A method, system, and medium for identifying the characteristics of carbon dioxide emission reduction potential curves.

Abstract

A method, device, and medium for identifying the characteristics of carbon dioxide emission reduction potential curves are disclosed. The method includes the following steps: functionalization of the carbon dioxide emission reduction potential curve; correlation analysis of the carbon dioxide emission reduction potential curve; functional principal component analysis of the carbon dioxide emission reduction potential curve; functional cluster analysis of the carbon dioxide emission reduction potential curve; and functional linear regression analysis of the carbon dioxide emission reduction potential curve. This invention provides a method, device, and medium for identifying the characteristics of carbon dioxide emission reduction potential curves at the enterprise, industry, and regional levels, uncovering potential emission reduction capabilities, emission reduction difficulties, and emission reduction characteristics. It technically solves the problem of the difficulty in interpreting the morphological meaning of carbon dioxide emission reduction potential curves.

Description

Technical Field

[0001] This invention relates to the field of new power system construction technology, and in particular to a method, system and medium for identifying carbon dioxide emission reduction potential curve features for new power system construction. Background Technology

[0002] As climate change intensifies, controlling greenhouse gas emissions has become a global issue. Countries around the world are adopting various emission reduction measures to reduce greenhouse gas emissions. The setting of emission reduction targets, the design of emission reduction schemes, and the allocation of emission reduction tasks for an industry or region need to be formulated in combination with the actual characteristics of each industry or region. However, in reality, the true potential and difficulty of carbon emission reduction vary from industry to industry or region to region. How to formulate and implement an effective emission reduction scheme based on the emission reduction potential characteristics of an industry is an important practical problem.

[0003] Existing technical solutions have three main shortcomings. First, the emission reduction potential curve characteristics vary and are correlated across regions and industries. Existing solutions either establish a unified emission reduction potential curve characteristic identification scheme for the entire country or only identify characteristics for a single region or industry. The former ignores the differences between different emission reduction potential curve characteristics, while the latter ignores their correlations. Therefore, this invention provides a unified identification scheme for all regions and industries, taking into account both the differences and correlations in emission reduction potential curve characteristics. The identified emission reduction potential curve characteristics can reflect both the uniqueness of an individual curve and the correlations between different curves.

[0004] Second, the characteristics of carbon dioxide emission reduction potential curves include various types, such as: the changing trend of emission reduction difficulty as emission reduction potential is continuously released, the similarity and heterogeneity between emission reduction potential curves in different industries, and the relationship between emission reduction potential curves and baseline carbon emission intensity. Ignoring any of these characteristics can lead to a significant decrease in the effectiveness of the proposed solution. This invention provides a systematic method for identifying the characteristics of carbon dioxide emission reduction potential curves, comprehensively identifying the characteristics of carbon dioxide emission reduction potential curves in samples.

[0005] Third, the identification of the characteristics of the carbon dioxide emission reduction potential curve is inevitably affected by random factors, which significantly reduces the accuracy of the identification results. This invention uses a functional data analysis method to restore the shape of the emission reduction potential curve as much as possible, reduce noise interference, and deeply identify the characteristics of the carbon dioxide emission reduction potential curve. Summary of the Invention

[0006] The purpose of this invention is to construct a method, system, and medium for identifying the characteristics of carbon dioxide emission reduction potential curves. This method considers both the differences and correlations in the characteristics of emission reduction potential curves, reduces interference from random factors, and comprehensively analyzes the changing trends of emission reduction difficulty for various entities as emission reduction potential is continuously released, the similarities and heterogeneities between emission reduction potential curves in different industries, and the relationship between emission reduction potential curves and baseline carbon emission intensity. A computer device is provided as the physical entity of the carbon dioxide emission reduction potential curve characteristic identification system. A computer-readable storage medium is also provided as the carrier of the required computer program.

