Grey prediction method and system based on periodic aggregation and periodic component factor

Abstract

The invention relates to the technical field of energy prediction, in particular to a grey prediction method and system based on periodic aggregation and periodic component factors, and the method comprises the following steps: S1, model establishment: forming a discrete grey prediction model on the basis of a DGM (1, 1) model; s2, data decomposition: utilizing a data decomposition algorithm to decompose trend, periodicity and random volatility in the original data; s3, periodicity and random fluctuation reconstruction: carrying out information mining and reconstruction on periodicity and random fluctuation components, combining seasonal factors and a time sequence theory, incorporating the periodicity and random fluctuation components into a discrete grey prediction model, and optimizing a prediction result; s4, result analysis: analyzing an overall prediction result; according to the method, long-term trend, periodic fluctuation and short-term random noise can be captured respectively, comprehensive modeling and optimization of different data characteristics are ensured, and the overall precision of prediction is improved.

Description

Technical Field

[0001] This invention relates to the field of energy forecasting technology, and in particular to a grey forecasting method and system based on periodic aggregation and periodic component factors. Background Technology

[0002] In recent years, climate issues and energy crises have intensified. To address these global challenges, achieving a green and low-carbon transformation has become an important development direction for countries around the world. Developing renewable energy is a key way to achieve low carbon emissions and promote sustainable development. However, due to the volatility, intermittency, and randomness of renewable energy, its stability in the power system is poor, which increases the cost of power generation and the difficulty of system operation. Therefore, accurate renewable energy forecasting technology is of great significance for alleviating the uncertainty of energy supply and optimizing the planning and management of the power system.

[0003] Currently, renewable energy forecasting technology has gradually developed into various methods, including mathematical-physical methods, statistical models, machine learning models, and their combined models. Mathematical-physical methods rely on numerical weather prediction models, but they require a large amount of computing resources and high-quality initial observation data, making them difficult to adapt to the complex and ever-changing energy forecasting needs. Statistical models have certain advantages in probabilistic prediction, but they have high requirements for the distribution and quality of data, making them difficult to effectively meet the needs of medium- and long-term forecasting. Machine learning methods have shown strong learning and feature extraction capabilities in the context of big data, but they rely on a large amount of data and are easily affected by insufficient data. In addition, in long-term forecasting, the accurate description of nonlinear periodic characteristics is also a challenge in model construction, which places higher demands on renewable energy forecasting.

[0004] The purpose of this invention is to provide a grey prediction method and system based on periodic aggregation and periodic component factors to overcome the shortcomings of existing technologies. It has strong adaptability and robustness, and can provide a more accurate and reliable solution for renewable energy prediction in complex time series. Summary of the Invention

[0005] This invention provides a grey prediction method and system based on periodic aggregation and periodic component factors.

[0006] A grey prediction method based on periodic aggregation and periodic component factors includes the following steps:

[0007] S1, Model Establishment: Based on the DGM(1,1) model, a discrete grey prediction model is formed to solve the problem of conversion from discrete form to continuous form;

[0008] S2, Data Decomposition: Using data decomposition algorithms to decompose the trends, periodicity and random fluctuations in the original data, and identify the trend parts that conform to the quasi-exponential law;

[0009] S3, Reconstruction of Periodicity and Random Fluctuations: Information mining and reconstruction of periodicity and random fluctuation components are performed, and combined with seasonal factors and time series theory, they are incorporated into the discrete grey prediction model to optimize the prediction results;

[0010] S4, Results Analysis: Combining the trend analysis and the optimized prediction results, the overall prediction results are analyzed.

[0011] Optionally, the model building in S1 includes:

[0012] S11, Data accumulation generation: Accumulate and generate the original data sequence {x0(1),x0(2),...,x0(n)} to obtain the accumulated generation sequence {x1(1),x1(2),...,x1(n)};

[0013] S12, Grey Model Establishment: Based on the accumulated generated data, a first-order difference equation is constructed, and a grey prediction model is built based on grey system theory.

[0014] S13, Solving parameters by least squares method: The parameters of the grey prediction model are estimated by least squares method to obtain the optimal values ​​of the model parameters;

[0015] S14, Predicted value calculation: Using the obtained model parameters, a grey prediction model is used to make predictions, calculate the predicted values ​​for the accumulated data, and restore the predicted values ​​of the original data through anti-accumulation generation (IAGO).

[0016] S15, Transformation to Continuous Form: After establishing the discrete grey prediction model, the transformation from discrete to continuous form is solved through inverse accumulation generation and parameter solving.

