Short-term wind speed multi-step prediction method based on combined CGRU model

Abstract

The application provides a short-term wind speed multi-step prediction method based on a combined CGRU model, and comprises the following steps: S1, decomposing an original wind speed signal; S2, reconstructing each wind speed subsequence and a secondary wind speed subsequence by using phase space reconstruction, and then performing feature selection on each reconstructed data by using a multi-label XGBoost feature selection method; S3, establishing a CGRU prediction model for each feature-selected subsequence, wherein the model extracts more effective features from each sub-signal by using a CNN, and identifies the time dependence between the extracted features and future wind speed by using a GRU; and S4, performing an accumulation operation on the prediction results of each subsequence to obtain a final prediction result. The prediction error is significantly reduced, and the accuracy and stability of wind speed prediction are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of wind speed prediction for wind power generation, and in particular to a short-term multi-step wind speed prediction method based on a combined CGRU model. Background Technology

[0002] With the escalating energy crisis and the increasing emphasis on carbon neutrality, renewable energy has garnered global attention, and wind power is widely considered one of the most promising renewable energy sources. Wind power generation largely depends on wind speed, and wind speed forecasting is crucial for the effective allocation of wind power resources. Accurate wind speed forecasting is essential for ensuring the stability of grid-connected power supply from wind power, peak shaving in the power system, safety analysis, and reducing operating costs. However, the inherent randomness, intermittency, and volatility of wind power itself pose significant challenges to accurate wind speed forecasting. Accurate wind speed forecasting remains a critical issue, and research on improving its accuracy has increased significantly in recent years, making it imperative to enhance the accuracy of wind speed forecasting.

[0003] In recent years, numerous wind speed prediction models have emerged. Based on their typical characteristics, these models can be categorized into two types: physical numerical weather prediction (NWP) models and data-driven models based on historical data. Physical models, based on computational fluid dynamics (CFD) models, utilize three-dimensional spatial and temporal meteorological information for prediction, including variables such as topography, air pressure, temperature, and humidity. However, physical models have some drawbacks, including high accuracy requirements for each weather variable and the need for significant computation time. Generally, the short-term prediction accuracy of physical models is often lower than that of data-driven models. In contrast, data-driven models, with their simpler model structures, require less data and do not necessitate a deep understanding of the physical phenomena.

[0004] Generally, data-driven models can be further divided into three categories: statistical models, intelligent models, and hybrid models. Regardless of whether it's a statistical model or an intelligent model, each model has its own advantages and limitations. Single models are sensitive to data structures, and the methods mentioned above all have limitations in modeling complex data structures. To overcome the limitations of single models, a large amount of research has focused on hybrid models. By combining different methods, the advantages of various approaches are integrated, thereby improving the predictive ability of the system.

[0005] One effective approach is to utilize heuristic optimization algorithms, such as Particle Swarm Optimization (PSO), Simulated Annealing (SA), Genetic Algorithm (GA), Differential Evolution (DE), and Artificial Bee Colony (ABC), to jointly optimize key parameters of the prediction model. While many optimization algorithms have been successfully applied to improve individual intelligent models, there is still no evidence that any single algorithm always performs best in all real-world situations.

[0006] Another effective approach is to combine several methods, especially in neural networks. By stacking hidden layers, the advantages of several models can be utilized layer by layer, and joint optimization algorithms can be used to improve prediction performance.

[0007] Other studies focus on feature selection for input variables in wind speed prediction. Feature selection can simplify data structure, avoid overfitting, and reduce computational costs. While these feature selection methods currently offer some help in simplifying data structure, reducing computational costs, and minimizing prediction errors, they are primarily applicable only to feature selection problems in single-step prediction.

[0008] Furthermore, most existing hybrid short-term wind speed models focus on improving prediction accuracy. Most models utilize decomposition methods to break down wind speed time series into different components and then predict each component. However, the complex data structure resulting from redundant features in wind speed prediction can easily lead to model overfitting, and research on computational costs has not received sufficient attention, especially in multi-step prediction. Currently, research on feature selection for multi-step wind speed prediction is still limited. Moreover, existing commonly used hybrid models may not fully exploit the deeper characteristics of different components. Summary of the Invention

[0009] This invention aims to at least solve the technical problems existing in the prior art, and in particular, it innovatively proposes a short-term wind speed multi-step prediction method based on a combined CGRU model.

[0010] To achieve the above-mentioned objectives of this invention, this invention provides a short-term wind speed multi-step prediction method based on a combined CGRU model, comprising the following steps:

[0011] S1, decompose the original wind speed signal:

[0012] S1-1, First, the original wind speed sequence is decomposed using EMD, which decomposes the original wind speed sequence into multiple wind speed subsequences and residual signals;

[0013] S1-2, after EMD decomposition, the unpredictability of each wind speed subsequence is estimated by sample entropy analysis. The most unpredictable subsequence is then further decomposed by VMD to obtain multiple secondary wind speed subsequences.

[0014] The secondary decomposition method decomposes the high-frequency subsequence with high unpredictability based on the primary decomposition, further extracting the frequency-varying characteristics of wind speed and obtaining more effective subsequences, thereby improving the predictive ability of the model.

[0015] S2, phase space reconstruction is used to reconstruct each wind speed subsequence, secondary wind speed subsequence and residual signal, and then the multi-label XGBoost feature selection method is used to select features for each reconstructed data;

[0016] The multi-label XGBoost feature selection method is an improvement on the single-label XGBoost method, resulting in a feature selection approach applicable to multi-step prediction tasks. This method extracts features with high relevance and low redundancy, simplifies the data structure, improves subsequent model training speed, and avoids overfitting.

[0017] S3, input the sub-sequences and residual signals after feature selection into the CGRU prediction model to obtain the prediction results. The model uses CNN to extract features from each sub-signal and uses GRU to identify the time dependence between the extracted features and future wind speed.

[0018] S4. The prediction results of each subsequence and the residual signal are accumulated to obtain the final prediction result.

[0019] In summary, due to the adoption of the above technical solution, the present invention has the following advantages:

[0020] (1) An MLXGBoost feature selection method suitable for multi-step prediction is proposed. This method selects the optimal input features for each IMF subsequence, which simplifies the data structure and improves the modeling efficiency.

[0021] (2) An efficient CGRU prediction model was developed. This model uses CNN to extract more effective features from each sub-signal, uses GRU to identify the time dependence between the extracted features and future wind speed, and uses GA to jointly optimize the important parameters of CGRU. The CGRU prediction model can adapt to long-term dependence and can extract effective information from the original data. Compared with existing models, the prediction error is significantly reduced, effectively improving the accuracy and stability of wind speed prediction.

[0022] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0024] Figure 1 This is a flowchart of the calculation process for the sample entropy of this invention.

[0025] Figure 2 This is the phase space recombination diagram predicted in one or more steps according to the present invention.

[0026] Figure 3 This is a schematic diagram of the structure of the GRU of the present invention.

[0027] Figure 4 This is a flowchart of the hybrid model of the present invention.

[0028] Figure 5 This is a time-series data graph of the original wind speed in a specific embodiment of the present invention.

[0029] Figure 6 This is a subsequence diagram after EMD decomposition in a specific embodiment of the present invention.

[0030] Figure 7 This is a subsequence diagram after VMD decomposition in a specific embodiment of the present invention.

[0031] Figure 8 This is a diagram showing the center frequency of each subsequence after VMD decomposition in a specific embodiment of the present invention.

[0032] Figure 9 This is a schematic diagram comparing the one-step prediction results of different decomposition methods in each season.

[0033] Figure 10 This is a comparative diagram of the 6-step prediction results of different decomposition methods in each season.

[0034] Figure 11 This is a diagram comparing the 10-step prediction results of different decomposition methods in each season.

[0035] Figure 12 This is a scatter plot of the actual and predicted values ​​of models using different decomposition methods in four datasets. Detailed Implementation

[0036] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0037] Raw wind speed signals are nonlinear and nonstationary. Directly establishing a prediction model often results in low accuracy. Therefore, this invention proposes a short-term multi-step wind speed prediction method based on a combined CGRU model, specifically an SD-MLXGBoost-GA-GRU combined model. The process is as follows: Figure 4 As shown, it includes the following steps:

[0038] S-1, performs signal stability detection on the original wind speed time series signal;

[0039] S-2 uses the Empirical Mode Decomposition (EMD) method and sample entropy analysis to decompose the original signal into a series of IMF signals from high frequency to low frequency and residual signals with certain fluctuation characteristics.

