CN102708296A - Energy supply and demand prediction method based on grey multi-factor prediction model - Google Patents

Abstract

The invention relates to a method for predicting energy supply and demand of a tobacco enterprise. The invention firstly utilizes a factor analysis method to reduce the dimension of the original number series, synthesizes the variables into a plurality of factors with less quantity so as to reproduce the mutual relation between the original variables and the factors, simultaneously classifies the variables according to different factors, carries out kernel smoothing treatment on the number series, gives larger weight to points near the time point, and then carries out grey prediction, thereby effectively improving the prediction precision.

Description

A kind of energy supply and demand Forecasting Methodology based on the multifactor forecast model of grey

Technical field

The invention belongs to the production of cigarettes technical field, be specifically related to a kind of energy supply and demand Forecasting Methodology based on the multifactor forecast model of grey.

Background technology

How China's tobacco enterprise under the prerequisite of guaranteeing stable supplying and safety in production, efficiently utilizes the limited energy, optimizes the supply and demand structure, makes full use of secondary energy, and reducing the waste that the energy supply and demand imbalance causes is an important problems.Be the basis with the prediction variation tendency, it is most important effectively to dispatch the energy.At present, the energy forecast of domestic majority tobacco enterprise is based on the short-term prediction of artificial experience, and dopester's experience is required to lack the support of forecast model than higher.Most of researchs about energy supply and demand all concentrate on the supply and demand prediction of the single energy or two kinds of energy, and the supply and demand prediction that comprises various energy resources is seldom arranged.

The system and method for at present relevant energy supply and demand prediction mainly contains following several kinds:

1. neural network model

Though have the higher non-linearity mapping ability, can approach nonlinear function with arbitrary accuracy, in actual computation, also have some problems: the computation process speed of convergence of (1) backpropagation is slow, generally needs hundreds and thousands of times iterative computation; (2) there is the minimal value of energy function; (3) implicit neuron number and the experience of often leaning on of choosing that is connected power; (4) convergence of network is relevant with the structure of network etc.

2. regression equation method

Because the tobacco enterprise energy resource system is complicated, related variety of energy sources is various, and is interrelated between the energy, is not suitable for predicting with regression equation.And use regression equation and estimate when predicting, can only estimate dependent variable, do not allow dependent variable to infer independent variable by independent variable.

Grey GM (1, n) model

Can see much with grey GM (1; N) during model is applied to actual system's match and forecasts; But effect is not very desirable, although (1, n) differential equation of model mechanism is very simple because explain grey GM; But actual the finding the solution of model is difficult to obtain, and the method for solving of equation has directly determined model fitting, prediction effect.Though grey GM (1, the n) mutual relationship between each factor in the model ability reactive system, it only is fit to the state model of the system that sets up, and is suitable for the performance analysis of each variable, is well-suited for the high order system modeling basis is provided, and is not suitable for prediction.

4. multifactor prediction MGM (1, n) model

Usually as systematic analysis, the modeling of the system that needs to consider multifactor mutual restriction, connect each other.(1, n) model is to come through setting up differential equation of first order that n relation factor is suitable for the prediction to the tobacco enterprise energy supply and demand to the wherein influence of certain factors vary in the reflection system to the multifactor prediction MGM of gray system theory.But because multivariate input and output problem variable number is many, and exists mutual relationship between variable and the variable, so precision of prediction is not very high.

5. factorial analysis

Factorial analysis is that the variable with intricate relation (or sample) comprehensively is several factors of negligible amounts; To reproduce the mutual relationship between the original variable and the factor; Can also classify to variable according to the different factors simultaneously; It belongs to a kind of statistical method of handling dimensionality reduction in the multivariate analysis, so we carry out factorial analysis before it is predicted, can effectively improve the grey prediction precision.

Therefore the multifactor prediction MGM of utilization (1, need combine with factor analysis when n) model is predicted the supply and demand of enterprise energy, with the raising precision of prediction.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art, a kind of energy supply and demand Forecasting Methodology based on the multifactor forecast model of grey that combines with factor analysis is provided.