[0017] Optionally, the data decomposition in S2 includes:

[0018] S21, Data decomposition model construction: Decompose the original data sequence {x0(1),x0(2),...,x0(n)} into trend term, period term and random fluctuation term;

[0019] S22, Trend Term Extraction: Identify the quasi-exponential regularity of the trend term T(k) in the original data, and extract the trend term T(k) using the moving average method;

[0020] S23, Periodic Term Extraction: The periodic term S(k) is extracted using Fast Fourier Transform (FFT), and the main periodic components in the data are identified through spectral analysis and decomposed as periodic terms.

[0021] S24, Extraction of random fluctuation term: Remove the trend term T(k) and periodic term S(k) from the original data x0(k), and the remaining part is taken as the random fluctuation term R(k).

[0022] Optionally, the periodic and random fluctuation reconstruction in S3 includes:

[0023] S31, Extraction and Modeling of Periodic Components: Wavelet analysis is used to perform in-depth information mining of periodic components, identify the main periodic frequencies, and construct a periodic component model based on the main periodic frequencies to capture the periodic fluctuations in the original data.

[0024] S32, Identification and smoothing of random fluctuation components: Information mining is performed on random fluctuation components to identify their fluctuation range and characteristics, and the exponential smoothing algorithm is used to reduce noise interference.

[0025] S33, Combining and Reconstructing Seasonal Factors: Combining seasonal factors in time series data, using seasonal assumptions and time series theory, the extracted periodic and processed random fluctuation components are reconstructed into the discrete grey prediction model.

[0026] Optionally, the extraction and modeling of the periodic components in S31 includes:

[0027] S311, Local periodicity feature extraction: Based on the initially extracted periodic components, wavelet analysis is used to decompose the original data at multiple scales to identify local periodicity features at different scales and further characterize the dynamic characteristics of periodic fluctuations.

[0028] S312, Construction of dynamic periodic model: Based on the local periodicity characteristics in wavelet transform, a dynamic periodic component model with different amplitudes and phases is constructed to capture the dynamic periodic changes in the original data.

[0029] Optionally, the identification and smoothing of the random fluctuation component in S32 includes:

[0030] S321, Random Fluctuation Feature Extraction: The random fluctuation component {R(k)} is extracted from the original data, and the standard deviation σ of the random fluctuation component is calculated. R To quantify its fluctuation range, and to evaluate the frequency characteristics of random fluctuations through autocorrelation analysis, the autocorrelation function ρ(l) is used to identify its main fluctuation period or frequency characteristics.

[0031] S322, Exponential Smoothing: The exponential smoothing algorithm is used to reduce noise in the random fluctuation component {R(k)}, thereby reducing the impact of random noise on the prediction results.

[0032] Optionally, the seasonal factor combination and reconstruction in S33 includes:

[0033] S331, Periodic Adjustment of Seasonal Factors: Based on the seasonality assumption, the extracted periodic term S(k) is periodically adjusted to enhance its seasonality.

[0034] S332, Seasonal smoothing of random fluctuation components: using the seasonality assumption to smooth the random fluctuation components Perform seasonal smoothing;

[0035] S333, Seasonal Reconstruction to Discrete Grey Prediction Model: The adjusted seasonal cyclical component S... season (k) and seasonal random fluctuation components Reconstructing the discrete grey prediction model to generate the final predicted value.

[0036] Optionally, the result analysis in S4 includes:

[0037] S41, Prediction Error Calculation: The mean squared error (MSE) and mean absolute percentage error (MAPE) are used to calculate the prediction error by comparing the actual data with the predicted value, which is used to evaluate the prediction accuracy.

[0038] S42, Residual Analysis of Trend and Seasonal Components: Calculate the residuals of the trend and seasonal components to identify any biases.

[0039] S43, Stability Analysis of Results: By calculating the mean square error (MSE) and mean absolute percentage error (MAPE) for multiple time periods, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed to verify its applicability and reliability.

[0040] Optionally, the stability analysis of the results in S43 includes:

[0041] S431, Time Period Division: Divide the overall time series data into several equal time periods {T1, T2, ..., T...} m Each time period contains a certain number of data points, which are used to evaluate the stability of the reconstructed discrete grey prediction model in each time period.

[0042] S432, Calculate the mean square error for each time period: For each time period T i Calculate the mean squared error to quantify the prediction accuracy for that time period;

[0043] S433, Calculate the mean absolute percentage error for each time period: For each time period T i Calculate the mean absolute percentage error to assess the relative error performance over that time period;

[0044] S434, Stability Analysis and Applicability Verification: By calculating the standard deviation of the mean square error and the mean absolute percentage error for each time period, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed.