[0007] This invention adopts the following technical solution. This invention provides a method for identifying the characteristics of a carbon dioxide emission reduction potential curve, the method comprising the following steps:

[0008] Step 1, Data Acquisition and Preprocessing

[0009] Step 2: Apply B-spline basis function fitting and coarse penalty method to smooth the original carbon dioxide emission reduction potential curve, and construct the function of the carbon dioxide emission reduction potential curve;

[0010] Step 3: Based on the fitted carbon dioxide emission reduction potential curves obtained in Step 2, determine the correlation between emission reduction potential curves of different industries through covariance and Pearson correlation coefficient.

[0011] Step 4: Extract principal components from the functionalized carbon dioxide emission reduction potential curve data, determine the number of principal components, obtain the principal component curves, and calculate the scores of each industrial sector on each principal component.

[0012] Step 5: Based on the principal component scores obtained in Step 4, perform functional clustering on the carbon dioxide emission reduction potential curves;

[0013] Step 6: Using the functionalized carbon dioxide emission reduction potential curve data as the explanatory variable and the carbon emission reduction efficiency index data as the explained variable, construct a functional linear regression model to obtain the correlation between the carbon dioxide emission reduction potential curve and the carbon emission reduction efficiency index.

[0014] Preferably, in step 1, the collected data includes: energy carbon emission data, emission reduction potential data, carbon emission reduction difficulty data, and carbon emission reduction efficiency data;

[0015] Preferably, in step 1, data preprocessing includes: calculation of the original carbon dioxide emission reduction potential curve and interpolation calculation of the original carbon dioxide emission reduction potential curve.

[0016] Preferably, in step 2, the formula for fitting the carbon dioxide emission reduction potential curve using the B-spline basis function is as follows:

[0017]

[0018] In the formula,

[0019] M represents the number of standard basis functions.

[0020] N represents the total number of fitted carbon dioxide emission reduction potential curves.

[0021] 's' represents the range of variation in cumulative emission reduction potential.

[0022] n represents the nth fitted carbon dioxide emission reduction potential curve.

[0023] x n (s) represents the nth fitted carbon dioxide emission reduction potential curve over the range s of cumulative emission reduction potential variation.

[0024] B m (s) represents the function expression of the m-th standard basis function over the range s of cumulative emission reduction potential.

[0025] c nm This represents the coefficient of the m-th standard basis function in the n-th fitted carbon dioxide emission reduction potential curve.

[0026] Preferably, in step 2, a rough penalty method is used to apply the coefficient c. nm The model that minimizes the sum of squares by applying a smoothing penalty is:

[0027]

[0028] In the formula,

[0029] PSS λ (c n1 ,…,c nm ) represents the sum of squared residuals.

[0030] X n (j) represents the true value of the nth carbon dioxide emission reduction potential curve at sample point j.

[0031] x n (j) represents the fitted value of the nth carbon dioxide emission reduction potential curve at sample point j.

[0032] L(x n ) represents a linear differential operator.

[0033] L(x n (s) represents x n The second derivative of (s),

[0034] λ represents the smoothing coefficient.

[0035] Preferably, in step 4, the principal component score expression of the carbon dioxide emission reduction curve is as follows:

[0036] f i =∫β i (s)x i (s)ds,i=1,2,…,,N

[0037] In the formula,

[0038] f i Represents the i-th carbon dioxide emission reduction curve x i Principal component scores,

[0039] β i (s) represents the weighting function of the i-th carbon dioxide emission reduction curve.

[0040] x i (s) represents the i-th fitted carbon dioxide emission reduction curve.

[0041] The weight function β1(s) for calculating the score of the first principal component is given by the following objective and constraints:

[0042]

[0043] Calculate the principal component score of the j-th function, and its weight function β j (s) is obtained by solving for the following objectives and constraints:

[0044]

[0045] In the formula,

[0046] β j (s) represents the weighting function of the j-th carbon dioxide emission reduction curve.

[0047] Preferably, in step 5, the carbon dioxide emission reduction potential curve samples are divided into different clusters based on the shortest Euclidean distance. The clustering method continuously expands and iterates the samples, determining the cluster centers and clustering results during the iterative process. The formula for calculating the clustering target is:

[0048]

[0049] In the formula,

[0050] C j Let j represent the sample set of the j-th class.

[0051] k represents the number of classes.

[0052] X i This indicates that the sample points of the carbon dioxide emission reduction potential curve belong to a subset of a certain class.

