Energy production prediction method containing fractional derivative partial grey model

Abstract

This invention relates to an energy production forecasting method using a partial grey model with fractional derivatives, belonging to the field of energy production forecasting. It first selects the current monthly production values ​​of different energy sources as a database to construct an original matrix sequence X. (0) As input to the model; secondly, fractional derivatives and fractional accumulation operators are introduced when constructing the model to dynamically predict energy output under the grey effects of exponential and sine functions; finally, the simulated value X of the model is calculated. (r) , Restore value X (0) Furthermore, the model was compared with a control model in various indicators; the particle swarm optimization algorithm was used to find the optimal parameter vector that minimizes the MAPE value; finally, the new model was applied to energy production forecasting. This invention introduces exponential and trigonometric functions, giving the model's time response function oscillatory characteristics, thus accurately capturing and effectively mapping data volatility, significantly improving adaptability and flexibility; the integration of fractional derivatives and fractional accumulation operators into the model significantly improves prediction accuracy.

Description

Technical Field

[0001] This invention belongs to the field of energy production forecasting and relates to an energy production forecasting method using a gray model with fractional derivatives. Background Technology

[0002] The proportion of clean energy needs to be increased, and low-carbon living remains key to development. Regarding energy supply and demand, my country's energy resources and load centers exhibit an inverse distribution, leading to significant energy supply and demand imbalances in some regions. During peak energy demand periods, some areas may experience coal and electricity shortages. Furthermore, my country's high dependence on imported crude oil and natural gas poses a weakness in ensuring energy security. Therefore, scientifically and rationally predicting energy production in certain regions is beneficial for timely adjustments to my country's energy structure and addressing supply and demand imbalances.

[0003] Energy production sequences include not only traditional structured data but also a large amount of unstructured data. Furthermore, there are often strong correlations between energy data; for example, there are certain substitution relationships between energy sources such as electricity, natural gas, and oil; and there are also connections between energy demand and supply in different regions. In addition, energy production sequences are affected by uncertain real-world factors such as economic conditions, policies, demand structures, and technological innovation, exhibiting characteristics of grey systems. Grey prediction models, operating under uncertain conditions with limited data and information, establish prediction models through data processing and phenomenon analysis. They primarily utilize the ability to extract the essence of data using differential equations to obtain relatively accurate prediction results, and are characterized by simple algorithms, short computation time, and wide applicability.

[0004] Reliable and accurate energy production data not only reflect a country's resource endowment and development capacity, but also its economic development level, industrial structure, technological progress, and the effectiveness of its energy policies. Therefore, scientifically and accurately predicting energy production is crucial for adjusting the energy structure, promoting the development of clean and renewable energy, and reducing dependence on fossil fuels. However, energy production forecasting faces many difficulties and challenges. First, exploring the nonlinearity and complexity of energy production series is a demanding task; second, considering the impact of potential unknown influencing factors on forecast accuracy further complicates the process.

[0005] Therefore, a new method for predicting energy production is urgently needed to solve the above problems. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an energy production prediction method using a partial grey model with fractional derivatives. It first selects the current monthly production values ​​of different energy sources as a database to construct an original matrix sequence X. (0)As input to the model; secondly, fractional derivatives and fractional accumulation operators are introduced when constructing the model to dynamically predict energy output under the grey effects of exponential and sine functions; finally, the simulated value X of the model is calculated. (r) , Restore value X (0) Furthermore, the model was compared with the control model in various indicators; the particle swarm optimization algorithm was used to find the optimal parameter vector that minimizes the MAPE value; finally, the new model was applied to energy production prediction.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] An energy production prediction method using a partial grey model with fractional derivatives, comprising the following steps:

[0009] S1: Select the current monthly output values ​​of different energy sources as the database to construct the original matrix sequence X. (0) ;

[0010] S2: Based on the original matrix sequence X (0) Calculate the cumulative sequence X of order r (r) The nearest mean generation sequence Z (r) and partial derivative sequence

[0011]

[0012] S3: Construct fractional derivative partial differential equations as whitening equations for the gray model CFFPGM(·), introduce fractional derivative operators and fractional accumulation operators into the gray model CFFPGM(·), and construct gray action combining exponential and sine functions to describe the oscillation of the data.

