Ocean Wind Speed Prediction Based on the Fusion of Spatial Clustering and an Improved Residual Graph Attention Network

Abstract

Accurately predicting wind speed is crucial for the generation efficiency of offshore wind energy. This paper proposes an ultra-short-term wind speed prediction method using a graph neural network with a multi-head attention mechanism. The methodology aims to effectively explore the spatio-temporal correlations present in offshore wind speed data to enhance the accuracy of wind speed predictions. Initially, the offshore buoys are organized into a graphical network. Subsequently, in order to cluster the nodes with comparable spatio-temporal features, it clusters the nearby nodes around the target node. Then, a multi-head attention mechanism is incorporated to prioritize the interconnections among distinct regions. In the construction of the graph neural network, a star topology structure is formed by connecting additional nodes to the target node at the center. The effectiveness of this methodology is validated and compared to other time series-based approaches through comparative testing. Metrics such as Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, and R yielded values of 0.364, 0.239, 0.489, and 0.985, respectively. The empirical findings indicate that graph neural networks utilizing a multi-head attention mechanism exhibit notable benefits in the prediction of offshore wind speed, particularly when confronted with intricate marine meteorological circumstances.

1. Introduction

The escalating growth of the economy and society has led to a significant increase in the consumption of fossil fuels in recent times, resulting in a heightened level of environmental pollution. Consequently, nations across the globe have begun to prioritize the advancement of clean and sustainable sources of energy [1]. Wind energy has experienced rapid global growth due to its environmentally friendly nature and renewable characteristics [2]. The fundamental concept behind wind power generation is harnessing the kinetic energy of wind to propel wind turbines, hence facilitating the conversion of this energy into electrical energy [3].

In contrast to onshore wind power resources, offshore wind resources exhibit a significant abundance. Hence, due to the expeditious advancement of offshore wind power technology, there has been a notable rise in the establishment of offshore wind farms. Consequently, the exploration and exploitation of offshore wind energy have garnered escalating interest from the global community [4]. Based on the 2023 Global Offshore Wind Report published by the GWEC, the global offshore wind market has experienced a compound annual growth rate of 21% over the previous ten years. This growth has resulted in a cumulative installed capacity of 64.3 GW by the conclusion of 2022, representing 7.1% of the overall global wind power capacity [5].

The power generation efficiency of offshore wind power is significantly impacted by the instability and unpredictability of offshore wind speeds. Consequently, this has a direct effect on the equilibrium between power grid supply and demand, posing substantial challenges to grid dispatching and jeopardizing the secure and steady operation of the grid [6]. Hence, the prediction of wind speed emerges as a crucial approach in addressing these issues. The utilization of this technology can offer significant insights and recommendations for the efficient management of power systems, electricity generation, transmission and distribution, energy storage administration, and decision making in energy markets [7,8,9]. In this context, the central question of our study revolves around how to enhance the accuracy and reliability of offshore wind speed predictions.

Presently, wind speed forecasting models can be primarily categorized into physical methodologies, statistical methodologies, artificial intelligence methodologies, and hybrid forecasting methodologies [10]. NWP and CM are commonly employed as physical approaches to estimate forthcoming wind speeds through the simulation and prediction of atmospheric motion [11,12] The conventional statistical models encompass ARMA models [13] and ARIMA models [14]. Physical approaches are predicated on the utilization of simulated environmental parameters, whilst statistical methods are contingent upon historical data. Due to their reliance on linear models and data-dependent assumptions, these methods are not adept at effectively addressing the nonlinear attributes inherent in wind power series.

In order to enhance the precision of wind speed prediction, scholars have been incorporating machine learning methods into the domain [15]. The initial introduction of machine learning methods encompassed neural networks, namely, biological neural networks, which had the ability to learn and adapt to their surrounding environment. The primary mechanism by which machine learning acquires knowledge is through iterative training of the neural network’s parameters, resulting in the determination of the weight parameters for the predictive model [16]. Several approaches commonly used in machine learning include Markov chains, SVM, KNN, ELM, and RF. In reference [17], Brahimi et al. described this approach for a model utilizes meteorological parameters such as air pressure, wind direction, total solar radiation and relative humidity as input features. The study conducted in [18] employed an enhanced SVM algorithm for the purpose of predicting short-term wind power. The utilization of large data and advancements in computing power have facilitated the widespread application of diverse deep learning models in the field of wind speed forecasting research. Several widely used deep learning models in the field of artificial intelligence include CNN, RNN, GRU, LSTM, and others.

