A composite elastic response prediction method based on adaptive characteristic modal decomposition

Abstract

The application discloses a kind of based on adaptive feature modal decomposition composite elastic response prediction method, the method first filters and load power strong correlation environmental characteristics, constructs response input set;Improved feature modal decomposition is combined with adaptive window function to carry out multi-scale decomposition to load signal;Based on sample entropy, autocorrelation, mutual information and energy proportion, mode comprehensive score function is constructed, and key elastic response component is filtered and reconstructed;High-dimensional nonlinear feature is reduced using kernel principal component analysis;Finally, the LSTM model of fusion time sequence attention mechanism and quantile regression is constructed, and the multi-quantile point load response prediction interval is output.The application can effectively suppress noise interference, reduce feature redundancy, significantly improve prediction accuracy and robustness, and can quantify prediction uncertainty, to provide reliable decision basis for complex working condition distribution network dispatching and demand side response.

Description

Technical Field

[0001] This invention relates to the field of power system load modeling and analysis technology, and in particular to a composite elastic response prediction method based on adaptive eigenmode decomposition. Background Technology

[0002] With the continuous development of new power systems and the large-scale integration of distributed energy resources, the formation mechanism of electricity load is gradually evolving from being driven by traditional single electricity consumption behavior to a complex process influenced by multiple factors such as meteorological conditions, user behavior, electricity price signals, and equipment operating status. In this context, load changes not only manifest as numerical fluctuations but also reflect dynamic response characteristics to external disturbances.

[0003] Most existing studies use load time series as the direct prediction object, focusing on estimating future load values ​​by fitting historical data, such as methods based on BP neural networks, support vector machines, and deep learning models. These methods can improve prediction accuracy to some extent, but they generally treat load as a passive variable, failing to adequately characterize the response relationship between load and external environmental factors, and making it difficult to reflect the elastic variation characteristics of load under different operating conditions.

[0004] With increasing fluctuations in meteorological conditions and growing complexity in electricity consumption structures, load sequences exhibit significant non-stationarity, multi-scale volatility, and strong randomness. Traditional single models are easily affected by noise interference and feature redundancy when dealing with such complex sequences, leading to a decline in model generalization ability. In addition, existing methods are mostly based on point prediction and lack the ability to characterize the uncertainty of load response, making it difficult to meet the analysis and decision-making needs under complex operating environments. Summary of the Invention

[0005] The purpose of this invention is to provide a composite elastic response prediction method based on adaptive eigenmode decomposition, in order to solve the technical problems of existing methods that lack the ability to characterize the coupling relationship between load and multi-source environmental factors and their response elastic characteristics, making it difficult to accurately reflect the intrinsic driving mechanism of load changes when facing non-stationary, multi-scale and strong random disturbance conditions, and easily resulting in feature redundancy, difficulty in eliminating noise interference and insufficient model generalization ability.

[0006] This invention is achieved using the following technical solution: a composite elastic response prediction method based on adaptive eigenmode decomposition, comprising the following steps: Step S1: Construct a candidate environmental feature set, analyze the correlation between each environmental feature and the load power sequence, screen out key driving variables, and form a response feature input set to characterize the basic response relationship of the load to external factors; Step S2: The original load signal is decomposed into multiple scales using an improved eigenmode decomposition method. The Hanning window or Blackman window is dynamically selected based on the signal frequency band characteristics through an adaptive window function selection mechanism, and the load signal is decomposed into multiple elastic response components at different time scales. Step S3: Evaluate the effectiveness of the composite elastic response of each modal component obtained by decomposition, calculate the sample entropy, autocorrelation peak, mutual information with the original load sequence and energy ratio of each modal component, and construct a modal comprehensive scoring function based on this. According to the scoring results, the modes are divided into trend response components, effective fluctuation response components and noise components. Key components are retained and reconstructed to obtain the denoised response signal. Step S4: The kernel principal component analysis method is used to perform nonlinear mapping and dimensionality reduction on the reconstructed response signal and the high-dimensional features composed of the response feature input set. The number of principal components to be retained is determined according to the cumulative contribution rate, so as to realize feature compression and redundant information removal. Step S5: Construct a long short-term memory network model that integrates temporal attention mechanism and quantile regression. Using the dimensionality-reduced features as input, the response information at different historical moments is weighted through temporal attention mechanism, and multiple quantile prediction results are output by combining quantile regression to obtain the load composite elastic response prediction range.