[0040] S-3 uses variational mode decomposition (VMD) to perform a second decomposition on the high-frequency signal, and then obtains the high-frequency re-decomposed IMF signal through sample entropy analysis;

[0041] S-4, each IMF signal and residual signal is recombined in phase space according to the requirements of embedding dimension m and delay time τ, respectively, to obtain M-dimensional space groups;

[0042] S-5, Multi-label XGBoost is used to select the optimal input features for each IMF signal and residual signal after phase space reconstruction.

[0043] S-6, establish corresponding CGRU models optimized by GA parameters for each IMF signal and residual signal to predict wind speed;

[0044] S-7, the prediction results of each IMF signal and residual signal are superimposed to obtain the superimposed wind speed prediction value;

[0045] S-8 compares the predicted results with the comparison model and the actual values ​​to draw experimental conclusions.

[0046] 1. Related technologies to the method of this invention

[0047] 1.1 Two-level decomposition method

[0048] 1.1.1 Empirical Mode Decomposition (EMD)

[0049] Empirical Mode Decomposition (EMD) is a method for smoothing nonlinear and nonstationary signals. EMD decomposes complex nonlinear signals into a series of smooth Intrinsic Mode Functions (IMFs). IMFs include local characteristic information of trends and fluctuations of the original signal at different scales, which helps in analyzing the true physical meaning of the signal. Wind speed data is nonlinear and nonstationary; EMD helps extract features and improve forecasting capabilities.

[0050] Empirical Mode Decomposition (EMD) decomposes signals based on the time-scale characteristics of the data itself. Therefore, it does not require pre-setting any basis function features. The EMD method can decompose any type of signal, and is particularly suitable for processing non-stationary and nonlinear data. The EMD method exhibits good integrity and orthogonality, preserving the inherent characteristics of the data during the decomposition process. The decomposition steps are as follows:

[0051] Solve for all local extrema of the signal s(t), then connect all the upper and lower extrema to obtain the upper and lower envelopes (all data lie between the upper and lower envelopes). Their average value is m1(t), and the difference between the s(t) signal and m1(t) is the first proto-IMF h1(t). The equation is shown in Equation (2):

[0052] h1(t)=s(t)-m1(t) (1)

[0053] Where s(t) represents the original signal (sequence), m1(t) represents the average value of the envelope formed by the local extrema of s(t), and h1(t) represents the decomposition quantity proto-IMF.

[0054] However, h1(t) generally does not conform to the definition of IMF. This is because a new extremum may appear when transforming from a rectangular coordinate system to a curvilinear coordinate system. Therefore, we should repeat the above steps and perform a selection process, using h1(t) as the input for the next iteration. The equation is shown in formula (3):

[0055] h 11 (t)=h1(t)-m 11 (t) (2)

[0056] Where m 11 (t) represents the average value of the envelope formed by the local extrema of h1(t); h 11 (t) represents the IMF component to be selected.

[0057] The filtering process will be repeated i times until h. 1i (t) becomes the true IMF. The equation is shown in formula (4):

[0058] h 1i (t)=h1(i-1) (t)-m 1i (t) (3)

[0059] Where m 1i (t) represents h 1(i-1) The average value of the envelope formed by the local extrema of (t), h 1i (t) represents the multiple IMF components to be selected in the i-th screening, h 1(i-1) (t) represents the candidate IMF component for the (i-1)th iteration; the output of equation (2) is used as the input of equation (3), and then the operation of equation (2) is repeated to obtain multiple candidate IMF components.

[0060] The Cauchy convergence criterion is the stopping condition. Specifically, the test requirement is defined as the normalized squared deviation between two consecutive screening operations. The equation is shown in formula (5):

[0061]

[0062] SD i This is used to determine the conditions for the IMF components to be selected above, and whether they meet the conditions to become true IMF decomposition components. When SD i When the value is less than 0.2, c1(t) = h 1i c1(t) is the first IMF. T is based on the stopping condition according to the Cauchy convergence criterion. SD i It is difficult to be less than 0.2, as this ensures that the frequency and amplitude of IMFs have sufficient physical meaning. j (t) represents the j-th IMF. The equations are shown in formulas (6)-(7):

[0063] c1(t)=h 1i (t) (5)

[0064] c j (t)=h ji (t) (6)

[0065] Among them, h ji (t) represents the j-th IMF component to be selected in the i-th screening;

[0066] The residual r1(t) can be obtained through equation (8), and r1(t) is used as a new signal. The screening process is then repeated. The residual r obtained in this process... j (t) is shown in equation (9).

[0067] r1(t)=s(t)-c1(t) (7)

[0068] r j (t)=r j-1(t)-c j (t),j=2,3,4…,n (8)

[0069] Where s(t) represents the original signal, c1(t) represents the first IMF component, and r1(t) represents the first residual; the steps are repeated using the residual as the input signal to obtain the next IMF signal, and the steps are repeated to continuously obtain a new residual r. j (t), r j-1 (t) represents the (j-1)th residual.

[0070] The signal s(t) can be represented by the intrinsic mode function C after EMD decomposition. j (t) and residual r n The equation is represented by (t). The equation is shown in formula (10):

[0071]

[0072] Where n is the number of IMFs obtained from the decomposition, C j (t) represents the j IMF components obtained from the decomposition, r n (t) represents the nth residual obtained from the last decomposition.

[0073] 1.1.2 Sample Entropy (SE)

[0074] Sample entropy, proposed by Richman and Moornan, is a novel measure of time series complexity. It's an algorithmic improvement on the approximation quotient. Sample entropy aims to reduce the error of approximate entropy and achieve closer consistency with the known random component. Compared to approximate entropy, sample entropy has two major advantages: First, it doesn't involve comparisons of its own data segments; it's the exact value of the negative average natural logarithm of conditional probabilities, thus its calculation is independent of data length. Second, it exhibits better consistency; if one time series has a higher entropy than another, it will also have a higher entropy for different dimensions and thresholds, with the entropy value directly proportional to the series complexity.

[0075] For a wind speed time series {x(i), i = 1, 2, 3, ..., n}, where n is the length of the original time series, the sample entropy calculation steps are as follows:

[0076] (1) Reconstruct the phase space of the wind speed time series x(i) to obtain the matrix X. m Let m be the dimension, then:

[0077]

[0078] (2) Define the subsequence X m (i) and X mThe distance d[X] of (j) m (i),X m [j] represents the absolute value of the maximum difference between the corresponding values ​​of the two. That is:

[0079] d[X m (i),X m (j)]=max|x(i+k)-x(j+k)|,k=(0,1,…,m-1),i≠j (11)

[0080] Among them, X m (i), X m (j) is matrix X m Any two rows of subsequences.

[0081] (3) For a given i-th row suborder X m (i), which has a maximum difference d[X] with all other subsequences. m (i),X m (j)],j(1≤j≤nm,j≠i), statistical d[X m (i),X m The number of (j)]≤r is denoted as B. i For 1≤i≤nm, the definition is:

[0082]

[0083] In the formula The maximum distance is the percentage of the number of rows whose absolute value (maximum distance) of the maximum difference between the corresponding values ​​in the i-th row and other rows is less than the threshold r.

[0084] Then n-m+1 The average value is expressed as:

[0085]

[0086] (4) Let m = m + 1, repeat (1) to (3) above, and calculate B. m+1 (r);

[0087] (5) The formula for calculating sample entropy is:

[0088]

[0089] The value of sample entropy SampEn(m,r,n) under the corresponding parameters m, r,n is related to the selection of parameters m, r,n. Different embedding dimensions (i.e., the dimension m) and similarity tolerance (i.e., the threshold r) correspond to different sample entropy values. Generally, r is taken as 0.1 to 0.25 times the standard deviation of the original data. When m=2, the value of SampEn(m,r,n) has the best dependence on the length n of the original time series, and the calculated sample entropy has more reasonable statistical characteristics. To more intuitively illustrate the calculation process, the sample entropy algorithm flowchart is as follows: Figure 1 As shown:

[0090] First, input a time series of length n, and set the parameter m. , The value of r is then used to reconstruct the phase space of the time series, and the proportion of rows whose maximum distance between the i-th row and all other rows is less than the threshold r is calculated. Calculate n-m+1 more The average value B of (i = 1, 2, ..., n-m+1) m (r), then let m = m + 1, and repeat the above steps to obtain B. m+1 (r), thus obtaining the final sample entropy value. Here, m, r, n are the parameters m, r, n, where m is the matrix X. m The dimension is the embedding dimension; n is the length of the original time series; r represents the similarity tolerance, i.e., the threshold.