[0045] A grey prediction system based on periodic aggregation and periodic component factors, used to implement the aforementioned grey prediction method based on periodic aggregation and periodic component factors, includes the following modules:

[0046] Model building module: Based on the DGM(1,1) model, a discrete grey prediction model is formed, completing the transformation from discrete form to continuous form;

[0047] Data decomposition module: Processes the raw data through data decomposition algorithms, decomposes it into trend, periodic and random fluctuation components, and identifies the trend part that conforms to the quasi-exponential law;

[0048] Periodic and Random Fluctuation Reconstruction Module: This module mines and reconstructs information on periodic and random fluctuation components, and integrates them with seasonal factors and time series theory into the discrete grey prediction model to optimize the prediction results.

[0049] Results Analysis Module: Combining the trend section and the optimized prediction results, this module analyzes the overall prediction results and evaluates the model's prediction accuracy and stability.

[0050] The beneficial effects of this invention are:

[0051] This invention systematically decomposes the trend, periodicity, and random volatility in time series data by introducing periodic aggregation and periodic component factors. Based on this, it reconstructs the periodic and random volatility components by combining seasonal factors, enabling the prediction model to flexibly and accurately handle complex multidimensional feature data. Data decomposition allows the model to capture long-term trends, periodic fluctuations, and short-term random noise separately, ensuring comprehensive modeling and optimization of different data characteristics and improving the overall accuracy of prediction.

[0052] This invention eliminates noise interference caused by random fluctuations by generating data through data accumulation and solving using the least squares method, forming a smooth prediction sequence, thereby enhancing the model's fitting degree and robustness. At the same time, by combining local periodic feature extraction and dynamic periodic model construction methods, it captures subtle periodic changes in data at different time periods, ensuring that the model has a high adaptability to variable periodic fluctuations, especially showing stronger stability and accuracy in complex scenarios with dynamic periodicity.

[0053] This invention, through comprehensive result analysis, including calculating the mean squared error (MSE) and mean absolute percentage error (MAPE) for each time period, residual analysis, and stability analysis, quantifies the overall prediction accuracy and stability of the model over different time periods. This not only ensures the robust performance of the model under different data scenarios but also provides effective data support for further optimization, making the model applicable to various complex time series data scenarios and significantly improving the accuracy and reliability of predictions. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in this 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 for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a schematic diagram of the prediction method flow according to an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the system functional modules according to an embodiment of the present invention. Detailed Implementation

[0057] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0058] It should be noted that the use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0059] Generally, terms can be understood at least partly from their use in context. For example, depending at least partly on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in a singular sense, or a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood not necessarily to convey an exclusive set of factors, but rather, alternatively, depending at least partly on the context, to allow for the presence of other factors that are not necessarily explicitly described.

[0060] like Figure 1 As shown, a grey prediction method based on periodic aggregation and periodic component factors includes the following steps:

[0061] S1, Model Establishment: Based on the DGM(1,1) model, a discrete grey prediction model is formed to solve the problem of conversion from discrete form to continuous form;

[0062] S2, Data Decomposition: Using data decomposition algorithms to decompose the trends, periodicity and random fluctuations in the original data, and identify the trend parts that conform to the quasi-exponential law;

[0063] S3, Reconstruction of Periodicity and Random Fluctuations: Information mining and reconstruction of periodicity and random fluctuation components are performed, and combined with seasonal factors and time series theory, they are incorporated into the discrete grey prediction model to optimize the prediction results;

[0064] S4, Results Analysis: Combining the trend analysis and the optimized prediction results, the overall prediction results are analyzed.

[0065] The above methods can effectively handle complex time series data containing trends, periodicity, and random fluctuations, achieving high-precision predictions with limited data. They are highly flexible and robust, and are particularly suitable for scenarios with incomplete data or significant periodic fluctuations, providing more accurate and reliable prediction results.

