Regional carbon emission factor calculation method based on ARIMA-PCA-grey correlation analysis

Abstract

The invention relates to a regional carbon emission factor calculation method based on ARIMA-PCA-grey correlation analysis, and the method comprises the steps: collecting the power production and consumption data of a target region, and carrying out the preprocessing; then, performing trend prediction on the preprocessed historical data by using an ARIMA model to obtain prediction data of power production and consumption data at a future moment; combining the preprocessed historical data with the predicted data to construct a data set, processing the data in the data set by using a PCA technology, and extracting a plurality of principal components which have the greatest influence on the carbon emission factor; then, a grey correlation analysis method is adopted to distribute weights for all principal components; finally, the carbon emission factors of the target area are calculated according to the principal components and the corresponding weights, and the method can improve the calculation precision, reduce the data processing difficulty and achieve refined management of the carbon emission factors.

Description

Technical Field

[0001] The invention relates to a method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis, and belongs to the field of environmental protection and energy management. Background Art

[0002] With the continued impact of global climate change, promoting the transformation of the economy and society towards a low-carbon direction has become a common goal of the international community. As an important indicator for measuring energy efficiency and environmental protection effectiveness, the accurate calculation of the carbon emission factor is crucial for guiding energy conservation and emission reduction measures. However, existing calculation methods are often limited to a single data source or an overly macroscopic perspective, making it difficult to adapt to the complex and changing situations in the field of electricity production and consumption, especially when the amount of data is large and the dimensions are numerous. Traditional methods have certain limitations. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the carbon emission factor calculation method in the prior art is difficult to adapt to the complex and changeable situations in the field of electricity production and consumption, and to provide a regional carbon emission factor calculation method based on ARIMA-PCA-grey correlation analysis.

[0004] In order to achieve the above object, the technical solution proposed by the present invention is: a method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis, comprising:

[0005] Step 1: Collect and pre-process the electricity production and consumption data of the target area;

[0006] Step 2: Use the ARIMA model to perform trend forecasting on the preprocessed historical data to obtain forecast data of power production and consumption data at future times;

[0007] Step 3: Combine the preprocessed historical data and forecast data to construct a data set, use PCA technology to process the data in the data set, and extract several principal components that have the greatest impact on carbon emission factors;

[0008] Step 4: Use grey correlation analysis to assign weights to each principal component;

[0009] Step 5: Calculate the carbon emission factor of the target area based on the principal components and the corresponding weights.

[0010] The above technical solution is further designed as follows: in step 1, the preprocessing of the electricity production and consumption data includes removing missing values, detecting outliers and standardizing.

[0011] In step 2, the data at the future moment is predicted using the ARIMA model as follows:

[0012]

[0013] in, is the predicted value at the future time point T+1, y T ,y T-1 ,…,y T-p+1 is the most recent p historical data points ∈ T ,∈ T-1 ,…,∈ T-q+1 are the most recent q error terms.

[0014] In step 2, the accuracy of the prediction results is evaluated using the mean square error of the predicted data:

[0015]

[0016] Where N is the number of steps to predict, y t is the actual value, is the predicted value.

[0017] In step 3, the process of extracting the main component specifically includes:

[0018] The data in the data set is standardized and then the covariance matrix is ​​calculated for the standardized data set:

[0019]

[0020] Where X is the standardized data matrix, is the mean of the data matrix;

[0021] Solve the eigenvalue λ and corresponding eigenvector v of the covariance matrix C;

[0022] Arrange the eigenvalues ​​in descending order and select the eigenvectors corresponding to the first k eigenvalues ​​as the principal components;

[0023] Compute the principal component score matrix for the principal components:

[0024]

[0025] Among them, V k is the matrix of the first k eigenvectors, and Z is the principal component score matrix.

[0026] The k-value selection method is to set a threshold so that the cumulative contribution rate of k eigenvalues ​​reaches the threshold;

[0027]

[0028] Where n is the total number of eigenvalues.

[0029] The threshold is 80%.