[0091] 1.1.3 Variational Mode Decomposition (VMD)

[0092] VMD is an adaptive, fully non-recursive modal variational and signal processing method that determines relevant frequency bands and extracts corresponding model components through a variational model. It overcomes the end-point effects and modal component aliasing problems of the EMD method and has a more robust mathematical foundation. It can reduce the non-stationarity of time series with high complexity and strong nonlinearity, decomposing them into relatively stationary subsequences containing multiple different frequency scales, making it suitable for non-stationary sequences. Based on the number of modal decompositions of the given sequence, the subsequent search and solution process can adaptively match the optimal center frequency and finite bandwidth for each mode, and can achieve effective separation of intrinsic modal components (IMFs), frequency domain partitioning of the signal, and thus obtain the effective decomposition components of the given signal, ultimately obtaining the optimal solution to the variational problem. Its constrained variational problem is:

[0093]

[0094] Where u k ,w k Let be the k-th mode and the center frequency, respectively, where K is the total number of modes, and δ(t) is the Dirac function. is the convolution operator. To solve the optimal solution of this constrained variational model, the Lagrange multiplier λ is introduced, transforming the constrained optimization problem into an unconstrained model, resulting in the Lagrange function:

[0095]

[0096] Here, α is a quadratic penalty factor, which reduces Gaussian noise interference. The alternating direction multiplier (ADMM) iterative algorithm is used to obtain each modal component and the center frequency. According to the ADMM algorithm, its u... k ,w k The update formula is as follows:

[0097]

[0098]

[0099]

[0100] Where n is the number of iterations, Corresponding to Fourier transforms of f(t), u(t), and λ(t).

[0101] This represents the k-th center frequency after the nth cycle (n iterations);

[0102] w represents the center frequency; express Fourier transform;

[0103] This represents the k-th component after the nth iteration (n iterations);

[0104] || 2 Represents the square of the absolute value;

[0105] Represents the Lagrange multiplier in the (n+1)th iteration;

[0106] Represents the Lagrange multiplier of the nth iteration;

[0107] γ represents the parameter to be updated;

[0108] f(t) represents the original sequence;

[0109] Represent the Fourier transform of f(t);

[0110] The iterative process of VMD mainly includes the following four steps:

[0111] Step 1: Given a sequence f(t), initialize the modes Center frequency and Lagrange multiplier

[0112] Step 2: For each mode μ k Update using formulas (17) and (18) respectively. and w k .

[0113] Step 3: Update using formula (19)

[0114] Step 4: If the termination condition is met, stop the iteration. It can be done The inverse Fourier transform of the real part is obtained. Otherwise, n is changed to n+1, and step 2 is continued.

[0115] 1.2 Feature Selection

[0116] 1.2.1 Phase Space Recombination

[0117] Select the first M steps (144 steps, or one day's worth of data, if the data interval is 10 minutes) as input features, and the last N steps as output labels.

[0118] Considering the chaotic nature of wind speed time series, PSR wind speed time series are used for phase space reconstruction. An embedding dimension *m* and a delay time *t* are defined. A sliding window is constructed using the given embedding dimension *m* and delay time *t*. Through the sliding window, the wind speed time series {x(i), i = 1, 2, 3, ..., n} is reconstructed in a high-dimensional phase space, yielding a data matrix. The processing here is similar to that described earlier, but the purpose is different; previously, the sample entropy was used for subsequent evaluation. This is the data structure required to construct the prediction model.

[0119] Embedding dimension m = M + N, delay time t = 1, the data structure after phase space recombination is as follows Figure 2 As shown:

[0120] The figure shows the data structure after phase space reconstruction for one-step or multi-step prediction. If there are M input features, each reconstructed row contains M consecutive input values. If the number of output labels is N, each row contains N consecutive output values. The number of rows L+1 depends on the embedding dimension m, the delay time t, and the length n of the original sequence. When t = 1, L+1 = n - m + 1.

[0121] 1.2.2 Multi-label XGBoost Feature Selection

[0122] Extreme gradient boosting (XGBoost), proposed by Chen et al. in 2016, is an efficient and scalable machine learning model. It's an improvement on gradient descent decision trees (GBDT), combining multiple classification and regression trees (CART) in a boosting manner. Its main idea is to use the residuals of previous models to train subsequent models, meaning the subsequent models can correct the errors produced by the previous models. XGBoost uses a second-order Taylor expansion to approximate the loss function to ensure model accuracy and adds a regularization term to the objective function to control model complexity, thereby achieving better generalization and avoiding overfitting.

[0123] XGBoost feature importance selection is a type of embedding method. During the training of XGBoost, we use gain to determine the optimal splitting node. Gain represents the gain score for each split of the tree. The final feature importance score is calculated by the average gain, which is the total gain of all trees divided by the total number of splits for each feature. The more times a feature is split, the greater the gain it brings to the model. It outputs the importance of each feature by calculating the gain. If the feature importance score is higher, the feature contributes more to the model construction and training process. We generally obtain the top-ranked features based on the descending order of feature importance scores. The gain calculation method is shown in formula (20):

[0124]

[0125] Where gain represents the gain;

[0126] Indicates multiple features in I L The first gradient on;

[0127] Indicates multiple features in I L The second gradient on;

[0128] g i h i These represent the first-order and second-order gradients, respectively.

[0129] i represents the i-th feature.

[0130] I L I R I represents the samples of the left and right nodes after segmentation, respectively. L I R Each includes multiple samples;

[0131] I = I L ∪I R λ and γ are penalty parameters.

[0132] This method is generally only applicable to single-label feature selection, i.e., obtaining the importance score of the input feature for a specific label. For multi-label feature selection problems, we improve this method to make it applicable to multi-label feature selection problems, called Multi-Label XGBoost (MLXGBoost) feature selection. First, we iteratively operate on the existing single-label feature selection method, performing XGBoost feature selection on each input feature and each label (i.e., each step of the multi-step prediction, let the number of labels be N), obtaining the importance score of each input feature for each label (predictor variable). Each input feature will obtain N importance score values. If there are 10 prediction steps, then each feature will have 10 importance scores (with 10 labels).

[0133] Then, two metrics are used to select the final required input features. One metric is the average score of each feature, that is, the average importance score of each feature to the N labels. The calculation formula is as follows:

[0134]

[0135] Average-score m This represents the average importance score of the m-th feature to the N labels;

[0136] gain mn This represents the importance score of the m-th feature relative to the n labels;

[0137] N is the total number of tags;

[0138] n represents the nth label. The features are sorted in descending order according to the average importance score of each feature across the N labels, and the p features with the highest average score (features that are highly correlated with multiple labels) are selected.

[0139] Another metric is the maximum score for each feature, which is the maximum importance score of each feature for the N labels. The calculation formula is as follows:

[0140] Highest-score m =Max{gain m1 gain m2 gain m3 ,…,gain mN}. (twenty two)

[0141] Among them, the highest score m This represents the maximum importance score of the m-th feature among the N labels;

[0142] The features are sorted in descending order based on their maximum importance scores across the N labels. The q features with the highest scores (features that are highly correlated with a particular step in the multi-step prediction process) are then selected.

[0143] Finally, the two indicators are combined to determine the final selected input features. If a feature is selected in both indicators, it is used as the final required input feature; if the number of features is insufficient, each indicator is weighted 50% for feature selection until the required number of selected input features is met.

[0144] 1.3 Prediction Methods

[0145] 1.3.1 Convolutionally Gated Recurrent Unit (CGRU)

[0146] The main trend components of each wind speed time subsequence obtained by the quadratic decomposition not only have long and short dependencies but also possess deep features. To predict these main trend components, a CGRU network was designed. In the CGRU network, convolutional layers (Conv1D) are used to capture deep features, while GRU layers are used to obtain the temporal dependencies of wind speed for wind speed prediction.

[0147] Convolutional Neural Networks (CNNs) use locally connected structures to share common weights across different locations, significantly reducing the number of parameters compared to fully connected neural networks. Common CNN architectures typically include convolutional layers, pooling layers, dropout layers, and fully connected layers, using activation functions for non-linear mapping. Convolutional layers can automatically extract features through multiple filters (kernels). During the forward propagation phase, each convolutional layer applies an activation function and convolution operation to the output of the previous layer. This characteristic of CNNs helps extract hidden information without being affected by its uncertainty.

