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Significant Wave Heights (SWH) is an important attribute to describe ocean waves, and SWH prediction is of great significance for ensuring the design of offshore engineering and the safety of offshore operations. In recent years, deep learning methods have been used to predict SWH, but the existing methods cannot effectively capture the long-term correlation of SWH, thus ignoring the local associations between multiple elements of the ocean. To this end, this paper proposes a SWH prediction model (Multi-elements Local and Global Correlation for Wave height Prediction, MLG-SWH) that combines local and global features of marine multi-elements. First, using multiple factors such as significant wave height, wind speed and period as input, a Local-Global Embedding (LGE) module is designed to embed local correlation and time information of ocean multi-elements. Then, an encoder-decoder structure is used to extract the features of ocean wave height, where a casual dilated convolution self-attention module is designed to effectively capture the global long-term correlation of ocean multi-element sequences and the generative prediction method in the decoder is adopted to avoid errors accumulated in the single-step iterative prediction. Finally, the data of two stations with different characteristics of SWH variation in the North Atlantic are selected for experimental evaluations. Compared with classical time-series forecasting models and mainstream deep learning methods, the MLG-SWH model achieves the lowest mean square error and mean absolute error in 24 and 48 hours SWH forecasting, having a greater advantage in long-term time series prediction. [ABSTRACT FROM AUTHOR]

In this paper, a 2-stage cascaded deep learning framework, Port Wave Prediction Network (PWPNet), is proposed for real-time prediction of significant wave height (SWH) distribution in a port. The PWP-out model of the first stage, predicting port-entrance wave parameters, utilizes three branches, the first branch using a Long Short Term Memory (LSTM) module to learn the temporal dependencies of time sequences of port-entrance wave parameters, the second branch using Wave and Wind field Feature Extraction (WWFE) modules, composed of a residual network with spatial and channel attention, to capture spatiotemporal characteristics of outside-port 2D wave and wind field data, the third branch using multi-scale time encoding to capture the periodic characteristics of waves and wind. The PWP-in model of the second stage, estimating the in-port SWH distribution, uses port-entrance wave parameters based on a customized Artificial Neural Network (ANN) and takes PWP-out's output as its input. A comparison of the performance of PWP-out and mainstream machine learning models including LSTM, GRU, BPNN, SVR, ELM, and RF at Hambantota Port shows that PWP-out outperforms all other models regarding medium-term (25–48 h), med–long-term (49–72 h), and long-term (73–96 h) predictions, and ablation experiments proved the effectiveness of the three branches. Furthermore, the performance comparison of our PWPNet and other 2-stage models of LSTM, GRU, BPNN, SVR, ELM, and RF cascaded with PWP-in shows that PWPNet outperforms those cascaded models for medium-term to long-term predictions of SWH distribution in a port. [ABSTRACT FROM AUTHOR]

Significant wave height prediction for the following hours is a necessity for the planning and operation of wave energy devices. For a site-specific and short-term prediction, classical numerical wave forecasting methods may not be justified as exhaustive climatological data and huge computational power are needed. In this paper, a combination of a decomposition approach and long short-term memory network was presented to forecast the significant wave heights. An improved version of complete ensemble empirical mode decomposition algorithm and recurrence quantification analysis were applied to separate the original time series into deterministic and stochastic components. Each decomposed series was forecasted by the long short-term memory network and the final predicted significant wave heights were obtained by integrating the deterministic and stochastic predictions. Wave data measured at three buoy stations along the eastern coast of the United States were utilized to verify the hybrid model. The performance of the proposed method in three different wave height ranges was evaluated. The results suggested that the hybrid model outperformed the stand-alone long short-term memory network adjusted on the unseparated signal; in particular, for longer lead times and larger wave heights. [ABSTRACT FROM AUTHOR]

