A wind power multi-scale decomposition prediction method

Abstract

A wind power multi-scale decomposition prediction method. At present, the single-point prediction is not comprehensive and accurate enough, and has been unable to adapt to the quantitative and accurate requirements of risk management of wind farm and power grid dispatching mechanism. After the actual wind power data is formed into an original wind power sequence, the feature selection and data decomposition processing are sequentially performed to form multi-scale modal data, a deep prediction model is constructed according to the multi-scale modal data, and the determination process of the probability prediction interval in the residual distribution mode deep prediction model is completed through the self-adaptive bandwidth kernel density estimation. After the actual wind power data is formed into an original wind power sequence, an initial model is established, the initial model is subjected to feature selection processing, that is, the SHAP algorithm is used to calculate the weighted marginal contribution of each feature of the initial model according to all involved feature subsets based on the Shapley value in the game theory, and the feature data acquisition process of the mutual dependence and interaction effect between the accurate quantification features is completed.

Description

Technical Field

[0001] This invention specifically relates to a multi-scale decomposition prediction method for wind power, belonging to the field of wind power assessment technology. Background Technology

[0002] Solar and wind power, among renewable energy sources, have become core drivers of global energy transition due to their zero-emission and sustainable advantages. By the end of 2025, global cumulative installed wind power capacity had climbed to approximately 1136 GW, with 117 GW of new capacity added in 2024, a record high. According to the International Energy Agency's "Net-Zero Emission Pathway" scenario, global annual wind power generation is projected to increase from approximately 5000 TWh in 2024 to approximately 7900 TWh in 2030. Wind and solar power together contributed over 95% of global new renewable energy capacity in 2024, significantly optimizing the traditional energy consumption structure. However, compared to hydropower and solar power, wind power exhibits greater randomness and volatility, necessitating intelligent forecasting technologies to improve prediction accuracy and reduce potential harm to the power grid. Deep learning, with its superior nonlinear computing capabilities, has made significant progress in wind power forecasting; for example, Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, and Transformer-based models are widely used in ultra-short-term and medium-to-long-term forecasts. Currently, wind power forecasting research mainly focuses on deterministic forecasting, failing to consider the dangers that wind power fluctuations and uncertainties pose to wind power grid connection. Wind power probabilistic forecasting can output probability density functions or confidence intervals, which can more intuitively reflect the uncertainty of wind power and thus play a more critical auxiliary decision-making role in power system dispatching and market clearing.

[0003] Currently, ultra-short-term wind power prediction (WPP) plays a crucial role in wind power grid-connected dispatch and electricity market transactions. With the increasing installed capacity of wind power, its nonlinear, non-stationary, and high-frequency fluctuation characteristics place higher demands on grid security and economy. To address this, researchers have proposed various hybrid models integrating deep learning and signal processing to improve prediction accuracy and robustness. For example, Yu Wang's Conv-ELSTM model combines Empirical Mode Decomposition (EMD) with a convolutional long short-term memory (LSTM) network architecture, modeling high- and low-frequency components in wind power data separately, and extracting key information through a feature fusion network, significantly improving prediction accuracy within one hour. In ultra-short-term prediction for offshore wind farms, Bin Zhou's PCA-SSA-VMD-BiLSTM model utilizes Principal Component Analysis (PCA) for dimensionality reduction, Sparrow Search Algorithm (SSA) to optimize Variational Mode Decomposition (VMD) parameters, and learns multi-scale features through bidirectional LSTM, achieving effective modeling of wind power volatility. Furthermore, Xiao Dong's STDHL model utilizes a dynamic hypergraph structure to model high-order spatial correlations between wind farms and combines it with a grouped temporal convolutional network to extract temporal features, demonstrating superior prediction performance on the GEFCom dataset. Keisler and Le Naour developed the WindDragon system, integrating automatic deep learning with numerical weather prediction (NWP) wind speed maps, achieving 1- to 6-hour wind power prediction. To further improve prediction performance, Zheng et al. proposed an LSTM-XGBoost hybrid model combining technical indicators, utilizing the extreme gradient boosting algorithm XGBoost to enhance the model's generalization ability, achieving excellent prediction results in an empirical study of wind farms in Inner Mongolia. In addition, the GFST-WSF model, combining a graph attention network (GAT) and a Transformer architecture, effectively captures the complex spatial dependencies between wind speed stations, improving the accuracy of 6- to 24-hour wind speed predictions. In summary, the main trends in current research on ultra-short-term wind power prediction include: improving the accuracy and stability of predictions by combining the advantages of multiple models; optimizing model parameters using advanced optimization algorithms to accelerate model convergence and improve prediction performance; introducing interpretability analysis and uncertainty assessment to enhance the transparency and practicality of models; and considering the spatial correlation between wind farms to improve the adaptability of models to complex environments.

[0004] While existing hybrid forecasting models have made significant progress in improving forecast accuracy, they often overlook the inherent instabilities and potential risks of wind power generation. To more comprehensively assess the volatility and uncertainty of wind power generation, introducing interval forecasting methods for wind power is of great significance. Existing research shows that interval forecasting models are superior to traditional point forecasting methods in quantifying the uncertainty of wind farm power generation per unit area (WPP). Existing literature analysis indicates that traditional physical and statistical methods are significantly insufficient in dealing with the increasing volume and complexity of meteorological data, limiting the accuracy of wind power forecasting WPP. In particular, existing wind power forecasting studies often employ one-to-one correlation analysis methods such as the maximum information coefficient (MIC) and Pearson correlation coefficient, using the magnitude of the obtained correlation coefficient as the main basis for feature selection. However, both MIC and Pearson correlation coefficient only measure the linear or nonlinear association between a single feature and the target variable, failing to characterize the interaction and synergistic effects between features. Because the "marginal contribution" of a feature in conjunction with other variables is not equivalent to its individual correlation, one-to-one correlation coefficients often underestimate or overestimate the importance of certain features that have a significant effect in a multivariate environment. While traditional machine learning (ML) models possess certain modeling capabilities, they are sensitive to input features when faced with large-scale, high-dimensional datasets and are susceptible to overfitting or underfitting. Relying on single-point prediction methods is neither comprehensive nor accurate enough to meet the quantitative and precise risk management requirements of wind farms and grid dispatching agencies. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a multi-scale decomposition prediction method for wind power.