While the current machine learning methods have demonstrated some efficacy in enhancing the precision of wind speed forecasting, it is important to acknowledge that each model possesses inherent constraints. For instance, DNN is not adept at accommodating temporal variations in time series data. Recurrent neural networks, on the other hand, often encounter the challenge of vanishing gradients [19]. Additionally, long short-term memory models suffer from the drawback of prolonged training durations. To address the limitations of individual models, researchers have started to explore ensemble forecasting techniques as a potential means of mitigating these weaknesses. Zhang et al. [20] conducted a VMD-PRBF-ARMA-E model is proposed. This model integrates decomposition algorithms with statistical approaches, and its effectiveness in enhancing the precision of wind speed prediction is demonstrated by an experimental analysis. In the cited work [21], Ren et al. introduce a novel model named EMD-SVR that integrates EMD with support vector regression. This model effectively decomposes wind speed data into several intrinsic mode functions and residual sequences, and subsequently employs SVR for training purposes. In the realm of wind power prediction, a pioneering study by Shahid et al. [22] introduces a revolutionary framework called genetic long short-term memory. This framework combines the principles of long short-term memory with GA to enhance the accuracy of short-term wind power forecasting. The incorporation of models enhances the robustness of wind speed prediction in these systems.

The occurrence of wind is a naturally-occurring phenomenon that arises from the persistent variation of air currents. As a result, there is typically a significant correlation between the speeds of wind in neighboring regions. Hence, the task of characterizing dynamic spatio-temporal correlation information and utilizing it to enhance wind power predictions has emerged as a prominent area of research [23]. The wind speed prediction model proposed in reference [24] combines a convolutional neural network and a multilayer perceptron to incorporate spatio-temporal correlation. Zhu et al. [25] have developed a deep architecture known as the Spatio-Temporal Forecasting Network, which integrates convolutional neural networks with long short-term memory for the purpose of wind speed prediction.

While CNN excels at capturing spatial neighborhood information in matrix representations, wind farms are frequently arranged in non-rectangular grid configurations. In contrast to CNN, GCN leverages the adjacency matrix in graph theory to represent the spatial interconnections among nodes, enabling the more efficient extraction of non-rectangular topological grid structure information. The framework proposed in reference [26] presents a methodology for ultra-short-term wind power forecasting. This methodology utilizes graph neural networks and NWP techniques. The framework constructs adjacency matrices based on geographical distance and focuses on predicting the power output of a cluster of wind farms. Khodayar et al. [27] developed Deep Learning Architecture (GCDLA). This architecture is motivated by the local first-order approximation of spectral graph convolution and utilizes extracted temporal characteristics to make predictions on wind speed time series over all nodes of the graph. The utilization of graph neural networks in constructing a graph structure is documented. Reference [28] forms a graph structure using graph neural networks. This graph structure is used to compute the spatio-temporal correlations between the target turbine and neighboring turbines. Then, a deep residual network (DRN) is used to train the short-term wind power prediction model. The model proposed in reference [29] is MCC-Stem-GNN, which integrates GFT for capturing spatial correlations and DFT for capturing temporal correlations.

Although most contemporary models perform satisfactorily, there are some shortcomings that need to be recognized. The above node building models using graph neural networks rely on manually defined thresholds to determine whether a node is connected to an edge. These methods lack the factor of adaptive graph building. In addition, the graph convolution process used by the GCN network does not consider the degree of importance associated with individual nodes. In this paper, we propose a novel method (DK-RGAT) that combines spatial clustering techniques with an enhanced residual graph attention network to construct the construction dynamic graph in a data-driven manner, and introduces an autonomous attention mechanism to solve the problem of importance weights. Our proposed model is designed to significantly improve the accuracy and effectiveness of wind power predictions and is scientifically innovative.

The primary contributions of this study can be succinctly described as follows:

• This study proposes a method that integrates the DTW and K-means algorithms to generate dynamic network adjacency matrices in a data-driven manner. This approach addresses the existing challenge of relying on manually defined thresholds to establish connections between nodes.
• A novel star topology network structure is developed for the purpose of predicting the target node. Empirical evidence demonstrates that the implementation of a star topology structure yields a notable enhancement in the accuracy of predictions.
• Attention strategies are utilized with the aim of mitigating the loss of previous information in wind power data and enhancing the impact of significant information. The enhancement in feature extraction efficiency in the proposed model leads to improved accuracy in wind power predictions.
• The enhancement of the GAT is achieved through the incorporation of residual structures within the network architecture. This integration effectively mitigates the issue of gradient vanishing that arises when there is an increase in the number of network layers.
• The efficacy and suitability of the proposed model are assessed using wind speed statistics obtained from the National Oceanic and Atmospheric Administration (NOAA) of the United States.

The subsequent sections of this work are structured in the following manner: Section 2 provides an overview of the data sources and information, focusing on their graphical aspects and provides an exposition of the conceptual framework employed in the prediction of spatio-temporal sequences. Section 3 of this report provides a comprehensive analysis of the experimental environment and assessment measures employed in the study. Section 4 provides the conclusions of the study and an analysis of the experimental findings. Section 5 presents an outlook on future work.