[0013] S4: Based on the r-order cumulative sequence X (r) The nearest mean generation sequence Z (r) and partial derivative sequence Construct matrices B and Y, and use the least squares method to estimate the parameter vector of the grey model CFFPGM(·);

[0014] S5: Calculate the simulated value X using both the time-response formula and the cumulative reduction formula. (r) and restoration value X (0) ;

[0015] S6: Calculate the mean square error, mean absolute percentage error, root mean square percentage error, mean absolute error, correlation coefficient, and statistical coefficient of the grey model CFFPGM(·) and several comparative models;

[0016] S7: To ensure the best prediction results, the particle swarm optimization algorithm is used to find the optimal parameters with the goal of minimizing the MAPE value; the optimal parameters are then substituted into the gray model CFFPGM(·) to calculate the simulation value and the MAPE value.

[0017] S8: Compare the prediction performance of the gray model CFFPGM(·) with that of each comparative model. If the prediction performance is better than all comparative models, save the optimal parameters and use them for energy production prediction. Otherwise, continue to use the particle swarm algorithm to find the optimal parameters.

[0018] Furthermore, in step S1, let X (0) The matrix sequence consists of n m×m matrices constructed from the database, with the current monthly output value of different energy sources as the basis:

[0019] X (0) =(X (0) (1),X (0) (2),…,X (0) (n))

[0020] Where, X (0) (k) (k = 1, 2, ..., n) is an m × m matrix, represented as:

[0021]

[0022] X represents (0) (k) is the value in row i and column j.

[0023] Furthermore, in step S2, the original matrix sequence X (0) r (r∈R) + ) order cumulative generation sequence X (r) Represented as:

[0024] X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n))

[0025] In the formula, X (r) (k) (k = 1, 2, ..., n) is an m × m matrix. X represents (r) (k) The value in row i and column j, where:

[0026]

[0027] and,

[0028]

[0029] Where t represents time, Γ(·) represents the gamma function, and X represents (0) (t) is the value in row i and column j;

[0030] Then the nearest mean generating sequence Z (r) Represented as:

[0031] Z (r) =(Z (r) (2),…,Z (r) (n))

[0032] Among them, Z (r) (k) (k = 2, 3, ..., n) is an m × m matrix. Z represents (r) (k) The value in row i, column j is represented as:

[0033]

[0034] in,

[0035] The nearest mean generation sequence Z (r) The horizontal and vertical partial derivative sequences Z x (r) and Z y (r) Satisfy the following formula:

[0036]

[0037] express The value in row i and column j, express The value in row i and column j.

[0038] Furthermore, in step S3, the gray model CFFPGM(·) is The abbreviation for is expressed as:

[0039]

[0040] In the formula, M represents the number of unknown parameters, M = 3m 2 +8, the whitening equation for the gray model CFFPGM(·) is expressed as:

[0041]

[0042] Where (r,α,α1)∈(0,1]a,b,c,ω,d are real constant parameter variables, and t is the value of X. (r) The time variables, x and y, are X (r)The spatial variables, α0, β0, β1 are m×m constant matrices, which are expressed as follows:

[0043]

[0044] In the formula, μ 011 ,μ 012 ,…,μ 0mm ,λ 011 ,λ 012 ,…,λ 0mm ,η 111 ,η 112 ,…,η 1mm It refers to all elements in the matrix α0, β0, β1.

[0045] Furthermore, in step S4, firstly, the gray model The least squares parameter estimation vector is represented as:

[0046]

[0047] Its satisfaction Where B and Y are matrices constructed based on the aforementioned sequence;

[0048] Where matrix B is m 2 (n-1)×(3m 2 A +3) order matrix, which is represented as:

[0049]

[0050] In matrix B, yes The value in row i, column j; and

[0051]

[0052] The constructed matrix Y is m 2 An (n-1)×1 matrix is ​​represented as:

[0053]

[0054] In matrix Y, It is X (r) (k) is the value in row i and column j.

[0055] Furthermore, in step S5, the gray model The time response is:

[0056]

[0057] in, for Simulated values ​​of the model The value in row i and column j;

[0058] Grey Model The final reduction formula is:

[0059]

[0060] in, for Model restoration value The value at coordinates (r, c);

[0061] Furthermore, in step S6, the comparison models include ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM, and ARIMA models, specifically targeting the grey model. Compared with all the comparison models, we have:

[0062] The formula for calculating the mean squared error (MSE) is:

[0063]

[0064] The formula for calculating the Mean Absolute Percentage Error (MAPE) is as follows:

[0065]

[0066] The formula for calculating the root mean square percentage error (RMSPE) is:

[0067]

[0068] The formula for calculating the Mean Absolute Error (MAE) is:

[0069]

[0070] The formula for calculating the correlation coefficient R is:

[0071]

[0072] In the formula, cov(·) represents the covariance, and Var(·) represents the variance.

