage 39, 3235–3271 (2025). doi: 10.1007/s11269-025-04105-w
Ghanbari-Adivi, E., Kermannezhad, J., Raeisi, A. (2025). 'Predicting the electrical conductivity of water using the Hicking CEEMD-LSSVM optimization algorithm', Water and Soil Management and Modelling, 5(4), pp. 323-348. doi: 10.22098/mmws.2025.18187.1657
Hasan, R. I., Yusuf, S. M., Mohd Rahim, M. S., & Alzubaidi, L. (2023). Automatic Clustering and Classification of Coffee Leaf Diseases Based on an Extended Kernel Density Estimation Approach. Plants. doi: 10.3390/plants12081603
Hou, X., Ge, F., Chen, D., Shen, L., & Zou, F. (2023). Temporal distribution-based prediction strategy for dynamic multi-objective optimization assisted by GRU neural network. Information Sciences. doi: 10.1016/j.ins.2023.119627
Huang, X., Ma, C., Zhao, Y., Wang, K., & Meng, W. (2023). A hybrid model of neural network with VMD–CNN–GRU for traffic flow prediction. International Journal of Modern Physics. doi: 10.1142/S0129183123501590
Ikram, R. M. A., Cao, X., Sadeghifar, T., Kuriqi, A., Kisi, O., & Shahid, S. (2023). Improving Significant Wave Height Prediction Using a Neuro-Fuzzy Approach and Marine Predators Algorithm. Journal of Marine Science and Engineering. doi: 10.3390/jmse11061163
Imani, M. (2023). Alzheimer’s diseases diagnosis using fusion of high informative BiLSTM and CNN features of EEG signal. Biomedical Signal Processing and Control. doi: 10.1016/j.bspc.2023.105298
Jamei, M., Ali, M., Karimi, B., Karbasi, M., Farooque, A. A., & Yaseen, Z. M. (2023). Surface water electrical conductivity and bicarbonate ion determination using a smart hybridization of optimal Boruta package with Elman recurrent neural network. Process Safety and Environmental Protection. doi: 10.1016/j.psep.2023.03.062
Jia, C., Tian, Y., Shi, Y., Jia, J., Wen, J., & Zeng, J. (2023). State of health prediction of lithium-ion batteries based on bidirectional gated recurrent unit and transformer. Energy. doi: 10.1016/j.energy.2023.129401
Kumar, N. P., Vijayabaskar, S., Murali, L., & Ramaswamy, K. (2023). Design of optimal Elman Recurrent Neural Network based prediction approach for biofuel production. Scientific Reports. doi: 10.1038/s41598-023-34764-x
Li, H., & Wu, X. J. (2024). CrossFuse: A novel cross attention mechanism based infrared and visible image fusion approach. Information Fusion. doi: 10.1016/j.inffus.2023.102147
Li, K., Huang, W., Hu, G., & Li, J. (2023). Ultra-short term power load forecasting based on CEEMDAN-SE and LSTM neural network. Energy and Buildings, 279, 112666
Li, L., Li, Y., Mao, R., Li, L., Hua, W., & Zhang, J. (2023). Remaining Useful Life Prediction for Lithium-Ion Batteries With a Hybrid Model Based on TCN-GRU-DNN and Dual Attention Mechanism. IEEE Transactions on Transportation Electrification. doi: 10.1109/TTE.2023.3247614
Li, Y., Peng, G., Du, T., Jiang, L., & Kong, X. Z. (2024). Advancing fractured geothermal system modeling with artificial neural network and bidirectional gated recurrent unit. Applied Energy, 372, 123826. doi: 10.1016/j.apenergy.2024.123826
Liu, F., & Liang, C. (2024). Short-term power load forecasting based on AC-BiLSTM model. Energy Reports. doi: 10.1016/j.egyr.2024.01.026
Liu, Z., Shao, T., & Zhang, X. (2024). BCG signal analysis based on improved VMD algorithm. Measurement, 231, 114631. doi: 10.1016/j.measurement.2024.114631
Luo, Q. R., Xu, H., & Bai, L. H. (2022). Prediction of significant wave height in hurricane area of the Atlantic Ocean using the Bi-LSTM with attention model. Ocean Engineering, 266, 112747. doi: 10.1016/j.oceaneng.2022.112747
Ma, P., Li, G., Zhang, H., Wang, C., & Li, X. (2024). Prediction of remaining useful life of rolling bearings based on multiscale efficient channel attention CNN and bidirectional GRU. IEEE Transactions on Instrumentation and Measurement, 73, 1-13. doi: 10.1109/TIM.2023.3347787
Mahdavi-Meymand, A., & Sulisz, W. (2023). Application of nested artificial neural network for the prediction of significant wave height. Renewable Energy. doi: 10.1016/j.renene.2023.03.118
Mahdavi-Meymand, A., & Sulisz, W. (2024). Development of pyramid neural networks for prediction of significant wave height for renewable energy farms. Applied Energy, 362, 123009. doi: 10.1016/j.apenergy.2024.123009