[0053] Z j Denotes the cluster center of the j-th class.

[0054] D(X i Z j () represents the distance function, and its calculation formula is:

[0055]

[0056] In the formula,

[0057] w ki The functional principal component score vector represents the sample points of the carbon dioxide emission reduction potential curve.

[0058] w kj This represents the cluster center vector.

[0059] Preferably, in step 6, the expression for the functional linear regression model is as follows:

[0060] Y=α+∫β(s)X(s)ds+ε

[0061] In the formula,

[0062] 'a' represents a constant term.

[0063] ε represents the random error term.

[0064] X(s) represents the carbon dioxide emission reduction potential curve data.

[0065] 's' represents the range of changes in the cumulative emission reduction potential percentage.

[0066] β(s) represents the coefficient function corresponding to the carbon dioxide emission reduction potential curve data.

[0067] Y represents the carbon emission reduction efficiency index.

[0068] Preferably, the least squares method with a penalty term is used to smooth the β(s) data, and the formula for calculating the minimum sum of squared errors is:

[0069]

[0070] In the formula,

[0071] Y represents the true value of the i-th sample point.

[0072] α represents the regression constant term.

[0073] X i (s) represents the carbon dioxide emission reduction potential curve data.

[0074] L(β(s)) denotes a linear differential operator, and L(β(s)) is equal to the second derivative of β(s).

[0075] β(s)=∑c i Bi (s),

[0076] In the formula,

[0077] c i The coefficients of the i-th basis function

[0078] B i (s) represents the standard basis functions.

[0079] A second aspect of the present invention provides a carbon dioxide emission reduction potential curve feature recognition system, and the carbon dioxide emission reduction potential curve feature recognition method is implemented. The recognition system includes: a data acquisition and preprocessing module, a data analysis module, and an output demonstration module.

[0080] The data acquisition and preprocessing module is used for the acquisition and preprocessing of energy carbon emission data, emission reduction potential data, carbon emission reduction difficulty data, and carbon emission reduction efficiency data.

[0081] The data analysis module is used to perform correlation analysis, principal component analysis, cluster analysis, and regression analysis.

[0082] The output demonstration module is used to showcase the characteristics and information contained in the carbon dioxide emission reduction potential curve.

[0083] A third aspect of the invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when executed by a processor, the program implements the steps of the method for identifying the features of a carbon dioxide emission reduction potential curve as claimed in the claims.

[0084] The beneficial effects of this invention are that, compared with the prior art,

[0085] (1) This invention applies functional data analysis methods to feature identification of carbon dioxide emission reduction potential curves. It involves data preprocessing methods such as B-spline fitting and penalty term smoothing, which more scientifically restore the curve shape and reduce noise interference. Functional principal component analysis is used to deeply explore the features of carbon dioxide emission reduction potential curves, and functional clustering and functional regression methods are used to draw conclusions with practical significance.

[0086] (2) This invention uses a quantitative method to analyze the carbon dioxide emission reduction potential curve, and provides a more in-depth analysis of the characteristics of the carbon dioxide emission reduction potential curve data. It is not limited to answering whether the carbon dioxide emission reduction potential curve of different industries has a significant impact on the carbon emission reduction efficiency index, but also analyzes the different impacts of different intervals of the carbon dioxide emission reduction potential curve, and which interval has a greater impact, so as to better help the government formulate reasonable and relevant emission reduction policies.

[0087] (3) This invention provides additional assistance for the design of emission reduction policies. Since there are few existing methods for the characteristic analysis of carbon dioxide emission reduction potential curves, functional data analysis, as an emerging mathematical statistics method, has been introduced into the characteristic identification of carbon dioxide emission reduction potential curves. It systematically performs functional correlation analysis, functional principal component analysis, functional cluster analysis, and functional regression analysis on carbon dioxide emission reduction potential curves, which is innovative in itself and provides theoretical support for the formulation of carbon emission reduction policies in different industrial sectors in my country. Attached Figure Description

[0088] Figure 1 This is a flowchart of a method for identifying the features of a carbon dioxide emission reduction potential curve according to the present invention;

[0089] Figure 2 This is a structural block diagram of a computer device for recognizing carbon dioxide emission reduction potential curve features according to the present invention. Detailed Implementation

[0090] The present application will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be construed as limiting the scope of protection of the present application.