[0073] The formula for calculating the statistical coefficient U1 is:

[0074]

[0075] The formula for calculating the statistical coefficient U² is:

[0076]

[0077] in, Corresponding to gray models And the original matrix sequence and the model restored value matrix sequence in all the comparison models.

[0078] Furthermore, in step S7, with the objective of minimizing the average relative error, considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established:

[0079]

[0080]

[0081]

[0082] The optimization model was optimized using the particle swarm optimization algorithm to obtain the optimal fractional order r, the parameters ω and d in the sine function, and the parameters α and α1 in the exponential function.

[0083] Furthermore, in step S8, the optimal parameters are substituted into... The model calculates various indicators and compares them with the indicator values ​​of the comparison models. If the error range is met and the correlation coefficient R value of the new model is higher than that of all comparison models, and other indicators are lower than those of all comparison models, then the new model is applied to energy production forecasting; otherwise, the particle swarm optimization algorithm is used to find the optimal parameters.

[0084] The beneficial effects of this invention are as follows:

[0085] This invention innovates upon traditional gray-based prediction models by constructing a gray-based prediction model based on fractional-order accumulation operators and fractional-order derivative operators, and by building a gray action with a combination of exponential and sine function terms. The introduction of exponential and trigonometric functions gives the model's time response function oscillatory characteristics, enabling it to accurately capture and effectively map data volatility, significantly improving the model's adaptability and flexibility. Furthermore, to further enhance the model's predictive performance, fractional-order derivatives and fractional-order accumulation operators are cleverly integrated into the new model. This not only enriches the model's theoretical framework but also significantly improves prediction accuracy in practical applications, providing robust and reliable tool support for data analysis and prediction in the energy production field.

[0086] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0087] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0088] Figure 1 This is an overall flowchart of an energy production prediction method using a grayish model with fractional derivatives according to the present invention.

[0089] Figure 2 This is a comparison chart of the overall fitting trends of the gray-toned model of this invention and other comparative models;

[0090] Figure 3 This is a comparison chart of the grayish model of the present invention with other comparative models using APE. Detailed Implementation

[0091] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0092] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0093] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0094] Please see Figures 1-3 This is an energy production prediction method using a partial grey model with fractional derivatives.

[0095] This invention provides a method for predicting energy production using a partial grey model with fractional derivatives. For example... Figure 1 As shown, the method specifically includes the following steps:

[0096] S1: Select the current monthly output values ​​of different energy sources as the database to construct the original matrix sequence X. (0) As input to the model;

[0097] S2: Process the original sequence and calculate the r-order cumulative sequence X. (r) The nearest mean generation sequence Z (r) and partial derivative sequence

[0098] S3: Construct a fractional derivative partial differential equation as the model To improve the prediction accuracy of the model, a whitening equation is proposed. A fractional derivative operator and a fractional accumulation operator are introduced into the model, and a gray action combining exponential and sine functions is constructed to describe the oscillation of the data.

[0099] S4: Construct matrices B and Y using the above sequence, and estimate the parameter vector using the least squares method;

[0100] S5: Calculate the simulated value X using both the time-response formula and the cumulative reduction formula. (r) and restoration value X (0) ;

[0101] S6: Computational Model The mean square error, mean absolute percentage error, root mean square percentage error, mean absolute error, correlation coefficient, and statistical coefficients of the six comparative models ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM, and ARIMA are shown in Table 1.

[0102] S7: While ensuring the best prediction results, use the particle swarm optimization algorithm to find the optimal parameters that minimize the MAPE value; substitute the optimal parameters into... The simulation values ​​and MAPE values ​​are calculated in the model;

[0103] S8: If the error range is met and the new model has better prediction performance, that is, the R value of the new model is higher than that of the comparison model, while the values ​​of the other six indicators are lower than those of the comparison model, then the new model can be applied to energy production prediction. Otherwise, continue to use the particle swarm optimization algorithm to find the optimal parameters.

