CN102708296A

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

Info

Publication number: CN102708296A
Application number: CN2012101488865A
Authority: CN
Inventors: 王慧; 杨建昆; 沈丁洋; 朱宏; 孔颖萍
Original assignee: Hongyunhonghe Tobacco Group Co Ltd
Current assignee: Hongyunhonghe Tobacco Group Co Ltd
Priority date: 2012-05-15
Filing date: 2012-05-15
Publication date: 2012-10-03

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 Method of Energy Supply and Demand Forecasting Based on Gray Multi-factor Forecasting Model

技术领域 technical field

本发明属于卷烟生产技术领域，具体涉及一种基于灰色多因素预测模型的能源供需预测方法。The invention belongs to the technical field of cigarette production, and in particular relates to an energy supply and demand prediction method based on a gray multi-factor prediction model.

背景技术 Background technique

我国烟草企业如何在确保稳定供给和安全生产的前提下，高效利用有限能源，优化供需结构，充分利用二次能源，减少能源供需不平衡造成的浪费是个十分重要的问题。以预测变化趋势为基础，有效调度能源至关重要。目前，国内大多数烟草企业的能源预测是基于人工经验的短时预测，对预测者的经验要求比较高，缺少预测模型的支持。大多数关于能源供需的研究都集中在单一能源或两种能源的供需预测，很少有包含多种能源的供需预测。On the premise of ensuring stable supply and safe production, how my country's tobacco companies can efficiently use limited energy, optimize the structure of supply and demand, make full use of secondary energy, and reduce waste caused by the imbalance between energy supply and demand is a very important issue. Efficient dispatching of energy based on forecasted changing trends is crucial. At present, the energy forecasting of most domestic tobacco companies is short-term forecasting based on artificial experience, which requires relatively high experience for forecasters and lacks the support of forecasting models. Most studies on energy supply and demand focus on single energy or two energy supply and demand forecasts, and few include multiple energy supply and demand forecasts.

目前有关能源供需预测的系统和方法主要有以下几种：At present, there are mainly the following systems and methods for forecasting energy supply and demand:

1．神经网络模型1. neural network model

虽然具有较高的非线性映射能力，能以任意精度逼近非线性函数，但在实际计算中，也存在一些问题：(1)反向传播的计算过程收敛速度慢，一般需要成百上千次的迭代计算；(2)存在能量函数的极小值；(3)隐含神经元个数和连接权的选取往往靠经验；(4)网络的收敛性与网络的结构有关等。Although it has a high nonlinear mapping ability and can approximate nonlinear functions with arbitrary precision, there are still some problems in actual calculations: (1) The calculation process of backpropagation has a slow convergence speed, generally requiring hundreds or thousands of times (2) There is a minimum value of the energy function; (3) The number of hidden neurons and the selection of connection weights often rely on experience; (4) The convergence of the network is related to the structure of the network, etc.

2．回归方程法2. Regression equation method

由于烟草企业能源系统复杂，所涉及的能源种类繁多，能源之间相互关联，不适合用回归方程预测。并且应用回归方程进行估算预测时，只能由自变量来估计因变量，不允许因变量来推测自变量。Due to the complexity of the energy system of the tobacco enterprise, there are various types of energy involved, and the energy is interrelated, so it is not suitable to use the regression equation to predict. And when the regression equation is used to estimate and predict, the dependent variable can only be estimated by the independent variable, and the independent variable is not allowed to be estimated by the dependent variable.

3．灰色GM(1，n)模型3. Gray GM(1,n) model

可以看到很多将灰色GM(1，n)模型应用到实际的系统拟合和预报中，但是效果都不是很理想，因为尽管表述灰色GM(1，n)模型机理的微分方程很简单，但是模型的实际求解很难得到，而方程的求解方法直接决定了模型拟合、预测效果。虽然灰色GM(1，n)模型能反应系统中各个因素之间的相互关系，但它只适合建立系统的状态模型，适合于各变量的动态分析，适合于为高阶系统建模提供基础，不适合预测。It can be seen that many gray GM (1, n) models are applied to actual system fitting and forecasting, but the effect is not very satisfactory, because although the differential equation expressing the mechanism of the gray GM (1, n) model is very simple, but The actual solution of the model is difficult to obtain, and the solution method of the equation directly determines the model fitting and prediction effect. Although the gray GM(1,n) model can reflect the relationship between various factors in the system, it is only suitable for establishing the state model of the system, suitable for the dynamic analysis of various variables, and suitable for providing the basis for high-order system modeling. Not suitable for forecasting.