2. Materials and Methods

2.1. Materials

The actual data used in this study corresponds to standard meteorological and wave measurements obtained from the National Oceanic and Atmospheric Administration (NOAA, www.ndbc.noaa.gov (accessed on 23 October 2023)) [30]. These NOAA buoys are typically operated and maintained by U.S. government agencies to report wind, wave, and other ocean conditions at strategic locations to support marine navigation, search and rescue operations, and scientific research. The measurements are made by sensors equipped on moored offshore buoys distributed throughout U.S. and international waters maintained by the National Data Buoy Center [31]. Figure 1 shows the exact locations of the experimental sites on the map.

Table 1. Specific information about the relevant buoy information.

Number of the Buoy	Longitude (°W)	Latitude (°N)	Data Number
41001	72.242	34.703	4320
41002	74.936	31.759	4320
41004	79.099	32.502	4320
41009	80.185	28.508	4320
41013	77.764	33.441	4320
44014	74.837	36.603	4320
41025	75.454	35.01	4320
41048	69.573	31.831	4320
42002	93.646	26.055	4320
42036	84.508	28.501	4320
42040	88.237	29.207	4320
42055	94.112	22.14	4320
44008	69.25	40.496	4320
44009	74.692	38.46	4320
44020	70.283	41.497	4320

provides details of the selected sites, including the exact position of each site, data time range used, and total amount of available data.

The target node is Buoy 41009, and other selected buoys should be as close to the target node as possible to capture real-time information about the meteorological and oceanographic conditions associated with the target node. Buoys in closer proximity can provide more accurate data since they are subject to similar meteorological and oceanographic influences, reducing spatial variability in the data. The historical data at the selected sites ranges from 1 April 2023 to 30 April 2023, with sampling every 10 min by the buoys, totaling 4320 data points. This data volume satisfies the requirements of the research or application.

The current concentration of wind power projects in nearshore regions is also considered. Buoy locations close to shore can better reflect nearshore meteorological and oceanographic conditions, which is crucial for the feasibility and efficiency of nearshore wind power projects. By selecting these nearshore sites, we can provide real-time meteorological and oceanographic data relevant to nearshore wind power projects, aiding in the planning, operation, and maintenance of wind farms.

2.2. Methods

2.2.1. Overview

This study proposes a novel approach that integrates spatial clustering and improved residual graph attention networks to enhance the accuracy of offshore wind speed predictions. Compared with current popular wind power forecasting methods, this approach dynamically constructs the graph structure in a data-driven manner, solving the problem of manually setting thresholds for graph construction. It also designs a multi-headed attention graph network incorporated with residual connections, comprehensively considering both spatial and temporal information. This not only improves prediction efficiency but also achieves more accurate predictions. Compared with methods that solely rely on time series, the proposed network framework fully utilizes the spatial correlations between meteorological stations in the target domain. It learns the topological structures in a data-driven manner and automatically learns the contributions of different regions through the attention mechanism. This allows the complex and dynamic meteorological conditions at sea to be better modeled.

Specifically, this study uses the dynamic time warping algorithm to calculate the similarity between wind speed sequences in different sea areas, and then classifies the wind speed sequences into clusters based on spatio-temporal characteristics using K-means clustering. This groups wind speed data from the same category for the target node into one cluster. Next, we construct the topological structure of the graph network with the target node at the center connected to other nodes, forming a star-shaped topology. Residual connections are introduced to alleviate the gradient vanishing problem in deep graph networks. On this basis, we design a multi-headed attention mechanism to capture correlations between different sea areas. Comparative experiments validate the effectiveness of the proposed method and compare it with conventional time series based approaches. Results show that graph neural networks fused with multi-headed attention can significantly improve wind speed prediction accuracy under complex marine meteorological conditions. This study provides an innovative approach to improving marine meteorological forecasting with broad application prospects in fields like marine resource management and meteorological disaster warning. A schematic of the proposed model workflow is shown in Figure 2.

2.2.2. Computing Time Series Similarity

DTW is a measure of the distance between two time series, where each data point in one time series can be matched to multiple data points in the other time series. This enables DTW to compute the distance between time series of differing lengths [32]. Figure 3 illustrates the calculation of distance between two time series objects with unequal temporal durations.

The computational process of the DTW algorithm is as follows:

Suppose we have two time series, a sequence $X=\left(x_1,x_2,\dots ,x_n\right)$ of length $n$, and a sequence $Y=\left(y_1,y_2,\dots ,y_m\right)$ of length $m$. First, create a matrix of size $n\times m$, This matrix is used to store the distances between each pair of points in the two time series, denoted as $d\left(x_i,y_j\right)$, which is typically computed using a distance measure like the Euclidean distance. In this paper, we use Euclidean distance. The Euclidean distance formula is as follows:

$$d(x,y)=\sqrt{\sum _{i=1}^n\sum _{j=1}^m{\left(x_i-y_j\right)}^2}$$

(1)

Initialize a matrix of the same size as the distance matrix to store cumulative distances. The first row and the first column of the cumulative distance matrix are usually set to a large value (e.g., positive infinity) to ensure that the first point is matched with all possible alignment points with a sufficiently large distance, as demonstrated below.