[0007] Furthermore, in step S1, the Pearson correlation coefficient is used to analyze the correlation between various environmental characteristics and the load power sequence. The formula for calculating the Pearson correlation coefficient is as follows: ; in, The sample length; For the first An environment variable at time... The possible values ​​of ; For a moment The load power; and These are the mean values ​​of the corresponding sequences.

[0008] Furthermore, in step S2, the adaptive window function selection mechanism specifically means that, for the frequency band to be decomposed, when the time corresponding to the local maximum value of the autocorrelation spectrum satisfies T>T th When this indicates that the frequency band has a trend and periodicity, the Blackman window with stronger sidelobe suppression capability is selected; when T≤T th When this is the case, it indicates that the frequency band has local fluctuation characteristics, so the Hanning window with higher main lobe resolution is selected; where T is the load fluctuation period estimated by the autocorrelation spectrum reaching a local maximum after crossing zero, T th This is a preset threshold.

[0009] Furthermore, the improved eigenmode decomposition method in step S2 uses correlation kurtosis as an index to construct constraints to update the filter coefficients, decomposing the original signal into K frequency bands, as defined below: ; in, For the first One decomposition mode; For the first One FIR filter function; Index variables representing operations; This is the filter length; Indicates length is The original signal; Indicates the photovoltaic fluctuation cycle; The shift order is... .

[0010] Furthermore, in step S3, the modal synthesis scoring function for the i-th modal component is expressed as: ; For the first The sample entropy of each modality characterizes the sequence complexity; This represents the peak value of the autocorrelation of this mode; This refers to the mutual information between the mode and the original load sequence; This refers to the proportion of energy in this mode to the total energy. , , , These are the weighting coefficients.

[0011] Furthermore, in step S3, the formula for calculating the energy proportion of the i-th modal component is: .

[0012] Furthermore, step S4 specifically includes: The input sample is Through nonlinear mapping Mapped to a high-dimensional feature space and a Gaussian kernel function is applied: Construct the kernel matrix: Where σ is the kernel width parameter; Perform eigenvalue decomposition on the centered kernel matrix: The number of principal components to be retained is determined based on the cumulative contribution rate. ; in, For the first One eigenvalue; For the corresponding feature vector; when the cumulative contribution rate When the contribution rate is greater than or equal to the preset contribution rate threshold, the first p principal components are selected as the features after dimensionality reduction.

[0013] Furthermore, in step S5, the temporal attention mechanism is expressed as: ; ; ; in, For a moment Attention score; These are the normalized attention weights; This is a weighted context vector; , , These are trainable parameters.

[0014] Furthermore, in step S5, the loss function for the quantile regression is the quantile loss function, which is defined as follows for a quantile q: ; in, This is the actual load value; This is the predicted value of the q-th quantile in the model output; The total loss function can be expressed as: ; In the formula, It is the set of quantiles.

[0015] Furthermore, the composite elastic response prediction method also includes the following steps: S6: The model performance is evaluated using root mean square error, mean absolute error, and coefficient of determination, and the predicted results of the composite elastic response under load and its range are output.

[0016] The beneficial effects of this invention are as follows: This invention utilizes an improved adaptive eigenmode decomposition (FMD) and adaptive window function selection mechanism to achieve multi-scale decomposition and effective separation of trend, fluctuation, and noise components in non-stationary, strongly random load signals. Based on this, a modal comprehensive scoring function is constructed using sample entropy, autocorrelation, mutual information, and energy proportion to accurately screen and reconstruct high-value response components, significantly suppressing random noise interference. Furthermore, kernel principal component analysis (KPCA) is used to reduce the dimensionality of high-dimensional nonlinear features, eliminating feature redundancy. Finally, a Long Short-Term Memory (LSTM) network integrating temporal attention mechanism and quantile regression not only enhances the ability to identify key response periods but also outputs a load response prediction interval containing quantile information, comprehensively characterizing the elastic variation range and uncertainty of the load under multi-source disturbance conditions.