[0104] In step S1 of this embodiment, let X (0) The matrix sequence consists of n m×m matrices constructed from the database, with the current monthly output value of different energy sources as the basis:

[0105] X(0) =(X (0) (1),X (0) (2),…,X (0) (n))

[0106] Where, X (0) (k) (k = 1, 2, ..., n) is an m × m matrix, represented as:

[0107]

[0108] X represents (0) (k) is the value in row i and column j.

[0109] In step S2 of this embodiment, the original sequence is processed, and the r-order cumulative sequence X is calculated. (r) The nearest mean generation sequence Z (r) and partial derivative sequence Specifically, it includes: X (r) (k) is X (0) (k) of r (r∈R) + ) order cumulative generation sequence:

[0110] X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n))

[0111] Where, X (r) (k) (k = 1, 2, ..., n) is an m × m matrix. X represents (r) The value of (k) in row i and column j is as follows:

[0112]

[0113] and:

[0114]

[0115] Where t represents time, Γ(·) represents the gamma function, and X represents (0) (t) is the value in row i and column j.

[0116] The nearest mean generation sequence Z (r) Represented as:

[0117] Z (r) =(Z (r) (2),…,Z (r) (n))

[0118] Among them, Z (r) (k) (k = 2, 3, ..., n) is an m × m matrix. Z represents (r) (k) The value in row i, column j, and Specifically as follows:

[0119]

[0120] The nearest mean generation sequence Z (r) The horizontal and vertical partial derivative sequences Z x (r) and Z y (r) Satisfy the following formula:

[0121]

[0122]

[0123] express The value in row i and column j, express The value in row i and column j.

[0124] In step S3 of this embodiment, The expression is:

[0125]

[0126] Where M = 3m 2 +8, k = 2, 3, ..., n; and its whitening equation is expressed as:

[0127]

[0128] Where (r,α,α1)∈(0,1]a,b,c,ω,d are real constant parameter variables, and t is the value of X. (r) The time variables, x and y, are X (r) The spatial variables, α0, β0, and β1, are m×m constant matrices, as detailed below:

[0129]

[0130] μ 011 ,μ 012 ,…,μ 0mm ,λ 011 ,λ 012 ,…,λ 0mm ,η 111 ,η 112 ,…,η 1mmIt refers to all elements in the matrix α0, β0, β1.

[0131] In step S4 of this embodiment, a matrix is ​​constructed using the above sequence, and the parameter vector is estimated using the least squares method. Specifically, this includes: for Model, least squares parameter estimation vector

[0132]

[0133] satisfy:

[0134] Where matrix B is m 2 (n-1)×(3m 2 A +3) order matrix, which is represented as:

[0135]

[0136] In matrix B, yes The value in row i, column j; and

[0137]

[0138] The constructed matrix Y is m 2 An (n-1)×1 matrix is ​​represented as:

[0139]

[0140] In matrix Y, It is X (r) (k) is the value in row i and column j.

[0141] In step S5 of this embodiment, the gray model The time response is:

[0142]

[0143] in, for Simulated values ​​of the model The value in row i and column j;

[0144] Grey Model The final reduction formula is:

[0145]

[0146] in, for Model restoration value The value at coordinates (i,j).

[0147] In step S6 of this embodiment, the model The formulas for the mean square error, mean absolute percentage error, root mean square percentage error, mean absolute error, correlation coefficient, and statistical coefficients of the six comparative models ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM, and ARIMA are shown in Table 1.

[0148] Table 1

[0149]

[0150]

[0151] The smaller the values ​​of MSE, MAPE, RMSPE, MAE, and U1 and U2, the higher the model accuracy. The closer the R-value is to 1, the better the model performance.

[0152] In step S7 of this embodiment, the particle swarm optimization algorithm is used to find the optimal parameters that minimize the MAPE value while ensuring the best prediction result; the optimal parameters are then substituted into... The process of calculating simulation values ​​and MAPE values ​​in the model is as follows:

[0153] With the objective of minimizing the average relative error, and considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established:

[0154]

[0155]

[0156] The optimization model was optimized using the particle swarm optimization algorithm to obtain the optimal fractional order r, the parameters ω and d in the sine function, and the parameters α and α1 in the exponential function.

[0157] In step S8 of this embodiment, the optimal parameters are substituted into The model calculates various indicators and compares them with the seven indicator values ​​of six comparative models. If the new model meets the error range and its predictive performance is better, it can be applied to energy production forecasting.