[0066] The model building in S1 includes:

[0067] S11, Data Accumulation Generation: Accumulate the original data sequence {x0(1),x0(2),...,x0(n)} to generate the accumulated generation sequence {x1(1),x1(2),...,x1(n)}, represented as:

[0068]

[0069] Where x1(k) is the kth data point in the accumulated data sequence, x0(i) is the ith data point in the original data sequence, and n is the total number of data points;

[0070] S12, Grey Model Establishment: Based on the accumulated generated data, a first-order difference equation is constructed. Based on grey system theory, a grey prediction model is built, expressed as:

[0071]

[0072] Where a and b are the parameters of the gray model, The predicted values ​​of the generated sequence accumulated in the grey prediction model;

[0073] S13, Solving for parameters using the least squares method: The parameters of the grey prediction model are estimated using the least squares method to obtain the optimal values ​​of the model parameters, expressed as:

[0074]

[0075] Where B is the accumulated data matrix, Y is the target vector, and B T Let B be the transpose of matrix B;

[0076] S14, Predicted Value Calculation: Using the obtained model parameters, a grey prediction model is used to make predictions, calculating the predicted values ​​for the accumulated data. The predicted values ​​for the original data are then recovered using Inverse Accumulation Generation (IAGO), as shown below:

[0077]

[0078] in, Let x1(k) be the predicted (k+1)th accumulated data point, and x1(k) be the kth data point in the accumulated generation sequence. The predicted value of the original data after restoration, for the (k+1)th prediction point. This is the predicted k-th accumulated data point;

[0079] S15, Transformation to Continuous Form: After establishing the discrete grey prediction model, the transformation from discrete to continuous form is solved through inverse accumulation generation and parameter solving.

[0080] The above methods effectively eliminate random fluctuations and noise in the data, making the data sequence smoother and thus improving the accuracy of prediction. At the same time, the use of the least squares method to solve the model parameters ensures a high degree of model fit, making it perform well when dealing with small samples and uncertain data. It not only solves the problem of converting from discrete to continuous form, but also enhances the adaptability and robustness of the model, making it suitable for a variety of complex time series prediction scenarios.

[0081] The data decomposition in S2 includes:

[0082] S21, Data Decomposition Model Construction: The original data sequence {x0(1),x0(2),...,x0(n)} is decomposed into a trend term, a periodic term, and a random fluctuation term, represented as:

[0083] x0(k)=T(k)+S(k)+R(k),k=1,2,…,n;

[0084] Where T(k) is the trend term, representing the long-term trend of change in the data; S(k) is the periodic term, representing the periodic fluctuations in the data; and R(k) is the random fluctuation term, representing the randomness or noise in the data.

[0085] S22, Trend Term Extraction: The trend term T(k) in the original data is identified using a quasi-exponential pattern. The trend term T(k) is extracted using the moving average method, and expressed as:

[0086]

[0087] Where m is the size of the sliding window;

[0088] S23, Periodic Term Extraction: Periodic terms S(k) are extracted using Fast Fourier Transform (FFT). The main periodic components in the data are identified through spectral analysis and decomposed as periodic terms. Specifically, this includes:

[0089] Applying Fast Fourier Transform: Performing Fast Fourier Transform on the original data sequence {x0(1),x0(2),...,x0(n)} yields the frequency domain representation {X(f1),X(f2),...,X(f... n )}, where each X(f k ) represents frequency f k The corresponding magnitude in complex form is expressed as:

[0090]

[0091] Where X(f) k ) represents frequency f k The Fourier transform coefficients (complex form) of x0(j) are given, where x0(j) is the j-th data point in the time series, and i is the imaginary unit, satisfying i 2 = -1, where n is the total number of data points;

[0092] Calculate the amplitude spectrum: Calculate the amplitude A(f) at each frequency. d ), that is, X(f k The modulus of ) is used to identify the main frequency components, and is represented as:

[0093]

[0094] Among them, A(f) k ) is the frequency f k The amplitude, Re(X(f) k )) and Im(X(f k )) are respectively X(f k The real and imaginary parts of ().

[0095] Identify the main periodic components: based on the amplitude spectrum A(f) k Select a frequency component f with a relatively large amplitude. k The main periodic components in the data corresponding to these frequencies, the periodic term S(k), are represented as a superposition of sine waves with amplitude, expressed as:

[0096]

[0097] Where m is the number of main periodic frequencies selected, and f k It is the frequency of each major periodic component, A(f k ) is the frequency f k The range, It is frequency f k The phase angle is usually determined by the phase of the Fourier transform coefficients;

[0098] S24, Extraction of the random fluctuation term: The trend term T(k) and the periodic term S(k) are removed from the original data x0(k), and the remaining part is taken as the random fluctuation term R(k), expressed as:

[0099] R(k) = x0(k) - T(k) - S(k);

[0100] By employing the above methods, we can process data characteristics of different natures, thereby significantly improving the accuracy and robustness of predictions. Trend extraction enables the model to capture the long-term trend of data changes, periodic extraction can reveal periodic fluctuations in the data, and random fluctuation separation helps to reduce the interference of noise. This allows the model to perform more accurate modeling and optimization for each component, making it particularly suitable for processing complex time series data and effectively improving the stability and applicability of overall predictions.