[0017] Experimental results show that, compared with the traditional model, the root mean square error (RMSE) and mean absolute percentage error (MAPE) of this invention are reduced by 28.9% and 25.6%, respectively, and the coefficient of determination (R²) is also reduced. 2 With a value as high as 0.9928, it still demonstrates excellent prediction accuracy, robustness, and generalization ability under complex operating conditions such as variable weather and drastic load fluctuations, providing reliable data support for distribution network dispatching, demand-side response, and operation analysis. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0019] Figure 1 FMD flowchart; Figure 2 This is a signal decomposition diagram; Figure 3 This is a decomposed signal spectrum diagram. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0023] Short-term load forecasting is a crucial foundation for supporting distribution network operation scheduling and resource optimization. However, actual load data typically exhibits significant non-stationarity, multi-scale fluctuations, and noise interference introduced by weather changes and user behavior. Directly inputting unprocessed data into the response model can easily lead to decreased prediction accuracy. To address these technical problems, this invention provides a composite elastic response prediction method based on adaptive eigenmode decomposition. This method no longer uses load values ​​as the sole prediction target but instead takes a response mechanism approach, characterizing the composite elasticity of the load to external disturbances through multi-scale decomposition and feature reconstruction, thus achieving a shift from numerical prediction to response modeling. The method mainly includes the following steps: Step S1: Construct a candidate environmental feature set, analyze the correlation between each environmental feature and the load power sequence, screen out key driving variables, and form a response feature input set to characterize the basic response relationship of the load to external factors; Step S2: The original load signal is decomposed into multiple scales using an improved eigenmode decomposition method. The Hanning window or Blackman window is dynamically selected based on the signal frequency band characteristics through an adaptive window function selection mechanism, and the load signal is decomposed into multiple elastic response components at different time scales. Step S3: Evaluate the effectiveness of the composite elastic response of each modal component obtained by decomposition, calculate the sample entropy, autocorrelation peak, mutual information with the original load sequence and energy ratio of each modal component, and construct a modal comprehensive scoring function based on this. According to the scoring results, the modes are divided into trend response components, effective fluctuation response components and noise components. Key components are retained and reconstructed to obtain the denoised response signal. Step S4: The kernel principal component analysis method is used to perform nonlinear mapping and dimensionality reduction on the reconstructed response signal and the high-dimensional features composed of the response feature input set. The number of principal components to be retained is determined according to the cumulative contribution rate, so as to realize feature compression and redundant information removal. Step S5: Construct a long short-term memory network model that integrates temporal attention mechanism and quantile regression. Using the dimensionality-reduced features as input, the response information at different historical moments is weighted through temporal attention mechanism, and multiple quantile prediction results are output by combining quantile regression to obtain the load composite elastic response prediction range. S6: The model performance is evaluated using root mean square error, mean absolute error, and coefficient of determination, and the predicted results of the composite elastic response under load and its range are output.

[0024] In this embodiment, step S1 specifically includes: to improve the representativeness and effectiveness of the input features, a candidate environmental feature set is first constructed, and its correlation with load power is analyzed. Candidate environmental features include meteorological variables such as maximum temperature, minimum temperature, average temperature, average relative humidity, and rainfall. Further auxiliary features such as temperature difference, time period number, weekday / rest day identifier, and historical lagging load can be introduced. The Pearson correlation coefficient is used to analyze the correlation between each driving factor and the load sequence, screening out key driving variables that have a significant impact on load changes, forming a response feature input set to characterize the basic response relationship of the load to external factors. Environmental Features With load power sequence The Pearson correlation coefficient is defined as: ; In the formula, The sample length; For the first An environment variable at time... The possible values ​​of ; For a moment The load power; and These are the mean values ​​of the corresponding sequences.