Deep learning methods have excellent prospects for application in wave forecasting research. This study employed the convolutional LSTM (ConvLSTM) algorithm to predict the South China Sea (SCS) significant wave height (SWH). Three prediction models were established to investigate the influences of setting different parameters and using multiple training data on the forecasting effects. Compared with the SWH data from the China–France Ocean Satellite (CFOSAT), the SWH of WAVEWATCH III (WWIII) from the pacific islands ocean observing system are accurate enough to be used as training data for the ConvLSTM-based SWH prediction model. Model A was preliminarily established by only using the SWH from WWIII as the training data, and 20 sensitivity experiments were carried out to investigate the influences of different parameter settings on the forecasting effect of Model A. The experimental results showed that Model A has the best forecasting effect when using three years of training data and three hourly input data. With the same parameter settings as the best prediction performance Model A, Model B and C were also established by using more different training data. Model B used the wind shear velocity and SWH as training and input data. When making a 24-h SWH forecast, compared with Model A, the root mean square error (RMSE) of Model B is decreased by 17.6%, the correlation coefficient (CC) is increased by 2.90%, and the mean absolute percentage error (MAPE) is reduced by 12.2%. Model C used the SWH, wind shear velocity, wind and wave direction as training and input data. When making a 24-h SWH forecast, compared with Model A, the RMSE of Model C decreased by 19.0%, the CC increased by 2.65%, and the MAPE decreased by 14.8%. As the performance of the ConvLSTM-based prediction model mainly rely on the SWH training data. All the ConvLSTM-based prediction models show a greater RMSE in the nearshore area than that in the deep area of SCS and also show a greater RMSE during the period of typhoon transit than that without typhoon. Considering the wind shear velocity, wind, and wave direction also used as training data will improve the performance of SWH prediction.

• A novel combined prediction system for SWH prediction is proposed. • Developed an integrated feature extraction method. • Multi-criteria decision-making method is introduced to select sub-models. • A multi-objective homogeneous nuclear molecular optimization is proposed. • A hybrid kernel density estimation method is developed. Accurate prediction of significant wave height is paramount for the effective design, operation, and maintenance of wave energy converters. However, current research falls short in achieving precise and stable point predictions, along with comprehensive uncertainty analysis of significant wave height. To address this gap, this study presents a comprehensive significant wave height combined prediction system. This integrated system encompasses outlier detection utilizing Autoencoders, sophisticated feature engineering, a multi-criteria decision-based model selection methodology, a multi-objective homogeneous nuclear molecular optimization algorithm, and a hybrid kernel density estimation technique. To tackle the critical issue of model selection within ensemble prediction, we introduce a multi-criteria compromise solution ranking algorithm known as VIKOR for the selection of sub-models. Additionally, a novel multi-objective homogeneous nuclear molecular optimization algorithm is proposed, which incorporates joint opposing selection and an elite retention strategy to effectively manage multiple objectives simultaneously, yielding Pareto optimal solutions for combining weights. Furthermore, a hybrid kernel density estimation approach is developed, surpassing previous methods reliant on a single kernel function and fixed bandwidth, thereby achieving a more precise fit to the distribution of wave height data. The effectiveness of the proposed model is rigorously evaluated using wave height datasets from three distinct locations. The experimental results convincingly demonstrate that the significant wave height combined prediction system outperforms existing solutions, excelling in both point and interval predictions of significant wave height. [ABSTRACT FROM AUTHOR]

In this paper, a 2-stage cascaded deep learning framework, Port Wave Prediction Network (PWPNet), is proposed for real-time prediction of significant wave height (SWH) distribution in a port. The PWP-out model of the first stage, predicting port-entrance wave parameters, utilizes three branches, the first branch using a Long Short Term Memory (LSTM) module to learn the temporal dependencies of time sequences of port-entrance wave parameters, the second branch using Wave and Wind field Feature Extraction (WWFE) modules, composed of a residual network with spatial and channel attention, to capture spatiotemporal characteristics of outside-port 2D wave and wind field data, the third branch using multi-scale time encoding to capture the periodic characteristics of waves and wind. The PWP-in model of the second stage, estimating the in-port SWH distribution, uses port-entrance wave parameters based on a customized Artificial Neural Network (ANN) and takes PWP-out’s output as its input. A comparison of the performance of PWP-out and mainstream machine learning models including LSTM, GRU, BPNN, SVR, ELM, and RF at Hambantota Port shows that PWP-out outperforms all other models regarding medium-term (25–48 h), med–long-term (49–72 h), and long-term (73–96 h) predictions, and ablation experiments proved the effectiveness of the three branches. Furthermore, the performance comparison of our PWPNet and other 2-stage models of LSTM, GRU, BPNN, SVR, ELM, and RF cascaded with PWP-in shows that PWPNet outperforms those cascaded models for medium-term to long-term predictions of SWH distribution in a port.