[0006] A method for predicting wind power multi-scale decomposition involves first forming an original wind power sequence from the actual acquired wind power data, then performing feature selection and data decomposition processing to form multi-scale modal data. After constructing a deep prediction model based on the multi-scale modal data, the method uses adaptive bandwidth kernel density estimation to determine the probability prediction interval in the deep prediction model based on the residual distribution.

[0007] As a preferred approach: the process of selecting features after forming the original wind power sequence from the actual acquired wind power data involves establishing an initial model from the original wind power sequence, and then performing feature selection on the initial model. Specifically, the SHAP algorithm, based on the Shapley value in game theory, is used to calculate the weighted marginal contribution of each feature in the initial model according to all involved feature subsets. This completes the feature data acquisition process for accurately quantifying the interdependence and interaction effects between features. The calculation process is as follows:

[0008] The Shapley value φ for each feature is obtained by calculating the marginal contribution of each feature to the model's prediction. jThe calculation formula is:

[0009]

[0010] In the above formula, φ0 is the predicted average value of all samples, φ j The contribution of the j-th feature, This represents the sum of the Shapley values ​​for all features;

[0011] XGBoost prediction was used as the basis for SHAP analysis, and the Shapley value φ for each feature in the training set was calculated using TreeExplainer. ij Then, its Mean Absolute SHAP is obtained as an importance indicator. The calculation process is as follows:

[0012]

[0013] In the above formula, n represents the nth sample, φ ij This represents the SHAP value of feature j of the nth sample.

[0014] As a preferred approach, the process of feature selection followed by data decomposition of the original wind power sequence involves performing FFT spectral analysis on the feature-selected wind power data to determine the range of K values. After determining the range of K values, normalization signal processing and variational mode decomposition are performed. The information entropy of each intrinsic mode function (IMF) and the average information entropy for each corresponding K value are then calculated sequentially. It is determined whether the information entropy and average information entropy have traversed all K values. If they have, the optimal K value is determined, and variational mode decomposition is performed on the optimal K value, saving the result data. If they have not, normalization signal processing and variational mode decomposition are performed again, and the information entropy of each IMF and the average information entropy for each corresponding K value are calculated again, until the information entropy and average information entropy have traversed all K values. Finally, the optimal K value is determined, and variational mode decomposition is performed on the optimal K value, saving the result data.

[0015] As a preferred approach, the specific process of performing feature selection on the original wind power sequence followed by data decomposition processing can be divided into the following steps:

[0016] Step 1: First, apply the Fast Fourier Transform (FFT) to extract the frequency components and calculate their Discrete Fourier Transform X(k), which is defined as follows:

[0017]

[0018] In the above formula, x(n) is the original wind power sequence, N is the sequence length, X(k) is the frequency domain component obtained after Fourier transform, and j is the imaginary unit. It is the kernel function of the DFT, used to project a time-domain signal into the frequency domain; it is used to calculate the wind power spectral density |X(k)|. 2 To identify the main periodic components in the signal, the number of the aforementioned peaks serves as preliminary data for estimating the number of modes required for VMD;

[0019] Step Two: Next, based on the initial basis provided by FFT, VMD decomposition is performed on all K values ​​within the range to calculate their information entropy, thereby completing the decomposition of the data signal f(t) into K modal components u with finite bandwidth. k In the processing of (t), each mode has its corresponding center frequency, which is defined by the following formula:

[0020]

[0021] In the above formula, f(t) represents the original input signal, K represents the preset number of mode decompositions, and u k (t) represents the k-th mode obtained from the decomposition, w k The center frequency of each component is represented by δ(t), which is the Dirac function, and j is the imaginary unit. It is a Hilbert transform kernel. To represent the Hilbert transform in order to construct its analytic signal, It is a complex exponential term used for frequency shifting of the signal; obtaining the optimal solution of the constrained variation is the process of introducing the Lagrange multiplier λ(t) to transform the constrained variation into an unconstrained variation, and the calculation formula is:

[0022]

[0023] In the above formula, u k It is the set of all modal components, ω k α represents the center frequencies corresponding to all modes, and α is the weight that adjusts the smoothness of the solution and the reconstruction error. It is the sum of all modal components; λ(t) is the Lagrange multiplier, which is updated iteratively by the Alternating Direction Multiplier Method (ADMM). k w k ,λ until convergence;

[0024] Information entropy is a metric for modal complexity. The optimal number of modes is selected by minimizing information entropy; its calculation method is as follows:

[0025]

[0026] In the above formula, K is the number of candidate modes, K * H is the final selected optimal number of modes.k Let H(K) be the information entropy of the Kth mode, and H(K) be the average information entropy when the number of modes is K, where k is the index of the mode component. The information entropy is calculated as follows:

[0027]

[0028] Step 3: Finally, the selected optimal number of modes K is used to perform the final VMD decomposition on the signal to obtain the data of each mode and residual component. Each mode and residual component data is the multi-scale mode data.

[0029] As a preferred approach, the prediction processing of multi-scale modal data involves fusing multi-scale temporal convolutional networks, bidirectional LSTMs, and temporal attention mechanisms to construct a deep prediction model based on the multi-scale modal data. Specifically:

[0030] A multi-scale TCN model is constructed, comprising a TCN structure with three parallel branches. Each branch consists of a one-dimensional convolutional layer and a Temporal Block. The kernel sizes are set to 1, 3, and 5, respectively. The kernel sizes in the Temporal Block are 3, 5, and 7, respectively, with dilation values ​​of 2 and 4. The calculation formula is as follows:

[0031] The output formula for the i-th branch is:

[0032] H i =TCN i (RELU(BN(Conv1D pre,i (X)))) (8)

[0033] In the above formula, X∈R H×T×C Represents the input sequence, Conv1D pre,i denoted as i-branch convolution, PIN represents batch normalization, where the outputs of multiple branches are connected along the channel dimension and then fused by a 1×1 convolution to unify the dimension;

[0034] H fused =ReLU(BN(Conv1D) 1×1 ([H1,H2,...,H n ]))) (9)

[0035] After fusion H fused Further into BILSTM, which employs a bidirectional LSTM structure, a temporal attention mechanism is added after BILSTM to improve the prediction performance of key prediction modules. The attention score in the temporal attention mechanism is calculated using the following formula:

[0036] Q,K,V=W Q H,W KH,W V H (10)

[0037]

[0038] H attn =AV (12)

[0039] In the above formula, H is the output hidden state sequence of the BiLSTM layer, d is the hidden state dimension, and W... Q W K W V These are the training weight matrices used to generate the linear transformation matrices for the query, key, and value; Q is the query matrix, K is the key matrix, and V is the value matrix. It is the attention score, A is the attention weight matrix, H ... attn It is the final output after being weighted by the time attention mechanism.