[0025] Environmental features are sorted according to their correlation coefficients, and features with high correlation to load power are selected as input signals. In this embodiment, five environmental features closely related to load power—maximum temperature, minimum temperature, average temperature, average relative humidity, and rainfall—are selected as basic inputs, and together with historical load sequences, they constitute the input dataset for subsequent decomposition and response models.

[0026] In this embodiment, step S2 specifically includes: The FMD method, by simultaneously considering the impulsive and periodic characteristics of the signal, exhibits strong noise and interference resistance. Addressing the non-stationarity and multi-scale characteristics of the load sequence, an improved FMD is used to decompose the load signal, representing it as multiple response components at different time scales. This method extracts decomposed modes based on an adaptive FIR filter, overcoming the limitations of traditional methods on filter shape, bandwidth, and center frequency, achieving more thorough signal decomposition. By introducing an adaptive window function selection mechanism, a Hanning window or Blackman window is dynamically selected based on frequency band characteristics, effectively separating the low-frequency trend response from the high-frequency fluctuation response, thereby extracting the elastic response components of the load at different time scales.

[0027] Using correlated kurtosis (CK) as an indicator, constraints are constructed to update the FIR filter coefficients, decomposing the original signal into K frequency bands, as defined below: ; ; ; In the formula For the first One decomposition mode; For the first One FIR filter function; Index variables representing operations; This is the filter length; Indicates length is The original signal; Indicates the photovoltaic fluctuation cycle; The shift order is... .

[0028] The low-frequency and high-frequency components of the signal are filtered using Hanning and Blackman windows, respectively. Under the constraints of the above formulas, the filter coefficients are updated iteratively with the goal of maximizing the correlation kurtosis. (Autocorrelation spectrum) The definition is as follows: ; In the formula It is the lag coefficient.

[0029] First of all The filter is updated iteratively a certain number of times. Initial modal components are obtained through filter deconvolution. The correlation coefficients between modes are calculated, and the two pairs of modes with the highest correlation are identified. Modes with low correlation kurtosis are then removed. After removal, the filter coefficients of the remaining modes are updated, and the iteration continues until the number of modal components reaches a preset value. n The process terminates at a certain time, and the relevant formula is as follows: ; In the formula and Each of the two modal components represents a separate modal component. and They are respectively and The average value of the modal components. The following is the process for improving FMD; please refer to [link / reference]. Figure 1 : (1) Initialization: Load the original load signal The input parameters include the sampling frequency, filter size, number of frequency band divisions, number of decomposed modes (ModeNum), and maximum number of iterations. These parameters are used to initialize the input information and define the range of each frequency band. When this indicates that the frequency band has a strong trend and periodicity, the Blackman window, which has a stronger sidelobe suppression capability, should be selected; when This indicates that the frequency band exhibits strong local fluctuation characteristics, thus a Hanning window with high main lobe resolution is selected. This allows for adaptive configuration of window functions for different frequency bands, thereby improving the separation accuracy between low-frequency trend terms and high-frequency disturbance terms. FIR filters Set the initial iteration counter. .

[0030] (2) Signal decomposition: decomposing the original signal Filtering is performed. The filter bank is used. Perform convolution on the signal to obtain the filtered modal components: ; Using the original signal Decompose the modal components and estimated load fluctuation cycle Update filter coefficients. Load fluctuation cycle. The autocorrelation spectrum reaches a local maximum after crossing zero. The timing is estimated. After completing one iteration, set... .

[0031] (3) Iteration termination judgment: Determine whether the number of iterations has reached the preset maximum number of iterations. If not, return to step 2 to continue iterating. If it has reached the maximum number of iterations, execute step (4).

[0032] (4) Modal component selection: The multi-scale decomposition algorithm (MCKD) is used to decompose the signal into multiple modes (IMF), and the correlation coefficient between two modes is calculated: ; In the formula It is a signal and covariance; and It is a signal and The standard deviation of . A value of size is obtained. The matrix of pairwise signal correlations is used to compare the correlation kurtosis of the two signals with the highest correlation coefficients, retaining the signal with the higher correlation kurtosis. By updating the signals and filters and removing redundant signals, the final result is obtained. One modality.

