Novel fractional time-delay multivariable grey model for carbon emission prediction

Abstract

The invention discloses a fractional time-delay multivariable grey model for carbon emission prediction, and belongs to the field of grey prediction models. The model comprises the following steps: S1, collecting dependent variable data and related influence factor data; s2, preprocessing the data; s3, constructing a parameter matrix, and calculating a parameter column of the model; s4, using a particle swarm optimization algorithm to optimize and identify to obtain a value of an optimal time-delay parameter, and constructing a fractional time-delay multivariable grey model; and S5, outputting a prediction result of the carbon emission system. The method has high interpretability and prediction accuracy, is applied to prediction of the total carbon dioxide emission in China, and is an efficient carbon emission prediction method.

Description

Technical Field

[0001] The invention relates to a multivariate grey prediction model, in particular to an improved multivariate time-lag grey prediction model, which is mainly used for the accurate prediction of carbon emissions. Background Art

[0002] Carbon emission forecasting is an important part of climate change prevention and control. It is a useful tool to assist and improve various social, economic, and environmental decision-making processes, so that energy and industrial activities are based on environmental coordination and sustainable development, and plays an important role in environmental management. Through the forecast of carbon emissions, we can understand its changing status, especially the carbon emission forecast under the background of dual carbon. Its accurate forecast can take effective treatment measures in time, which will provide technical guarantee for mitigating climate change, protecting the ecological environment, improving people's quality of life, ensuring social stability, and sustainable development of the social economy and environment.

[0003] To address this problem, managers and researchers have established many prediction models, such as regression analysis, grey models, machine learning, artificial neural networks, etc. In predictive modeling, the size of the data sample directly affects the modeling effect. Under the dual carbon background, there is less data available. In the case of a small data sample size, a fractional time-lag multivariate grey prediction model is proposed to solve the problem of carbon emission prediction under sample missing conditions. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, this patent application proposes a fractional time-lag multivariate grey prediction model suitable for carbon emissions under the dual carbon background.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A novel fractional time-lag multivariate grey model for carbon emission forecasting includes the following steps:

[0007] S1: Collect dependent variable data and its related influencing factors;

[0008] S2: preprocess the data;

[0009] S3: construct parameter matrix and calculate parameter columns of the model;

[0010] S4: Use the particle swarm optimization algorithm to optimize and identify the optimal value of the time-lag parameter τ and construct the fractional time-lag multivariate grey model NSGM(1,N,τ);

[0011] S5: Output of carbon emission system prediction results.

[0012] Furthermore, the step of collecting data in step S1 also includes: collecting dependent variable data and relevant factor data affecting the dependent variable, and then determining the key factors affecting the dependent variable, that is, the independent variables in the model, by searching relevant literature or according to the grey correlation degree, wherein the grey correlation degree is determined as:

[0013]

[0014] where ζ is called the resolution coefficient, γ(X0,X i ) is called the grey relational degree of X0 and X1. i ) to select the independent variable.

[0015] Furthermore, the specific steps of step S2 are:

[0016] A1: Calculate the 1-AGO cumulative generation sequence of the dependent variable;

[0017]

[0018] in,

[0019] A2: Calculate the adjacent mean value of the dependent variable to generate a sequence;

[0020]

[0021] in

[0022] A3: Use cubic spline interpolation function to calculate the 1-AGO cumulative generation sequence of all independent variables The specific steps include:

[0023] B1: Split the time axis and divide the time range τ into three small intervals, namely [0,1], (1,2] and (2,3], so as to perform interpolation calculation in each small interval;

[0024] B2: Estimate using cubic spline interpolation function Value

[0025] (1)S(x j )=f(x j ),j=0,1,L,n, ensuring that at each interpolation point x j At this point, the value of the interpolation function S(x) is equal to the original data point f(x j )

[0026] (2) Ensure that the interpolation function is continuous and smooth at the endpoints of all intervals

[0027] B3: Identify the optimal time delay value based on the optimization algorithm;

[0028] B4: Generate a set of independent variable sequences.

[0029] Furthermore, the specific steps of step S3 are:

[0030] C1: Construct parameter matrices B and Y; specifically;

[0031]

[0032] C2: Parameter column of the calculation model

[0033] The least squares parameter list of the NSGM(1,N,τ) model satisfy:

[0034] When m=N+3 and |B|≠0,

[0035] When m>N+3 and |B|≠0,

[0036] When m<N+3 and |B|≠0,

[0037] C3: If the "singular matrix" phenomenon occurs, dedimensionalize the variables to avoid such phenomenon.