[0030] In step 4, allocating weights to each principal component specifically includes:

[0031] Non-dimensionalize the k principal components;

[0032]

[0033] Among them, x ij is the jth principal component value of the ith data sample, min(x j ) and max(x j ) are the minimum and maximum values ​​of the jth principal component respectively;

[0034] Calculate the correlation coefficient between each sample and the reference sequence:

[0035]

[0036] Where m is the number of data samples and δ is the resolution coefficient;

[0037] Calculate the correlation of each principal component:

[0038]

[0039] Among them, γ ij is the correlation between the jth principal component and the reference sequence;

[0040] Assign weights based on the degree of association:

[0041]

[0042] Among them, w j is the weight of the jth principal component.

[0043] The best values ​​of the principal component values ​​corresponding to the k principal components are selected as the reference sequence.

[0044] The carbon emission factor in step 5 is:

[0045]

[0046] Among them, CE n is the carbon emission factor of region n, w j is the weight of the jth principal component, z nj is the jth principal component score of region n.

[0047] The beneficial effects of the present invention are:

[0048] The method of the present invention uses the ARIMA model to predict the trend of electricity production and consumption data, and uses the PCA dimensionality reduction technology to extract the main influencing factors, then uses the grey correlation analysis method to determine the importance weights of each influencing factor, and finally calculates the carbon emission factors of various cities through a comprehensive model, thereby improving the calculation accuracy, reducing the difficulty of data processing, and realizing the refined management of carbon emission factors. It can adapt to the complex and changeable situations in the field of electricity production and consumption, provide a scientific basis for carbon emission management in various regions, and provide important technical support for promoting the low-carbon transformation of energy consumption and achieving sustainable development. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0050] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Embodiment 1

[0052] The carbon emission factor calculation method of this embodiment includes the following steps:

[0053] Step 1: Collect and pre-process the electricity production and consumption data of the target area;

[0054] Step 2: Use the ARIMA model to perform trend forecasting on the preprocessed historical data to obtain forecast data of power production and consumption data at future times;

[0055] Step 3: Combine the preprocessed historical data and forecast data to construct a data set, use PCA technology to process the data in the data set, and extract several principal components that have the greatest impact on carbon emission factors;

[0056] Step 4: Use grey correlation analysis to assign weights to each principal component;

[0057] Step 5: Calculate the carbon emission factor of the target area based on the principal components and the corresponding weights.

[0058] Embodiment 2

[0059] This embodiment is further designed on the basis of the first embodiment. Figure 1 As shown, specifically:

[0060] Step 1: Collect electricity production and consumption data in various parts of the target area in time series and pre-process the data to ensure data quality.

[0061] Electricity production data includes power generation data of each power plant, power generation data of different types of power generation methods (such as thermal power, hydropower, wind power, solar power, etc.) and carbon emission data of power plants.

[0062] Electricity consumption data include electricity consumption data for various cities, electricity consumption data for different industries (such as industry, commerce, and residents), and time distribution data of electricity consumption (such as hours, days, weeks, months, etc.).

[0063] The electricity production data includes carbon emission data, such as the carbon emission factors of power plants and emission factor data of regional power grids.

[0064] The data preprocessing is as follows:

[0065] (1) Remove missing values ​​and delete data points with missing values;

[0066] D={(x i ,y i )|x i and y i have no missing values}

[0067] (2) Use the Z-score method to detect outliers;

[0068]

[0069] ∣z i ∣≤3, it is determined that there are no outliers;

[0070] (3) The data are standardized and converted into a standard normal distribution with a mean of 0 and a variance of 1.

[0071]

[0072] in, is the sample mean, and s is the sample standard deviation.

[0073] Combine data from different sources into one unified dataset.

[0074] D={(x 1 ,y 1 ),(x 2 ,y 2 ),…,(x n ,y n )}

[0075] Among them, x i represents the feature vector of the i-th observation, y i represents the target variable for the ith observation.

[0076] In the data set, each observation point (i.e., each sample) contains input variables (feature vectors) and output variables (target variables).