$$\left[\begin{array}{cccccc}\mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }& \mathrm{\infty }& \cdots & \mathrm{\infty }\\ \mathrm{\infty }& 0& 0& 0& \cdots & 0\\ \mathrm{\infty }& 0& 0& 0& \cdots & 0\\ \mathrm{\infty }& 0& 0& 0& \cdots & 0\\ ⋮& ⋮& ⋮& ⋮& \ddots & ⋮\\ \mathrm{\infty }& 0& 0& 0& \cdots & 0\end{array}\right]$$

Starting from the second row and the second column of the cumulative distance matrix, calculate the cumulative distances using the following recursive formula:

$$\omega \left(X,Y\right)=d\left(x_i,y_j\right)+\min \left\{\omega \left(i-1,j-1\right),\omega \left(i-1,j\right),\omega \left(i,j-1\right)\right\}$$

(2)

Here, $min$ represents the minimum of the cumulative distances of the adjacent elements. This formula indicates that the cumulative distance at the current point $\left(i,j\right)$ is the distance $d\left(x_i,y_j\right)$ between the current points plus the minimum cumulative distance among the three adjacent points: upper-left, upper, and left.

$$D[i,j]=DTW(X,Y)=\sqrt{\omega (X,Y)}$$

(3)

Here, $D$ is an $m\ast n$ sized distance matrix, and $D[i,j]$ represents the DTW distance between time series $X\left[i\right]$ and$Y\left[j\right]$. The DTW distance between the two time series $X$ and $Y$ can be obtained by taking the square root of the value in the bottom-right corner of the matrix.

2.2.3. Clustering Algorithm

Clustering algorithms group objects into clusters such that the similarity between objects within the same cluster is maximized, while the similarity between objects from different clusters is minimized.

In this paper, we use k-means clustering, where the clusters are represented by a central vector or point called the centroid. The centroid of each cluster is the mean of all the points assigned to that cluster. The k-means algorithm iteratively reassigns points to their closest centroid and recalculates the centroids based on the current cluster membership until the centroids stabilize. Therefore, k-means clustering aims to partition observations into k clusters where each observation belongs to the cluster with the nearest mean.

First, select the number of clusters k for clustering. Randomly select k time series as the initial centroids or use other initialization methods. Iterate until a stop condition is met; for each time series $X,$calculate its DTW distance to each centroid $C\left[j\right]$.

Assign $X$ to the cluster with the nearest centroid:

$$\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}(i)=\arg \underset{j}{min}D[i,j]$$

(4)

Update the centroids of each cluster based on the assigned data points:

$$\mathrm{Centroid}[k]=\frac{1}{\left|C_k\right|}\sum _{i\in C_k}X[i]$$

(5)

Here, $k$ represents the number of clusters, $Centroid\left[k\right]$ denotes the centroid of the k-th cluster, $C_k$ represents the set of members in the k-th cluster, $X\left[i\right]$ signifies the i-th data point in the time series, and $\left|C_k\right|$ indicates the number of members in the k-th cluster.

2.2.4. Use of the Improved Residual GAT Network

Based on the results of spatial clustering, we constructed an improved residual GAT for wind speed predictions over the ocean. GAT networks learn representations for each node by aggregating information from neighboring nodes, which can handle data with arbitrary graph structures. Meanwhile, the residual structure helps alleviate the gradient vanishing problem during network training. Therefore, this study designed a multi-headed attention GAT network incorporated with residual connections. The overall network architecture is illustrated in Figure 4.

First, the original dataset is converted into a feature matrix using a sliding window method and input to the RGAT network structure. In the network structure, a linear transformation is first performed to generate a hidden matrix. The hidden matrix and its transpose matrix are then used to generate an attention matrix. The attention matrix and hidden matrix are then input to a residual structure. The output of the residual structure is then input to a multi-head attention mechanism. Finally, a linear transformation is performed to obtain the output matrix.

The input to the graph attention mechanism is:

$$X=\left\{\overrightarrow{X_1},\overrightarrow{X_2},\cdots ,\overrightarrow{X_N}\right\},\overrightarrow{X_i}\in {\mathbb{R}}^C$$

(6)

Here, $N$ represents the number of nodes and $C$ represents the number of features. This indicates that the input data contains $N$ nodes, each with $C$ features.

Then a shared self-attention operation is performed on the nodes:

$$e_{ij}=a\left(\mathrm{W}{\overrightarrow{X}}_i,\mathrm{W}{\overrightarrow{X}}_j\right)$$

(7)

Here, the attention coefficient$e_{ij}$ represents the attention weights of a node to other nodes.

In the graph structure, a masked attention approach is adopted, where node $i$ only attends to its neighbor nodes ${\mathcal{N}}_i$ in the graph, and ${\mathcal{N}}_i$ is the neighborhood of node $i$ in the graph.