[0038] Furthermore, a new time-lag fractional-order grey multivariate prediction model is constructed. The specific steps include:

[0039] D1: Use the particle swarm optimization (PSO) algorithm to optimize and identify the value of the optimal time-delay parameter τ. The specific steps include:

[0040] E1: Determine the range of the time lag parameter t, start the search from the start time, and use the time lag parameter at the selected step size. The method stops at the upper limit of the search;

[0041] E2: The parameter vector Substituting the time response function into the model, we get An estimated value of

[0042] E3: Construct constraint equations to calculate the minimum error. In order to evaluate the effectiveness of the model and its results, the value range of t is [0,3];

[0043]

[0044] D2: Construct fractional time-lag multivariate grey model NSGM(1,N,τ)

[0045] 1) Time response formula of NSGM(1,N,τ) model:

[0046]

[0047] 2) The final reduction formula of the NSGM (1, N, τ) model:

[0048]

[0049] in

[0050] Furthermore, the specific steps for outputting the carbon emission prediction results are: according to the training input-output mode, new data is input into the new time-lag fractional grey multivariate prediction model, and the model output is the prediction result of carbon emissions.

[0051] Beneficial Effects

[0052] (1) When fractional lags establish the dependency relationship between variables in the model, they can better explore the lag effect between independent variables and dependent variables and have strong explanatory power;

[0053] (2) Cubic spline interpolation enables the carbon emission dataset under dual carbon to use a smooth and continuous curve, avoiding the oscillation problem of high-order polynomial interpolation and providing good computational efficiency while ensuring accuracy.

[0054] (3) It provides an effective way to solve other small sample prediction problems. Description of the drawings:

[0055] Figure 1 This is a system flow chart of a novel fractional time-lag multivariate grey model for carbon emission prediction according to the present invention;

[0056] Figure 2 The present invention provides a flow chart for optimizing the time lag parameters of a novel fractional time lag multivariate grey model for carbon emission prediction. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0058] A new fractional time-lag multivariate grey model for carbon emission prediction is proposed. By adding the time-lag parameter τ to the traditional NSGM (1, N) model, the model includes the following steps:

[0059] S1: Collect dependent variable data and its related influencing factors;

[0060] S2: preprocess the data;

[0061] S3: construct parameter matrix and calculate parameter columns of the model;

[0062] S4: Use the particle swarm optimization algorithm to optimize and identify the optimal value of the time-lag parameter τ and construct the fractional time-lag multivariate grey model NSGM(1,N,τ);

[0063] S5: Output of carbon emission system prediction results.

[0064] Optimized, the step of collecting data in step S1 also includes: collecting dependent variable data and relevant factor data affecting the dependent variable, and then determining the key factors affecting the dependent variable by searching relevant literature or according to the grey correlation degree, that is, the independent variable in the model, wherein the grey correlation degree is determined as:

[0065]

[0066] where ζ is called the resolution coefficient, γ(X0,X i ) is called the grey relational degree of X0 and X1. i ) to select the independent variable.

[0067] The specific steps of step S2 are optimized as follows:

[0068] A1: Calculate the 1-AGO cumulative generation sequence of the dependent variable;

[0069]

[0070] in,

[0071] A2: Calculate the adjacent mean value of the dependent variable to generate a sequence;

[0072]

[0073] in

[0074] A3: Use cubic spline interpolation function to calculate the 1-AGO cumulative generation sequence of all independent variables The specific steps include:

[0075] B1: Split the time axis and divide the time range τ into three small intervals, namely [0,1], (1,2] and (2,3], so as to perform interpolation calculation in each small interval;

[0076] B2: Estimate using cubic spline interpolation function Value

[0077] (1)S(x j )=f(x j ),j=0,1,L,n, ensuring that at each interpolation point xj At this point, the value of the interpolation function S(x) is equal to the original data point f(x j )

[0078] (2) Ensure that the interpolation function is continuous and smooth at the endpoints of all intervals

[0079] B3: Identify the optimal time delay value based on the optimization algorithm;

[0080] B4: Generate a set of independent variable sequences.

[0081] Furthermore, the specific steps of step S3 are:

[0082] C1: Construct parameter matrices B and Y; specifically;

[0083]

[0084] C2: Parameter column of the calculation model

[0085] The least squares parameter list of the NSGM(1,N,τ) model satisfy:

[0086] When m=N+3 and |B|≠0,

[0087] When m>N+3 and |B|≠0,

[0088] When m<N+3 and |B|≠0,

[0089] C3: If the "singular matrix" phenomenon occurs, dedimensionalize the variables to avoid such phenomenon.