[0040] As a preferred approach: The KDE method is used to model probabilistic prediction. After obtaining the predicted values ​​through a multi-scale TCN model, the distribution of the residuals calculated from the predicted values ​​is estimated. A Gaussian kernel function is used for calculation. For a given confidence level and corresponding bandwidth, the formula for the estimated distribution function of the residual set is:

[0041]

[0042] In the above formula, φ(·) is the standard normal function, and h α It is the bandwidth used to control the smoothness of the kernel function;

[0043] The prediction interval is constructed based on the estimated distribution of the residuals. First, the solution is obtained. The value at the quantile, for the lower quantile. and upper quantile The following formula is satisfied:

[0044]

[0045] The corresponding formula for the 1-α confidence interval is:

[0046]

[0047] As a preferred approach, a corresponding evaluation process is performed on the probability prediction interval. This process begins by generating a bandwidth for the corresponding confidence interval based on Silverman's rule. Starting with this bandwidth, a symmetric network is constructed at 1.5 times its size. A grid search cross-validation method is used to evaluate the performance of the prediction interval under different bandwidths. If no bandwidth superior to that generated by Silverman's rule is found, the bandwidth generated by Silverman's rule is used for the probability prediction process. The probability prediction process involves dividing the training data into a 5-fold validation set, sequentially fitting the residual distribution with a portion of the data, and predicting the interval coverage of the other portion. The evaluation metric uses a weighted interval prediction coverage criterion, ensuring that the coverage rate meets the target while reducing the interval width. The metrics are calculated using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), Predicted Interval Coverage Rate (PICP), Normalized Average Width of Predicted Interval (PINAW), and Comprehensive Evaluation Index (CWC). The calculation formula is as follows:

[0048]

[0049] In the above formula, the prediction interval is labeled [L]. i U i The actual value is y. i , c is the predicted value of the i-th sample. i It is a coverage indicator; when the true value falls within the prediction interval, c i The corresponding value is 1; when the actual value does not fall within the prediction interval, c i The corresponding value is 0; R is the range of the target variable in the entire training dataset, and N is the total number of samples; γ and η are the adjustment parameters of the penalty factor.

[0050] Compared with existing technologies, this invention provides a multi-scale decomposition prediction method for wind power, which has the following beneficial effects:

[0051] I. This invention presents a prediction method for evaluating wind power based on a probabilistic prediction model using ensemble decomposition and deep learning. Feature selection is performed using XGBoost-SHAP to extract key influencing factors. An improved variational mode decomposition (FVMD) is used to decompose the original wind power sequence into multi-scale modes, reducing non-stationarity. Then, a deep prediction model integrating a multi-scale temporal convolutional network (MTCN), a bidirectional LSTM, and a temporal attention mechanism (TATTAN) is constructed to effectively model multi-frequency features. Finally, adaptive bandwidth kernel density estimation (AKDE) is used to model the residual distribution and construct the probabilistic prediction interval.

[0052] Second, the model established by this invention is superior to existing mainstream models in both point prediction and probability prediction, with higher prediction accuracy and more stable interval coverage performance, providing standardized and accurate data support for wind power dispatch and grid-connected operation.

[0053] Third, by constructing prediction intervals at multiple confidence levels, this invention not only improves the information content and reliability of prediction results, but also helps the power system better adapt to the unpredictability of wind power, thereby enhancing the safety and stability of grid operation. It provides reliable forward-looking data guidance for wind power grid connection and effective utilization, and can form a quantitative and standardized early warning assessment process for wind power, which is conducive to providing a standardized processing method for the real-time quantitative assessment process of wind power. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the data decomposition process of this invention.

[0055] Figure 2 This is a flowchart illustrating the model formation process in this invention. In the diagram, Conv1d is a 1D convolution, k is the kernel size, TemporalBlock is the basic building block in the TCN model, Dilation is the dilation rate, Dilated CausalConv is the dilated causal convolutional layer, WeightNorm is the weight normalization, ReLU is the activation function, and Dropout is a regularization technique to prevent overfitting.

[0056] Figure 3 This is a schematic diagram of the probability prediction process in this invention;

[0057] Figure 4 This is a block diagram illustrating the implementation principle of the multi-scale decomposition prediction process for wind power in this invention.

[0058] Figure 5 A bar chart showing the SHAP value results;

[0059] Figure 6 A comparison chart of VMD decomposition results;

[0060] Figure 7 A line graph showing the information entropy results for each K value;

[0061] Figure 8 A comparison chart of model fitting results;

[0062] Figure 9 A comparative diagram of evaluation indicators for various models applicable to complex wind power characteristics;

[0063] Figure 10 This is a diagram comparing the evaluation indicators of various models. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Specific implementation method one: Combining Figures 1 to 10 This embodiment describes a method for predicting wind power using a multi-scale decomposition. The method involves first generating an original wind power sequence from the acquired wind power data, then sequentially performing feature selection and data decomposition to generate multi-scale modal data. Based on this multi-scale modal data, a deep prediction model is constructed. Finally, adaptive bandwidth kernel density estimation is used to determine the probability prediction interval within the deep prediction model based on the residual distribution.

[0066] Combination Figure 4 As shown, the wind power multi-scale decomposition prediction process in this embodiment can be further divided into several steps: step 1 is the feature selection process from the original data, step 2 is the data decomposition process of the selected data, and step 3 is the prediction and standardization evaluation process of the decomposed data.