[0091] Embodiment 1 of the present invention provides a method for identifying the features of a carbon dioxide emission reduction potential curve, such as... Figure 1 As shown, it includes the following steps:

[0092] Step 1: Data Collection and Preprocessing. Obtain data on energy carbon emissions, emission reduction potential, carbon emission reduction difficulty, and carbon emission reduction efficiency for the research industry and its affiliated companies.

[0093] Data preprocessing:

[0094] The calculation of the original carbon dioxide emission reduction potential curve involves first mapping the different emission reduction potentials of various enterprises in the same industry to their emission reduction difficulties, arranging them in order of increasing emission reduction difficulty, accumulating the emission reduction potentials of each industry, and interpolating for missing observation points. Based on the accumulated emission reduction potential and emission reduction difficulty data, the original carbon dioxide emission reduction potential curve is plotted.

[0095] To address the issue of inconsistent observation points corresponding to the cumulative emission reduction potential curves across different industries, the observation points in the original carbon dioxide emission reduction potential curves for each industry are interpolated and uniformly mapped to equidistant intervals of 100 or 1000 points. The 1000-point equidistant interval data is used for functional principal component analysis, as its finer granularity better reflects the curve's shape. The 100-point equidistant interval data is used for functional linear regression analysis. Since the regression analysis of the carbon dioxide emission reduction potential curve based on 1000 points takes too long, using 100-point granular data in the regression analysis still effectively reflects the correlation in the regression results.

[0096] Step 2: Functionalization of the carbon dioxide emission reduction potential curve.

[0097] The functionalized calculation of the original carbon dioxide emission reduction potential curve, using B-spline basis function fitting and rough penalty method to smooth the original carbon dioxide emission reduction potential curve, can reduce the impact of observation error and solve the problem of large step phenomenon in the original curve, which makes data analysis difficult. The functionalized carbon dioxide emission reduction potential curve is more likely to extract the changing trend of emission reduction difficulty of each subject as the emission reduction potential is continuously released, the similarity and heterogeneity between emission reduction potential curves of different industries, and the relationship between emission reduction potential curve and baseline carbon emission intensity.

[0098] B-spline basis function fitting combines the convenience and flexibility of polynomial calculation. It can fit the original data more accurately using fewer basis functions, making up for the shortcomings of traditional spline basis function interpolation. This reduces the disturbance caused by observation errors to the feature extraction of carbon dioxide emission reduction potential curves, and is suitable for fitting non-periodic curves such as carbon dioxide emission reduction potential curves.

[0099] The formula for fitting the carbon dioxide emission reduction potential curve using B-spline basis functions is:

[0100]

[0101] In the formula,

[0102] M represents the number of standard basis functions.

[0103] N represents the total number of fitted carbon dioxide emission reduction potential curves.

[0104] 's' represents the range of changes in cumulative emission reduction potential.

[0105] n represents the nth fitted carbon dioxide emission reduction potential curve.

[0106] x n(s) represents the nth fitted carbon dioxide emission reduction potential curve over the range s of cumulative emission reduction potential change.

[0107] B m (s) represents the function expression of the m-th standard basis function over the range s of cumulative emission reduction potential.

[0108] c nm This represents the coefficient of the m-th standard basis function in the n-th fitted carbon dioxide emission reduction potential curve.

[0109] Roughness-penalized smoothing avoids overfitting and preserves the smoothing effect of basis function expansion, better representing various characteristics of the original sample data and maintaining the smoothness of the curve. Roughness smoothing will result in a better fit between the estimated curve and the data, and minimize the sum of squared residuals.

[0110] The rough penalty method is used to apply the coefficient c. nm The model that minimizes the sum of squares by applying a smoothing penalty is:

[0111]

[0112] In the formula,

[0113] PSS λ (c n1 ,…,c nm ) represents the sum of squared residuals.