To make the weights comparable, the attention coefficients are normalized as follows:

$${\alpha }_{ij}=\frac{\exp \left(\mathrm{LeakyReLU}\left({\overrightarrow{\mathrm{a}}}^T\left[\mathrm{W}{\overrightarrow{X}}_i\parallel \mathrm{W}{\overrightarrow{X}}_j\right]\right)\right)}{\sum _{k\in {\mathcal{N}}_i}\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{LeakyReLU}\left({\overrightarrow{\mathrm{a}}}^T\left[\mathrm{W}{\overrightarrow{X}}_i\parallel \mathrm{W}{\overrightarrow{X}}_k\right]\right)\right)}$$

(8)

where ${.}^T$ represents transposition and $\parallel$ is the concatenation operation.

In GAT networks, hierarchical non-linear feature transformations extract high-level features, which gradually weaken low-level information. Each layer only aggregates first-order neighbor features, resulting in limited information sources. Deeper nodes cannot obtain sufficient gradient information, making the training process unstable. This paper introduces residual connections to aggregate low-level information into high-level representations, alleviating the vanishing gradient problem. The computation is as follows:

$${\mathrm{H}}^{\prime }=\mathrm{H}+\mathrm{O}$$

(9)

$$\mathrm{O}=\mathrm{A}\mathrm{H}\in {\mathbb{R}}^{B\times N\times D}$$

(10)

$$\mathrm{H}=\mathrm{X}\mathrm{W}\in {\mathbb{R}}^{B\times N\times D}$$

(11)

Here, ${\mathrm{H}}^{\prime }$ is the output from the residual structure, $\mathrm{H}$ is the hidden space matrix after linear transformation of the feature matrix, and $\mathrm{O}$ is the attention matrix.

3. Experimental Results and Analysis

In this section, experiments are designed to validate the feasibility of the proposed model. Actual datasets from a wind farm are used to predict the actual wind speed to compare the effect of the proposed prediction model with other models.

3.1. Experiment Design

All the experiments in this paper were conducted on a personal computer running on a Windows 11 operating system. The computer is equipped with a 12th Gen Intel(R) Core(TM) i7-12700 processor (Manufacturer: Intel, Santa Clara, CA, USA) and 1660 Super graphics card (Manufacturer: Nvidia, Santa Clara, CA, USA), and uses a 256 GB SN740 NVMe WD solid state drive for storage (Manufacturer: Western Digital, San Jose, CA, USA). In addition, the PyTorch version used in this paper is 2.1, and the CUDA version is 12.1. The following experimental results are the average values obtained by repeating experiments five times.

3.2. Evaluation Criteria

In order to evaluate the model’s ability to make accurate predictions, we employ several measures, including Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), and Pearson’s correlation coefficient (R correlation coefficient). MAE measures the average absolute value of the model’s prediction error and is insensitive to outliers, thus providing a comprehensive reflection of the overall accuracy of the model. In contrast, MSE and RMSE take into account the squared error, exhibiting greater sensitivity to large errors and aiding in the more effective capture of bias in predictions. Additionally, RMSE, being on the same scale as the predictor variables, is more interpretable compared to MSE.

These measures are utilized to assess the mistakes and correlation of the model over the forecasting period. In the interval [0, 1], lower values of MSE and RMSE imply superior performance of the model, whereas a smaller MAE implies a stronger alignment with the real data. Moreover, a higher R correlation value indicates a more robust association between the model and the observed data. The formulas pertaining to these measurements are as follows:

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n\left|Y_i-{\widehat{Y}}_i\right|$$

(12)

$$\mathrm{M}\mathrm{S}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2$$

(13)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\mathrm{M}\mathrm{S}\mathrm{E}}$$

(14)

$$R=\frac{\sum _{i=1}^n\left(Y_i-\overline{Y}\right)\left({\widehat{Y}}_i-\widehat{\overline{Y}}\right)}{\sqrt{\sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2\sum _{i=1}^n{\left({\widehat{Y}}_i-\widehat{\overline{Y}}\right)}^2}}$$

(15)

where $n$ is the number of data points.$Y_i$ is the actual value, ${\widehat{Y}}_i$is the predicted value,$\overline{Y}$is the mean of actual values, and $\widehat{\overline{Y}}$is the mean of predicted values.

3.3. Prediction Results

3.3.1. Spatial Clustering

In this section, we conducted an in-depth analysis and discussion of the prediction results. In order to better understand the predictive capabilities of the model and identify correlations between different regions, we introduced the concept of spatial clustering. To achieve this goal, we adopted an approach that combines DTW and k-means clustering.

During the spatial clustering process, we first computed the DTW distances between all regions, and then performed clustering based on these distances. DTW is a technique used to measure the similarity between two time series by warping the time axis to find the best match between them. As shown in Figure 5, the correlation heat map of the 15 buoys is illustrated in Table 1.

The heat map visually represents the relationship between the color intensity and the magnitude of the dynamic time warping distance. Darker colors indicate higher DTW distances, indicating greater dissimilarity in wind speed time series between the two buoys. In contrast, it can be observed that the greater the lightness of the color, the higher the degree of similarity between the two time series.