Meng, F., Song, T., Xu, D., Xie, P., & Li, Y. (2021). Forecasting tropical cyclones wave height using bidirectional gated recurrent unit. Ocean Engineering, 234, 108795. doi: 10.1016/j.oceaneng.2021.108795
Mumuni, A., & Mumuni, F. (2022). Data augmentation: A comprehensive survey of modern approaches. In Array. doi: 10.1016/j.array.2022.100258
Qian, S., Peng, T., Tao, Z., Li, X., Nazir, M. S., & Zhang, C. (2024). An evolutionary deep learning model based on XGBoost feature selection and Gaussian data augmentation for AQI prediction. Process Safety and Environmental Protection, 191, 836-851. doi: 10.1016/j.psep.2024.08.119
Qin, C., Huang, G., Yu, H., Zhang, Z., Tao, J., & Liu, C. (2024). Adaptive VMD and multi-stage stabilized transformer-based long-distance forecasting for multiple shield machine tunneling parameters. Automation in Construction, 165, 105563. doi: 10.1016/j.autcon.2024.105563
Rezaei, M., Mohammadifar, A., Gholami, H., Mina, M., Riksen, M. J. P. M., & Ritsema, C. (2023). Mapping of the wind erodible fraction of soil by bidirectional gated recurrent unit (BiGRU) and bidirectional recurrent neural network (BiRNN) deep learning models. Catena. doi: 10.1016/j.catena.2023.106953
Sheng, A., Xie, L., Zhou, Y., Wang, Z., & Liu, Y. (2023). A Hybrid Model Based on Complete Ensemble Empirical Mode Decomposition With Adaptive Noise, GRU Network and Whale Optimization Algorithm for Wind Power Prediction. IEEE Access. doi: 10.1109/ACCESS.2023.3287319
Shi, J., Su, T., Li, X., Wang, F., Cui, J., Liu, Z., & Wang, J. (2023). A Machine-Learning Approach Based on Attention Mechanism for Significant Wave Height Forecasting. Journal of Marine Science and Engineering. doi: 10.3390/jmse11091821
Sivasakthi, B., & Selvanayagi, D. (2023). Prediction of Osteoporosis Disease Using Enhanced Elman Recurrent Neural Network with Bacterial Colony Optimization. doi: 10.1007/978-981-19-9819-5_16
Wan, A., Chang, Q., AL-Bukhaiti, K., & He, J. (2023). Short-term power load forecasting for combined heat and power using CNN-LSTM enhanced by attention mechanism. Energy. doi: 10.1016/j.energy.2023.128274
Wang, M., & Ying, F. (2023a). A hybrid model for multistep-ahead significant wave height prediction using an innovative decomposition–reconstruction framework and E-GRU. Applied Ocean Research, 140, 103752. doi: 10.1016/j.apor.2023.103752
Wang, M., & Ying, F. (2023b). Point and interval prediction for significant wave height based on LSTM-GRU and KDE. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.116247
Wang, M., Ying, F., & Nan, Q. (2024). Refined offshore wind speed prediction: Leveraging a two-layer decomposition technique, gated recurrent unit, and kernel density estimation for precise point and interval forecasts. Engineering Applications of Artificial Intelligence, 133, 108435. doi: 10.1016/j.engappai.2024.108435
Wang, Z., Peng, T., Zhang, X., Chen, J., Qian, S., & Zhang, C. (2025). Enhancing multi-step short-term solar radiation forecasting based on optimized generalized regularized extreme learning machine and multi-scale Gaussian data augmentation technique. Applied Energy, 377, 124708. doi: 10.1016/j.apenergy.2024.124708
Wei, A., Li, X., Yan, L., Wang, Z., & Yu, X. (2023). Machine learning models combined with wavelet transform and phase space reconstruction for groundwater level forecasting. Computers and Geosciences. doi: 10.1016/j.cageo.2023.105386
Wu, S., Guo, H., Zhang, X., & Wang, F. (2024). Short-Term Photovoltaic Power Prediction Based on CEEMDAN and Hybrid Neural Networks. IEEE Journal of Photovoltaics. doi: 10.1007/978-3-031-73407-6_33.
Xian, S., & Feng, X. (2023). Meerkat optimization algorithm: A new meta-heuristic optimization algorithm for solving constrained engineering problems. Expert Systems with Applications. doi: 10.1016/j.eswa.2023.120482
Xin, J., Zhou, C., Jiang, Y., Tang, Q., Yang, X., & Zhou, J. (2023). A signal recovery method for bridge monitoring system using TVFEMD and encoder-decoder aided LSTM. Measurement: Journal of the International Measurement Confederation. doi: 10.1016/j.measurement.2023.112797
Yang, H., Gu, D., Fu, S., Lu, Q., & Wang, J. (2025, May). A Long-Term Prediction Method of Gas Concentration Signal with Noise in Fully Mechanized Coal Mining Face Using CEEMDAN Combined with GRU. In International conference on the Efficiency and Performance Engineering Network (pp. 343-356). Cham: Springer Nature Switzerland. doi: 10.1007/978-3-031-73407-6_33.