The objective of the invention is to realize like this:

A kind of energy supply and demand Forecasting Methodology based on the multifactor forecast model of grey; Utilize the method for factorial analysis earlier, the dimension that reduces original ordered series of numbers is several factors of negligible amounts with aggregation of variable, to reproduce the mutual relationship between the original variable and the factor; Classify according to different factor pair variablees simultaneously; Ordered series of numbers is examined smoothing processing again, give big flexible strategy near the point the time point, and then carry out gray prediction.

Wherein, specifically comprise the steps:

Set up the r mode factor analysis mathematical model, comprising:

Utilize measured data that numerous indexs of tobacco enterprise energy supply and demand are set up supply and demand r mode factor analysis mathematical model,

With the raw data standardization,

Set up the related coefficient battle array of variable,

Ask characteristic root and the corresponding unit character vector of R, and extract m characteristic root as requested and corresponding proper vector is write out factor loading battle array A,

A is implemented the rotation of variance maximum orthogonality,

The calculated factor score shows each index of energy supply and demand with common factor respectively;

The nuclear smoothing processing gives big flexible strategy near the data major component time point that proposes; Computation bandwidth h makes repeated attempts and revises, the ordered series of numbers after the nuclear smoothing processing that must make new advances;

Set up MGM (1, n) forecast model comprises:

Influence system variable to after factorial analysis, drawing n in the energy supply and demand,

Set up MGM (1, n) model,

Try to achieve the match value and the predicted value of each factor in the system through calculating,

Result of calculation is analyzed, matrix of coefficients is suitably adjusted or controlled, coordinate repeatedly, till trying to achieve satisfactory result,

Each index of energy supply and demand index to prediction is set up GM (1,1) residual error correction model respectively;

Each index of energy supply and demand index to prediction is set up GM (1,1) residual error correction model respectively, comprising:

S4.1, to the prediction after the energy supply and demand amount set up residual sequence,

S4.2, set up Residual GM (1,1) model,

S4.3, compare with actual value the residual error that makes new advances, the checking precision.

Compared with prior art, the present invention has following advantage:

Utilize the method for factorial analysis earlier; The aggregation of variable that the dimension that reduces original ordered series of numbers will have intricate relation is several factors of negligible amounts; To reproduce the mutual relationship between the original variable and the factor, can also classify to variable according to the different factors simultaneously.Ordered series of numbers is examined smoothing processing again, give big flexible strategy near the point the time point.And then carry out grey prediction, can effectively improve its precision of prediction.

Description of drawings

Fig. 1 be of the present invention a kind of based on grey Multiple-Factor Model MGM (1, the parameter configuration process flow diagram of energy supply and demand Forecasting Methodology n);

Fig. 2 is an energy supply and demand prediction module algorithm flow chart of the present invention;

Fig. 3 is a prognoses system functional structure chart of the present invention.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is made further explain, but never in any form the present invention is limited, according to training centre of the present invention do any change or replacement, all belong to protection scope of the present invention.

Fig. 1～Fig. 3 is a kind of embodiment of the present invention.

Fig. 1 is the parameter configuration process flow diagram of this Forecasting Methodology.From the database of actual measurement, extract the energy supply and demand data, respectively factorial analysis is carried out in supply and demand, examine smoothing processing then; (1, n) model is predicted supply and demand to pretreated data M GM; Compare with measured result, model coefficient is revised as dissatisfied.The satisfaction that obtains each type that predicts the outcome is set up GM (1,1) model and further revised, make to predict the outcome more accurately, at last model is kept in the algorithms library.

Fig. 2 is an energy supply and demand prediction module algorithm flow chart of the present invention.From database, extract the measured data of modeling, and data are carried out pre-service, from algorithms library, extract corresponding forecast model coefficient information, use the model of pretreated data and extraction to predict and correction result then, export the result at last.