The regions were classified into several groups with the k-means method. The selection of an adequate K value, which represents the number of clusters, is of utmost importance in order to achieve clustering results that are relevant and reliable. In this study, three distinct values of K, namely, 2, 3, 4, and 5, were employed to assess the clustering outcomes. The corresponding clustering results are presented in

Table 2. K-means clustering result chart.

K=	Target Node Cluster	Cluster 2	Cluster 3	Cluster 4	Cluster 5
2	41002, 41004, 41009, 41048, 42002, 42036, 42040	41001, 41013, 41025, 44008, 44009, 44014, 44020, 44065
3	41002, 41004, 41009, 41013, 41048, 42002, 42036, 42040	44008, 44009, 44014, 44020, 44065	44008, 44009, 44014, 44020, 44065
4	41002, 41004, 41009, 41013, 41048, 42002, 44014	44008, 44009, 44020, 44065	42036, 42040	41001, 41025
5	41002, 41009, 41048, 42002	41001, 41025	41004, 41013, 44014	42036, 42040	44008, 44009, 44020, 44065

.

Based on the findings presented in Table 2, it can be observed that an increase in the value of K is associated with a progressive rise in the number of clusters, leading to more intricate and detailed outcomes. The designated prediction node utilized in this research is Buoy 41009. Hence, the central emphasis is placed on the Target Node Cluster, specifically the location of Buoy 41009. The data reveals that there is minimal variation in the buoys within the same cluster as Buoy 41009 as the value of K grows. This observation suggests a significant link between these buoys and Buoy 41009. Nevertheless, when the value of K is set to 4, the quantity of buoys within the identical cluster as the target node diminishes to 4 as a result of the increased level of granularity. As shown in Table 2, considering the data volume requirements for the graph network prediction, the buoy data clustered with K = 4 were utilized as the dataset for subsequent graph network prediction in this study. The first 24 days of data served as the training set, while the last 6 days constituted the test set. The output data comprised wind speed prediction results for the target node (Buoy 41009).

In order to enhance the accuracy of future graph network predictions, it is necessary to establish a clear definition of nodes and edges. Each buoy within cluster K = 4, including Buoy 41009, will be denoted as a node within the graph. The core node for the cluster will be Buoy 41009, with other buoys in the cluster connecting to it. This will result in a star-shaped topology, as depicted in Figure 6.

3.3.2. DK-RGAT Network Prediction

To showcase the efficacy and exceptional performance of the DK-RGAT model in wind power forecasting, a series of comparative experiments were undertaken. These tests involved the evaluation of several networks such as BI-LISTM, CNN, GRU, LSTM, RNN, XGBOOST, and others. Bi-LSTM is a variant of a recurrent neural network with hidden layers that can learn from the context in both forward and backward directions, allowing it to better capture dependencies in sequence data. CNN, while mainly applied to image processing, can also extract features from time-series data effectively through convolution operations. GRU is a type of RNN with a simpler structure than LSTM, using gating mechanisms to memorize important information in sequences. LSTM networks are a special type of RNN that mitigates the vanishing and exploding gradient problems in a traditional RNN through its long short-term memory cell design. RNN refers to the basic recurrent network structure, while XGBoost is a gradient boosting decision tree model representing a non-neural network approach.

The purpose of these experiments was to compare and contrast the performance of these networks with the proposed DK-RGAT model. The parameters are defined below. The DK-RGAT model incorporates two multi-head attention heads. Each CNN layer is equipped with 64 convolution kernels of size 1, employing Rectified Linear Units (ReLU) activation and causal padding. The hidden units of the LSTM, GRU, and Bi-LSTM layers are set to 64. The dropout rate is 0.3. The training parameters for all models are the same. The experiment consists of performing 100 iterations using the Adam optimizer with a batch size of 64. The time window size is set to 6 for the training set and the test set, that is, using the past 6 time points to predict one point in the future.

The findings of all models, including MAE, MSE, RMSE, and R2 values, are presented in

Table 3. Error table for benchmark experiments.

	DK-RGAT	BI-LSTM	CNN	GRU	LSTM	RNN	XGBOOST
MAE	0.364	0.811	0.731	0.811	0.646	0.731	0.786
MSE	0.239	1.253	0.857	0.897	0.685	0.857	0.936
RMSE	0.489	1.119	0.926	0.947	0.828	0.926	0.968
R	0.985	0.903	0.966	0.970	0.967	0.966	0.982

after conducting trials on the complete dataset. The bold values indicate the optimal values among all forecasts made by the models. Furthermore, the results of these predictions are graphically shown in Figure 7, while Figure 8 presents histograms to facilitate a visual comparison of the inaccuracies.

Based on the analysis of Figure 7 and Figure 8, it is evident that the projected values derived from the DK-RGAT model exhibit a strong degree of concordance with the observed values. Based on the data presented in Table 3, it is evident that DK-RGAT exhibited superior performance across various evaluation measures, including MAE, MSE, RMSE, and R. Specifically, DK-RGAT attained values of 0.364, 0.239, 0.489, and 0.985 for these respective metrics.