[0067] The multi-scale decomposition prediction method for wind power in this embodiment can improve the accuracy and reliability of ultra-short-term wind power prediction. Specifically, it achieves the quantitative and standardized prediction process through an integrated decomposition and deep learning probabilistic prediction model. The integrated decomposition and deep learning probabilistic prediction model is a model that integrates multiple methods in sequence, namely FS-FVMD-MTCN-BILSTM-TATTAN-AKDE. The specific formation process of this model is as follows: first, feature selection is performed through XGBoost-SHAP to extract key influencing factors; then, the improved variational mode decomposition FVMD is used to decompose the original wind power sequence into multi-scale modes to reduce non-stationarity; then, a deep prediction model integrating multi-scale temporal convolutional network MTCN, bidirectional LSTM (BiLSTM), and time attention mechanism TATTAN is constructed to achieve effective modeling of multi-frequency features; finally, adaptive bandwidth kernel density estimation AKDE is used to model the residual distribution and construct the probabilistic prediction interval. This invention also verifies the model using wind farm data. The results show that the proposed model outperforms existing mainstream models in both point prediction and probability prediction, and has higher prediction accuracy and more stable interval coverage performance, providing effective data support for wind power dispatch and grid-connected operation.

[0068] Specific Implementation Method Two: This implementation method further defines Specific Implementation Method One. In this method, the process of selecting features after forming the original wind power sequence from the actual acquired wind power data involves establishing an initial model after forming the original wind power sequence from the actual acquired wind power data, and then performing feature selection processing on the initial model. Specifically, the SHAP algorithm, based on the Shapley value in game theory, is used to calculate the weighted marginal contribution of each feature in the initial model according to all involved feature subsets. This completes the feature data acquisition process of accurately quantifying the interdependence and interaction effects between features. The calculation process is as follows:

[0069] The Shapley value φ for each feature is obtained by calculating the marginal contribution of each feature to the model's prediction. j The calculation formula is:

[0070]

[0071] In the above formula, φ0 is the predicted average value of all samples, φ j The contribution of the j-th feature, This represents the sum of the Shapley values ​​for all features, which is the sum of the Shapley values ​​for all features.

[0072] XGBoost prediction was used as the basis for SHAP analysis, and the Shapley value φ for each feature in the training set was calculated using TreeExplainer. ij Then, its Mean Absolute SHAP is obtained as an importance indicator. The calculation process is as follows:

[0073]

[0074] In the above formula, n represents the nth sample, φ ij This represents the SHAP value of feature j of the nth sample.

[0075] In this embodiment, the SHAP algorithm is a feature contribution interpretation method based on game theory. Based on the Shapley value in game theory, the SHAP algorithm can calculate the weighted marginal contribution of each feature in the model prediction according to all possible feature subsets. Theoretically, it can accurately quantify the interdependence and interaction effects between features.

[0076] Specific Implementation Method Three: This implementation method further defines Specific Implementation Method One or Two. In this method, the wind power multi-scale decomposition prediction method includes a data decomposition process. To reduce the impact of the non-stationarity of the wind power sequence on prediction performance, this method introduces Variational Mode Decomposition (VMD). VMD preprocesses the original power sequence, thereby improving the model's time-series modeling capability and prediction accuracy. VMD, as an advanced signal decomposition technique, can decompose complex signals into several eigenmode functions with finite bandwidth, exhibiting good adaptability and time-frequency locality. However, the performance of traditional VMD decomposition is highly dependent on the set number of modes K. If K is not properly selected, it may lead to mode aliasing or information redundancy, thus affecting the performance of subsequent prediction models. This invention constructs an improved decomposition framework, FVMD, based on an adaptive mode selection mechanism combining frequency domain analysis and complexity measurement, for efficient data decomposition. Compared to most structures that use optimization algorithms for selection, this structure significantly improves computational efficiency from a quantization perspective.

[0077] In this embodiment, the process of feature selection followed by data decomposition of the original wind power sequence involves performing FFT spectral analysis on the feature-selected wind power data to determine the range of K values. The determined K value range is then subjected to normalized signal processing and variational mode decomposition (MODE decomposition). The information entropy of each intrinsic mode function (IMF) and the average information entropy for each corresponding K value are calculated sequentially. It is then determined whether the information entropy and average information entropy have traversed all K values. If they have, the optimal K value is determined, and the optimal K value is subjected to MODE decomposition and the result data is saved. If they have not, the normalized signal processing and MODE decomposition are repeated, and the information entropy of each IMF and the average information entropy for each corresponding K value are calculated again. This process continues until the information entropy and average information entropy have traversed all K values. Finally, the optimal K value is determined, and the optimal K value is subjected to MODE decomposition and the result data is saved.

[0078] Specific Implementation Method Four: This implementation method is a further limitation of Specific Implementation Methods One, Two, or Three. In this implementation method, the specific process of performing feature selection on the original wind power sequence followed by data decomposition processing is divided into the following steps:

[0079] Step 1: First, apply the Fast Fourier Transform (FFT) to extract the frequency components and calculate their Discrete Fourier Transform X(k), which is defined as follows:

[0080]

[0081] In the above formula, x(n) is the original wind power sequence, N is the sequence length, X(k) is the frequency domain component obtained after Fourier transform, and j is the imaginary unit. It is the kernel function of the DFT, used to project a time-domain signal into the frequency domain; it is used to calculate the wind power spectral density |X(k)|. 2 To identify the main periodic components in the signal, the number of the aforementioned peaks serves as preliminary data for estimating the number of modes required for VMD;

[0082] Step Two: Next, based on the initial basis provided by FFT, VMD decomposition is performed on all K values ​​within the range to calculate their information entropy, thereby completing the decomposition of the data signal f(t) into K modal components u with finite bandwidth. k In the processing of (t), each mode has its corresponding center frequency, which is defined by the following formula:

[0083]

[0084] In the above formula, f(t) represents the original input signal, K represents the preset number of mode decompositions, and u k (t) represents the k-th mode obtained from the decomposition, w k The center frequency of each component is represented by δ(t), which is the Dirac function, and j is the imaginary unit. It is a Hilbert transform kernel. To represent the Hilbert transform in order to construct its analytic signal, It is a complex exponential term used for frequency shifting of the signal; obtaining the optimal solution of the constrained variation is the process of introducing the Lagrange multiplier λ(t) to transform the constrained variation into an unconstrained variation, and the calculation formula is:

[0085]

[0086] In the above formula, u k It is the set of all modal components, ω k α represents the center frequencies corresponding to all modes, and α is the weight that adjusts the smoothness of the solution and the reconstruction error. It is the sum of all modal components; λ(t) is the Lagrange multiplier, which is updated iteratively by the Alternating Direction Multiplier Method (ADMM). k w k ,λ until convergence;

[0087] Information entropy is a metric for modal complexity. The optimal number of modes is selected by minimizing information entropy; its calculation method is as follows:

[0088]

[0089] In the above formula, K is the number of candidate modes, K * H is the final selected optimal number of modes.k Let H(K) be the information entropy of the Kth mode, and H(K) be the average information entropy when the number of modes is K, where k is the index of the mode component. The information entropy is calculated as follows:

[0090]

[0091] Step 3: Finally, the selected optimal number of modes K is used to perform the final VMD decomposition on the signal to obtain the data of each mode and residual component. Each mode and residual component data is the multi-scale mode data.