Fig. 3 is a prognoses system functional structure chart of the present invention.The energy supply and demand class Modules that mainly comprises required prediction is surveyed data module of all categories, the parameter module of energy supply and demand forecast model, prediction residual correcting module.

Present embodiment is to following to tobacco enterprise energy supply and demand forecasting process:

The tobacco enterprise energy supply and demand is set up the r mode factor analysis mathematical model

Step (1) actual measurement one all each time period data are chosen representational data;

Step (2) utilizes measured data that numerous indexs of tobacco enterprise energy supply and demand are set up supply and demand r mode factor analysis mathematical model;

The measured data index is set up following factorial analysis mathematical model:

$\left\{\begin{array}{c}{X}_1=a_{11}{F}_1+a_{12}{F}_2+\·\·\·+a_{1m}{F}_m+{\mathrm{\ϵ}}_1\\ x_2=a_{21}{F}_1+a_{22}{F}_2+\·\·\·+a_{2m}{F}_m+{\mathrm{\ϵ}}_2\\ \·\\ \·\\ \·\\ X_p=a_{p1}{F}_1+a_{p2}{F}_2+\·\·\·+a_{\mathrm{pm}}{F}_m+{\mathrm{\ϵ}}_p\end{array}\right.$

Use matrix representation:

$\left[\begin{array}{c}{X}_1\\ X_2\\ \·\\ \·\\ \·\\ X_p\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \·\·\·& a_{1m}\\ a_{21}& a_{22}& \·\·\·& a_{2m}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ a_{p1}& a_{p2}& \·\·\·& a_{\mathrm{pm}}\end{array}\right]\left[\begin{array}{c}{F}_1\\ F_2\\ \·\\ \·\\ \·\\ F_m\end{array}\right]+\left[\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ \·\\ \·\\ \·\\ {\mathrm{\ϵ}}_p\end{array}\right]$

And satisfy:

①m≤p；

2. (F ε)=0 is that F and ε are incoherent to Cov;

3.

Be F ₁F _mUncorrelated and variance is all 1. Be ε ₁..., ε _pUncorrelated, and variance is different.The purpose of factorial analysis replaces X through model X=AF+ ε with F exactly, because m p, and m＜n, thus reach the hope of simplifying the variable dimension.

Step (3) is with the raw data standardization, for writing the convenient X that still is designated as _Ij

Step (4) is set up the related coefficient battle array R=(r of variable _Ij) _{P * p}, wherein

Step (5) is asked characteristic root and the corresponding unit character vector of R, is designated as λ respectively ₁>=λ ₂>=...>=λ _p>0 and u ₁, u ₂..., u _p, note $U=(u_2,\·\·\·,u_p)=\left[\begin{array}{cccc}{u}_{11}& u_{12}& \·\·\·& u_{1p}\\ u_{21}& u_{22}& \·\·\·& u_{2p}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ & & \·& \\ & & \·& \\ u_{p1}& u_{p2}& \·& u_{\mathrm{pp}}\end{array}\right]$

According to the requirement of contribution rate of accumulative total, extract m characteristic root and corresponding proper vector and write out the factor loading battle array: $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \·\·\·& a_{1m}\\ a_{21}& a_{22}& \·\·\·& a_{2m}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ & & \·& \\ & & \·& \\ a_{p1}& u_{p2}& \·& u_{\mathrm{pm}}\end{array}\right]=\left[\begin{array}{cccc}{u}_{11}\sqrt{{\mathrm{\λ}}_1}& u_{12}\sqrt{{\mathrm{\λ}}_2}& \·\·\·& u_{1m}\sqrt{{\mathrm{\λ}}_m}\\ u_{21}\sqrt{{\mathrm{\λ}}_1}& u_{22}\sqrt{{\mathrm{\λ}}_2}& \·\·\·& u_{2m}\sqrt{{\mathrm{\λ}}_m}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ & & \·& \\ & & \·& \\ u_{p1}\sqrt{{\mathrm{\λ}}_1}& u_{p2}\sqrt{{\mathrm{\λ}}_2}& \·& u_{\mathrm{pm}}\sqrt{{\mathrm{\λ}}_m}\end{array}\right]$

Step (6) is implemented the rotation of variance maximum orthogonality to A;

Step (7) shows each index of tobacco enterprise energy supply and demand respectively with common factor, can find out the contributive rate of its each factor of influence through this formula;

Step (8) calculated factor score.