[0077] The feature vector is a set of input variables that describe the observation points (samples). In this embodiment, the feature vector generally includes various indicators related to electricity production and consumption, such as: total electricity production, industrial electricity consumption, residential electricity consumption, commercial electricity consumption, and other factors that may affect carbon emissions (such as weather conditions, economic activity levels, etc.);

[0078] Assuming there are n observation points and each observation point has p characteristic variables, the characteristic vector of the i-th observation can be expressed as:

[0079] x i =(x i1 ,x i2 ,…,x ip )x i =(x i1 ,x i2 ,…,x ip )

[0080] Among them, x ij Represents the value of the jth characteristic variable at the i-th observation point.

[0081] The target variable is the output variable of each observation point, that is, the variable that is expected to be predicted or calculated. In this embodiment, the target variable is the carbon emission factor. Assuming there are n observation points, the target variable of the i-th observation can be expressed as: y i

[0082] Among them, y i Represents the carbon emission factor of the ith observation point.

[0083] Step 2: Use the ARIMA model to predict the trend of the preprocessed historical data. Specifically:

[0084] Use the trained model to make predictions about future data:

[0085]

[0086] in, is the predicted value at the future time point T+1, y T ,y T-1 ,…,y T-p+1 is the most recent p historical data points ∈ T ,∈ T-1 ,…,∈ T-q+1 are the most recent q error terms.

[0087] Evaluate the prediction results: Use mean square error (MSE) or other evaluation indicators to evaluate the accuracy of the prediction results. In this embodiment, mean square error is used for evaluation:

[0088]

[0089] Where N is the number of steps to predict, y t is the actual value, is the predicted value.

[0090] This embodiment uses the ARIMA model to perform trend forecasting on preprocessed historical data, which can provide forecast values ​​of power production and consumption data in the future. These forecast values ​​can be used as part of the basic data for subsequent calculation of carbon emission factors, ensuring the accuracy and reliability of input data. And trend forecasting through the ARIMA model can eliminate random fluctuations and noise in the data, making the data smoother, thereby improving the accuracy of subsequent analysis.

[0091] The ARIMA model is established as follows:

[0092] For time series data y t Build an autoregressive model;

[0093] y t =c+φ 1 y t-1 +φ 2 y t-2 +…+φ p y t-p +∈ t

[0094] Among them, φ i is the autoregressive coefficient, p is the autoregressive order, ∈ t is the error term. Through the autoregressive model, the lag term characteristics of the time series are obtained.

[0095] Differencing the time series to make it stationary;

[0096] Δ d y t =y t -y t-d

[0097] Where d is the difference order. d = 1 or d = 2 can make the series stable. Through difference processing, the trend characteristics of the time series are obtained.

[0098] Establish a moving average model for the differenced sequence;

[0099] ∈ t =θ 1 ∈ t-1 +θ 2 ∈ t-2 +…+θ q ∈ t-q +η t

[0100] Among them, θ i is the moving average coefficient, q is the moving average order, η t is the new error term. Through the moving average model, the random fluctuation characteristics of the time series are obtained.

[0101] The maximum likelihood estimation (MLE) method is used to estimate the model parameters, so that the probability of the observed sample data is maximized, ensuring the reliability and effectiveness of the model;

[0102]

[0103] in, and are the estimates of the autoregressive coefficient and the moving average coefficient, respectively.

[0104] The best model was selected using the AIC criterion, ensuring the simplicity and generalization ability of the model;

[0105]

[0106] Where k is the number of model parameters, n is the number of samples, is the value of the maximum likelihood function.

[0107] Step 3: Use PCA dimensionality reduction technology to remove redundant information in the data set and extract the principal components that have the greatest impact on carbon emission factors; it is used to reduce the dimension of the data while retaining most of the information in the data.

[0108] Specifically, the predicted data is merged into the data set and standardized, and the covariance matrix is ​​calculated based on the standardized data.

[0109]

[0110] Where X is the standardized data matrix, is the mean of the data matrix.

[0111] Solve for the eigenvalues ​​λ and eigenvectors v of the covariance matrix C.