[0114] X n (j) represents the true value of the nth carbon dioxide emission reduction potential curve at sample point j.

[0115] x n (j) represents the fitted value of the nth carbon dioxide emission reduction potential curve at sample point j.

[0116] L(x n ) represents a linear differential operator.

[0117] L(x n (s) represents x n The second derivative of (s),

[0118] λ represents the smoothing coefficient, the magnitude of which controls the smoothness of the curve. To balance overfitting and oversmoothing, the value of λ is preferably determined using generalized cross-validation.

[0119] Step 3: Based on the fitted carbon dioxide emission reduction potential curve obtained in Step 2, determine the correlation between emission reduction potential curves of different industries through covariance and Pearson correlation coefficient.

[0120] Based on the coefficients of the carbon dioxide emission reduction potential curves of each industry after functionalization, the covariance and Pearson correlation coefficient of the coefficients of different industries are calculated to obtain the changing trend of the emission reduction difficulty of each subject as the emission reduction potential is continuously released, and whether different industries have similar characteristics.

[0121] Step 4: Extraction of principal components of the carbon dioxide emission reduction potential curve.

[0122] The functionalized carbon dioxide emission reduction potential curve data is subjected to functional principal component extraction to determine the number of principal components, obtain the principal component curves, and calculate the scores of each industrial sector on each principal component.

[0123] Functional principal component extraction (PCE) can extract the eigenvalues ​​and eigenvectors of a data matrix to find the direction of greatest data variation. Unlike traditional PCE analysis, it transforms the weight vector β and data variable x into high-dimensional data β(s) and c(s), turning a discrete exponent into a continuous exponent, corresponding to the i-th carbon dioxide emission reduction curve x. i The principal component score expression is:

[0124] f i =∫β i (s)x i (s)ds,i=1,2,…,,N

[0125] In the formula,

[0126] f i Represents the i-th carbon dioxide emission reduction curve x i Principal component scores,

[0127] β i (s) represents the weighting function of the i-th carbon dioxide emission reduction curve.

[0128] x i (s) represents the i-th fitted carbon dioxide emission reduction curve.

[0129] Furthermore, the weighting function β1(s) of the score of the first principal component can be calculated, with the objective and constraints as follows:

[0130]

[0131] The first line defines the objective as maximizing the mean square value, which identifies the most significant direction of change within the function. The square integral constraint on the weight function in the second line is a necessary condition for achieving the objective. Without this constraint, the mean square value can be arbitrarily large.

[0132] Similarly, we can further obtain the principal component score of the j-th function, and its weight function β. j (s) is obtained by solving for the following objectives and constraints:

[0133]

[0134] In the formula,

[0135] β j (s) represents the weighting function of the j-th carbon dioxide emission reduction curve.

[0136] Step 5: Based on the principal component scores obtained in Step 4, perform functional clustering on the carbon dioxide emission reduction potential curves. Since there is no correlation between the principal components, the scores of the first two or more principal components can be used as the expansion dimension to expand all industrial sector carbon dioxide emission reduction potential curve samples into a two-dimensional or higher-dimensional scatter plot, and then cluster them using the K-means clustering method.

[0137] In functional clustering analysis, since there is no correlation between principal components, the K-means method is used for clustering after expanding the principal component scores. The clustering is based on the shortest Euclidean distance, assigning samples to different clusters. This clustering method requires continuous expansion and iteration of the samples, determining cluster centers and clustering results during the iterative process. The formula for calculating the clustering objective is:

[0138]

[0139] In the formula,

[0140] C j Let j represent the sample set of the j-th class.

[0141] k represents the number of classes.

[0142] X i This indicates that the sample points of the carbon dioxide emission reduction potential curve belong to a subset of a certain class.

[0143] Z j Denotes the cluster center of the j-th class.

[0144] D(X i Z j () represents the distance function, and its calculation formula is:

[0145]

[0146] In the formula,

[0147] w ki The functional principal component score vector represents the sample points of the carbon dioxide emission reduction potential curve.

[0148] w kj This represents the cluster center vector.