[0148] It can be defined as:

[0149]

[0150] in, This represents the output after convolution;

[0151] f represents the activation function;

[0152] W k This represents the weights of the k-th convolutional kernel;

[0153] x represents the input;

[0154] (W k *x) ij This means that the input x is processed by the convolution kernel W. k To perform a convolution operation, the number of convolution kernel operations required horizontally and vertically are i and j, respectively.

[0155] b k This indicates the bias of the k-th convolution operation.

[0156] k represents the number of convolution kernels. Each convolution kernel (containing weights) performs a convolution operation with the input, and an offset b is added. k The output is then nonlinearized using an activation function f. For two-dimensional data, i and j represent the number of convolution kernel operations required horizontally and vertically, respectively.

[0157] In deep learning, RNNs are a useful method for handling chaotic time series. However, their insufficient ability to handle long-range information can lead to problems such as vanishing gradients. LSTM is a variant of RNN, but GRU effectively considers long-term dependencies, has a simpler structure than LSTM, and is an improved algorithm. LSTM has three gates: input gate, forget gate, and output gate, while GRU only has two gates: update gate and reset gate. For GRU, the update gate can replace the input and forget gates of LSTM, and the reset gate can directly process previous hidden states. Therefore, GRU is faster to train than LSTM.

[0158] Memory cells such as Figure 3 As shown, it consists of an update gate and a reset gate.

[0159] The calculation can be expressed as:

[0160] z t =σ(W z *[h t-1 x t ]+b z ) (twenty four)

[0161] r t =σ(W r *[h t-1 x t ]+b r (25)

[0162]

[0163]

[0164] Where σ() is the sigmoid function, [h t-1 x t ] indicates that h t-1 x t Perform a door reset operation, h t-1 W represents the output information from the previous step. z b z These represent the input weights and biases for this step, respectively.

[0165] This indicates that the output of the update gate is multiplied by the output of the previous step, and then weighted and biased by the input of this step, before being processed by the Tanh activation function. ⊙ represents element-wise multiplication; the symbols are shown in Table 1 below:

[0166] Table 1

[0167] <![CDATA[h t ]]> The hidden layer vectors in GRU, t = 1, 2, ..., n-1, n <![CDATA[x t ]]> The output vector in the GRU, t = 1, 2, ..., n-1, n <![CDATA[z t ]]> The update gate in GRU, t = 1, 2, ..., n-1, n <![CDATA[r t ]]> The reset gate in GRU, t = 1, 2, ..., n-1, n <![CDATA[W z ]]> The parameter matrix of the update gate in GRU <![CDATA[W r ]]> Parameter matrix of reset gate in GRU <![CDATA[W h ]]> Parameter matrix of hidden layers in GRU <![CDATA[b z ]]> GRU update gate bias vector <![CDATA[b r ]]> Bias vector of reset gate in GRU <![CDATA[b h ]]> Bias vector of hidden layer in GRU σ, tanh Activation function

[0168] The CGRU network of this invention consists of one convolutional layer (Conv1D) and two GRU layers. The loss function is mean squared error, and the optimization function is the Adam algorithm. The structure of CGRU is as follows: Figure 3 As shown.

[0169] 1.3.2 Genetic Algorithm (GA)

[0170] Genetic algorithms are adaptive global optimization probabilistic search algorithms that simulate the heredity and evolution of organisms in their natural environment. The algorithm uses the principle of survival of the fittest, including heredity, gene mutation, natural selection, and hybridization. It automatically acquires and accumulates knowledge about the search space during the search process and adaptively controls the search process to calculate the globally optimal solution.

[0171] Genetic algorithms are a population-based search technique that uses chromosomes in the population during the search process, with each chromosome representing a feasible solution. This paper uses a Bernoulli distribution to define a randomly initialized binary array encoding as the genetic representation of our solution, i.e., the genetic code.

[0172] The main process of the genetic algorithm is as follows:

[0173] First, the population is initialized, and a first-generation population is randomly generated. Each chromosome in the population contains feasible solutions. Next, for each chromosome in the current population, training is performed using the training set, and its fitness is calculated on the validation set using a fitness function. Then, roulette wheel selection is used to make chromosomes with higher fitness values ​​more likely to be selected for genetic operations. Through chromosome crossover and low-probability gene mutations, a new generation of individuals is generated, achieving population evolution. Through this series of selection, crossover, and mutation processes, a new generation of individuals is generated, and each generation evolves towards higher fitness, because better individuals are always more likely to be selected to produce the next generation, while individuals with low fitness are gradually eliminated. This process is repeated until the termination condition is met.

[0174] Selection involves repeatedly choosing a chromosome from the current population and adding it to a new population until a suitable reproductive ratio is achieved. This study employs an elitist strategy, meaning that chromosomes with higher fitness in the current population have a greater probability of being selected and added to the new population. The probability of an individual being selected is P(x...). i The calculation formula is as follows:

[0175]

[0176]

[0177] Where fitness(x) i For individual x i fitness, x i Let i represent the i-th individual in the population, which goes through NP cycles.

[0178] Crossover is an operation that involves repeatedly selecting two chromosomes from the current population as parental chromosomes, generating and adding two offspring chromosomes to a new population, until the crossover ratio is reached. This study uses uniform crossover. With uniform crossover, each value in the offspring chromosomes is independently selected from two values ​​at the same corresponding position on the two parental chromosomes. Allowing individuals to cross over in pairs to produce the next generation ensures that superior genes from the previous generation are retained in the next, while inferior genes are replaced by the genes from the other half of the individual.

[0179] Mutation involves repeatedly selecting a chromosome from the current population, modifying it to generate a mutant, and adding this mutant to a new population until a mutation ratio is reached. This study employs single-point mutation, injecting small, random changes into the selected chromosome through low-probability events. This mutation introduces diversity into the population and avoids local optima.

[0180] The basic genetic algorithm can be defined as a 7-tuple:

[0181] GA=F(k,f,s,c,m,Px i ,P c ,P m (29)

[0182] Where F() is the computation function of the genetic algorithm, k is the population size; f is the individual fitness evaluation function; s is the selection operator; c is the crossover operator; m is the mutation operator; P(xi) is the crossover probability; P c P represents the crossover probability. m This represents the probability of mutation.

[0183] 2. Validity Analysis of the Model Proposed in This Invention

[0184] 2.1 Data Collection

[0185] The data in this paper comes from historical wind speed data from multiple measuring points at a wind farm in Shandong Province, China, in 2011. We selected partial data from one measuring point across four seasons as experimental data, with a sampling interval of 10 minutes. The experimental part of this paper uses the electricity data from the first 15 days of January, April, July, and October 2011 for modeling, totaling 4*2160 data points. 70% of the data from each season was used as the training set, and 30% as the test set. The original wind speed dataset is shown in Table 2. Figure 5 As shown.

[0186] Table 2 describes the wind speed dataset.

[0187]

[0188] 2.2 Evaluation Indicators

[0189] Using a single error evaluation metric cannot accurately reflect the overall performance of a prediction model; therefore, multiple different error evaluation metrics are needed to comprehensively measure the model's quality. The following three evaluation metrics can be used to judge the quality of prediction results: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The calculation formulas are shown below:

[0190]

[0191]

[0192]

[0193] In the formula: N is the total number of samples; y i Let be the measured value of the i-th sample; Let be the predicted value for the i-th sample.

[0194] This paper uses three improvement metrics to show the progress of one model relative to another, including the percentage improvement in RMSE (P0.05). RMSE Percentage improvement in MAE (P) MAE And the percentage improvement of MAPE P MAPE The equations are defined as formulas (18)-(20).

[0195]

[0196]

[0197]

[0198] RMSE1, MAE1, and MAPE1 are the evaluation metrics for the baseline model, while RMSE2, MAE2, and MAPE2 are the evaluation metrics for the comparison model.

[0199] 2.3 Dataset Decomposition

[0200] Taking the January dataset (Dataset1) as an example: First, the original wind speed sequence is decomposed using EMD (through experiments, the wind speed signal can be decomposed into a maximum of 7 IMF signals using the EMD method). The signal is first decomposed into 7 IMF signals and 1 residual signal, and then sample entropy analysis is performed on each sub-signal. The sample entropy analysis results are shown in Table 3 below:

[0201] Table 3. Sample entropy results of the 8 subsequences after EMD decomposition.