2. nuclear smoothing processing

Step (9) gives big flexible strategy by following formula near the data major component time point that is proposed;

${\hat{f}}_{t_0}=\frac{{\mathrm{\Σ}}_{t=1}^T{X}_{t}K\left(\frac{t-t_0}{h}\right)}{{\mathrm{\Σ}}_{t=1}^{T}K\left(\frac{t-t_0}{h}\right)}$

In the formula: { X _t---the known time sequence data;

---examine level and smooth ordered series of numbers;

K (u)---kernel function;

H---bandwidth.

Step (10) computation bandwidth h, big bandwidth can produce excessively level and smooth estimation, some the possible details on the tolerance of omission trend and estimated peak and paddy; When using little bandwidth, only there are several innings data to be used, reduced the variance of estimating, but causing gained to be estimated is the curve of a fluctuation; Need make repeated attempts and revise generally;

The ordered series of numbers after the nuclear smoothing processing that step (11) must make new advances.

3. set up MGM (1, n) forecast model

This model can reflect that n relation factor is to the wherein influence of certain factors vary rate; We mainly seek in n the relation factor; Relation in the energy supply and demand between certain variable and the other factors, this influence factor are n the major components that proposes in the factorial analysis process, and it is predicted.

Step (12) is to there being n to influence system variable after factorial analysis in the supply and demand of the energy, each variable has the wherein corresponding one-accumulate formation sequence of n data

constantly for

promptly:

$X_i^{\left(1\right)}\left(k\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{X}_i^{\left(0\right)}\left(k\right)$

In the formula: i=1,2 ..., N.

Step (13) set up MGM (1, n) model;

MGM (1, n) model is set up n unit One first-order ordinary differential equation group to this formation sequence exactly:

$\left\{\begin{array}{c}\frac{{\mathrm{dX}}_1^{\left(1\right)}}{\mathrm{dt}}=a_{11}{X}_1^{\left(1\right)}+a_{12}{X}_2^{\left(1\right)}+\·\·\·+a_{1n}{X}_n^{\left(1\right)}+b_1\\ \frac{{\mathrm{dX}}_2^{\left(1\right)}}{\mathrm{dt}}=a_{21}{X}_1^{\left(1\right)}+a_{22}{X}_2^{\left(1\right)}+\·\·\·+a_{2n}{X}_n^{\left(1\right)}+b_2\\ \·\\ \·\\ \·\\ \frac{{\mathrm{dX}}_n^{\left(1\right)}}{\mathrm{dt}}=a_{n1}{X}_1^{\left(1\right)}+a_{n2}{X}_2^{\left(1\right)}+\·\·\·+a_{\mathrm{nn}}{X}_n^{\left(1\right)}+b_n\end{array}\right.$

Order:

$X^{\left(0\right)}\left(k\right)={[X_1^{\left(0\right)}\left(k\right),X_2^{\left(0\right)}\left(k\right),\·\·\·,X_n^{\left(0\right)}\left(k\right)]}^T$

$X^{\left(1\right)}\left(k\right)={[X_1^{\left(1\right)}\left(k\right),X_2^{\left(1\right)}\left(k\right),\·\·\·,X_n^{\left(1\right)}\left(k\right)]}^T$

$A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \·\·\·& a_{1n}\\ a_{21}& a_{22}& \·\·\·& a_{2n}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ a_{n1}& a_{n2}& \·\·\·& a_{\mathrm{nn}}\end{array}\right]$

$B=\left[\begin{array}{c}{b}_1\\ b_2\\ \·\\ \·\\ \·\\ b_n\end{array}\right]$

In the formula: A, B---be called identified parameters.