[0092] Specific Implementation Method Five: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, or Four. This implementation method combines... Figure 2 As shown, the multi-scale decomposition prediction method for wind power also includes a data prediction process to improve the accuracy and stability of wind power prediction. Specifically, it is a deep learning model that integrates a multi-scale temporal convolutional network (MS-TCN), a bidirectional long short-term memory network (Bi-LSTM), and a temporal attention mechanism. This model fully mines feature information at different time scales and combines the attention mechanism to improve the ability to model temporal dependencies, thereby improving prediction performance.

[0093] The data prediction process enhances the modeling of short-term dynamic changes. Specifically, it involves processing multi-scale modal data for prediction by fusing multi-scale temporal convolutional networks, bidirectional LSTMs, and temporal attention mechanisms to construct a deep prediction model. Specifically:

[0094] A multi-scale TCN model is constructed, comprising a TCN structure with three parallel branches. Each branch consists of a one-dimensional convolutional layer and a Temporal Block. The kernel sizes are set to 1, 3, and 5, respectively. The kernel sizes in the Temporal Block are 3, 5, and 7, respectively, with dilation values ​​of 2 and 4. The calculation formula is as follows:

[0095] The output formula for the i-th branch is:

[0096] H i =TCN i (RELU(BN(Conv1D pre,i (X)))) (8)

[0097] In the above formula, X∈R H×T×C Represents the input sequence, Conv1D pre,idenoted as i-branch convolution, PIN represents batch normalization, where the outputs of multiple branches are connected along the channel dimension and then fused by a 1×1 convolution to unify the dimension;

[0098] H fused =ReLU(BN(Conv1D) 1×1 ([H1,H2,...,H n ]))) (9)

[0099] After fusion H fused Further into BILSTM, BILSTM adopts a bidirectional LSTM structure, which has better performance in time series prediction compared to the LSTM structure.

[0100] To enhance the capabilities of key prediction modules, a temporal attention mechanism is added after BILSTM. The attention score is calculated using the following formula:

[0101] Q,K,V=W Q H,W K H,W V H (10)

[0102]

[0103] H attn =AV (12)

[0104] In the above formula, H is the output hidden state sequence of the BiLSTM layer, d is the hidden state dimension, and W... Q W K W V These are the training weight matrices used to generate the linear transformation matrices for the query, key, and value; Q is the query matrix, K is the key matrix, and V is the value matrix. It is the attention score, A is the attention weight matrix, H ... attn This is the final output after being weighted by a temporal attention mechanism. This attention structure can effectively utilize contextual information at a specific time, thus improving the model's predictive performance.

[0105] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, or Five. In this implementation method, the KDE method is used to model probabilistic prediction. After obtaining the predicted value through the multi-scale TCN model, the distribution of the residuals calculated from the predicted value is estimated. A Gaussian kernel function is used for calculation. For the corresponding bandwidth at a given confidence level, the formula for the estimated distribution function of the residual set is:

[0106]

[0107] In the above formula, φ(·) is the standard normal function, and hα It is the bandwidth used to control the smoothness of the kernel function;

[0108] The prediction interval is constructed based on the estimated distribution of the residuals. First, the solution is obtained. The value at the quantile, for the lower quantile. and upper quantile The following formula is satisfied:

[0109]

[0110] The corresponding formula for the 1-α confidence interval is:

[0111]

[0112] The KDE method in this embodiment is a nonparametric method. Its advantage lies in that it does not require prior assumptions about the data distribution and can flexibly describe the shape of the data distribution. The predicted values ​​are obtained using the constructed model, and the distribution of the residuals calculated from the predicted values ​​is estimated. A Gaussian kernel function is selected for calculation because it provides a stable fit to the data, is sensitive to outliers, and can characterize the details of the residuals.

[0113] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Method One, Two, Three, Four, Five or Six. In this implementation method, the choice of bandwidth is particularly important for kernel density estimation. Excessively wide bandwidth can make the estimated distribution too smooth and ignore details, while too small a bandwidth will introduce too much estimation noise. When evaluating the probability prediction interval, the corresponding evaluation process involves first generating a bandwidth for the corresponding confidence interval according to Silverman's rule. Starting with this bandwidth, a symmetric network is constructed at 1.5 times its size. A grid search cross-validation method is used to evaluate the performance of the prediction interval under different bandwidths. If no bandwidth better than that generated by Silverman's rule is found, the bandwidth generated by Silverman's rule is used for the probability prediction process. The probability prediction process involves dividing the training data into a 5-fold validation set, fitting the residual distribution with a portion of the data, and predicting the interval coverage of the other portion of the data. The evaluation metric uses a weighted interval prediction coverage criterion to ensure that the coverage rate meets the target while reducing the interval width. The metrics are calculated using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), Predicted Interval Coverage (PICP), Normalized Average Width of Predicted Interval (PINAW), and Comprehensive Evaluation Index (CWC). The calculation formula is as follows:

[0114]

[0115]

[0116] The prediction interval is labeled [L] iU i The actual value is y. i The total number of samples is N.

[0117]

[0118] In the above formula, the prediction interval is labeled [L]. i U i The actual value is y. i , c is the predicted value of the i-th sample. i It is a coverage indicator; when the true value falls within the prediction interval, c i The corresponding value is 1; when the actual value does not fall within the prediction interval, c i The corresponding value is 0; R is the range of the target variable in the entire training dataset, and N is the total number of samples; γ and η are the adjustment parameters of the penalty factor; μ is the required confidence level, and γ and μ are the penalty coefficients, with values ​​of 50 and 10, respectively.