[0202] Sample Entropy 1.6038 0.7875 0.4972 0.2371 0.0617 0.0129 0.0136 0.0056

[0203] It can be seen that the sample entropy value after IMF5 is close to 0, so we decompose the original signal into 4 IMF signals and 1 residual signal. The decomposition results are as follows. Figure 6 As shown, Figure 6 The darker areas represent the training set, and the lighter areas represent the test set. As shown in the figure, after preprocessing with the EMD algorithm, the wind speed signal is divided into five groups of decomposed signals, ranging from high frequency to low frequency. The low-frequency main signal waveform changes smoothly without spikes, while the high-frequency signal contains spike noise. The sample entropy analysis results of each decomposed sub-signal are shown in Table 4 below:

[0204] Table 4. Sample entropy results of the 5 subsequences after EMD decomposition.

[0205] Sample Entropy 1.6038 0.7875 0.4972 0.2371 0.0381

[0206] Considering that the prediction error after EMD algorithm decomposition mainly comes from high-frequency signals, sample entropy is used to analyze each decomposed signal. Sample entropy analysis measures the time series complexity by measuring the probability of new patterns arising in the signal; the higher the probability of new patterns arising, the greater the complexity of the sequence. The lower the sample entropy value, the higher the self-similarity of the sequence; the higher the sample entropy value, the more complex the sample sequence. Therefore, it is necessary to further decompose signals with high sample entropy values. It can be seen that the time series of high-frequency signals is more complex, so the high-frequency signal IMF1 is further decomposed.

[0207] The VMD algorithm is used to further decompose the sub-signal IMF1. First, the signal is decomposed into six IMF components stepwise from high frequency to low frequency. Then, each IMF... 1k Sample entropy analysis was also performed, and the results are shown in Table 5:

[0208] Table 5. Sample entropy results of the 5 subsequences after VMD decomposition.

[0209] Sample Entropy 0.5387 0.5018 0.5247 0.5529 0.5322 0.5644

[0210] Table 5 shows that the sample entropy value of IMF1 decreased significantly after VMD decomposition, but the entropy values ​​of each IMF... 1k The sample entropy values ​​are very close, so IMF1 can be decomposed into 3 sub-signals using VMD. The results are shown in Table 6 below:

[0211] Table 6 shows the sample entropy results of the five subsequences after VMD decomposition.

[0212] Sample Entropy 0.5604 0.6580 0.6085

[0213] The VMD decomposition results are as follows: Figure 7 As shown, by analyzing the center frequency, the hyperparameters of VMD are set to K=5 and alpha=100. The center frequency diagram is shown below. Figure 8 As shown, by Figure 8 It can be seen that the center frequencies of each component are dispersed, effectively separating the signals of each frequency band.

[0214] 2.4 Multi-label XGBoost Feature Selection

[0215] A sliding window is designed to reorganize the phase space of data for each subsequence, using the first 144 steps (24 hours) as input features. Each subsequence ultimately yields a 144-dimensional feature matrix as its input set. The first 70% of the data is selected as the training set. Feature importance is evaluated based on the gain of the XGBoost algorithm's structure score. In the multi-step prediction task, a multi-label-specific XGBoost feature selection method is used, ranking features based on their importance scores across two metrics.

[0216] Table 7. Ranking of the Importance of IMF Features in Single-Step Prediction

[0217]

[0218] As shown in the table above, the features ranked third in importance and beyond have very low scores, meaning these input features have minimal impact on the prediction results. Using these features as input would only increase redundancy. Therefore, the top three features in importance are selected as the input features for single-step prediction.

[0219] Table 8. Ranking of Importance Scores of IMF Features in the 6-Step Prediction Process

[0220]

[0221] Based on the ranking of the average score and the maximum score of each input feature, the six features with the highest feature importance scores are selected as the input features of each sub-signal.

[0222] Table 9. Ranking of Importance Scores of IMF Features in the 10-Step Prediction Process

[0223]

[0224] By combining the average score and the maximum score of each input feature, the input features for each component in the ten-step prediction are selected. Based on the average score and the maximum score of the features, six features are selected as the input features.

[0225] The feature importance scores of the input features in multi-step predictions show that in IMF2, IMF3, IMF4, and Residue multi-step predictions, the first step before the initial prediction plays a major role in subsequent multi-step predictions. This means it has a significant impact on the baseline of the subsequent N-step predictions, but little impact on volatility. However, in IMF11, IMF12, and IMF13 multi-step predictions, approximately the first five steps before the initial prediction play a major role in subsequent multi-step predictions. This means it has a relatively large impact on the volatility of the subsequent N-step predictions. This further illustrates that by using quadratic decomposition to reasonably divide the wind speed fluctuation characteristics into subsequences of different frequency bands, the accuracy of the predictions is effectively improved.

[0226] Meanwhile, this feature selection method effectively extracts a small number of important features as input, extracts effective information and removes invalid information, reduces model redundancy, reduces the difficulty of subsequent modeling, and significantly reduces the time spent on parameter optimization and modeling.

[0227] Based on the comprehensive feature scores in the table above, the input features selected by multi-label XGBoost feature selection for the January dataset are shown in Table 10 below:

[0228] Table 10 Results of Feature Selection

[0229]

[0230]

[0231] 2.5 GA Optimization of GRU

[0232] The CGRU prediction model is established, and the parameters of learning rate, batch size, and the number of filters in the convolutional recurrent layers have a significant impact on the model's prediction accuracy. Therefore, these parameters need to be optimized. The steps for implementing model prediction can be summarized as follows:

[0233] Step 1: Divide the training samples and prediction samples appropriately. Set several parameters for the search range.

[0234] Step 2: Determine the fitness function of the CGRU model. This paper selects the root mean square error as the fitness function, as described in the following equation:

[0235]

[0236] In the formula, y i Let be the measured value of the i-th sample; Let be the predicted value of the i-th sample, and N be the total number of samples.

[0237] Step 3: Set the population size k, maximum number of iterations T, and mutation probability P for the GA algorithm. m The probability P of selecting the number of elites xi Crossover probability P c Set the current iteration number t=0 and initialize the particle position and velocity.

[0238] Step 4: Initialize the population and generate the first generation population.

[0239] Step 5: Calculate the target fitness value based on equation (36) and evaluate it.

[0240] Step 6: Select, cross over, and mutate the previous generation population based on the elite selection rate, crossover probability, and mutation probability to generate the next generation population.

[0241] Step 7: Determine if the GA algorithm meets the termination condition. If it does, proceed to Step 8; otherwise, let t = t + 1 and execute Steps 5 through 7.

[0242] Step 8: Output the global optimal individual spatial location and fitness value of the GA algorithm, which is the optimal solution to the problem to be optimized.

[0243] Step 9: Use the optimal learning rate, batch size, and number of neurons obtained by the GA algorithm to optimize the CGRU and substitute them into the GA-CGRU model to predict the samples.

[0244] Table 11 shows the results of GRU parameter optimization for each IMF and residual after single-step and multi-step phase space reconstruction using GA.

[0245]

[0246]

[0247] Finally, the final prediction results are obtained by summarizing the prediction results for each IMF and residual.

[0248] 2.6 Verify the accuracy and stability of the model proposed in this invention.

[0249] To verify the accuracy and stability of the proposed model, experiments were conducted using wind speed datasets from four seasons. The single-step and multi-step wind speed prediction results of the SD-MLXGBoost-GA-CGRU model were thoroughly compared with multiple comparative models using various evaluation metrics. The comparisons were mainly divided into: comparisons of different decomposition methods, comparisons of combined models, and comparisons of commonly used models. Hybrid prediction models based on different decomposition methods were used as comparison models, namely EMD-MLXGBoost-GA-CGRU and VMD-MLXGBoost-GA-CGRU. The only difference between them is the data decomposition method, allowing for the analysis of the impact of SD. Combined models such as MLXGBoost-GA-CGRU, SD-GA-CGRU, and SD-MLXGBoost-CGRU (included in SD-MLXGBoost-GA-CGRU) were used as comparison models to analyze the influence of each component of the proposed model. SD-PSO-LSTM, DE-GRU, MLXGBoost-ANN, LSTM, SVM, and ANN were used for comparison as individual prediction models, demonstrating the advantages of the proposed prediction model.