[0033] In this embodiment, step S3 specifically includes: For each modal component obtained from the decomposition, the present invention evaluates its effectiveness from the perspective of composite elastic response modeling. Indicators such as sample entropy, autocorrelation characteristics, mutual information, and energy proportion are calculated respectively to construct a modal comprehensive evaluation function to measure the contribution of each component to the load response characterization. Existing methods often rely on modal correlation or correlation kurtosis for screening, but these indicators focus on statistical characteristics and are difficult to reflect the actual role of the mode in the load response process, easily leading to confusion between effective and noise components. Therefore, based on the comprehensive evaluation results, the modes are divided into trend response components, effective fluctuation response components, and noise components. Key components are retained and reconstructed to obtain a denoised response signal, thereby suppressing random noise while retaining the main response characteristics and improving model stability and reliability.

[0034] For the Modality The sample entropy, autocorrelation peak, mutual information with the original load sequence, and energy proportion were calculated respectively, and a modal comprehensive scoring function was constructed: ; In the formula, For the first The sample entropy of each modality characterizes the sequence complexity; This represents the peak value of the autocorrelation of this mode; This refers to the mutual information between the mode and the original load sequence; This refers to the proportion of energy in this mode to the total energy. , , , Let be the weighting coefficients, and satisfy: ; Among them, the Energy percentage of each mode Represented as: ; Based on the overall score The magnitude of the value determines the mode type, which is divided into trend mode, effective fluctuation mode, and noise mode. When Greater than the preset threshold If the prediction value is high, it is considered a high-predictive-value mode and retained; otherwise, it is considered a low-predictive-value mode and suppressed or eliminated.

[0035] The retained trend mode and effective fluctuation mode are reconstructed to obtain the noise-reduced reconstructed signal. : ; In the formula, A set of indices for preserving modalities.

[0036] This step effectively mitigates the adverse effects of high-frequency random noise on subsequent feature extraction and response model training while preserving the main trends and key fluctuation information.

[0037] In this embodiment, step S4 specifically includes: After modal decomposition and reconstruction, the input feature dimension is still high, and there may be strong nonlinear correlations between different features. To address this, the present invention employs kernel principal component analysis (KPCA) to perform nonlinear mapping and dimensionality reduction on the features. By constructing a kernel matrix and performing feature decomposition, the number of principal components is determined based on the cumulative contribution rate, thereby achieving feature compression and redundant information removal, and improving the efficiency of subsequent model training.

[0038] Let the input sample be Through nonlinear mapping Map it to a high-dimensional feature space and construct the kernel matrix: ; The present invention preferably uses a Gaussian kernel function: In the formula, This is the kernel width parameter.

[0039] Perform eigenvalue decomposition on the centered kernel matrix: In the formula, For the first One eigenvalue; This is the corresponding feature vector.

[0040] The number of principal components to be retained is determined based on the cumulative contribution rate. The cumulative contribution rate is defined as: ; when When, select the previous The principal components serve as the feature inputs after dimensionality reduction.

[0041] In practice, kernel function parameters can also be jointly optimized through cross-validation. Furthermore, the cumulative contribution rate and the prediction error of the validation set are taken into account to enhance the adaptability of the dimensionality reduction results to subsequent response modeling tasks.

[0042] In this embodiment, step S5 specifically includes: While traditional Long Short-Term Memory (LSTM) networks can uncover long-term dependencies in time series, their ability to distinguish the importance of different historical moments is limited, and they typically only output a single predicted value, making it difficult to characterize the uncertainty of load response. To address these issues, this invention constructs an LSTM model that integrates a time-series attention mechanism and quantile regression to model the composite elastic response behavior of the load. By introducing an attention mechanism, the response information at different historical moments is weighted, enhancing the model's ability to identify key response periods; simultaneously, combined with quantile regression, multiple quantile results are output to obtain the load response interval, which characterizes the range of elastic changes in load under multi-source disturbance conditions.

[0043] To highlight the impact of key historical information on the current response prediction result, this invention introduces a temporal attention mechanism after the LSTM output layer. This attention mechanism is applied to the historical hidden states. Calculate its importance weight: ; ; ; In the formula, For a moment Attention score; These are the normalized attention weights; This is a weighted context vector; , , These are trainable parameters.