[0101] The periodic and random fluctuation reconstructions in S3 include:

[0102] S31, Extraction and Modeling of Periodic Components: Wavelet analysis is used to perform in-depth information mining of periodic components, identify the main periodic frequencies, and construct a periodic component model based on the main periodic frequencies to capture the periodic fluctuations in the original data.

[0103] S32, Identification and smoothing of random fluctuation components: Information mining is performed on random fluctuation components to identify their fluctuation range and characteristics. The exponential smoothing algorithm is used to reduce noise interference and process them into modelable residual terms, thereby enhancing the robustness of the model when facing random data.

[0104] S33, Combination and Reconstruction of Seasonal Factors: Combining seasonal factors in time series, using seasonal assumptions and time series theory, the extracted periodic and processed random fluctuation components are reconstructed into the discrete grey prediction model. By introducing seasonal factors, the adaptability of the discrete grey prediction model to periodic and random fluctuations is optimized, thereby improving the accuracy of the overall prediction results.

[0105] Through the above, periodic and random fluctuation components are systematically extracted and reconstructed, and the model is optimized by combining seasonal factors, making the prediction more accurate and reliable. The modeling of periodic components ensures the effective capture of regular fluctuations in the data, the smoothing of random fluctuations reduces the impact of noise and improves the robustness of the model, and the introduction of seasonal factors further enhances the model's adaptability to periodic and random fluctuations, significantly improving the model's performance in complex time series, making it more advantageous in terms of accuracy and stability, and suitable for application in real data scenarios with variable periodicity and volatility.

[0106] The extraction and modeling of periodic components in S31 includes:

[0107] S311, Local Periodicity Feature Extraction: Based on the initially extracted periodic components, wavelet analysis is used to decompose the original data at multiple scales to identify local periodicities at different scales, further characterizing the dynamic properties of periodic fluctuations, as shown below:

[0108]

[0109] Among them, W x (p,q) represents the wavelet coefficients at scale p and location q, used for local feature extraction, where p and q are the scale parameter and time translation parameter, respectively. For the mother wavelet function;

[0110] S312, Construction of Dynamic Periodic Model: Based on the local periodicity characteristics in wavelet transform, a dynamic periodic component model with different amplitudes and phases is constructed to capture the dynamic periodic changes in the original data, expressed as:

[0111]

[0112] Among them, S d (k) is a dynamic periodic component, A j (q) and These represent the amplitude and phase of the periodic component at different local locations q, respectively, to characterize local periodic changes;

[0113] The above methods can capture subtle periodic changes in data over different time periods, thereby addressing unstable periodic fluctuations and improving the model's adaptability to complex periodic data. This results in more accurate and robust predictions, especially in time series data with dynamic periodic characteristics, demonstrating higher prediction accuracy and practicality.

[0114] The identification and smoothing of random fluctuation components in S32 include:

[0115] S321, Random Fluctuation Feature Extraction: The random fluctuation component {R(k)} is extracted from the original data, and the standard deviation σ of the random fluctuation component is calculated. R To quantify its fluctuation range, and to evaluate the frequency characteristics of random fluctuations through autocorrelation analysis, the main fluctuation period or frequency characteristics are identified using the autocorrelation function ρ(l), expressed as:

[0116]

[0117]

[0118] Where, σ R Let be the standard deviation of the random fluctuation component, representing its fluctuation range, and R(k) be the k-th data point of the random fluctuation component. Let n be the mean of the random fluctuation component, and n be the total number of data points.

[0119]

[0120] Where ρ(l) is the autocorrelation coefficient of lag l, used to quantify the correlation between lag time l and random fluctuation component, and R(k) and R(k+l) are the k-th and k+l-th random fluctuation data points, respectively.

[0121] S322, Exponential Smoothing: The exponential smoothing algorithm is used to reduce noise in the random fluctuation component {R(k)}, thereby reducing the impact of random noise on the prediction results. This is expressed as:

[0122]

[0123] in, R(k) represents the smoothed random fluctuation component, which is the smoothed result of the k-th data point. R(k) is the original random fluctuation component, and α is the smoothing coefficient, which takes values ​​in the range of 0 < α < 1 and is used to control the degree of smoothing.