[0119] The prediction model used in this invention is specifically an ensemble model of FS-FVMD-MTCN-BILSTM-TATTAN-AKDE, which is used for ultra-short-term wind power probabilistic prediction. Here, FS represents the feature extraction module, FVMD is an adaptive variational mode decomposition model that selects the k-value, MTCN is a multi-scale feature extraction model based on a TCN structure, TATTAN is a time attention layer adapted for time series prediction, and AKDE is an adaptive bandwidth kernel density estimation model. The purpose of this ensemble model is to improve the accuracy of point prediction and probabilistic prediction, thereby assisting in power system dispatching decisions. The key advantages of this invention are as follows:

[0120] First, in the feature extraction module, a combination of XGBoost and SHAP is used to determine the importance of each feature, extract important features, and improve the prediction efficiency of wind power.

[0121] Second: In the data decomposition module, the FVMD method is proposed to decompose the wind power series, reduce data non-stationarity, and improve prediction accuracy. The FVMD method uses FFT and minimum information entropy to determine the most critical parameter k in VMD.

[0122] Third: In the deterministic prediction module, the MSTCN-BILSTM-TATTAN model is proposed to capture complex wind power characteristics. A multi-scale TCN structure, namely MSTCN, is constructed to capture the real-time, short-term and long-term trends of wind power data. Then, BILSTM is used for wind power prediction. A time attention mechanism is introduced to assign different weights to the hidden states in the BILSTM model to enhance the model's attention to key information.

[0123] Fourth: In the probability prediction module, the adaptive kernel density estimation method AKDE is used to predict wind power probability. Based on Silverman's rule, different bandwidths are generated for different confidence intervals. Then, the grid search cross-validation method is used to find the optimal bandwidth under different confidence intervals. Finally, the probability prediction results are generated by the KDE model.

[0124] Fifth: This invention is a prediction method adapted to the ultra-short-term wind power probability prediction integrated model, which can provide excellent prediction results, provide reliable forward-looking data guidance for wind power grid connection and effective utilization of wind power, and provide a standardized processing method for early warning assessment of wind power.

[0125] Combination Figures 1 to 10 As shown, the accuracy of prediction in this invention has also been verified in practice, and the specific process is as follows:

[0126] Taking a wind farm as the research object, this study uses multivariate time-series data of active power from wind turbines with a total installed capacity of 96MW from January 1st to December 31st, 2019, for case analysis. The data was sampled in 15-minute intervals, totaling 35,037 records, with 80% used for the training set, 10% for the validation set, and 10% for the test set. The collected features included: wind speed of 10m / s at 10m height, 30m / s at 30m height, 50m / s at 50m height, 70m / s at 70m height, wind direction at 70m height, wind azimuth, atmospheric temperature, atmospheric pressure, relative humidity, and active power output from the wind turbines. Input features were selected, and the SHAP value for each feature was calculated using a combination of XGBoost and SHAP. Features with SHAP values ​​greater than 1 were selected for prediction to increase the model's efficiency. The results are as follows: Figure 5 As shown, this invention selects seven features as inputs to the model, including wind speed at 10m height, wind speed at 30m height, wind speed at 50m height, wind speed at 70m height, wind direction at 70m height, atmospheric temperature, and relative humidity.

[0127] To reduce noise interference with the sequence, FVMD was used to decompose the original sequence. The K-value search result was 3, and the penalty factor was set to 1000. The decomposition result is as follows: Figure 6 As shown in Table 1, the information entropy results for each K value are illustrated in the line graph below. Figure 7 As shown, IMF1 is the low-frequency component, which shows the long-term trend of wind power; IMF2 is the medium-frequency component, which reflects the daily variation of wind power; and IMF3 is the high-frequency component, which shows the short-term rapid fluctuation of wind power.

[0128] Table 1 Information Entropy Results

[0129]

[0130] The model comparison experiment process in this invention is as follows:

[0131] To demonstrate the effectiveness of the model, this invention compared various model types, and the results are shown in Table 3. The fitting plots are shown below. Figure 8 As shown, the model FVMD-MTCN-BILSTM-TATTAN proposed in this invention performs best in terms of evaluation metrics. The lookback step size of all models is 24, and the prediction step size is 1. The detailed parameters of the models are shown in Table 2. The common parameters of other models are loss_function (MSELoss), optimizer (AdamW), and learning rate (0.001). In the comparison results in Table 3, all models whose names do not include LASSO use XGBoost-SAHP feature selection, while those with LASSO use LASSO feature selection. The features corresponding to each IMF component selected by LASSO are as follows: IMF1 is 10mspeed, 30mspeed, 50mspeed, 70mspeed, 70mdirection, hubspeed, WDHH(°), AP(hPa), and IMF2 and IMF3 are 10mspeed, 30mspeed, 70mspeed, WDHH(°), AP(hPa).

[0132] The model ablation experiment process in this invention is as follows: In order to prove the effectiveness of the improved model, the improved model is first subjected to an ablation experiment. As shown in Table 3, BILSTM improves MAE, MSE and RMSE by 2.50%, 1.06% and 0.49% respectively compared with LSTM. This is because the bidirectional structure of BILSTM can consider forward and backward dependencies at the same time, and can learn richer feature representations compared with LSTM.

[0133] Table 2 Parameters of the MTCN-BILSTM-TATTAN model

[0134]

[0135] Table 3 Model Comparison Experiment

[0136]

[0137] The BILSTM-TATTAN model improves upon the BILSTM model in terms of MAE, MSE, and RMSE by 8.58%, 23.18%, and 12.35%, respectively. This is because the BILSTM-TATTAN model incorporates a temporal attention mechanism, enhancing its ability to focus on key time points in the wind power sequence and thus improving its predictive capabilities. The TCN-BILSTM-TATTAN model improves upon the BILSTM-TATTAN model in terms of MAE, MSE, and RMSE by 9.14%, 5.17%, and 2.61%, respectively. The TCN-BILSTM-TATTAN model adds a TCN structure to the BILSTM-TATTAN model to extract features within the time window, increasing the model's overall feature extraction capability and providing a more discriminative temporal representation for subsequent BILSTM-TATTAN predictions, thereby improving predictive performance. The FVMD-TCN-BILSTM-TATTAN model improves upon the TCN-BILSTM-TATTAN model in MAE, MSE, and RMSE by 34.78%, 63.91%, and 39.91%, respectively. This is because FVMD decomposes the original wind power sequence into three subsequences: low-frequency, mid-frequency, and high-frequency, significantly reducing the instability of the wind power sequence and improving its predictability. The final model FVMD-MTCN-BILSTM-TATTAN proposed in this invention improves upon FVMD-TCN-BILSTM-TATTAN in MAE, MSE, and RMSE by 41.82%, 57.73%, and 34.93%, respectively. This improvement is attributed to MTCN's multi-scale modeling capability, which comprehensively captures the periodic changes in short-term wind power, providing rich and comprehensive feature representations for subsequent predictions and improving overall prediction stability and accuracy.