[0044] This mechanism enables the model to adaptively focus on historical moments that are more indicative of current load changes, thereby improving forecast accuracy.

[0045] To reflect the uncertainty in short-term composite elasticity response prediction, this invention uses quantile regression to output multiple quantile prediction values, such as quantiles q=0.1, 0.5, and 0.9, corresponding to the lower bound, median, and upper bound response prediction results, respectively. For quantile q, the quantile loss function is defined as: ; In the formula, This is the actual load value; This is the predicted value of the q-th quantile in the model output.

[0046] The total loss function can be expressed as: In the formula, It is the set of quantiles.

[0047] When q=0.5, it can be used as the load point response prediction result; when q=0.1 and q=0.9 are output simultaneously, the composite elastic response prediction range can be obtained. It is used to characterize prediction uncertainty.

[0048] In this embodiment, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) are used to evaluate the model performance, and the load response prediction results and their range are output to provide a basis for power system dispatching and operation analysis.

[0049] Furthermore, to verify the effectiveness of the composite elastic response prediction method proposed in this invention, short-term load data from a city distribution network in eastern China was selected as the implementation object. The data time range was from July 1st to July 15th, 2020, with a sampling interval of 15 minutes, resulting in 1344 sets of load response data. The load data came from actual measurement records on the low-voltage side of the main transformer of the city's 110kV substation. To fully reflect the characteristics of power load affected by meteorological conditions, this invention simultaneously collected the following five typical meteorological factors (strongly correlated with load): maximum temperature (°C), minimum temperature (°C), average temperature (°C), average relative humidity (%), and rainfall (mm).

[0050] The meteorological data mentioned above comes from the China Meteorological Administration's ground observation stations, and the time period is consistent with the load data at 15-minute intervals. Due to potential issues such as packet loss and jumps in load monitoring, this invention cleans the data on a daily basis. When the load or a certain meteorological characteristic shows consecutive zeros or unreasonable jumps (exceeding 50%), it is considered missing and repaired using cubic spline interpolation. Considering that the load changes most drastically between 07:00 and 22:00, the interval is set as the peak load sensitive period of 07:00–22:00 daily.

[0051] This invention employs a proposed FMD-KPCA-LSTM combined model for predicting composite elastic responses. In FMD decomposition, the filter size is set to 20, the number of split points is 4, the number of modes is 4, and the maximum number of iterations is 30. KPCA uses a Gaussian kernel function with a kernel parameter of 1, which, according to preliminary experiments, significantly improves dimensionality reduction efficiency. The LSTM model has a maximum training epoch of 100, an initial learning rate of 0.01, and adaptive decay after 70 iterations, with a regularization coefficient of 0.01. The model input time step is 1, the input dimension is 5 (five types of meteorological features), there is one hidden layer containing 50 neurons, and the output dimension is 1 (short-term load). The training batch size is 25, and the data is divided into training and test sets in a 7:3 ratio.

[0052] The load response sequence exhibits a clear superposition of periodicity and randomness under the influence of multi-source disturbances, and is driven by factors such as weather conditions and lifestyle habits, containing multiple types of information including trends, oscillations, and high-frequency disturbances. To enhance the model's ability to perceive changes in features, this invention utilizes FMD decomposition to perform modal reconstruction of the original load sequence, obtaining a total of 539×20 sets of decomposed feature sequences.

[0053] From the decomposition results of the signal Figure 2 It can be observed that: IMF1 mainly characterizes the low-frequency trend component of load response; IMF2 and IMF3 reflect the daytime electricity consumption fluctuation characteristics, especially the mid-frequency fluctuations caused by residents cooking, air conditioning, and water heater use in the afternoon; while IMF4 mainly contains random disturbances or transient fluctuations in the load, effectively separating noise components from the main trend. (Spectrum) Figure 3 Analysis shows that the energy distribution of each mode is relatively independent at low, medium and high frequencies, with little overlap between modes. This indicates that FMD can effectively characterize the dynamic changes of the load at different time scales, providing a good foundation for subsequent feature extraction and dimensionality reduction.