• Applied various soft-computing techniques for Significant Wave Height prediction. • Used data from diverse geographical locations from Canadian and Chinese Stations. • Demonstrated that ANFIS (SC) and BiGRU models provide the highest accuracy. • Models can help to reduce greenhouse gas emissions in marine transportation. • Findings can enhance maritime safety and disaster management. Predicting significant wave height (SWH) is critical to ocean engineering, navigation, and renewable energy harvesting. This study comprehensively analyzes several machine learning (ML) and deep learning (DL) models. These include the adaptive neuro-fuzzy inference system with subtractive clustering ANFIS (SC), an artificial neural network with Bayesian regularization ANN (BR), bidirectional long-short-term memory (BiLSTM), bidirectional gated recurrent unit (BiGRU), and BiGRU with attention mechanism (AM), all employed for the prediction of SWH. The models were evaluated using data from three stations: a Canadian station in the North Atlantic Ocean and two Chinese stations in the East China Sea. Our study demonstrates the superior performance of the ANFIS (SC) model across all stations. For instance, the ANFIS model achieved an R2 value of 0.9979 at the Canadian station, outperforming the gated recurrent unit (GRU) based model with an R2 of 0.9127 from previous research. Similarly, at the Lianyungang (LYG) station, the ANFIS model achieved an R2 value of 0.9812, surpassing the performance of the GRU network used in prior studies, which reached an R2 of 0.6436 for 6-hour forecasts. Moreover, our study outperforms the convolutional neural network (CNN) based BiGRUAM model used for shale oil production prediction regarding R2 values. Furthermore, compared to the dynamic ensemble ESN model used for wave height prediction, our ANFIS model demonstrated more robust and consistent performance. Therefore, this research significantly contributes to the field of SWH prediction by presenting the superior performance of the ANFIS model across different geographical locations and conditions. This research opens new avenues for future research and practical applications in oceanography, weather forecasting, and renewable energy harvesting. The architecture of the ML and DL based Significant Wave Height Prediction System [Display omitted] [ABSTRACT FROM AUTHOR]

Significant wave height (SWH) prediction plays an important role in marine engineering areas such as fishery, exploration, power generation, and ocean transportation. For long-term forecasting of a specific location, classical numerical model wave height forecasting methods often require detailed climatic data and incur considerable calculation costs, which are often impractical in emergencies. In addition, how to capture and use the dynamic correlation between multiple variables is also a major research challenge for multivariate SWH prediction. To explore a new method for predicting SWH, this paper proposes a deep neural network model for multivariate time series SWH prediction—namely, CLTS-Net. In this study, the sea surface wind and wave height in the ERA5 dataset of the relevant points P1, P2, and P3 from 2011 to 2018 were used as input information to train the model and evaluate the model’s SWH prediction performance. The results show that the correlation coefficients (R) of CLTS-Net are 0.99 and 0.99, respectively, in the 24 h and 48 h SWH forecasts at point P1 along the coast. Compared with the current mainstream artificial intelligence-based SWH solutions, it is much higher than ANN (0.79, 0.70), RNN (0.82, 0.83), LSTM (0.93, 0.91), and Bi-LSTM (0.95, 0.94). Point P3 is located in the deep sea. In the 24 h and 48 h SWH forecasts, the R of CLTS-Net is 0.97 and 0.98, respectively, which are much higher than ANN (0.71, 0.72), RNN (0.85, 0.78), LSTM (0.85, 0.78), and Bi-LSTM (0.93, 0.93). Especially in the 72 h SWH forecast, when other methods have too large errors and have lost their practical application value, the R of CLTS-Net at P1, P2, and P3 can still reach 0.81, 0.71, and 0.98. The results also show that CLTS-Net can capture the short-term and long-term dependencies of data, so as to accurately predict long-term SWH, and has wide applicability in different sea areas.

Accurate significant wave height (Hs) prediction is crucial for marine renewable energy development. The hybrid models combining multi-resolution analysis techniques such as empirical mode decomposition and wavelet transform with intelligence algorithm have flourished in Hs forecasting. However, these hybrid models cannot fit multivariable input mode well. In this study, a novel multivariable hybrid model is proposed. The improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and recurrence quantification analysis (RQA) were integrated as the deterministic and stochastic components decomposition (DSD) method. Then three machine learning models was integrated with DSD method as hybrid models, respectively. For more sufficient forecasting information, wind speed (Ws), wind direction (Wd) and Hs were adopted as inputs to construct multivariable hybrid models. The forecasting experiment was benchmarked with those from univariate hybrid models, multivariable single models and univariate single models. Three buoy-measured datasets were utilized for validation. Results revealed the positive effect of wind data on long-term prediction and the improvement to prediction by the DSD method. Benefiting from the advantages of both, multivariable hybrid models outperformed other benchmark models. Among them, the multivariable hybrid model based on long short-term memory (LSTM) network, DSD-LSTM-m, achieved the best forecasting performance. • A multivariable hybrid model for significant wave height forecasting is proposed. • The influence of multivariable input was revealed. • The characteristic of multivariable and univariate hybrid model was analyzed. • Comprehensive tests on various scenarios were performed for model verification. [ABSTRACT FROM AUTHOR]