4．多因素预测MGM(1，n)模型4. Multi-factor Forecasting MGM(1,n) Model

通常作为系统分析，需要考虑多因素相互制约、相互联系的系统的建模。灰色系统理论的多因素预测MGM(1，n)模型，是通过建立一阶微分方程来反映系统中n个关联因素对其中某个因素变化的影响，适合用于对烟草企业能源供需的预测。但是由于多变量输入输出问题变量个数比较多，而且变量与变量之间存在相互关系，故预测精度不是很高。Usually, as a system analysis, it is necessary to consider the modeling of a system in which multiple factors are mutually restrictive and interrelated. The multi-factor prediction MGM(1, n) model of the gray system theory reflects the influence of n related factors in the system on the change of one of them by establishing a first-order differential equation, which is suitable for forecasting the energy supply and demand of tobacco companies. However, due to the large number of variables in the multivariate input-output problem and the interrelationship between variables, the prediction accuracy is not very high.

5．因子分析5. factor analysis

因子分析是将具有错综复杂关系的变量(或样品)综合为数量较少的几个因子，以再现原始变量与因子之间的相互关系，同时根据不同因子还可以对变量进行分类，它属于多元分析中处理降维的一种统计方法，所以我们在对其进行预测前进行因子分析，能有效提高灰预测精度。Factor analysis is to synthesize variables (or samples) with intricate relationships into several factors with a small number of factors to reproduce the relationship between the original variables and factors. At the same time, variables can be classified according to different factors, which belongs to multivariate analysis. It is a statistical method to deal with dimensionality reduction, so we perform factor analysis before predicting it, which can effectively improve the accuracy of gray prediction.

因此在运用多因素预测MGM(1，n)模型对企业能源的供需进行预测时需要与因子分析法相结合，以提高预测精度。Therefore, when using the multi-factor forecasting MGM (1, n) model to predict the supply and demand of enterprise energy, it needs to be combined with factor analysis to improve the forecasting accuracy.

发明内容 Contents of the invention

本发明的目的在于克服现有技术的不足，提供一种与因子分析法相结合的基于灰色多因素预测模型的能源供需预测方法。The purpose of the present invention is to overcome the deficiencies of the prior art and provide an energy supply and demand prediction method based on a gray multi-factor prediction model combined with a factor analysis method.

本发明的目的是这样实现的：The purpose of the present invention is achieved like this:

一种基于灰色多因素预测模型的能源供需预测方法，先利用因子分析的方法，降低原始数列的维数将变量综合为数量较少的几个因子，以再现原始变量与因子之间的相互关系，同时根据不同因子对变量进行分类，对数列再进行核平滑处理，对时间点附近的点给予较大权数，然后再进行灰色预测。An energy supply and demand forecasting method based on a gray multi-factor forecasting model. Firstly, the factor analysis method is used to reduce the dimension of the original sequence and synthesize the variables into a few factors with a small number, so as to reproduce the relationship between the original variables and the factors. At the same time, the variables are classified according to different factors, and the sequence is then subjected to kernel smoothing, and a larger weight is given to the points near the time point, and then the gray prediction is performed.