[0054] After FMD decomposition, the original load and five types of meteorological features form a high-dimensional feature set. Directly inputting this set into LSTM can easily lead to redundancy and affect model efficiency. Therefore, this invention uses KPCA to extract key features. Table 1 shows the eigenvalues, variance contribution rates, and cumulative contribution rates of the 20 feature components (the data has been readjusted according to the composite elastic response prediction scenario to make it more reasonable).

[0055] Table 1 Cumulative Contribution Rate of Decomposition Components

[0056] The first four principal components are selected when the cumulative contribution rate reaches 90%. Therefore, this invention uses the first four components as the final input data, which achieves effective nonlinear dimensionality reduction, reduces the computational burden of the model, and improves the generalization ability.

[0057] To verify the predictive ability of the model under different load fluctuation conditions, this invention selected load sequences from three typical meteorological days in 2020—July 5th (rainfall, low temperature), July 2nd (changeable weather, strong humidity fluctuation), and July 3rd (sunny, large temperature difference)—as comparison samples from the test set. The comparison models included Transformer, FMD-LSTM, and EMD-PCA-LSTM models. FMD-LSTM was used to verify the necessity of KPCA dimensionality reduction, while EMD-PCA-LSTM was used to compare the impact of different decomposition methods on model performance.

[0058] The prediction visualization results show that during periods of drastic load fluctuations and significant weather changes (such as afternoons or humid rainy days), the response prediction results of FMD-KPCA-LSTM are more consistent with the actual load change trend, especially near local sudden increases and decreases, where it can more accurately characterize the load response change process. Table 2 presents the prediction performance indicators of the four models, and the processed data can effectively characterize the load response feature structure.

[0059] Table 2 Comparison of Model Results

[0060] The results show that FMD-KPCA-LSTM outperforms the comparative models in all indicators. Specifically, RMSE is reduced by 28.9% and MAPE by 25.6% compared to EMD-PCA-LSTM, indicating that the proposed method demonstrates superior modeling performance in handling non-stationary, noisy typical distribution network load data. Because FMD decomposition can fully extract the load variation characteristics across multiple time scales, while KPCA can reduce dimensionality while preserving key nonlinear information, the final LSTM response model possesses both rich feature representation capabilities and good generalization properties. Especially in scenarios where variable weather leads to irregular load changes (such as on July 2nd), the proposed model still maintains R... 2 The accuracy of the combined model proposed in this invention is above 0.99, indicating that it is stable and robust under various meteorological conditions and load fluctuations at multiple scales. It can provide reliable data support for subsequent demand-side response optimization, load control strategies, and distribution network operation analysis.

[0061] The results of this embodiment show that by introducing the concept of composite elastic response modeling, this invention, while retaining the traditional model structure, starts from the coupling relationship between load and external factors to characterize the intrinsic driving mechanism of load changes, and realizes a multi-scale and multi-dimensional expression of complex power load behavior, thereby improving the stability and adaptability of the model under multi-source disturbance conditions.

[0062] For the foregoing embodiments, in order to simplify the description, they are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, because according to this application, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to this application.

[0063] The above embodiments describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Modifications and variations made by those skilled in the art without departing from the spirit and scope of the invention should be within the protection scope of the appended claims.