In relation to the metric of MAE, the DK-RGAT model has an MAE value of 0.364, which is notably reduced by 43.7~55.1% compared to alternative models. The MSE of DK-RGAT, which is 0.239, exhibits a reduction of 65.1~80.9% compared to other models. In relation to the RMSE, the value of 0.489 achieved by DK-RGAT exhibits a reduction of approximately 40.9~56.3% when compared to the values obtained using other models. The correlation coefficient (R) of DK-RGAT (0.985) is marginally greater than that of BI-LSTM (0.903), CNN (0.966), GRU (0.970), LSTM (0.967), RNN (0.966), and XGBoost (0.982).

The comparative assessment underscores the efficacy of the DK-RGAT framework in the realm of wind power predictions, surpassing alternative models such as BI-LISTM, CNN, GRU, and others. The findings suggest that DK-RGAT exhibits a high level of precision in forecasting wind power, hence highlighting its efficacy in this specific domain.

3.3.3. Multi-Head Attention Experiments

The DK-RGAT model, as described in the present study, incorporates a multi-head attention mechanism to effectively capture crucial information from individual nodes. The multi-head attention method is capable of efficiently capturing global correlations across many representation subspaces, hence enabling the model to acquire more comprehensive feature representations. In contrast to a singular global attention mechanism, multi-head attention incorporates information from distinct subspaces by means of concatenation processes, resulting in more comprehensive and global feature representations.

The selection of the number of heads will have an impact on the diversity and comprehensiveness of the feature representations that are acquired by the model. An insufficient quantity of heads may result in a restricted capacity for feature expressions, whereas an excessive quantity may result in inefficient utilization of processing resources. Hence, striking a balance between the effectiveness and efficiency of the model necessitates the identification of an appropriate number of multi-head attention heads that can adequately capture feature representations while taking into account computational constraints. The guiding relevance of this is crucial for the creation of the DK-RGAT model discussed in this study, as well as for the interpretation of the experimental data.

To conduct more comprehensive research and design a series of experiments, the models are, respectively, Model 1, Model 2, Model 3, Model 4, Model 5 and Model 6 every time the amount of the heads range from 1 to 6. The anticipated value is depicted in Figure 9, whereas Figure 10 displays the error representation. Additionally,

Table 4. Prediction error table for different numbers of attention heads.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
MAE	0.558	0.364	0.756	0.805	1.049	1.288
MSE	0.579	0.239	1.092	1.274	1.919	2.797
RMSE	0.761	0.489	1.045	1.129	1.385	1.672
R	0.971	0.985	0.922	0.904	0.916	0.834

presents the pertinent error outcomes.

When the number of attention heads of the model is configured to 2, the best indicators are obtained. In comparison to alternative models, this model showcases superior performance characterised by minimal error fluctuation and exceptional stability. Nevertheless, when the number of attention heads is increased, there is a progressive increase in both the average error and standard deviation of the model. This finding suggests that augmenting the number of attention heads within a specific threshold contributes to enhancing the performance of the model. However, values over this threshold can result in a deterioration of performance and inefficient utilization of computational resources.

The model’s ability to generalize effectively without overfitting the training data is indicated by the low average error and standard deviation observed when utilizing 2 attention heads. The observed rise in mistakes can be attributed to the phenomena of overparameterization and overfitting, which occur when an excessive number of heads are included. There is a threshold for the number of attention heads beyond which the model’s complexity becomes unneeded relative to the complexity of the problem. The crucial aspect lies in achieving an optimal equilibrium between the expressiveness of the model and the implementation of regularization techniques.

With respect to the metric of Mean Absolute Error, Model 2 has an MAE value of 0.364, demonstrating a significant reduction ranging from 45.0% to 83.7% when compared to alternative models. Model 2 demonstrates a Mean Squared Error of 0.239, indicating a reduction ranging from 65.9% to 91.4% in comparison to alternative models. With regards to the Root Mean Squared Error, Model 2 has attained a value of 0.489, indicating a reduction of around 27.8~68.6% compared to the values produced by other models. The correlation coefficient of Model 2 (0.985) exhibits a slight superiority compared to Model 1 (0.971), Model 3 (0.922), Model 4 (0.904), Model 5 (0.916), and Model 6 (0.834).

In general, the findings indicate that employing two attention heads effectively captures the interdependencies within the data, resulting in a reduction in prediction error. However, the inclusion of extra attention heads yields diminishing benefits and may potentially lead to a decline in performance in this particular scenario.