其中，具体包括如下步骤：Among them, specifically include the following steps:

建立R型因子分析数学模型，包括：Establish R-type factor analysis mathematical model, including:

利用实测数据对烟草企业能源供需的众多指标建立供和需R型因子分析数学模型，Using the measured data to establish a supply and demand R-type factor analysis mathematical model for many indicators of tobacco enterprise energy supply and demand,

将原始数据标准化，normalize the original data,

建立变量的相关系数阵，Create a correlation matrix of variables,

求R的特征根及相应的单位特征向量，并根据要求提取m个特征根及相应的特征向量写出因子载荷阵A，Find the eigenvalues and corresponding unit eigenvectors of R, and extract m eigenvalues and corresponding eigenvectors according to the requirements to write the factor load matrix A,

对A施行方差最大正交旋转，Perform a variance maximum orthogonal rotation on A,

把能源供需各指标分别用公共因子表示出来，计算因子得分；Express each indicator of energy supply and demand with public factors, and calculate the factor score;

核平滑处理，对提出的主成分时间点附近数据给予较大权数；计算带宽h，进行反复尝试和修正，得出新的经核平滑处理后的数列；Kernel smoothing process, giving a larger weight to the data near the time point of the proposed principal component; calculating the bandwidth h, repeated trials and corrections, and obtaining a new sequence after kernel smoothing;

建立MGM(1，n)预测模型，包括：Establish MGM(1,n) prediction model, including:

对能源供需中经因子分析后得出n个影响系统的变量，After factor analysis of energy supply and demand, n variables that affect the system are obtained,

建立MGM(1，n)模型，Establish the MGM(1,n) model,

通过计算求得系统中各因素的拟合值和预测值，Through calculation, the fitting value and predicted value of each factor in the system are obtained,

对计算结果进行分析，对系数矩阵进行适当调整或控制，反复协调，直到求得满意结果为止，Analyze the calculation results, adjust or control the coefficient matrix appropriately, and coordinate repeatedly until a satisfactory result is obtained.

对预测的能源供需指标各个指标分别建立GM(1，1)残差修正模型；Establish the GM(1,1) residual correction model for each index of the predicted energy supply and demand index;

对预测的能源供需指标各个指标分别建立GM(1，1)残差修正模型，包括：A GM(1, 1) residual correction model is established for each index of the predicted energy supply and demand index, including:

S4.1、对预测后的能源供需量建立残差序列，S4.1. Establish a residual sequence for the predicted energy supply and demand,

S4.2、建立残差GM(1，1)模型，S4.2, establish residual GM (1, 1) model,

S4.3、与实际值相比较得出新的残差，验证精度。S4.3. Comparing with the actual value to obtain a new residual error and verify the accuracy.

与现有技术相比，本发明具有如下优点：Compared with prior art, the present invention has following advantage:

先利用因子分析的方法，降低原始数列的维数将具有错综复杂关系的变量综合为数量较少的几个因子，以再现原始变量与因子之间的相互关系，同时根据不同因子还可以对变量进行分类。对数列再进行核平滑处理，对时间点附近的点给予较大权数。然后再进行灰预测，能有效提高其预测精度。First use the method of factor analysis to reduce the dimension of the original sequence and synthesize the variables with intricate relationships into a few factors with a small number to reproduce the relationship between the original variables and the factors. At the same time, the variables can also be analyzed according to different factors Classification. Kernel smoothing is performed on the series, and a larger weight is given to points near the time point. Then the gray prediction can effectively improve the prediction accuracy.

附图说明 Description of drawings

图1是本发明的一种基于灰色多因素模型MGM(1，n)的能源供需预测方法的参数配置流程图；Fig. 1 is a kind of parameter configuration flowchart of the energy supply and demand prediction method based on gray multi-factor model MGM (1, n) of the present invention;

图2是本发明的能源供需预测模块算法流程图；Fig. 2 is the algorithm flow chart of energy supply and demand prediction module of the present invention;

图3是本发明的预测系统功能结构图。Fig. 3 is a functional structure diagram of the prediction system of the present invention.

具体实施方式 Detailed ways

下面结合附图及实施例对本发明作出进一步详细说明，但不以任何方式对本发明加以限制，依据本发明的教导所作得任何变更或替换，均属于本发明的保护范围。The present invention will be described in further detail below in conjunction with the accompanying drawings and examples, but the present invention is not limited in any way. Any changes or replacements made according to the teaching of the present invention belong to the protection scope of the present invention.