[0250] 2.6.1 Setting parameters for each model

[0251] The parameter settings of the proposed model and some comparative models are shown in Table 12:

[0252] Table 12 Parameters for each model

[0253]

[0254] The output set of each model consists of wind speed values ​​at 1, 6, and 10 steps after the input set. However, the input set is different for each model depending on its requirements. The input set of a model that has undergone feature selection is the result of feature selection, while the input set of a model that has not undergone feature selection requires us to select the values ​​N steps earlier as the model input. The structure of the input set for each model is shown in Table 13.

[0255] Table 13 Structure of each model input set

[0256] SD-GA-CGRU Wind speed data 1440 minutes in advance (144 steps in advance) CGRU Wind speed data 1440 minutes in advance (144 steps in advance) SD-PSO-LSTM Wind speed data 200 minutes in advance (20 steps ahead) DE-GRU Wind speed data 200 minutes in advance (20 steps ahead) LSTM Wind speed data 200 minutes in advance (20 steps ahead) SVM Wind speed data 200 minutes in advance (20 steps ahead) ANN Wind speed data 200 minutes in advance (20 steps ahead)

[0257] 2.6.2 Comparison of the proposed model with different decomposition prediction models

[0258] The prediction results of SD-MLXGBoost-GA-CGRU on wind speed datasets for four seasons were compared with those of two hybrid models based on other decomposition methods. The two comparison models were EMD-MLXGBoost-GA-CGRU and VMD-MLXGBoost-GA-CGRU, the only difference being their data decomposition methods. The comparisons of the 1-step, 6-step, and 10-step prediction curves of the three models with the actual values ​​for the four seasonal datasets are shown below. Figures 9-11 As shown.

[0259] The comparison graphs of predicted results and actual values ​​for each step and season show that the SD-MLXGBoost-GA-CGRU model proposed in this paper has the best fit to the actual values, especially in multi-step prediction, where it is evident that the proposed model has better predictive ability compared to models using other decomposition methods. In the multi-step prediction task, we can see that the EMD decomposition method model's predictive ability significantly decreases when wind speed rises or falls rapidly. The VMD decomposition method model's predictive performance is less than ideal when wind speed fluctuates repeatedly. Therefore, the SD-MLXGBoost-GA-CGRU model proposed in this paper exhibits high stability.

[0260] In addition, the error evaluation results of the 1-step, 6-step, and 10-step predictions of the three models in the four seasonal datasets are shown in Table 14:

[0261] Table 14 Comparison of average prediction errors for different decomposition methods in each season

[0262]

[0263] The 6-Step prediction map represents the predicted value of the sixth step on the test set of the 6-Step prediction, and the 10-Step prediction map represents the predicted value of the tenth step on the test set of the 10-Step prediction.

[0264] Based on the results in Table 14, we can see that in all four seasonal datasets, the SD-MLXGBoost-GA-CGRU model exhibits the lowest RMSE, MAE, and MAPE values ​​for both single-step and multi-step predictions, indicating that this model provides the most accurate and stable results. Furthermore, the RMSE, MAE, and MAPE values ​​show that in multi-step predictions, the SD decomposition method's prediction model shows larger differences in RMSE, MAE, and MAPE compared to the other two comparative models. This further demonstrates the greater advantage of the proposed method in multi-step predictions.

[0265] To further illustrate the impact of different decomposition methods on prediction performance, we used scatter plots to visually represent the prediction results. The scatter plots of the prediction results and actual values ​​for the four models on four datasets are shown below. Figure 9 As shown, the closer the predicted value is to the actual value, the closer it is to the regression line in the graph. Each subplot in the graph also provides the correlation coefficient R, which describes the degree of collinearity between the predicted results of the four models and the actual values. The R value ranges from 0 to 1. The closer the R value is to 1, the better the correlation with the actual value, and thus the better the prediction effect.

[0266] from Figure 12 As can be seen, regardless of whether it's single-step or multi-step prediction, the SD decomposition method model has the most evenly distributed scatter points near the regression line in different seasonal datasets, and is also closest to the regression line. Furthermore, the R-values ​​of the SD-MLXGBoost-GA-CGRU model's predictions are the largest for 1-step, 6-step, and 10-step predictions across the four seasonal datasets. This demonstrates that SD is the most effective decomposition method for improving predictive power compared to EMD and VMD.

[0267] 2.6.3 Comparison of the proposed model with other comprehensive prediction models

[0268] By using combined prediction models such as MLXGBoost-GA-CGRU, SD-GA-CGRU, SD-MLXGBoost-CGRU and SD-MLXGBoost-GA-GRU included in SD-MLXGBoost-GA-CGRU as comparative models, the impact of each component of the proposed model is analyzed.

[0269] The SD-MLXGBoost-GA-CGRU model showed the best fit to actual wind speed curves in 1-step, 6-step, and 10-step predictions across all seasonal datasets. SD-MLXGBoost-CGRU followed, while MLXGBoost-GA-CGRU and MLXGBoost-CGRU performed poorly in multi-step predictions, with CGRU showing the worst performance. This indicates that GA parameter optimization improves the model's performance; the SD-optimized model shows a significant improvement in fit compared to the unoptimized model, particularly in multi-step predictions. While the SD-MLXGBoost-GA-GRU model performed well in single-step predictions, significant disconnects occurred in 10-step predictions on the July and October datasets during periods of decreasing and rapid increases in wind speed. This demonstrates that adding convolutional layers to the GRU model significantly enhances its multi-step prediction capabilities. The SD-GA-CGRU model exhibits significant local imbalance and instability, indicating that the MLXGBoost feature selection method can simplify the data structure, improve relevance, reduce redundancy, and avoid overfitting, thereby improving prediction performance.

[0270] In addition, the error evaluation results of the 1-step, 6-step, and 10-step predictions of each model in the four seasonal datasets are shown in Table 15:

[0271] Table 15 Comparison of Average Prediction Errors for Different Combined Models in Each Season

[0272]

[0273]

[0274] Based on the results in Table 15, we can see that in the datasets for each month, the SD-MLXGBoost-GA-CGRU model has the lowest RMSE, MAE, and MAPE for both single-step and multi-step predictions. This indicates that each component of the model contributes to its improvement.

[0275] The SD-MLXGBoost-GA-CGRU model proposed in this paper achieves average RMSE, MAE, and MAPE of 0.3432, 0.2544, and 4.7440% respectively for one-step prediction on four seasonal datasets, and average RMSE, MAE, and MAPE of 0.5687, 0.4124, and 8.3583% respectively for six-step prediction.

[0276] The average RMSE, MAE, and MAPE of the 10-step advance prediction are 0.7457, 0.5369, and 11.0820%, respectively. We can see that the prediction performance of models without SD, whether single-step or multi-step prediction, is significantly lower than that of other models with SD. The MLXGBoost-GA-CGRU model achieves average RMSE, MAE, and MAPE of 0.6739, 0.4934, and 9.3707% for 1-step advance prediction on four seasonal datasets, which is considerably lower than the proposed SD-MLXGBoost-GA-CGRU model. In 10-step advance prediction, the average RMSE, MAE, and MAPE reach 1.3167, 0.9684, and 19.6040%, respectively, showing an even more significant difference and demonstrating the substantial advantage of the SD method. The RMSE, MAE, and MAPE values ​​of the SD-GA-CGRU, SD-MLXGBoost-CGRU, and SD-MLXGBoost-GA-GRU models are all higher than those of the proposed SD-MLXGBoost-GA-CGRU model in both single-step and multi-step predictions, with the difference being even greater in multi-step predictions. This indicates that MLXGBoost, GA, and CNN all improve the prediction performance of the model to a certain extent, especially in multi-step predictions.

[0277] 2.6.4 Improvement effect of the proposed model

[0278] Table 16 lists the percentage improvement of the proposed SD-MLXGBoost-GA-CGRU model compared to other combined models on four seasonal datasets.

[0279] Table 16

[0280]

[0281]

[0282] Models such as D-MLXGBoost-CGRU and SD-MLXGBoost-GA-GRU show improvements to some extent. Taking the 10-step advance prediction model, which shows a significant improvement, the average improvement across four seasonal datasets reveals that, compared to MLXGBoost-GA-CGRU, SD-GA-CGRU, SD-MLXGBoost-CGRU, and SD-MLXGBoost-GA-GRU, the proposed SD-MLXGBoost-GA-CGRU model achieves reductions in RMSE (43.35%, 17.52%, 13.35%, and 17.15%, respectively), MAE (44.56%, 14.41%, 10.86%, and 15.05%, respectively), and MAPE (43.47%, 11.22%, 8.71%, and 15.27%, respectively). This demonstrates that the proposed SD-MLXGBoost-GA-CGRU model is an effective short-term wind speed prediction model, especially advantageous in multi-step prediction.