3.3.4. Topological Structure Comparison

The prediction of graph network architectures is subject to significant variation, depending on the specific graph creation methods employed. This study introduces a star-shaped topological structure graph designed for the target node, and investigates how the amount of connections from different nodes can influence the prediction outcomes for the target node. Various configurations of models, each with a different number of buoys linked to Buoy 41009, have been established. In Model 1, two buoys (41002, 41004) are connected. Model 2 expands the connections to four buoys (41002, 41004, 41013, 41048), while Model 3 incorporates six buoys (41002, 41004, 41013, 41048, 42002, 44014). Building upon Model 3, Model 4 establishes a connection directly to Buoy 41009 itself. Contrasting with Model 4, Model 5 and Model 6 extend their connections to two low-correlation nodes (41013, 41025) and four low-correlation nodes (41013, 41025, 44020, 44065), respectively. The anticipated value is depicted in Figure 11, whereas Figure 12 displays the error representation. Additionally,

Table 5. Error table for different numbers of nodes.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
MAE	1.528	1.254	0.499	0.364	0.495	0.809
MSE	3.661	2.288	0.449	0.239	0.472	1.127
RMSE	1.913	1.512	0.670	0.489	0.687	1.061
R	0.766	0.883	0.968	0.985	0.966	0.935

presents the pertinent error outcomes.

Based on the evaluation results, it can be concluded that Model 4 exhibits superior predictive performance compared to the other models. The system has a topological configuration characterized by a star-shaped structure consisting of seven interconnected nodes. When compared to alternative models, Model 4 exhibits the most favorable performance in terms of the lowest Mean Absolute Error, Mean Squared Error, and Root Mean Squared Error values. Additionally, it demonstrates the highest correlation coefficient of 0.985. In relation to the metrics of Mean Absolute Error, Mean Squared Error, and Root Mean Squared Error, Model 4 exhibits a reduction in values ranging from 76.2% to 83.7%, 65.9% to 91.4%, and 27.8% to 68.6%, accordingly, when compared to other models. This indicates that Model 4 demonstrates superior predictive ability overall. This observation suggests that there is a positive correlation between the number of connected nodes in a star-shaped topology and the prediction performance of the target node.

The prediction accuracy of Model 1 for the target node is significantly low, mostly attributed to its excessively simplistic network structure comprising only two interconnected nodes. The inclusion of nodes (41013, 41025) in Model 5 and (41013, 41025, 44020, 44065) in Model 6 does not yield an enhancement in prediction performance. Instead, it leads to an increase in the values of Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, and a drop in the coefficient of determination. This implies that in the process of developing graph networks, it is necessary for the interconnected nodes to have a specific level of correlation. The act of connecting nodes without considering their correlation strength in a blind manner does not contribute to enhancing the predictive capacity of the model.

4. Conclusions and Discussion

This paper presents a novel approach to offshore wind speed predictions, which involves the enhancement of the residual graph attention network method through the incorporation of spatial clustering techniques. The objective of this research is to achieve both efficiency and accuracy in wind power forecasting. The primary concept underlying the suggested model is the aggregation of sites that exhibit similar wind speed sequences through the use of spatial clustering techniques. This is followed by the building of a graph, wherein residual networks and multi-head attention mechanisms are integrated into deep learning models. Residual networks are employed to mitigate the problem of disappearing gradients, and multi-head attention mechanisms are utilized to capture the significance of pertinent information. Various machine learning and deep learning techniques were employed in our study to forecast offshore wind speed factors. Compared with the literature [19,20,21,22], the graph network neural prediction method proposed in this paper integrates spatial information, and compared with the literature [23,24,25], it solves the shortcomings of static mapping and the problem that each node has different importance degrees. The utilization of geographical clustering, residual networks, and multi-head attention in the suggested model enhances its capability to capture temporal correlations within the wind speed data, hence facilitating more precise predictions.

The findings obtained from the analysis of wind speed data collected from NOAA systems illustrate the possible applications and significance of the suggested model.

• The prediction accuracy of the suggested hybrid model approach, which incorporates enhanced residual and spatial clustering techniques, surpasses that of baseline models by effectively extracting data correlations.
• Attention mechanisms and residual structures have been found to enhance the performance of models when comparing the behaviours of several modules.
• The wind speed data exhibits nonlinearity, and the suggested model effectively reflects the inherent variability in these nonlinear fluctuations.
• The performance of the suggested model can be effectively enhanced by judiciously selecting the number of heads to stack multi-head attention.

5. Future Works

In the future, our intention is to gather additional wind speed datasets from real-world sources in order to assess the effectiveness of wind speed prediction models. The aforementioned datasets encompass a broader range of variables that have an impact on wind velocities. The use of the provided datasets in conjunction with the suggested deep learning models enables the acquisition of elevated-level representations pertaining to a greater number of parameters. Consequently, this facilitates the generation of more efficient long-term predictions. For instance, the inclusion of humidity and temperature variables may facilitate the identification of potential nonlinear patterns within the dataset. The clustering algorithm employed in this study, known as DTW, is based on Euclidean clustering, which has limitations in effectively characterizing features. In forthcoming times, deep learning techniques will be employed to accomplish the task of sequence-to-sequence clustering. Our objective is to enhance the level of prediction accuracy and improve the comprehensibility of model development. In order to enhance the precision of the proposed wind power forecasting model, we intend to investigate additional hyperparameter optimization techniques, including Bayesian optimization and random search methodologies.