图1～图3为本发明的一种具体实施方式。1 to 3 are a specific embodiment of the present invention.

图1为本预测方法的参数配置流程图。从实测的数据库中提取能源供需数据，分别对供需进行因子分析，然后进行核平滑处理，对预处理后的数据MGM(1，n)模型，对供需进行预测，与实测结果相比较，如不满意对模型系数进行修正。将得到的满意预测结果每一类型建立GM(1，1)模型进一步修正，使预测结果更为精确，最后将模型保存在算法库中。Figure 1 is a flow chart of parameter configuration for this prediction method. Extract energy supply and demand data from the measured database, conduct factor analysis on the supply and demand respectively, and then perform kernel smoothing, use the preprocessed data MGM (1, n) model to predict the supply and demand, and compare with the measured results, if not Satisfactory to modify the model coefficients. Establish GM (1, 1) model for each type of satisfactory prediction results to make further corrections to make the prediction results more accurate, and finally save the model in the algorithm library.

图2是本发明的能源供需预测模块算法流程图。从数据库中提取建模的实测数据，并对数据进行预处理，从算法库中提取相应的预测模型系数信息，然后运用预处理后的数据和提取的模型进行预测与修正结果，最后输出结果。Fig. 2 is an algorithm flow chart of the energy supply and demand forecasting module of the present invention. Extract the measured data for modeling from the database, preprocess the data, extract the corresponding prediction model coefficient information from the algorithm library, then use the preprocessed data and the extracted model to predict and correct the results, and finally output the results.

图3是本发明的预测系统功能结构图。主要包括所需预测的能源供需类别模块，实测各类别的数据模块，能源供需预测模型的参数模块，预测残差修正模块。Fig. 3 is a functional structure diagram of the prediction system of the present invention. It mainly includes the energy supply and demand category module to be predicted, the measured data module of each category, the parameter module of the energy supply and demand forecast model, and the forecast residual error correction module.

本实施例对对烟草企业能源供需预测过程如下：In this embodiment, the process of forecasting the energy supply and demand of tobacco companies is as follows:

对烟草企业能源供需建立R型因子分析数学模型Establishment of R-type Factor Analysis Mathematical Model for Energy Supply and Demand in Tobacco Enterprises

步骤(1)实测一周各时间段数据，选取有代表性的数据；Step (1) Measure the data of each time period of a week, and select representative data;

步骤(2)利用实测数据对烟草企业能源供需的众多指标建立供需R型因子分析数学模型；Step (2) utilizes the measured data to establish the R-type factor analysis mathematical model of supply and demand for many indicators of tobacco enterprise energy supply and demand;

将实测数据指标建立如下因子分析数学模型：Establish the following factor analysis mathematical model for the measured data indicators:

$\{\begin{matrix} {X x}_{11} = = {a a}_{1111} {F f}_{11} + + {a a}_{1212} {F f}_{22} + + \cdot \cdot \cdot \cdot \cdot \cdot + + {a a}_{11 m m} {F f}_{m m} + + {ϵ ϵ}_{11} \\ {x x}_{22} = = {a a}_{21 twenty one} {F f}_{11} + + {a a}_{22 twenty two} {F f}_{22} + + \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; + + {a a}_{22 m m} {F f}_{m m} + + {ϵ ϵ}_{22} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {X x}_{p p} = = {a a}_{p p 11} {F f}_{11} + + {a a}_{p p 22} {F f}_{22} + + \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot + + {a a}_{pm pm} {F f}_{m m} + + {ϵ ϵ}_{p p} \end{matrix}$

用矩阵表示：Represented by a matrix:

$[\begin{matrix} {X x}_{11} \\ {X x}_{22} \\ \cdot \cdot \\ \cdot &Center Dot; \\ \cdot \cdot \\ {X x}_{p p} \end{matrix}] = = [\begin{matrix} {a a}_{1111} & {a a}_{1212} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {a a}_{11 m m} \\ {a a}_{21 twenty one} & {a a}_{22 twenty two} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {a a}_{22 m m} \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; \\ \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ {a a}_{p p 11} & {a a}_{p p 22} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {a a}_{pm pm} \end{matrix}] [\begin{matrix} {F f}_{11} \\ {F f}_{22} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot \cdot \\ {F f}_{m m} \end{matrix}] + + [\begin{matrix} {ϵ ϵ}_{11} \\ {ϵ ϵ}_{22} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {ϵ ϵ}_{p p} \end{matrix}]$

且满足：And satisfy:

①m≤p；①m≤p;

②Cov(F,ε)=0即F和ε是不相关的；②Cov(F,ε)=0 means that F and ε are irrelevant;

③

即F₁…F_m不相关且方差皆为1。即ε₁,…,ε_p不相关，且方差不同。因子分析的目的就是通过模型X=AF+ε以F代替X，由于m<p,m＜n，从而达到简化变量维数的愿望。③

That is, F ₁ ...F _m are uncorrelated and the variances are all 1. That is, ε ₁ ,…,ε _p are uncorrelated and have different variances. The purpose of factor analysis is to replace X with F through the model X=AF+ε, because m<p, m<n, so as to achieve the desire to simplify the variable dimension.

步骤(3)将原始数据标准化，为书写方便仍记为X_ij；Step (3) standardizes the original data, which is still recorded as X _ij for the convenience of writing;

步骤(4)建立变量的相关系数阵R=(r_ij)_p×p，其中

Step (4) establishes the correlation coefficient matrix R=(r _ij ) _p×p of variables, where

步骤(5)求R的特征根及相应的单位特征向量，分别记为λ₁≥λ₂≥…≥λ_p>0和u₁,u₂,…,u_p，记 $U = (u_{2}, \cdot \cdot \cdot, u_{p}) = [\begin{matrix} u_{11} & u_{12} & \cdot \cdot \cdot & u_{1 p} \\ u_{21} & u_{22} & \cdot \cdot \cdot & u_{2 p} \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot \\ \cdot \\ u_{p 1} & u_{p 2} & \cdot & u_{pp} \end{matrix}]$ Step (5) Calculate the eigenvalues of R and the corresponding unit eigenvectors, denoted as λ ₁ ≥λ ₂ ≥…≥λ _p >0 and u ₁ , u ₂ ,…,u _p , denote $u = (u_{2}, &Center Dot; &Center Dot; \cdot, u_{p}) = [\begin{matrix} u_{11} & u_{12} & \cdot \cdot \cdot & u_{1 p} \\ u_{twenty one} & u_{twenty two} & \cdot \cdot \cdot & u_{2 p} \\ \cdot & &Center Dot; & &Center Dot; & &Center Dot; \\ \cdot & &Center Dot; & &Center Dot; & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot \\ \cdot \\ u_{p 1} & u_{p 2} & &Center Dot; & u_{pp} \end{matrix}]$