[0149] Step 6: Functional linear regression analysis of the carbon dioxide emission reduction potential curve. Using the coefficients of the functionalized carbon dioxide emission reduction potential curve obtained in Step 3 as explanatory variables and the carbon emission reduction efficiency index data as the explained variable, a functional linear regression model is constructed to explore the correlation between the carbon dioxide emission reduction potential curve and the carbon emission reduction efficiency index.

[0150] In functional linear regression, the explanatory variable is the carbon dioxide emission reduction potential curve data, which is functional data; the explained variable is the carbon emission reduction efficiency index, which is scalar data. The regression expression is as follows:

[0151] Y=a+∫β(s)X(s)ds+ε

[0152] In the formula,

[0153] 'a' represents a constant term.

[0154] ε represents the random error term.

[0155] X(s) represents the carbon dioxide emission reduction potential curve data.

[0156] 's' represents the range of changes in the cumulative emission reduction potential percentage.

[0157] β(s) represents the coefficient function corresponding to the carbon dioxide emission reduction potential curve data.

[0158] Y represents the carbon emission reduction efficiency index.

[0159] The purpose of regression analysis is to estimate β(s). However, since the trend of functional data β(s) is complex and difficult to interpret, the least squares method with a penalized term is used to smooth the β(s) data to reveal the main changing characteristics of the β(s) coefficient. The formula for calculating the minimum sum of squared errors is as follows:

[0160]

[0161] In the formula,

[0162] Y i This represents the true value of the i-th sample point.

[0163] α represents the regression constant term.

[0164] X i (s) represents the carbon dioxide emission reduction potential curve data for the ... sample point.

[0165] L(β(s)) denotes a linear differential operator, and L(β(s)) is equal to the second derivative of β(s).

[0166] β(s)=∑c i B i (s),

[0167] In the formula,

[0168] c i The coefficients of the i-th basis function

[0169] B i (s) represents the standard basis functions.

[0170] Its coefficients are still a linear combination of basis functions. The addition of the linear differential operator makes the calculation of the minimum error sum of squares take into account the magnitude of the second derivative of β(s), so that the second derivative of β(s) is as small as possible in the final calculation. The second derivative represents the acceleration of the curve. The smaller the acceleration, the smoother the curve, thus achieving the purpose of smoothing the coefficient function β(s).

[0171] The aforementioned functional data analysis method treats a curve as a whole, with each curve representing only a "sample point." Using this as the basis for analysis, it maps infinite-dimensional functions to finite-dimensional functions, transforming difficult-to-analyze data changes into analyzable specific features.

[0172] This method eliminates the interference of random factors, transforms the chaotic raw data into functional data that can be used for analysis, and then explores the correlation between the shape characteristics of the emission reduction potential cost curve and the carbon intensity growth rate in the industry. It analyzes the magnitude and significance of the impact of different parts of the emission reduction potential curve on the carbon intensity growth rate, and further analyzes the impact mechanism and possible reasons of the emission reduction potential curve on the carbon intensity growth rate.

[0173] Embodiment 2 of the present invention also provides a carbon dioxide emission reduction potential curve feature recognition system, which runs the carbon dioxide emission reduction potential curve feature recognition method. The recognition system includes: a data acquisition and preprocessing module, a data analysis module, and an output demonstration module.

[0174] The data acquisition and preprocessing module is used for the acquisition and preprocessing of energy carbon emission data, emission reduction potential data, carbon emission reduction difficulty data, and carbon emission reduction efficiency data.

[0175] The data analysis module is used to perform correlation analysis, principal component analysis, cluster analysis, and regression analysis.

[0176] The output demonstration module is used to showcase the characteristics and information contained in the carbon dioxide emission reduction potential curve.