[0112] Given a covariance matrix C, its eigenvalues ​​and eigenvectors can be obtained by solving the following eigenvalue problem:

[0113] (1) Define eigenvalues;

[0114] Find the eigenvalue λ and the corresponding eigenvector v by solving the following system of equations:

[0115] Cv=λv

[0116] Where: C is the covariance matrix, v is the eigenvector, and λ is the corresponding eigenvalue.

[0117] (2) Rewrite the equation;

[0118] Cv-λv=0, that is: (C-λI)v=0

[0119] Where I is the identity matrix

[0120] (3) Non-zero solution conditions;

[0121] det(C-λI)=0

[0122] For the above equation to have a non-zero solution v, the determinant condition must be satisfied:

[0123] (4) Solving the eigenvalues;

[0124] Calculating det(C-λI) and setting it equal to zero gives a polynomial equation, called the characteristic polynomial. Solving this polynomial equation gives the eigenvalue λ.

[0125] (5) Solve the eigenvector;

[0126] For each eigenvalue λ, substitute it back into the original equation (C-λI)v=0, and then solve the homogeneous linear system of equations. There will usually be one free variable, so the eigenvectors v are not unique, but they are all proportional.

[0127] Arrange the obtained eigenvalues ​​in descending order, select the first k eigenvectors with larger eigenvalues ​​as principal components, and calculate the principal component scores;

[0128]

[0129] Among them, V k is the matrix of the first k eigenvectors, and Z is the principal component score matrix.

[0130] The principal component score matrix Z represents the projection of the data in the principal component space and the score of each observation in the principal component space. These scores retain the main variation information of the data and are helpful for subsequent analysis and modeling.

[0131] In this embodiment, the k value is selected by calculating the cumulative contribution rate of the first k principal components so that the cumulative contribution rate reaches a threshold value (such as 80%);

[0132]

[0133] Selecting appropriate principal components retains the principal components that have the greatest impact on the data variation.

[0134] Step 4: Use grey correlation analysis to determine the importance weight of each principal component, specifically:

[0135] Non-dimensionalize the k principal components;

[0136]

[0137] Among them, x ij is the jth principal component value of the ith data sample, min(x j ) and max(x j ) are the minimum and maximum values ​​of the jth principal component, respectively.

[0138] The principal component values ​​are new eigenvalues ​​extracted from the original data by the principal component analysis (PCA) algorithm. These principal components are a linear transformation of the original data. They are arranged in order. The first principal component contains the most information about the original data changes, the second principal component contains the second most information about the changes, and so on. ij It refers to the projection value of the i-th data sample on the j-th principal component or the coordinate value in this new feature space.

[0139] Calculate the correlation coefficient between each principal component and the reference sequence (ideal state);

[0140]

[0141] In grey relational analysis, the reference sequence usually refers to an ideal or expected state, which is used to compare with other sample sequences to determine the degree of similarity between each sample and the ideal state. The reference sequence can be selected by the following methods:

[0142] The best value (i.e., optimal state) of the principal component value corresponding to each principal component is selected as the reference sequence. For example, if the goal is to minimize carbon emissions, the minimum value of each variable can be used as the corresponding value of the reference sequence. Suppose there are m samples, each with n variables, denoted by x ij (where i = 1, 2, ..., m represents a sample and j = 1, 2, ..., n represents a variable). Reference sequence x 0 It can be defined as:

[0143] x 0 =(min(x 11 ,c 21 ,…,c m1 ),min(x 12 ,x 22 ,…,x m2 ),…,min(x 1n ,x 2n ,…,x mn ))

[0144] Where m is the number of data points and δ is the resolution factor (usually 0.5).

[0145] Calculate the correlation between each principal component and the reference sequence;

[0146]

[0147] Among them, γ ij is the correlation between the jth principal component and the reference sequence.

[0148] Assign weights based on the degree of association;

[0149]

[0150] Among them, w j is the weight of the jth principal component.

[0151] The weight of each principal component is determined by the ratio of its correlation to the total correlation of all principal components in which it is located. This can highlight the role of principal components with higher correlation with the reference sequence, while weakening the influence of principal components with lower correlation.