[0158] This embodiment applies the model to predict the production of raw coal and gasoline in three Chinese provinces, as well as the production of coalbed methane in Shanxi and natural gas in Qinghai, demonstrating the model's effectiveness from different perspectives. Through comprehensive analysis using seven evaluation indicators, the results show that the model's simulation and prediction accuracy is significantly superior to the other six comparative prediction models, demonstrating the new model's superior ability to predict the production of different regions and types of energy.

[0159] This embodiment compares the prediction model of the present invention with other models. The trend comparison chart of the prediction model of the present invention and other models is shown below. Figure 2 As shown in the comparison chart of APE, Figure 3 As shown. This case study uses coalbed methane (CBM) energy production data from Shanxi Province, sourced from the National Bureau of Statistics (https: / / data.stats.gov.cn / ) for monthly energy production data of various provinces in China. Since data is unavailable for some months, and the lack of data for these months exhibits no regularity, the data is incomplete. This small sample size and incomplete information align with the scope of grey system theory research. Twenty CBM production data points from Shanxi Province for May-December 2021, March-December 2022, and March-April 2023 were selected. A 2×2 matrix was constructed for each four months, resulting in five 2×2 matrix sequences. These matrix sequences were then input into different prediction models for analysis. The CFPGM model was compared with ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM, and ARIMA models. In this embodiment, the ARIMA model structure calculated based on the original data is the ARIMA(1,0,1) model. The optimal parameter vector of the CFFPGM model is (r,α,d,ω,α1)=(0.7388,0.0067,584.7848,431.0233,160.2397), and the optimal parameter vector of the EPGM model is (τ,r1,r2)=(1.0000,1.0000,1.0000). Simulations were performed to compare the seven models. The calculation results of the evaluation indicators for the seven models are shown in Table 2.

[0160] Table 2

[0161]

[0162] As shown in Table 2, the MAPE value of the CFFPGM model is only 1.3992%, while other comparative models all have values ​​greater than 2.5%, and the CFFPGM model also has the best performance across the other six metrics. The maximum value of the evaluation metric R is 1; a higher R value indicates higher model accuracy. The R value of the CFFPGM model is 0.9535, the highest among the comparative models. This demonstrates the effectiveness of the CFFPGM model. Furthermore, Table 2 shows that the traditional statistical method ARIMA and the neural network model LSTM have poor overall simulation performance, while the improved grayscale model CFFPGM outperforms ARIMA and LSTM. This indicates that the grayscale model can not only be applied to situations with large sample sizes, but more importantly, it outperforms time series models and neural network models that typically require large training datasets.

[0163] To more intuitively demonstrate the effectiveness of the CFFPGM model, the above results are visualized. See the model trend comparison chart below. Figure 2 See the APE comparison chart. Figure 3 .like Figure 2 As shown, the new model is closest to the original data and has the highest degree of overlap with the other models, while the other models are farthest from the original data. Figure 3 The APE box plots show that the CFFPGM model has the smallest mean, the shortest box, the most concentrated data, and the least dispersion, followed by the TDGM and ARIMA models. The ARGM, EPGM, NGM, and LSTM models perform relatively poorly. Therefore, the new CFFPGM model has the highest fitting accuracy.

[0164] Secondly, from Figure 2 The trend graph further demonstrates that the FPGM proposed in this invention outperforms other grey prediction models such as ARGM, EPGM, NGM, TDGM, as well as statistical methods and neural networks in predicting non-periodic oscillating data. This fact proves the effectiveness of introducing fractional derivative operators, fractional accumulation operators, exponential function terms, and sinusoidal grey actions into the model. Optimizing the model parameters using the particle swarm optimization algorithm allows the new model to more accurately predict non-monotonic oscillating data.