[0177] Embodiment 3 of the present invention also provides a computer device for identifying carbon dioxide emission reduction potential curve features, comprising: a processor, a memory, and computer programs and data stored in the memory for identifying carbon dioxide emission reduction potential curve features. Wherein:

[0178] Figure 2This is a structural block diagram of a computer device for identifying carbon dioxide emission reduction potential curve features according to the present invention. Before program execution, collected external data must be stored in the memory. An external source issues an instruction to the processor to begin identifying carbon dioxide emission reduction potential curve features; after determining the instruction type, the processor requests a call from the memory; the memory retrieves the corresponding computer program and data according to the instruction and provides it to the processor; the processor runs the computer program provided by the memory and outputs the results externally. The processor can call the computer program and data in the memory to perform the following methods: functionalization of carbon dioxide emission reduction potential curves; correlation analysis of carbon dioxide emission reduction potential curves; functional principal component analysis of carbon dioxide emission reduction potential curves; functional cluster analysis of carbon dioxide emission reduction potential curves; and functional linear regression analysis of carbon dioxide emission reduction potential curves.

[0179] Embodiment 4 of the present invention also provides a computer-readable storage medium for identifying carbon dioxide emission reduction potential curve features. The computer-readable storage medium stores a computer program, which, when executed by a processor, can implement the carbon dioxide emission reduction potential curve feature identification method in Embodiment 1.

[0180] Compared with traditional multivariate statistical analysis methods, this invention has many advantages:

[0181] (1) The analytical model has fewer prior assumptions and is more applicable, suitable for curves with cumulative emission reduction potential as the horizontal axis, such as the carbon dioxide emission reduction potential curve.

[0182] (2) The observation data need not be at equally spaced observation points, and different samples do not need to have the same number of observations. However, the carbon dioxide emission reduction potential curves of different industries often have inconsistent observation points, which reduces the limitation of being unable to analyze and compare due to inconsistent observation points.

[0183] (3) Functional data analysis can not only explore the characteristics of the original data itself, but also estimate the first derivative or higher derivative of the data to explore the more in-depth changes in the data.

[0184] (4) Smoothing the original data using functional data analysis methods can, to some extent, correct the observation errors in the observed data. Some industries' original carbon dioxide emission reduction potential curves exhibit obvious step phenomena. Smoothing the emission reduction potential curves by smoothing the curves can provide a more scientific analysis of the curve's morphological characteristics.

[0185] (5) The original data is fitted into a carbon dioxide emission reduction potential curve by the basis function expansion method, and the changing trend of emission reduction difficulty as emission reduction potential is continuously released, the similarity and heterogeneity between emission reduction potential curves of different industries, and the relationship between emission reduction potential curve and benchmark carbon emission intensity are captured.