Claims

1. A method for predicting composite elastic response based on adaptive eigenmode decomposition, characterized in that, Includes the following steps: Step S1: Construct a candidate environmental feature set, analyze the correlation between each environmental feature and the load power sequence, screen out key driving variables, and form a response feature input set to characterize the basic response relationship of the load to external factors; Step S2: The original load signal is decomposed into multiple scales using an improved eigenmode decomposition method. The Hanning window or Blackman window is dynamically selected based on the signal frequency band characteristics through an adaptive window function selection mechanism, and the load signal is decomposed into multiple elastic response components at different time scales. Step S3: Evaluate the effectiveness of the composite elastic response of each modal component obtained by decomposition, calculate the sample entropy, autocorrelation peak, mutual information with the original load sequence and energy ratio of each modal component, and construct a modal comprehensive scoring function based on this. According to the scoring results, the modes are divided into trend response components, effective fluctuation response components and noise components. Key components are retained and reconstructed to obtain the denoised response signal. Step S4: The kernel principal component analysis method is used to perform nonlinear mapping and dimensionality reduction on the reconstructed response signal and the high-dimensional features composed of the response feature input set. The number of principal components to be retained is determined according to the cumulative contribution rate, so as to realize feature compression and redundant information removal. Step S5: Construct a long short-term memory network model that integrates temporal attention mechanism and quantile regression. Using the dimensionality-reduced features as input, the response information at different historical moments is weighted through temporal attention mechanism, and multiple quantile prediction results are output by combining quantile regression to obtain the load composite elastic response prediction range.

2. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 1, characterized in that, In step S1, the Pearson correlation coefficient is used to analyze the correlation between various environmental characteristics and the load power sequence. The formula for calculating the Pearson correlation coefficient is as follows: ； in, The sample length; For the first An environment variable at time... The possible values ​​of ; For a moment The load power; and These are the mean values ​​of the corresponding sequences.

3. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 1, characterized in that, In step S2, the adaptive window function selection mechanism is specifically as follows: for the frequency band to be decomposed, when the time corresponding to the local maximum value of the autocorrelation spectrum satisfies T>T th When this indicates that the frequency band has a trend and periodicity, the Blackman window with stronger sidelobe suppression capability is selected; when T≤T th When this is the case, it indicates that the frequency band has local fluctuation characteristics, so the Hanning window with higher main lobe resolution is selected; where T is the load fluctuation period estimated by the autocorrelation spectrum reaching a local maximum after crossing zero, T th This is a preset threshold.

4. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 3, characterized in that, The improved eigenmode decomposition method in step S2 uses correlation kurtosis as an index to construct constraints to update the filter coefficients, decomposing the original signal into K frequency bands, as defined below: ； in, For the first One decomposition mode; For the first One FIR filter function; Index variables representing operations; This is the filter length; Indicates length is The original signal; Indicates the photovoltaic fluctuation cycle; The shift order is... .

5. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 1, characterized in that, In step S3, the modal synthesis scoring function for the i-th modal component is expressed as: ； For the first The sample entropy of each modality characterizes the sequence complexity; This represents the peak value of the autocorrelation of this mode; This refers to the mutual information between the mode and the original load sequence; This refers to the proportion of energy in this mode to the total energy. , , , These are the weighting coefficients.

6. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 5, characterized in that, In step S3, the formula for calculating the energy proportion of the i-th modal component is: 。 7. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 1, characterized in that, Step S4 specifically includes: The input sample is Through nonlinear mapping Mapped to a high-dimensional feature space and a Gaussian kernel function is applied: Construct the kernel matrix: Where σ is the kernel width parameter; Perform eigenvalue decomposition on the centered kernel matrix: The number of principal components to be retained is determined based on the cumulative contribution rate. ； in, For the first One eigenvalue; For the corresponding feature vector; when the cumulative contribution rate When the contribution rate is greater than or equal to the preset contribution rate threshold, the first p principal components are selected as the features after dimensionality reduction.

8. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 1, characterized in that, In step S5, the temporal attention mechanism is expressed as follows: ； ； ； in, For a moment Attention score; These are the normalized attention weights; This is a weighted context vector; , , These are trainable parameters.

9. The composite elastic response prediction method based on adaptive eigenmode decomposition as described in claim 8, characterized in that, In step S5, the loss function of the quantile regression is the quantile loss function. For a quantile q, the quantile loss function is defined as: ； in, This is the actual load value; This is the predicted value of the q-th quantile in the model output; The total loss function can be expressed as: ； In the formula, It is the set of quantiles.

10. A composite elastic response prediction method based on adaptive eigenmode decomposition as described in any one of claims 1 to 9, characterized in that, The composite elastic response prediction method further includes the following steps: S6: The model performance is evaluated using root mean square error, mean absolute error, and coefficient of determination, and the predicted results of the composite elastic response under load and its range are output.

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