[0138] In this invention, model comparison experiments were conducted to further demonstrate the predictive performance of the proposed model. Classic single models such as GRU, TCN, and CNN were compared. As shown in Table 3, the MTCN-BILSTM-TATTAN model achieved the best results in terms of prediction metrics, demonstrating its superior predictive performance to a certain extent. The FVMD-MTCN-BILSTM-TATTAN model improved MAE, MSE, and RMSE by 38.04%, 54.65%, and 32.57% respectively compared to the ICEEMDAN-MTCN-BILSTM-TATTAN model. This indicates the effectiveness of FVMD decomposition, demonstrating a faster decomposition speed and superior mode extraction and structure matching capabilities compared to ICEEMDAN. The IVMD-LASSO-BIGRU model

[40] is a structure proposed in the second half of 2004 for ultra-short-term wind power prediction. It relies on the decomposition of IVMD and the targeted feature selection of LASSO to make the prediction performance of the whole model excellent. The model proposed in this invention improves the MAE, MSE and RMSE by 15.02%, 16.85% and 8.78% respectively compared with IVMD-LASSO-BIGRU. The idea of ​​feature selection for each IMF component proposed in IVMD-LASSO-BIGRU is excellent, but the BIGRU model is slightly insufficient for multi-cycle and unstable wind power prediction.

[0139] The MTCN-BILSTM-TATTAN model used in this invention supplements these deficiencies to some extent. The FVMD-MTCN-BILSTM-TATTAN model shows slight improvements in MAE, MSE, and RMSE compared to the FVMD-LASSO-MTCN-BILSTM-TATTAN model, indicating that the feature selection method XGBoost-SAHP proposed in this invention can consider the nonlinear relationships between various features and reveal their synergistic effects, making it more suitable for situations with complex wind power characteristics. The evaluation metrics for each model are as follows: Figure 10 As shown.

[0140] This invention employs an automatic bandwidth kernel density estimation method for probabilistic prediction, using a Gaussian kernel for kernel density estimation. The interval prediction results based on the FVMD-MTCN-BILSTM-TATTAN model are shown in the figure below. Figure 9As shown in Table 4, the final results indicate that the probability prediction (PICP) value increases with the increase of PINAW. However, the magnitude of these two values ​​cannot judge the final prediction result of KDE. Therefore, this invention uses the comprehensive evaluation index CWC to verify the merits of the KDE model. When PICP is greater than its corresponding confidence level, the CWC value is equal to the PINAW value. That is, the goal of CWC is to minimize bandwidth while satisfying the PICP condition. Table 4 shows that, under the same confidence level, only when the IVMD-LASSO-BIGRU model has a 95% confidence level do the two kernel density estimation results match. For other AKDE optimizations, the bandwidth is superior to the empirically selected bandwidth of KDE. Comparing the metrics of the two models, for example, under a 95% confidence level AKDE, the CWC of the FVMD-MTCN-BILSTM-TATTAN model is 7.47% higher than that of the IVMD-LASSO-BIGRU model. This indicates that, at the same confidence level, the predicted probability interval of the FVMD-MTCN-BILSTM-TATTAN model has a smaller bandwidth.

[0141] Table 4. Experimental results of probability prediction using different models

[0142]

[0143]

[0144] The proposed model FS-FVMD-MTCN-BILSTM-TATTAN-AKDE possesses excellent point and interval prediction capabilities, providing crucial data support for wind farm operation. This model first employs XGBoost-SHAP for feature selection, reducing the dimensionality of raw wind power data to accelerate computational efficiency. Secondly, FVMD decomposition enhances the stability of wind power data, increasing its predictability. Compared to traditional optimization algorithms for VMD, this method offers a significant quantitative improvement in computational efficiency. Subsequently, MTCN enhances the model's feature extraction capabilities. MTCN's layer-by-layer expansion of the receptive field better adapts to short-term wind power variations, providing more comprehensive data support for subsequent BILSTM-TATTAN predictions. Finally, AKDE probabilistic prediction is performed based on the point prediction structure. The grid search cross-validation method in AKDE optimizes bandwidth selection, providing higher-quality prediction intervals compared to empirical bandwidth selection. The FS-FVMD-MTCN-BILSTM-TATTAN-AKDE model is an efficient model that combines deterministic and probabilistic prediction of wind power, enabling decision-makers to make more rational choices in the face of uncertainty and volatility in wind power.