[0165] In summary, the CFFPGM model processes energy production data in the form of a matrix sequence, increasing the sample size. Furthermore, the exponential and trigonometric function terms in the model effectively capture the trends and oscillations in the data. In addition, the use of fractional-order accumulation operators and fractional-order derivatives can further improve the model's fitting accuracy. This model can accurately provide a method for energy production forecasting, possessing certain theoretical basis and practical value, and has performed well in energy production forecasting tasks in China.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting energy production using a partial grey model with fractional derivatives, characterized in that: The method includes the following steps: S1: Select the current monthly output values ​​of different energy sources as the database to construct the original matrix sequence. ; S2: Based on the original matrix sequence calculate 1st order cumulative sequence Neighboring mean generation sequence and partial derivative sequence ; S3: Construct fractional derivative partial differential equations as a grey model The whitening equation in the gray model We introduce fractional derivative operators and fractional accumulation operators, and construct a grey action combining exponential and sine functions to describe the oscillation of the data. S4: According to 1st order cumulative sequence Neighboring mean generation sequence and partial derivative sequence Construct matrices B and Y, and estimate the grey model using the least squares method. The parameter vector; S5: Calculate the simulated values ​​using both time-response and cumulative reduction formulas. and restoration value ; S6: Calculate the grey model The mean squared error, mean absolute percentage error, root mean square percentage error, mean absolute error, correlation coefficient, and statistical coefficients of several comparative models; S7: While ensuring optimal prediction results, the goal is to minimize the MAPE value. The particle swarm optimization algorithm is used to find the optimal parameters; these optimal parameters are then substituted into the grey model. Calculate the simulation values ​​and MAPE values ​​in the middle; S8: Comparison of Gray Models Compare the prediction results with those of the comparison models. If the prediction results are better than all the comparison models, save the optimal parameters and use them for energy production prediction. Otherwise, continue to use the particle swarm optimization algorithm to find the optimal parameters. In step S3, the gray model for The abbreviation for is expressed as: In the formula, the model Indicates the number of unknown parameters, and Grey model The whitening equation is expressed as: in, , It is a real constant parameter variable. yes The time variable, yes Spatial variables, They are The order constant matrices are represented as follows: In the formula, It is a matrix All elements in; In step S4, firstly, the gray model The least squares parameter estimation vector is represented as: Its satisfaction ,in, This is a matrix constructed based on the aforementioned sequence; Among them, matrix for An dimensional matrix, represented as: In the matrix middle, yes exist OK, The values ​​of the column; and Constructed matrix for An ordinal matrix, represented as: In the matrix middle, yes exist OK The value of the column; In step S5, the gray model The time response is: in, for Simulated values ​​of the model exist OK The value of the column; Grey Model The final reduction formula is: in, for Model restoration value In coordinates The value of .

2. The energy production prediction method using a partial grey model with fractional derivatives as described in claim 1, characterized in that: In step S1, let The database is constructed using the current monthly production value of different energy sources. indivual A matrix sequence composed of two matrices of order: in, yes An ordinal matrix, represented as: express exist OK The values ​​of the column, where, .

3. The energy production prediction method using a partial grey model with fractional derivatives as described in claim 2, characterized in that: In step S2, the original matrix sequence of Accumulation generation sequence Represented as: In the formula, yes 1-th order matrix express exist OK The value of the column, ,in: and, in, Indicates time, Represents the gamma function, and , express exist OK The value of the column; Then the nearest mean generation sequence Represented as: in, yes 1-th order matrix express exist OK, The value of the column, It is represented as: in, ; Neighboring mean generation sequence Horizontal and vertical partial derivative sequences and Satisfy the following formula: express exist OK The value of the column, express exist OK The value of the column, .

4. The energy production prediction method using a partial grey model with fractional derivatives as described in claim 3, characterized in that: In step S6, the comparison models include ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM, and ARIMA models, targeting the grey model. Compared with all the comparison models, we have: The formula for calculating the mean squared error (MSE) is: The formula for calculating the Mean Absolute Percentage Error (MAPE) is as follows: The formula for calculating the root mean square percentage error (RMSPE) is: The formula for calculating the Mean Absolute Error (MAE) is: The formula for calculating the correlation coefficient R is: In the formula, Describing covariance, Indicates variance; The formula for calculating the statistical coefficient U1 is: The formula for calculating the statistical coefficient U² is: in, Corresponding to gray models And the original matrix sequence and the model restored value matrix sequence in all the comparison models.

5. The energy production prediction method using a partial grey model with fractional derivatives as described in claim 4, characterized in that: In step S7, with the objective of minimizing the average relative error, considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established: The optimal fractional order was obtained by optimizing the model using the particle swarm optimization algorithm. Parameters in the sine function and and the parameters in the exponential function and .

6. The energy production prediction method using a partial grey model with fractional derivatives as described in claim 5, characterized in that: In step S8, the optimal parameters are substituted into The model calculates various indicators and compares them with the indicator values ​​of the comparison models. If the error range is met and the correlation coefficient R value of the new model is higher than that of all comparison models, and other indicators are lower than those of all comparison models, then the new model is applied to energy production forecasting; otherwise, the particle swarm optimization algorithm is used to find the optimal parameters.

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