[0283] The comparison results with the MLXGBoost-GA-CGRU model show that the SD method significantly improves the model's prediction performance, contributing the most to the improvement among various enhancement methods. Comparing the results of the SD-GA-CGRU model reveals that MLXGBoost feature selection reduces the redundancy of irrelevant features, resulting in a significant improvement in prediction performance. Comparing the results of the SD-MLXGBoost-CGRU model shows that GA parameter optimization of CGRU improves the model's prediction performance to some extent. Comparing the results of the SD-MLXGBoost-GA-GRU model, the proposed model consistently performs well, indicating that extracting deep features through CNNs helps to further improve prediction performance. Therefore, the proposed CGRU model can fully utilize the advantages of CNNs and GRUs to provide more robust and effective prediction results.

[0284] 2.6.5 Comparison of the proposed model with six commonly used models

[0285] Six comparative models were included: SD-PSO-LSTM, DE-GRU, MLXGBoost-ANN, LSTM, SVM, and ANN. The prediction results of SD-MLXGBoost-GA-CGRU and the six comparative models were compared with actual values ​​on four seasonal datasets at 1-step, 6-step, and 10-step intervals. As the number of wind speed forecast steps increased, the forecast error gradually increased on each seasonal dataset. Regardless of whether it was single-step or multi-step prediction, the SD-MLXGBoost-GA-CGRU model, compared to the other comparative models, better tracked the changing trends of wind speed signals.

[0286] In 1-step advance prediction, the SVM model's predictive ability on the January and April datasets showed a significant decline when wind speed fluctuated dramatically. Most other models were able to fit the trend of wind speed changes well, and the difference in prediction performance was not significant in single-step prediction. However, in 6-step and 10-step advance prediction, the proposed model was more sensitive to changes in wind speed signals compared to the comparison models, further demonstrating its predictive performance advantage. For example, in the 6-step advance prediction of the four seasonal datasets, when wind speed rose or fell rapidly, several comparison models failed to keep up with the large changes in wind speed, exhibiting lag, while SD-MLXGBoost-GA-CGRU still managed to track the trend of wind speed changes well. In the 10-step advance prediction of four seasonal datasets, we can see that SD-PSO-LSTM, DE-GRU, MLXGBoost-ANN, LSTM, SVM, and ANN all exhibit significant underfitting, especially on the April and July datasets. SVM, ANN, and LSTM all show lag issues when wind speed fluctuates repeatedly, while SD-PSO-LSTM fluctuates excessively when wind speed fluctuates upwards or downwards. The fit of DE-GRU and MLXGBoost-ANN also drops sharply. The SD-MLXGBoost-GA-CGRU model also shows a significant decrease in fit in 10-step advance prediction compared to 1-step and 6-step prediction, but its fit is still relatively good compared to other comparative models.

[0287] Furthermore, Table 17 shows a comparison of the error evaluation results of the proposed model with six other commonly used models for 1-step, 6-step, and 10-step predictions in four seasonal datasets:

[0288] Table 17 Comparison of average prediction errors for different models in each season

[0289]

[0290]

[0291] Based on Table 17, the following conclusions can be drawn: Overall, the SD-MLXGBoost-GA-CGRU model outperforms the comparative models in wind speed prediction across the four datasets, demonstrating its effective and stable predictive performance. The three error evaluation metrics (MAE, MAPE, and RMSE) of the proposed model are all lower than those of the other comparative models. Especially in multi-step prediction tasks, compared to LSTM, SVM, ANN, and the undecomposed DE-GRU and MLXGBoost-ANN, the proposed method shows significant advantages, with significantly reduced MAE, MAPE, and RMSE values.

[0292] The comparison results between ANN and MLXGBoost-ANN show that the proposed MLXGBoost feature selection method improves prediction performance to a certain extent. This method extracts features with high relevance and low redundancy, simplifies the data structure, avoids overfitting, and thus improves prediction performance. The model after SD decomposition significantly outperforms other models, especially in multi-step prediction tasks. These results indicate that SD and MLXGBoost can improve the prediction performance of the model, with SD contributing more than MLXGBoost. Combining SD and MLXGBoost can achieve even greater improvements. CGRU combined with deep neural networks has strong learning capabilities, can capture irregular trends and time dependencies in wind speed, and improve prediction performance.

[0293] 2.6.6 Frequency of Error Distribution

[0294] The error metric mentioned earlier is to prevent positive and negative errors from canceling each other out. It is the result of averaging the overall error based on the absolute value or square calculation. To understand the true distribution of prediction errors for each prediction model, probability density histograms and kernel density curves of the error distribution for single-step and multi-step predictions of the proposed SD-MLXGBoost-GA-CGRU prediction model and other comparative models were plotted for four seasons. These graphs provide a more intuitive view of the error distribution. The probability density distribution of the prediction error of the SD-MLXGBoost-GA-CGRU model in 1-step, 6-step, and 10-step advance predictions in each seasonal dataset all exhibit a sharp peak. Although the contraction on both sides slows down with the increase of the prediction steps, its probability density distribution is still optimal compared to other comparative models.

[0295] The probability density distribution histogram of the 1-step prediction error for each seasonal dataset clearly shows that the SD-MLXGBoost-GA-CGRU model exhibits a significant spike in the middle, which is much higher than other comparative models. The two sides are generally lower than other models and shrink earlier. This indicates that the 1-step prediction error of the SD-MLXGBoost-GA-CGRU model on each seasonal dataset is concentrated at small error values ​​(-0.5m / s to 0.5m / s), and large error values ​​above ±1m / s are relatively rare. The 1-step prediction performance is significantly better than the comparative models.

[0296] In the probability density distribution histograms of 6-step and 10-step advance prediction errors for the January and April datasets, the SD-MLXGBoost-GA-CGRU model significantly outperforms the comparison model. The probability density of prediction errors is higher near the "0" value, indicating that prediction errors are concentrated at small error values, with fewer cases of large errors, resulting in better prediction performance. In the histograms of 6-step and 10-step advance prediction errors for the July and October datasets, the SD-PSO-LSTM model also shows a good probability density distribution of prediction errors, similar to the SD-MLXGBoost-GA-CGRU model. However, we can see that although the peak values ​​at small errors are similar, the curve contraction of the SD-MLXGBoost-GA-CGRU model occurs slightly earlier than that of the SD-PSO-LSTM model. Specifically, the SD-MLXGBoost-GA-CGRU model has fewer errors exceeding ±1.5 m / s in 6-step advance prediction and ±2.0 m / s in 10-step advance prediction compared to the SD-PSO-LSTM model.

[0297] Based on the above analysis of the probability density distribution histograms of 1-step, 6-step, and 10-step advance prediction errors in the datasets for each season, we can see that the SD-MLXGBoost-GA-CGRU model has superior performance in 1-step, 6-step, and 10-step advance predictions, with its prediction errors concentrated at small error points, demonstrating its advantages in multi-step prediction tasks.

[0298] 2.6.7 Average time to build prediction models for different models

[0299] Table 18 shows the average computation time of the model in different wind speed prediction steps.

[0300]

[0301] As we can see from Table 18, the average computation time of LSTM, SVM and ANN models is relatively short, and they can complete the training of the model quickly. However, their prediction performance is generally poor, and there is a large gap compared with the SD-MLXGBoost-GA-CGRU model.

[0302] The average computation time of the SD-MLXGBoost-GA-CGRU model is significantly reduced compared to the SD-GA-CGRU model, especially in multi-step prediction modeling. This demonstrates that MLXGBoost feature selection greatly improves the speed of model building, a conclusion also reached by comparing the average computation time of ANN and MLXGBoost-ANN. The MLXGBoost feature selection method simplifies the data structure by extracting highly relevant and low-redundancy features, and its improvement in training speed is more significant than its improvement in prediction error.

[0303] The average computation time of the SD-MLXGBoost-GA-CGRU model is longer than that of the MLXGBoost-GA-CGRU model. This is because the SD model decomposes the model into multiple IMF subsequences with different frequency features. Each subsequence needs to be modeled separately, which requires more computation time. However, the SD method significantly improves the predictive performance of the model, so spending more computation time is necessary.