[0124] The above methods effectively reduce the interference of random noise, weaken short-term fluctuations, and maintain long-term trends, thereby making the prediction model more stable and accurate, improving the model's adaptability to irregular fluctuations, and making the prediction results more reliable and resistant to interference in complex environments.

[0125] The combination and reconstruction of seasonal factors in S33 include:

[0126] S331, Periodic Adjustment of Seasonal Factors: Based on the seasonality assumption, the extracted periodic term S(k) is periodically adjusted to enhance its seasonality. Assuming the original data has periodic seasonal fluctuations, the seasonal reconstruction of the periodic component S(k) is expressed as follows:

[0127] S season (k)=S(k)·F(k);

[0128] Among them, S season (k) is the seasonally adjusted periodic component, S(k) is the extracted initial periodic component, and F(k) is the seasonality factor;

[0129] S332, Seasonal smoothing of random fluctuation components: using the seasonality assumption to smooth the random fluctuation components Seasonal smoothing is performed to ensure that the variation characteristics of random fluctuations in different seasons are preserved, as shown below:

[0130]

[0131] in, The random fluctuation component is seasonally smoothed. The processed random fluctuation component is represented by F(k), which is the seasonality factor.

[0132] S333, Seasonal Reconstruction to Discrete Grey Prediction Model: The adjusted seasonal cyclical component S... season (k) and seasonal random fluctuation components Reconstructing the discrete grey prediction model to generate the final predicted value. Represented as:

[0133]

[0134] in, This is the final forecast value after seasonal reconstruction. The trend forecast value, S, comes from the trend term of the discrete grey prediction model. season (k) is the seasonally adjusted cyclical component. This is the random fluctuation component after seasonal smoothing;

[0135] Through the above methods, the periodic and random fluctuation components are seasonally adjusted and smoothed, enabling the model to adapt to the fluctuation characteristics of different seasons. By reconstructing the seasonally adjusted components into the discrete grey prediction model, the model more accurately captures the seasonal changes in the time series, significantly improving the accuracy and stability of the prediction results, enhancing the model's adaptability and robustness, and making the predictions perform better in the context of complex periodic and random fluctuations.

[0136] The results analysis in S4 includes:

[0137] S41, Prediction Error Calculation: Using the mean squared error (MSE) and mean absolute percentage error (MAPE), the prediction error is calculated by comparing the actual data with the predicted values. This error is used to evaluate the prediction accuracy and is expressed as follows:

[0138]

[0139] Where x0(k) is the kth actual data point, Let k be the kth predicted data point, and n be the total number of data points;

[0140] S42, Residual Analysis of Trend and Seasonal Components: Calculate the residuals of the trend and seasonal components to identify any biases, expressed as:

[0141]

[0142] Where Residual(k) is the residual of the k-th data point. S is the trend forecast value. season (k) is a seasonal cyclical component. This is the random fluctuation component after seasonal smoothing;

[0143] S43, Stability Analysis of Results: By calculating the mean square error (MSE) and mean absolute percentage error (MAPE) for multiple time periods, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed to verify its applicability and reliability.

[0144] Through the above, the model's prediction accuracy and reliability were systematically evaluated. Mean squared error (MSE) and mean absolute percentage error (MAPE) quantified the model's overall accuracy. Residual analysis revealed potential biases in the predictions, while stability analysis over different time periods ensured the model's robust performance under various data fluctuation scenarios. This not only verified the accuracy of the prediction results but also provided data support for the continuous optimization of the model, making it more adaptable to complex time series data applications.

[0145] The stability analysis of the results in S43 includes:

[0146] S431, Time Period Division: Divide the overall time series data into several equal time periods {T1, T2, ..., T...} m Each time period contains a certain number of data points, which are used to evaluate the stability of the reconstructed discrete grey prediction model in each time period.

[0147] S432, Calculate the mean square error for each time period: For each time period T i The mean squared error is calculated to quantify the prediction accuracy for that time period, and is expressed as:

[0148]

[0149] in, For time period T i The mean square error, where x0(k) is the kth actual data point. For the k-th prediction data point, n i For time period T i The total number of data points within;

[0150] S433, Calculate the mean absolute percentage error for each time period: For each time period T i The mean absolute percentage error is calculated to evaluate the relative error performance over that time period, and is expressed as:

[0151]

[0152] in, For time period T i The mean absolute percentage error, x0(k) is the kth actual data point. This is the k-th predicted data point;

[0153] S434, Stability Analysis and Applicability Verification: By calculating the standard deviation of the mean square error and the mean absolute percentage error for each time period, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed, as follows:

[0154]

[0155] Where, σ MSE σ represents the standard deviation of the mean square error for each time period. MAPE The standard deviation of the mean absolute percentage error for each time period. These are the mean squared error and the mean absolute percentage error for all time periods, respectively.