Claims

1. A method for multi-scale decomposition prediction of wind power, characterized in that: After the actual wind power data is formed into the original wind power sequence, feature selection and data decomposition are performed sequentially to form multi-scale modal data. After constructing a deep prediction model based on the multi-scale modal data, the probability prediction interval in the deep prediction model with residual distribution is determined by adaptive bandwidth kernel density estimation. The process of feature selection after forming the original wind power sequence from the actual acquired wind power data involves establishing an initial model, and then performing feature selection on the initial model. Specifically, the SHAP algorithm, based on the Shapley value in game theory, is used to calculate the weighted marginal contribution of each feature in the initial model according to all involved feature subsets. This completes the feature data acquisition process for accurately quantifying the interdependence and interaction effects between features. The calculation process is as follows: The Shapley value for each feature is obtained by calculating the marginal contribution of each feature to the model's prediction. The calculation formula is: (1) In the above formula, The predicted average for all samples. For the first The contribution of each feature This represents the sum of the Shapley values ​​for all features; XGBoost prediction is used as the basis for SHAP analysis, and the Shapley value of each feature in the training set is calculated using TreeExplainer. Then, its Mean Absolute SHAP is obtained as an importance indicator. The calculation process is as follows: (2) In the above formula, This represents the nth sample. Represents the SHAP value of feature j of the nth sample; The process of feature selection followed by data decomposition of the original wind power sequence involves performing FFT spectral analysis on the feature-selected wind power data to determine the range of K values. After determining the range of K values, normalization signal processing and variational mode decomposition (MODED) are performed. The information entropy of each intrinsic mode function (IMF) and the average information entropy for each corresponding K value are calculated sequentially. It is then determined whether the information entropy and average information entropy have traversed all K values. If they have, the optimal K value is determined, and MODED is performed on the optimal K value, and the result data is saved. If they have not, normalization signal processing and MODED are performed again, and the information entropy of each IMF and the average information entropy for each corresponding K value are calculated again, until the information entropy and average information entropy have traversed all K values. Finally, the optimal K value is determined, and MODED is performed on the optimal K value, and the result data is saved. The specific process of performing feature selection and data decomposition on the original wind power sequence can be divided into the following steps: Step 1: First, apply the Fast Fourier Transform (FFT) to extract the frequency components and calculate their Discrete Fourier Transform. Its definition is as follows: (3) In the above formula, It is the original wind power sequence. It is the sequence length. It is the frequency domain component obtained through Fourier transform. It is the imaginary unit. It is a kernel function of the DFT, used to project a time-domain signal into the frequency domain; it is used to calculate the wind power spectral density. To identify the main periodic components in the signal, the number of the aforementioned peaks serves as preliminary data for estimating the number of modes required for VMD; Step Two: Next, based on the initial basis provided by FFT, VMD decomposition is performed on all K values ​​within the range to calculate their information entropy, thereby completing the data signal... Decomposed into K modal components with finite bandwidth In the processing, each mode has its corresponding center frequency, which is defined by the following formula: (4) In the above formula, Represents the original input signal. This represents the preset number of modal decompositions. This represents the k-th mode obtained from the decomposition. Indicates the center frequency of each component. It is the Dirac function. It is the imaginary unit. It is a Hilbert transform kernel. To represent the Hilbert transform in order to construct its analytic signal, It is a complex exponential term used for frequency shifting of the signal; obtaining the optimal solution of the constrained variation is the process of introducing the Lagrange multiplier λ(t) to transform the constrained variation into an unconstrained variation, and the calculation formula is: (5) In the above formula, It is the set of all modal components. These are the center frequencies corresponding to all modes. It is the weight of adjusting the smoothness of the solution and the reconstruction error. It is the sum of all modal components; It is a Lagrange multiplier, iteratively updated using the Alternating Direction Multiplier Method (ADMM). Until convergence; Information entropy is a metric for modal complexity. The optimal number of modes is selected by minimizing information entropy; its calculation method is as follows: (6) In the above formula, K is the number of candidate modes. It is the final selected optimal number of modes. It is the information entropy of the Kth mode. It is the average information entropy when the number of modes is K. It is the index of the modal component, and the information entropy is calculated as follows: (7) Step 3: Finally, the selected optimal number of modes K is used to perform the final VMD decomposition on the signal to obtain the data of each mode and the residual component. Each mode and the residual component data is the multi-scale mode data. Predictive processing of multi-scale modal data involves fusing multi-scale temporal convolutional networks, bidirectional LSTMs, and temporal attention mechanisms to construct a deep prediction model based on the multi-scale modal data. Specifically: A multi-scale TCN model is constructed, comprising a TCN structure with three parallel branches. Each branch consists of a one-dimensional convolutional layer and a Temporal Block. The kernel sizes are set to 1, 3, and 5, respectively. The kernel sizes in the Temporal Block are 3, 5, and 7, respectively, with dilation values ​​of 2 and 4. The calculation formula is as follows: The output formula for the i-th branch is: (8) In the above formula, Represents the input sequence. express Convolution of each branch, This indicates batch standardization; multiple branch outputs are connected along the channel dimension, and then... Unifying dimensions after convolutional fusion; (9) After fusion Further into BILSTM, which employs a bidirectional LSTM structure, a temporal attention mechanism is added after BILSTM to improve the prediction performance of key prediction modules. The attention score in the temporal attention mechanism is calculated using the following formula: (10) (11) (12) In the above formula, The output hidden state sequence of the BiLSTM layer. To hide the state dimension, These are the training weight matrices used to generate the linear transformation matrices for query, key, and value; It is a query matrix. It is a key matrix. It is a value matrix. It's an attention score. It is the attention weight matrix. It is the final output after being weighted by the time attention mechanism.

2. The wind power multi-scale decomposition prediction method according to claim 1, characterized in that: The KDE method is used to model probabilistic prediction. After obtaining the predicted values ​​through a multi-scale TCN model, the distribution of the residuals calculated from the predicted values ​​is estimated. A Gaussian kernel function is used for calculation. For a given confidence level and corresponding bandwidth, the estimated distribution function formula for the residual set is: (13) In the above formula, It is a standard normal function. It is the bandwidth used to control the smoothness of the kernel function; The prediction interval is constructed based on the estimated distribution of the residuals. First, the solution is obtained. The value at the quantile, for the lower quantile. and upper quantile The following formula is satisfied: (14) Then the corresponding The formula corresponding to the confidence interval is: (15)。 3. The wind power multi-scale decomposition prediction method according to claim 1 or 2, characterized in that: The evaluation process for the probability prediction intervals involves first generating a bandwidth for the corresponding confidence interval according to Silverman's rule. Using this bandwidth as a starting point, a symmetric network is constructed at 1.5 times its size. A grid search cross-validation method is used to evaluate the performance of the prediction intervals under different bandwidths. If no bandwidth superior to that generated by Silverman's rule is found, the bandwidth generated by Silverman's rule is used for the probability prediction process. The probability prediction process involves dividing the training data into a 5-fold validation set, successively fitting the residual distribution with a portion of the data, and predicting the interval coverage of the other portion. The evaluation metric adopts a weighted interval prediction coverage criterion, ensuring that the coverage rate meets the target while reducing the interval width. The metrics are calculated using Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE), Predicted Interval Coverage Rate (PICP), Normalized Average Width of Predicted Interval (PINAW), and Comprehensive Evaluation Index (CWC). The calculation formula is as follows: (16) (17) (18) (19) (20) (21) In the above formula, the prediction interval is labeled as The actual value is , It is the first The predicted value for each sample, It is a coverage indicator; when the true value falls within the prediction interval, The corresponding value is 1; when the actual value does not fall within the prediction interval, The corresponding value is 0; It represents the range of the target variable in the entire training dataset, and N is the total number of samples; and It is the adjustment parameter of the penalty factor.

Images