[0304] In summary, this invention proposes a novel GA-CGRU multi-step wind speed prediction model based on multi-label specific XGBoost feature selection and secondary decomposition. This model combines decomposition methods, multi-label feature selection methods, optimization models, and hybrid prediction models, demonstrating excellent performance in multi-step wind speed prediction tasks. Based on wind speed data collected from a wind farm in Shandong, China, across several seasons, experimental analysis with several comparative models verifies the stability and superiority of the proposed model. The main conclusions are summarized below.

[0305] 1) The proposed quadratic decomposition method can decompose the subsequences obtained from the first decomposition into high-frequency subsequences with high unpredictability, and further extract the frequency-specific fluctuation characteristics of wind speed. The more effective subsequences further improve the model's forecasting ability, especially in multi-step forecasting.

[0306] 2) The XGBoost feature selection method for multi-label proposed in this paper can extract highly relevant and low-redundancy features, simplify the data structure, improve training speed, and avoid overfitting.

[0307] 3) This paper establishes a GA-CGRU prediction model. Convolutional layers are used to capture deep features, GRU layers are used to obtain the temporal dependence of wind speed, and GA is used to optimize the parameters for wind speed forecasting. This model outperforms popular models in prediction accuracy, especially in multi-step prediction tasks.

[0308] 4) Judging from the overall trend, error distribution, goodness of fit, RMSE, MAE, MAPE, correlation coefficient and other error evaluation indicators, the proposed SD-MLXGboost-GA-CGRU method is better than the benchmark model in wind speed forecasting.

[0309] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A short-term wind speed multi-step prediction method based on a combined CGRU model, characterized in that, Includes the following steps: S1, decompose the original wind speed signal: S1-1, First, the original wind speed sequence is decomposed using EMD, which decomposes the original wind speed sequence into multiple wind speed subsequences and residual signals; S1-2, after EMD decomposition, the unpredictability of each wind speed subsequence is estimated by sample entropy analysis. The most unpredictable subsequence is then further decomposed by VMD to obtain multiple secondary wind speed subsequences. S2, phase space reconstruction is used to reconstruct each wind speed subsequence, secondary wind speed subsequence, and residual signal, and then the multi-label XGBoost feature selection method is used to select features from each reconstructed data; the feature selection of each reconstructed subsequence using the multi-label XGBoost feature selection method includes the following steps: S200, the first M columns of the data matrix obtained after phase space reconstruction are used as M input features, then... Column as The system outputs labels in multiple steps; then, XGBoost feature selection is performed on the input features and each label to obtain the importance score of each input feature for each label. Each input feature will then receive... Each importance score; S201 uses two metrics to select the final required input features: One metric is the average score of each feature, that is, the score of each feature for... The average importance score of each tag is calculated using the following formula: ， in Indicates the first Each feature for The average importance score of each tag; Indicates the first Each feature for Importance score of each tag; Total number of tags; According to each characteristic The p features with the highest average importance scores on each label are selected in descending order. Another metric is the maximum score for each feature, i.e., the score for each feature relative to the maximum score for ... The maximum value among the importance scores of each tag is calculated using the following formula: ， in, Indicates the first Each feature for The maximum value among the importance scores of each label; According to each characteristic The importance scores of each label are sorted in descending order, and the q features with the highest scores are selected. Finally, the two indicators are combined to determine the final selected input features. If a feature is selected in both indicators, it will be used as the final required input feature. S3, input the sub-sequences and residual signals after feature selection into the CGRU prediction model to obtain the prediction results. The model uses CNN to extract features from each sub-signal and uses GRU to identify the time dependence between the extracted features and future wind speed. S4. The prediction results of each subsequence and the residual signal are accumulated to obtain the final prediction result.

2. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 1, characterized in that, The method of estimating the unpredictability of each wind speed subsequence using sample entropy analysis involves calculating the sample entropy of each wind speed subsequence and selecting the top Q wind speed subsequences with the highest sample entropy (ranked from highest to lowest) as the most unpredictable subsequences. The sample entropy calculation steps are as follows: SA, for wind speed subsequence, i.e., wind speed time series Reconstructing the phase space yields the matrix. , Let be the dimension, then: ， in For matrix The total number of rows in the subsequence; SB, defines a subsequence and distance It is the absolute value of the maximum difference between the two corresponding values, that is: ， in, , For matrix Any two rows of subsequences; 0~ A number between, Indicates the first row and number The difference between corresponding values ​​in a row subsequence; For matrix dimensionality; SC, for a given SC row subsequence It has a maximum difference from all other subsequences. , ,statistics The number, recorded as ;for definition: ， in, For dimension Time The maximum distance between the corresponding values ​​of a row and other rows is less than a threshold. The proportion of the number of values ​​to all maximum differences; For matrix dimensionality; The length of the original time series; but indivual The average value is expressed as: ， SD, making Repeat steps SA~SC to calculate... ; SE, the formula for calculating sample entropy is: ， The dimension is time value; Indicates the first The maximum distance between the corresponding values ​​of a row and other rows is less than a threshold. The proportion of the number of values ​​to all maximum differences; express indivual The average value; This indicates the similarity tolerance, or threshold.

3. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 2, characterized in that, Also includes: Before selecting wind speed subsequences with higher sample entropy, wind speed subsequences with sample entropy values ​​close to 0 are first removed.

4. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 1, characterized in that, The iterative process of further decomposing the subsequence using VMD includes the following steps: Step 1: Given a sequence Initialize the modality { }, center frequency { } and Lagrange multiplier ; Step 2: For each mode Update using the following formulas respectively. and ; ， ， in, The number of iterations; express Fourier transform; Indicates the first After the nth iteration One component; express Fourier transform; Represents the original sequence; Indicates the first After the nth iteration One center frequency; It is a secondary penalty factor; Indicates the center frequency; The center frequency is represented by the first Each component Represents the square of the absolute value; Step 3: Update the Lagrange multipliers using the following formula. ; ， in Indicates that the parameter is being updated; Indicates the first Lagrange multipliers in the next cycle; Indicates the first Lagrange multipliers in the next cycle; Step 4: If the termination condition is met, stop the iteration. It can be done The inverse Fourier transform of the real part is obtained; otherwise, Become Then proceed to Step 2.

5. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 1, characterized in that, The specific steps for reconstructing each wind speed subsequence using phase space reconstruction include: S20, Set Embedding Dimension and delay time ; S21, through a given embedding dimension and delay time Build a sliding window; S23, wind speed time series via a sliding window. The data matrix is ​​obtained by reconstructing it in a high-dimensional phase space.

6. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 1, characterized in that, The CGRU prediction model includes one convolutional layer and two GRU layers, wherein the convolutional layer uses one-dimensional convolution.

7. A short-term wind speed multi-step prediction method based on a combined CGRU model according to claim 6, characterized in that, The loss function of the CGRU prediction model is the mean squared error, the optimization function is the Adam algorithm, and the evaluation metrics are root mean squared error, mean absolute error, and mean absolute percentage error.

8. The short-term wind speed multi-step prediction method based on the combined CGRU model according to claim 1, characterized in that, S3 further includes: jointly optimizing the parameters of the CGRU prediction model using GA, wherein the parameters include the learning rate, batch size, and the number of filters in the convolutional recurrent layer, and the specific steps are as follows: Step 1: Divide the training samples and prediction samples, and set the search range of the parameters; Step 2: Determine the fitness function of the CGRU model. Root mean square error is chosen as the fitness function, as described in the following equation: ， in, For the first Measured values ​​of a sample; For the first Predicted values ​​for each sample; This represents the total number of samples. These represent the minimum learning rate and the maximum learning rate, respectively. These represent the minimum batch size and the maximum batch size, respectively. These represent the minimum and maximum number of filters, respectively. Step 3: Set the population size for the GA algorithm Maximum number of iterations T, mutation probability The probability of selecting the number of elites Crossover probability Set the current iteration number t=0, and initialize the particle position and velocity; Step 4: Initialize the population and generate the first generation population; Step 5: Calculate the target fitness value based on Step 2 and evaluate it, i.e., minimize the root mean square error of the predicted samples; Step 6: Select, cross over, and mutate the previous generation population based on the elite selection rate, crossover probability, and mutation probability to generate the next generation population; Step 7: Determine if the GA algorithm meets the termination condition. If it does, proceed to Step 8; otherwise, let t = t + 1 and execute Step 5 to Step 7. Step 8: Output the global optimal individual spatial location and fitness value of the GA algorithm, which is the optimal solution to the problem to be optimized.

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