[0152] Step 5: Construct a comprehensive model to calculate the carbon emission factors of cities, specifically:

[0153] Integrate the principal component scores obtained by PCA dimension reduction in step 3 and the weights obtained by grey relational analysis in step 4;

[0154] D integrated ={(z 1 ,w 1 ),(z 2 ,w 2 ),…,(z n ,w n )}

[0155] Among them, z i is the principal component score after PCA dimensionality reduction, w i It is the weight obtained through grey relational analysis.

[0156] The principal component scores are combined with the weights to calculate the carbon emission factors for each region;

[0157]

[0158] Among them, CE n is the carbon emission factor of region n, w j is the weight of the jth principal component, z nj is the j-th principal component score of region n.

[0159] This embodiment can also use historical data to train the above carbon emission factor calculation model, and calibrate the model through a cross-validation method to ensure the accuracy and stability of the model.

[0160] The technical solutions of the present invention are not limited to the above-mentioned embodiments, and any technical solutions obtained by equivalent replacement methods fall within the scope of protection required by the present invention.

Claims

1. A method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis, characterized in that: include: Step 1: Collect and pre-process the electricity production and consumption data of the target area; Step 2: Use the ARIMA model to perform trend forecasting on the preprocessed historical data to obtain forecast data of power production and consumption data at future times; Step 3: Combine the preprocessed historical data and forecast data to construct a data set, use PCA technology to process the data in the data set, and extract several principal components that have the greatest impact on carbon emission factors; Step 4: Use grey correlation analysis to assign weights to each principal component; Step 5: Calculate the carbon emission factor of the target area based on the principal components and the corresponding weights.

2. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 1, characterized in that: In step 1, preprocessing of the electricity production and consumption data includes removing missing values, detecting outliers and standardizing.

3. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 2 is characterized in that: In step 2, the data at the future moment is predicted using the ARIMA model as follows: in, is the predicted value at the future time point T+1, y T ,y T-1 ,…,y T-p+1 is the most recent p historical data points ∈ T ,∈ T-1 ,…,∈ T-q+1 are the most recent q error terms.

4. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 3 is characterized in that: In step 2, the accuracy of the prediction results is evaluated using the mean square error of the predicted data: Where N is the number of steps to predict, y t is the actual value, is the predicted value.

5. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 4 is characterized in that: In step 3, the process of extracting the main component specifically includes: The data in the data set is standardized and then the covariance matrix is ​​calculated for the standardized data set: Where X is the standardized data matrix, is the mean of the data matrix; Solve the eigenvalue λ and corresponding eigenvector v of the covariance matrix C; Arrange the eigenvalues ​​in descending order and select the eigenvectors corresponding to the first k eigenvalues ​​as the principal components; Compute the principal component score matrix for the principal components: Among them, V k is the matrix of the first k eigenvectors, and Z is the principal component score matrix.

6. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 5 is characterized in that: The k-value selection method is to set a threshold so that the cumulative contribution rate of k eigenvalues ​​reaches the threshold; Where n is the total number of eigenvalues.

7. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 6, characterized in that: The threshold is 80%.

8. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 7 is characterized in that: In step 4, allocating weights to each principal component specifically includes: The k principal components are dimensionless; Among them, x ij is the jth principal component value of the ith data sample, min(x j ) and max(x j ) are the minimum and maximum values ​​of the jth principal component respectively; Calculate the correlation coefficient between each sample and the reference sequence: Where m is the number of data samples and δ is the resolution coefficient; Calculate the correlation of each principal component: Among them, γ ij is the correlation between the jth principal component and the reference sequence; Assign weights based on the degree of association: Among them, w j is the weight of the jth principal component.

9. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 8, characterized in that: The best values ​​of the principal component values ​​corresponding to the k principal components are selected as the reference sequence.

10. The method for calculating regional carbon emission factors based on ARIMA-PCA-grey correlation analysis according to claim 9, characterized in that: The carbon emission factor in step 5 is: Among them, CE n is the carbon emission factor of region n, w j is the weight of the jth principal component, z nj is the jth principal component score of region n.

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