Significant wave height forecasting is an important aspect of many ocean related engineering and scientific phenomena. However, due to the complicated and chaotic nature of ocean waves, in general, data in hand has to be decomposed into its deterministic and stochastic features before feeding into the predictive model. The present study introduces a refined singular value decomposition (SVD) based algorithm for decomposing raw data into its hierarchally energetic pertinent features. SVD-fuzzy model is developed via hybridizing Adaptive Neuro-Fuzzy Inference Systems (ANFIS) model with the proposed algorithm. SVD-fuzzy model is compared with stand-alone fuzzy and combination of a widely used wavelet transformation and fuzzy logic (wavelet-fuzzy) models in predicting SWH in five distinctive Pacific Ocean locations for future lead times 1 h, 2 h, 3 h, 4 h, 5 h, 6 h, 12 h, 18 h and 24 h from two previous hourly SWH data. According to mean square error (MSE), the Nash-Sutcliffe coefficient of efficiency (CE), coefficient of determination (R2), and mean absolute error (MAE) model evaluation metrics, it is found that SVD-fuzzy model outperformed the stand-alone fuzzy model for all lead times and data (Maximum CE of SVD-Fuzzy model is 0.991). Further, SVD-fuzzy model results compare well with those of Wavelet-Fuzzy model. The outcomes of this study indicate that the integrated SVD-fuzzy modeling approach, with no underlying assumptions a priori, is a promising principled tool for its possible future applications not only for coastal and ocean problems but in engineering and scientific disciplines where future state space prediction of a complex and stochastic dynamical system is significant. • A data preprocessing algorithm based on singular value decomposition (SVD) proposed. • SVD based algorithm combined with adaptive neural fuzzy inference system (ANFIS). • Hybrid SVD-fuzzy models developed for significant wave height (SWH) forecasting. • SVD-fuzzy model outperformed fuzzy model for all three Pacific buoy stations' data. • SVD-based model found superior both in short and long time SWH forecasting. [ABSTRACT FROM AUTHOR]

In this paper we propose to apply the Support Vector Regression (SVR) methodology to significant wave height estimation using the shadowing effect, that is visible on the X-band marine radar images of the sea surface due to the presence of high waves. One of the main problems of using sea clutter images is that, for a given sea state conditions, the shadowing effect depends on the radar antenna installation features, such as the angle of incidence. On the other hand, for a given radar antenna location, the shadowing properties depend on the different sea state parameters, like wave periods, and wave lengths. Thus, in this paper we show that SVR can be successfully trained from simulation-based data. We propose a simulation process for X-band marine radar images derived from simulated wave elevation fields using the stochastic wave theory. We show the performance of the SVR in simulation data and how SVR outperforms alternative algorithms such as neural networks. Finally, we show that the simulation process is reliable by applying the SVR methodology trained in the simulation-based data to real measured data, obtaining good prediction results in wave height, which indicates the goodness of our proposal. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative method for nowcasting significant wave height (H s) through the development of hierarchical machine learning classification models. In testing the hypothesis that hierarchical classification can improve H s prediction, flat and hierarchical classifiers were developed and tested on field-data recorded on a coastal jetty located in the southern coasts of Cyprus. A comprehensive investigation of the performance of flat over hierarchical classification models yields that the proposed method provides greater flexibility throughout the model development stages. This flexibility is attributed to the manipulation of data before training, optimization of classifier's hyperparameters during training, and the curtailment of features post-training at each level of the hierarchy. It is demonstrated that, the hierarchical approach resulted in better classification performance across a plethora of performance metrics established for a comprehensive comparison. It is also shown that the increased performance of the proposed approach comes at the expense of complexity arising from performing computationally expensive operations and the requirement for development of multiple local classifiers. Still, the increased classification performance of the hierarchical approach highlights the potential of this original method and the requirement for a rigid framework to be constructed for the development of hierarchical models for H s prediction. • Hierarchical classification can be successfully applied to the significant wave height prediction problem. • Unsupervised learning techniques can be deployed to identify the natural hierarchical structure of significant wave heights. • Training multiple binary and multiclass classifiers along the hierarchy provides flexibility pre, during and post-training. • Increased flexibility in the hierarchical approach yields better classification models across various performance metrics. [ABSTRACT FROM AUTHOR]