[0090] Optimized, a new time-lag fractional-order grey multivariate prediction model is constructed. The specific steps include:

[0091] D1: Use the particle swarm optimization (PSO) algorithm to optimize and identify the value of the optimal time-delay parameter τ. The specific steps include:

[0092] E1: Determine the range of the time lag parameter t, start the search from the start time, and use the time lag parameter at the selected step size. The method stops at the upper limit of the search;

[0093] E2: The parameter vector Substituting the time response function into the model, we get An estimated value of

[0094] E3: Construct constraint equations to calculate the minimum error. In order to evaluate the effectiveness of the model and its results, the value range of t is [0,3];

[0095]

[0096] D2: Construct fractional time-lag multivariate grey model NSGM(1,N,τ)

[0097] 1) Time response formula of NSGM(1,N,τ) model:

[0098]

[0099] 2) The final reduction formula of the NSGM (1, N, τ) model:

[0100]

[0101] in

[0102] The optimized fractional time-lag multivariate grey model for carbon emission prediction has the following specific steps for outputting the result: according to the training input-output mode, the model output is the prediction result of carbon emissions.

[0103] Beneficial Effects

[0104] (1) When fractional lags establish the dependency relationship between variables in the model, they can better explore the lag effect between independent variables and dependent variables and have strong explanatory power;

[0105] (2) Cubic spline interpolation enables the carbon emission dataset under dual carbon to use a smooth and continuous curve, avoiding the oscillation problem of high-order polynomial interpolation and providing good computational efficiency while ensuring accuracy.

[0106] (3) It provides an effective way to solve other small sample prediction problems.

[0107] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A fractional time-lag multivariate grey model for carbon emission prediction, characterized in that: By adding the time lag parameter τ to the traditional NSGM (1, N) model, the following steps are included: S1: Collect dependent variable data and its related influencing factors; S2: preprocess the data; S3: construct parameter matrix and calculate parameter columns of the model; S4: Use the particle swarm optimization algorithm to optimize and identify the optimal value of the time-lag parameter τ and construct the fractional time-lag multivariate grey model NSGM(1,N,τ); S5: Output of carbon emission system prediction results.

2. The fractional time-lag multivariate grey model for carbon emission prediction according to claim 1, characterized in that: The step of collecting relevant influencing factors in step S1 also includes: determining the key factors affecting the dependent variable according to the grey correlation degree, where ζ is called the resolution coefficient, γ(X0,X i ) is called the grey relational degree of X0 and X1. i ) to select the independent variable.

3. According to the fractional time-lag multivariate grey model for carbon emission prediction according to claim 2, the selected raw data is preprocessed, and step S2 specifically comprises: A1: Calculate the 1-AGO cumulative generation sequence of the dependent variable in, A2: Calculate the adjacent mean of the dependent variable to generate a sequence; in A3: Use cubic spline interpolation function to calculate the 1-AGO cumulative generation sequence of all independent variables The specific steps include: B1: Split the time axis and divide the time range τ into three small intervals, namely [0,1], (1,2] and (2,3], so as to perform interpolation calculation in each small interval; B2: Estimate using cubic spline interpolation function Value (1)S(x j )=f(x j ),j=0,1,L,n, ensuring that at each interpolation point x j At this point, the value of the interpolation function S(x) is equal to the original data point f(x j ) (2) Ensure that the interpolation function is continuous and smooth at the endpoints of all intervals B3: Identify the optimal time delay value based on the optimization algorithm; B4: Generate a set of independent variable sequences.

4. The fractional time-lag multivariate grey model for carbon emission prediction according to claim 3, wherein the parameter estimation step S3 specifically comprises: C1: construct parameter matrices B and Y; C2: Parameter column of the calculation model The least squares parameter list of the NSGM(1,N,τ) model satisfy: When m=N+3 and |B|≠0, When m>N+3 and |B|≠0, When m<N+3 and |B|≠0, C3: If the "singular matrix" phenomenon occurs, dedimensionalize the variables to avoid such phenomenon.

5. The fractional time-lag multivariate grey model according to claim 4, wherein the model building step specifically comprises: D1: Use the particle swarm optimization (PSO) algorithm to optimize and identify the value of the optimal time-delay parameter τ. The specific steps include: E1: Determine the range of the time lag parameter t, start the search from the start time, and use the time lag parameter at the selected step size. The method stops at the upper limit of the search; E2: The parameter vector Substituting the time response function into the model, we get An estimated value of E3: Construct constraint equations to calculate the minimum error. In order to evaluate the effectiveness of the model and its results, the value range of t is [0,3]; D2: Construct fractional time-lag multivariate grey model NSGM(1,N,τ) 1) Time response formula of NSGM(1,N,τ) model: 2) The final reduction formula of the NSGM (1, N, τ) model: in 6. The fractional time-lag multivariate grey model for carbon emission prediction according to claim 5, characterized in that: The specific steps of the result output are: according to the training input-output mode, the model output is the predicted result of carbon emissions.

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