[0156] The above steps ensure the comprehensiveness and consistency of prediction accuracy. By analyzing the standard deviation of the error, the stability of the model in different time periods can be revealed, clarifying its applicability and reliability. For time periods with large fluctuations, the stability analysis of the results can also help identify potential prediction biases, providing a basis for further optimization, enhancing the robustness of the model in complex time series data, and making predictions more accurate and reliable.

[0157] like Figure 2 As shown, a grey prediction system based on periodic aggregation and periodic component factors is used to implement the aforementioned grey prediction method based on periodic aggregation and periodic component factors, and includes the following modules:

[0158] Model building module: Based on the DGM(1,1) model, a discrete grey prediction model is formed, completing the transformation from discrete form to continuous form;

[0159] Data decomposition module: Processes the raw data through data decomposition algorithms, decomposes it into trend, periodic and random fluctuation components, and identifies the trend part that conforms to the quasi-exponential law;

[0160] Periodic and Random Fluctuation Reconstruction Module: This module mines and reconstructs information on periodic and random fluctuation components, and integrates them with seasonal factors and time series theory into the discrete grey prediction model to optimize the prediction results.

[0161] Results Analysis Module: Combining the trend section and the optimized prediction results, this module analyzes the overall prediction results and evaluates the model's prediction accuracy and stability.

[0162] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0163] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A grey prediction method based on periodic aggregation and periodic component factors, characterized in that, Includes the following steps: S1, Model Establishment: Based on the DGM(1,1) model, a discrete grey prediction model is formed to solve the problem of conversion from discrete form to continuous form; S2, Data Decomposition: Using data decomposition algorithms to decompose the trends, periodicity and random fluctuations in the original data, and identify the trend parts that conform to the quasi-exponential law; S3, Reconstruction of Periodicity and Random Fluctuations: Information mining and reconstruction of periodicity and random fluctuation components are performed, and combined with seasonal factors and time series theory, they are incorporated into the discrete grey prediction model to optimize the prediction results; S4, Results Analysis: Combining the trend analysis and the optimized prediction results, the overall prediction results are analyzed.

2. The grey prediction method based on periodic aggregation and periodic component factors according to claim 1, characterized in that, The model establishment in S1 includes: S11, Data accumulation generation: Accumulate and generate the original data sequence {x0(1),x0(2),...,x0(n)} to obtain the accumulated generation sequence {x1(1),x1(2),...,x1(n)}; S12, Grey Model Establishment: Based on the accumulated generated data, a first-order difference equation is constructed, and a grey prediction model is built based on grey system theory. S13, Solving parameters by least squares method: The parameters of the grey prediction model are estimated by least squares method to obtain the optimal values ​​of the model parameters; S14, Predicted value calculation: Using the obtained model parameters, a grey prediction model is used to make predictions, calculate the predicted values ​​for the accumulated data, and restore the predicted values ​​of the original data through anti-accumulation generation; S15, Transformation to Continuous Form: After establishing the discrete grey prediction model, the transformation from discrete to continuous form is solved through inverse accumulation generation and parameter solving.

3. The grey prediction method based on periodic aggregation and periodic component factors according to claim 2, characterized in that, The data decomposition in S2 includes: S21, Data decomposition model construction: Decompose the original data sequence {x0(1),x0(2),...,x0(n)} into trend term, period term and random fluctuation term; S22, Trend Term Extraction: Identify the quasi-exponential regularity of the trend term T(k) in the original data, and extract the trend term T(k) using the moving average method; S23, Periodic Term Extraction: The periodic term S(k) is extracted using Fast Fourier Transform, and the main periodic components in the data are identified through spectral analysis and decomposed as periodic terms. S24, Extraction of random fluctuation term: Remove the trend term T(k) and periodic term S(k) from the original data x0(k), and the remaining part is taken as the random fluctuation term R(k).

4. The grey prediction method based on periodic aggregation and periodic component factors according to claim 3, characterized in that, The periodic and random fluctuation reconstruction in S3 includes: S31, Extraction and Modeling of Periodic Components: Wavelet analysis is used to perform in-depth information mining of periodic components, identify the main periodic frequencies, and construct a periodic component model based on the main periodic frequencies to capture the periodic fluctuations in the original data. S32, Identification and smoothing of random fluctuation components: Information mining is performed on random fluctuation components to identify their fluctuation range and characteristics, and the exponential smoothing algorithm is used to reduce noise interference. S33, Combining and Reconstructing Seasonal Factors: Combining seasonal factors in time series data, using seasonal assumptions and time series theory, the extracted periodic and processed random fluctuation components are reconstructed into the discrete grey prediction model.