Significant wave height (SWH) prediction plays an important role in marine engineering areas such as fishery, exploration, power generation, and ocean transportation. For long-term forecasting of a specific location, classical numerical model wave height forecasting methods often require detailed climatic data and incur considerable calculation costs, which are often impractical in emergencies. In addition, how to capture and use the dynamic correlation between multiple variables is also a major research challenge for multivariate SWH prediction. To explore a new method for predicting SWH, this paper proposes a deep neural network model for multivariate time series SWH prediction—namely, CLTS-Net. In this study, the sea surface wind and wave height in the ERA5 dataset of the relevant points P1, P2, and P3 from 2011 to 2018 were used as input information to train the model and evaluate the model's SWH prediction performance. The results show that the correlation coefficients (R) of CLTS-Net are 0.99 and 0.99, respectively, in the 24 h and 48 h SWH forecasts at point P1 along the coast. Compared with the current mainstream artificial intelligence-based SWH solutions, it is much higher than ANN (0.79, 0.70), RNN (0.82, 0.83), LSTM (0.93, 0.91), and Bi-LSTM (0.95, 0.94). Point P3 is located in the deep sea. In the 24 h and 48 h SWH forecasts, the R of CLTS-Net is 0.97 and 0.98, respectively, which are much higher than ANN (0.71, 0.72), RNN (0.85, 0.78), LSTM (0.85, 0.78), and Bi-LSTM (0.93, 0.93). Especially in the 72 h SWH forecast, when other methods have too large errors and have lost their practical application value, the R of CLTS-Net at P1, P2, and P3 can still reach 0.81, 0.71, and 0.98. The results also show that CLTS-Net can capture the short-term and long-term dependencies of data, so as to accurately predict long-term SWH, and has wide applicability in different sea areas. [ABSTRACT FROM AUTHOR]

Explicit wave models and expensive sensor equipment capable of predicting and measuring wave parameters often carry a prohibitive computational and financial expense. To counter this, this paper proposes an alternative method for nowcasting coastal zone significant wave heights through the joint use of meteorological and structural data in the training of supervised machine learning models. In testing the hypothesis that structural data can improve model classification, artificial neural network and decision tree models were developed, trained and tested on field data recorded on a coastal jetty located in the southern coasts of Cyprus. A comprehensive investigation of the different models yields that the joint use of meteorological and structural features can improve classification performance, regardless of the network choice. It is also demonstrated that redundancy of training parameters could inject unwanted overfitting, reducing model generalization. To address this, a method for quantifying feature importance has been proposed by exploiting the nature of decision tree algorithms and the Gini impurity index, reaffirming that structural features do indeed benefit model classification. These results highlight the potential of tapping into the untapped pool of structural data for significant wave height prediction, paving the way for new research to be undertaken in this direction. • Structural acceleration data can be leveraged to obtain better classification models, aiding the prediction of significant wave height. • Neural networks and tree ensemble classification algorithms are effective in the prediction of significant wave height. • Network complexity and structural feature redundancy increases chances of overfitting, compromising model generalization. • Gini impurity index is a viable feature importance indicator, aiding the robustness of the models post feature curtailement. [ABSTRACT FROM AUTHOR]

A long short-term memory (LSTM) network is proposed for the quick prediction of significant wave height with higher accuracy than conventional neural network. The LSTM network is used for 1-h and 6-h predictions at ten stations with different environmental conditions. Using the wind speed of the past 4 h and the wave height and wind direction of the past 1 h as input parameters, the LSTM prediction results were obtained, and compared with results from a back propagation neural network, extreme learning machine, support vector machine, residual network, and random forest algorithm. Five statistical indicators were used to evaluate the results comprehensively. The minimum mean absolute error percentage of the 1-h and 6-h forecasts was 5.14% and 5.24%, respectively. The results demonstrate that the LSTM can achieve stable prediction effects, with accurate 1-h predictions and satisfactory 6-h predictions. In addition, predictions for four time spans, namely 12 h, 1 day, 2 days, and 3 days, were determined for Station 41008. The results show the powerful ability of LSTM to perform long-term prediction. The simulating waves nearshore-LSTM (SWAN-LSTM) model was proposed to make a single-point prediction, and it outperformed the standard SWAN model with an improvement in accuracy of over 65%. • LSTM neural network method is used for significant wave height prediction. • Significant wave height predictions are simulated by 6 algorithms in 10 stations. • Every 1hr, 6 h s, 12 h s, 1 day, 2 days, 3 days wave height predictions are carried out. • 5 indicators are used to evaluate the prediction results of different data volumes. • A SWAN-LSTM model are proposed to improve the accuracy of SWAN model. [ABSTRACT FROM AUTHOR]