Step (14) is according to the MGM model, and being write as matrix form has:

$\frac{{\mathrm{dX}}^{\left(1\right)}}{\mathrm{dt}}{\mathrm{AX}}^{\left(1\right)}+B$

Step (15) is used MATLAB, finds the solution matrix equation;

Step (16) is separated equation, does to tire out to subtract reduction, promptly tries to achieve the match value and the predicted value of each factor in the system;

Step (17) is analyzed result of calculation, as dissatisfied, or does not reach top phase target, can grey area based on each coefficient between, coefficient matrix is suitably adjusted or is controlled, remake simulation calculation.Coordinate so repeatedly, till trying to achieve satisfactory result.

4. each index of energy supply and demand index of prediction is set up GM (1,1) residual error correction model respectively

Step (18) is set up residual sequence to the energy supply and demand amount after predicting;

Step (19) is to the requirement of residual sequence;

1. non-negative: e >=0;

2. dull liter the: e (K+1) >=e (K);

If 3. have in the residual sequence e (h) 0, then should on residual error, add a suitable positive number, make wherein that minimum value becomes 0, obtain new residual sequence.

Step (20) is set up Residual GM (1,1) model;

Step (21) to obtain

calculate

Step (22) compare with actual value the residual error that makes new advances, can verify that its precision of prediction increases.

The above only is a preferred implementation of the present invention; Should be pointed out that for those skilled in the art, under the prerequisite that does not break away from know-why of the present invention; Can also make some improvement and distortion, these improvement and distortion also should be regarded as protection scope of the present invention.

Claims (2)

1. the energy supply and demand Forecasting Methodology based on the multifactor forecast model of grey is characterized in that, utilizes the method for factorial analysis earlier; The dimension that reduces original ordered series of numbers is several factors of negligible amounts with aggregation of variable; To reproduce the mutual relationship between the original variable and the factor, classify according to different factor pair variablees simultaneously, ordered series of numbers is examined smoothing processing again; Give big flexible strategy near the point the time point, and then carry out gray prediction.

2. according to claim 1 based on the energy supply and demand Forecasting Methodology of the multifactor forecast model of grey, it is characterized in that, comprise the steps:

Set up the r mode factor analysis mathematical model, comprising:

Utilize measured data that numerous indexs of tobacco enterprise energy supply and demand are set up supply and demand r mode factor analysis mathematical model,

With the raw data standardization,

Set up the related coefficient battle array of variable,

Ask characteristic root and the corresponding unit character vector of R, and extract m characteristic root as requested and corresponding proper vector is write out factor loading battle array A,

A is implemented the rotation of variance maximum orthogonality,

The calculated factor score shows each index of energy supply and demand with common factor respectively;

The nuclear smoothing processing gives big flexible strategy near the data major component time point that proposes; Computation bandwidth h makes repeated attempts and revises, the ordered series of numbers after the nuclear smoothing processing that must make new advances;

Set up MGM (1, n) forecast model comprises:

Influence system variable to after factorial analysis, drawing n in the energy supply and demand,

Set up MGM (1, n) model,

Try to achieve the match value and the predicted value of each factor in the system through calculating,

Result of calculation is analyzed, matrix of coefficients is suitably adjusted or controlled, coordinate repeatedly, till trying to achieve satisfactory result,

Each index of energy supply and demand index to prediction is set up GM (1,1) residual error correction model respectively;

Each index of energy supply and demand index to prediction is set up GM (1,1) residual error correction model respectively, comprising:

Energy supply and demand amount to after the prediction is set up residual sequence,

Set up Residual GM (1,1) model,

Compare with actual value the residual error that makes new advances, the checking precision.

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