Yang, X., & Li, S. (2023). Prediction of COVID-19 Using a WOA-BILSTM Model. Bioengineering. doi: 10.3390/bioengineering10080883
Yang, Y., Yang, Y., Zhou, S., Li, H., Zhu, W., Liu, Y., Xie, C. and Zhang, R. (2024). Degradation prediction of proton exchange membrane fuel cell based on mixed gated units under multiple operating conditions. International Journal of Hydrogen Energy, 67, 268-281. doi: 10.1016/j.ijhydene.2024.04.186
Yeganeh-Bakhtiary, A., EyvazOghli, H., Shabakhty, N., & Abolfathi, S. (2023). Machine learning prediction of wave characteristics: Comparison between semi-empirical approaches and DT model. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.115583
Yuan, L., Ma, Y., & Liu, Y. (2023). Ensemble deep learning models for protein secondary structure prediction using bidirectional temporal convolution and bidirectional long short-term memory. Frontiers in Bioengineering and Biotechnology, 11, 1051268. doi: 10.3389/fbioe.2023.1051268
Zhang, H., Wu, W., Song, X., & Chen, Z. (2024). Improving density logging resolution by VMD-CEEMDAN-ICWT method and its application in thin layer identification. Geoenergy Science and Engineering, 239, 212993. doi: 10.1016/j.geoen.2024.212993
Zhang, J., Xin, X., Shang, Y., Wang, Y., & Zhang, L. (2023). Nonstationary significant wave height forecasting with a hybrid VMD-CNN model. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.115338
Zhang, R., & Dai, H. (2023). Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion. Computer Methods in Applied Mechanics and Engineering. doi: 10.1016/j.cma.2022.115689
Zhao, L., Li, J., Feng, K., Wei, X., Song, J., & Jiao, Y. (2023). A hybrid optimization algorithm for GWO Fine-tuning GRU-Aided AKF during GPS outage. Measurement: Journal of the International Measurement Confederation. doi: 10.1016/j.measurement.2022.112302
Zhao, L., Li, Z., Zhang, J., & Teng, B. (2023). An integrated complete ensemble empirical mode decomposition with adaptive noise to optimize LSTM for significant wave height forecasting. Journal of Marine Science and Engineering, 11(2), 435. doi: 10.3390/jmse11020435
Zhao, Z., Yun, S., Jia, L., Guo, J., Meng, Y., He, N., Li, X., Shi, J., & Yang, L. (2023). Hybrid VMD-CNN-GRU-based model for short-term forecasting of wind power considering spatio-temporal features. Engineering Applications of Artificial Intelligence. doi: 10.1016/j.engappai.2023.105982
Zheng, Z., Ali, M., Jamei, M., Xiang, Y., Abdulla, S., Yaseen, Z. M., & Farooque, A. A. (2023). Multivariate data decomposition based deep learning approach to forecast one-day ahead significant wave height for ocean energy generation. Renewable and Sustainable Energy Reviews. doi: 10.1016/j.rser.2023.113645
Zhou, S., Zhang, Z. X., Luo, X., Niu, S., Jiang, N., & Yao, Y. (2023). Developing a hybrid CEEMDAN-PE-HE-SWT method to remove the noise of measured carbon dioxide blast wave. Measurement, 223, 113797. doi: 10.1016/j.measurement.2023.113797
Zhou, T., Yang, X., Ren, H., Li, C., & Han, J. (2023). The prediction of ship motion attitude in seaway based on BSO-VMD-GRU combination model. Ocean Engineering. doi: 10.1016/j.oceaneng.2023.115977
Zhu, R., Gao, J., Li, M., Gao, Q., Wu, X., & Zhang, Y. (2023). A ppb-level online detection system for gas concentrations in CS2/SO2 mixtures based on UV-DOAS combined with VMD-CNN-TL model. Sensors and Actuators B: Chemical. doi: 10.1016/j.snb.2023.134440
Zulqarnain, M., Ghazali, R., Aamir, M., & Hassim, Y. M. M. (2024). An efficient two-state GRU based on feature attention mechanism for sentiment analysis. Multimedia Tools and Applications. doi: 10.1007/s11042-022-13339-4
مدل سازی و مدیریت آب و خاک
دوره 6، Special Issue
Guest Editor: Dr. Raoof Mostafazadeh
خرداد 1405
صفحه 140-170

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  • تاریخ دریافت: 03 آبان 1404
  • تاریخ بازنگری: 05 آذر 1404
  • تاریخ پذیرش: 06 آذر 1404

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