5. The grey prediction method based on periodic aggregation and periodic component factors according to claim 4, characterized in that, The extraction and modeling of the periodic components in S31 includes: S311, Local periodicity feature extraction: Based on the initially extracted periodic components, wavelet analysis is used to decompose the original data at multiple scales to identify local periodicity features at different scales and further characterize the dynamic characteristics of periodic fluctuations. S312, Dynamic Periodic Model Construction: Based on the local periodicity characteristics in wavelet transform, a dynamic periodic component model with different amplitudes and phases is constructed to capture the dynamic periodic changes in the original data.

6. The grey prediction method based on periodic aggregation and periodic component factors according to claim 5, characterized in that, The identification and smoothing of the random fluctuation component in S32 includes: S321, Random Fluctuation Feature Extraction: The random fluctuation component {R(k)} is extracted from the original data, and the standard deviation σ of the random fluctuation component is calculated. R To quantify its fluctuation range, and to evaluate the frequency characteristics of random fluctuations through autocorrelation analysis, the autocorrelation function ρ(l) is used to identify its main fluctuation period or frequency characteristics. S322, Exponential Smoothing: The exponential smoothing algorithm is used to reduce noise in the random fluctuation component {R(k)}, thereby reducing the impact of random noise on the prediction results.

7. The grey prediction method based on periodic aggregation and periodic component factors according to claim 6, characterized in that, The seasonal factor combination and reconstruction in S33 includes: S331, Periodic Adjustment of Seasonal Factors: Based on the seasonality assumption, the extracted periodic term S(k) is periodically adjusted to enhance its seasonality. S332, Seasonal smoothing of random fluctuation components: using the seasonality assumption to smooth the random fluctuation components Perform seasonal smoothing; S333, Seasonal Reconstruction to Discrete Grey Prediction Model: The adjusted seasonal cyclical component S... season (k) and seasonal random fluctuation components Reconstructing the discrete grey prediction model to generate the final predicted value.

8. The grey prediction method based on periodic aggregation and periodic component factors according to claim 7, characterized in that, The result analysis in S4 includes: S41, Prediction Error Calculation: The mean square error and mean absolute percentage error are used to calculate the prediction error by comparing the actual data with the predicted value, which is used to evaluate the prediction accuracy. S42, Residual Analysis of Trend and Seasonal Components: Calculate the residuals of the trend and seasonal components to identify any biases. S43, Stability Analysis of Results: By calculating the mean square error and mean absolute percentage error over multiple time periods, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed to verify its applicability and reliability.

9. The grey prediction method based on periodic aggregation and periodic component factors according to claim 8, characterized in that, The stability analysis of the results in S43 includes: S431, Time Period Division: Divide the overall time series data into several equal time periods {T1, T2, ..., T...} m Each time period contains a certain number of data points, which are used to evaluate the stability of the reconstructed discrete grey prediction model in each time period. S432, Calculate the mean square error for each time period: For each time period T i Calculate the mean squared error to quantify the prediction accuracy for that time period; S433, Calculate the mean absolute percentage error for each time period: For each time period T i Calculate the mean absolute percentage error to assess the relative error performance over that time period; S434, Stability Analysis and Applicability Verification: By calculating the standard deviation of the mean square error and the mean absolute percentage error for each time period, the stability of the reconstructed discrete grey prediction model in different time periods is analyzed.

10. A grey prediction system based on periodic aggregation and periodic component factors, used to implement the grey prediction method based on periodic aggregation and periodic component factors as described in any one of claims 1-9, characterized in that, Includes the following modules: Model building module: Based on the DGM(1,1) model, a discrete grey prediction model is formed, completing the transformation from discrete form to continuous form; Data decomposition module: Processes the raw data through data decomposition algorithms, decomposes it into trend, periodic and random fluctuation components, and identifies the trend part that conforms to the quasi-exponential law; Periodic and Random Fluctuation Reconstruction Module: This module mines and reconstructs information on periodic and random fluctuation components, and integrates them with seasonal factors and time series theory into the discrete grey prediction model to optimize the prediction results. Results Analysis Module: Combining the trend section and the optimized prediction results, this module analyzes the overall prediction results and evaluates the model's prediction accuracy and stability.

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