[0186] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0187] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0188] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0189] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0190] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0191] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0192] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0193] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for identifying the characteristics of a carbon dioxide emission reduction potential curve, characterized in that, The method includes the following steps: Step 1, data collection and preprocessing. The collected data includes: energy carbon emissions data, emission reduction potential data, carbon emission reduction difficulty data, and carbon emission reduction efficiency data. Step 2: Apply B-spline basis function fitting and coarse penalty method to smooth the original carbon dioxide emission reduction potential curve, and construct the function of the carbon dioxide emission reduction potential curve; The formula for fitting the carbon dioxide emission reduction potential curve using B-spline basis functions is as follows: In the formula, M represents the number of standard basis functions, N represents the total number of fitted carbon dioxide emission reduction potential curves, s represents the range of cumulative emission reduction potential, n represents the nth fitted carbon dioxide emission reduction potential curve, and x n (s) represents the nth fitted carbon dioxide emission reduction potential curve over the cumulative emission reduction potential range s, B m (s) represents the function of the m-th standard basis function over the range s of cumulative emission reduction potential, c nm This represents the coefficient of the m-th standard basis function in the n-th fitted carbon dioxide emission reduction potential curve; The rough penalty method is used to apply the coefficient c. nm The model that minimizes the sum of squares by applying a smoothing penalty is: In the formula, PSS λ (c n1 ,…,c nm X represents the sum of squared residuals. n (j) represents the true value of the nth carbon dioxide emission reduction potential curve at sample point j, x n (j) represents the fitted value of the nth carbon dioxide emission reduction potential curve at sample point j, L(x n (s) represents x n The second derivative of (s), where λ represents the smoothing coefficient; Step 3: Based on the fitted carbon dioxide emission reduction potential curves obtained in Step 2, determine the correlation between emission reduction potential curves of different industries through covariance and Pearson correlation coefficient. Step 4: Extract principal components from the functionalized carbon dioxide emission reduction potential curve data, determine the number of principal components, obtain the principal component curves, and calculate the scores of each industrial sector on each principal component. The principal component score expression for the carbon dioxide emission reduction curve is shown below: f i =∫β i (s)x i (s)ds,i=1,2,…,N In the formula, f i Represents the i-th carbon dioxide emission reduction curve x i Principal component score, β i (s) represents the weighting function of the i-th carbon dioxide emission reduction curve, x i (s) represents the i-th fitted carbon dioxide emission reduction curve, and the weight function β1(s) is used to calculate the score of the first principal component. Its objective and constraints are as follows: Calculate the principal component score of the j-th function, and its weight function β j (s) is obtained by solving for the following objectives and constraints: In the formula, β j (s) represents the weighting function of the j-th carbon dioxide emission reduction curve; Step 5: Based on the principal component scores obtained in Step 4, perform functional clustering on the carbon dioxide emission reduction potential curves; Based on the shortest Euclidean distance, the carbon dioxide emission reduction potential curve samples are divided into different clusters. The clustering method continuously expands and iterates the samples, determining the cluster centers and clustering results during the iterative process. The formula for calculating the clustering objective is as follows: In the formula, C j Let X represent the sample set of class j, K represent the number of classes, and X represent the sample set of class j. i Z represents a subset of the sample points of the carbon dioxide emission reduction potential curve within a certain class. j Let D(X) represent the cluster center of the j-th class. i Z j () represents the distance function, and its calculation formula is: In the formula, w ki w represents the functional principal component score vector of the sample points of the carbon dioxide emission reduction potential curve. kj Represents the cluster center vector; Step 6: Using the functionalized carbon dioxide emission reduction potential curve data as the explanatory variable and the carbon emission reduction efficiency index data as the explained variable, construct a functional linear regression model to obtain the correlation between the carbon dioxide emission reduction potential curve and the carbon emission reduction efficiency index.

2. The method for identifying the characteristics of a carbon dioxide emission reduction potential curve according to claim 1, characterized in that: In step 1, data preprocessing includes: calculation of the original carbon dioxide emission reduction potential curve and interpolation calculation of the original carbon dioxide emission reduction potential curve.

3. The method for identifying the characteristics of a carbon dioxide emission reduction potential curve according to claim 1, characterized in that: In step 6, the expression for the functional linear regression model is as follows: Y=a+∫β(s)X(s)ds+ε In the formula, 'a' represents a constant term. ε represents the random error term. X(s) represents the carbon dioxide emission reduction potential curve data. 's' represents the range of changes in the cumulative emission reduction potential percentage. β(s) represents the coefficient function corresponding to the carbon dioxide emission reduction potential curve data. Y represents the carbon emission reduction efficiency index.

4. The method for identifying the characteristics of a carbon dioxide emission reduction potential curve according to claim 3, characterized in that: The formula for calculating the minimum sum of squared errors when smoothing β(s) data using the least squares method with a penalty term is: In the formula, Y i This represents the true value of the i-th sample point. α represents the regression constant term. X i (s) represents the carbon dioxide emission reduction potential curve data. L(β(s)) represents the second derivative of β(s). β(s)=∑c i B i (s), In the formula, c i The coefficients of the i-th basis function B i (s) represents the standard basis functions.

5. A carbon dioxide emission reduction potential curve feature identification system, operating the carbon dioxide emission reduction potential curve feature identification method as described in any one of claims 1 to 4, wherein the identification system comprises: The data acquisition and preprocessing module, the data analysis module, and the output demonstration module are characterized by: The data acquisition and preprocessing module is used for the acquisition and preprocessing of energy carbon emission data, emission reduction potential data, carbon emission reduction difficulty data, and carbon emission reduction efficiency data. The data analysis module is used to perform correlation analysis, principal component analysis, cluster analysis, and regression analysis. The output demonstration module is used to showcase the characteristics and information contained in the carbon dioxide emission reduction potential curve.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the carbon dioxide emission reduction potential curve feature identification method according to any one of claims 1-4.

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