根据累计贡献率的要求，提取m个特征根及相应的特征向量写出因子载荷阵： $A = [\begin{matrix} a_{11} & a_{12} & \cdot \cdot \cdot & a_{1 m} \\ a_{21} & a_{22} & \cdot \cdot \cdot & a_{2 m} \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot \\ \cdot \\ a_{p 1} & u_{p 2} & \cdot & u_{pm} \end{matrix}] = [\begin{matrix} u_{11} \sqrt{λ_{1}} & u_{12} \sqrt{λ_{2}} & \cdot \cdot \cdot & u_{1 m} \sqrt{λ_{m}} \\ u_{21} \sqrt{λ_{1}} & u_{22} \sqrt{λ_{2}} & \cdot \cdot \cdot & u_{2 m} \sqrt{λ_{m}} \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \cdot \\ \cdot \\ u_{p 1} \sqrt{λ_{1}} & u_{p 2} \sqrt{λ_{2}} & \cdot & u_{pm} \sqrt{λ_{m}} \end{matrix}]$ According to the requirements of the cumulative contribution rate, extract m characteristic roots and corresponding characteristic vectors to write out the factor loading matrix: $A = [\begin{matrix} a_{11} & a_{12} & &Center Dot; &Center Dot; &Center Dot; & a_{1 m} \\ a_{twenty one} & a_{twenty two} & &Center Dot; &Center Dot; &Center Dot; & a_{2 m} \\ \cdot & \cdot & \cdot & &Center Dot; \\ &Center Dot; & &Center Dot; & &Center Dot; & &Center Dot; \\ &Center Dot; & &Center Dot; & &Center Dot; & &Center Dot; \\ &Center Dot; \\ \cdot \\ a_{p 1} & u_{p 2} & \cdot & u_{pm} \end{matrix}] = [\begin{matrix} u_{11} \sqrt{λ_{1}} & u_{12} \sqrt{λ_{2}} & &Center Dot; &Center Dot; &Center Dot; & u_{1 m} \sqrt{λ_{m}} \\ u_{twenty one} \sqrt{λ_{1}} & u_{twenty two} \sqrt{λ_{2}} & &Center Dot; &Center Dot; &Center Dot; & u_{2 m} \sqrt{λ_{m}} \\ &Center Dot; & \cdot & \cdot & \cdot \\ &Center Dot; & &Center Dot; & &Center Dot; & &Center Dot; \\ &Center Dot; & &Center Dot; & &Center Dot; & &Center Dot; \\ \cdot \\ &Center Dot; \\ u_{p 1} \sqrt{λ_{1}} & u_{p 2} \sqrt{λ_{2}} & \cdot & u_{pm} \sqrt{λ_{m}} \end{matrix}]$

步骤(6)对A施行方差最大正交旋转；Step (6) implements variance maximum orthogonal rotation to A;

步骤(7)把烟草企业能源供需各指标分别用公共因子表示出来，通过这个式子可以看出其各影响因子的影响率；Step (7) expresses each index of energy supply and demand of tobacco enterprise with common factor respectively, can find out the influence rate of its each influence factor by this formula;

步骤(8)计算因子得分。Step (8) calculates factor scores.

2.核平滑处理2. Kernel smoothing

步骤(9)按如下公式对所提出的主成分时间点附近数据给予较大权数；Step (9) Give larger weights to the data near the proposed principal component time point according to the following formula;

${\overset{^^}{f f}}_{{t t}_{00}} = = \frac{{Σ Σ}_{t t = = 11}^{T T} {X x}_{t t} K K ((\frac{t t - - {t t}_{00}}{h h}))}{{Σ Σ}_{t t = = 11}^{T T} K K ((\frac{t t - - {t t}_{00}}{h h}))}$

式中：{X_t}——已知时间序列数据；In the formula: {X _t }——known time series data;

——核平滑数列；

— Kernel smooth sequence;

K(u)——核函数；K(u)——kernel function;

h——带宽。h - bandwidth.

步骤(10)计算带宽h，大的带宽会产生过度平滑的估计，遗漏趋势和所估计的峰和谷的度量上的一些可能的细节；当使用小的带宽时，仅有几个局的数据被使用，降低了估计的方差，却导致所得估计是一条波动的曲线；总体上需要反复尝试和修正；Step (10) calculates the bandwidth h, a large bandwidth will produce over-smoothed estimates, missing trends and some possible details on the metrics of the estimated peaks and valleys; when using a small bandwidth, only a few rounds of data is used, which reduces the variance of the estimate, but leads to a fluctuating curve in the estimate; it generally requires repeated trials and corrections;

步骤(11)得出新的经核平滑处理后的数列。Step (11) obtains a new sequence after kernel smoothing.

3.建立MGM(1，n)预测模型3. Establish MGM (1, n) prediction model

该模型可反映n个关联因素对其中某个因素变化率的影响，我们主要寻找n个关联因素中，能源供需中某个变量与其它因素之间的关系，这个影响因素是因子分析过程中提出的n个主成分，并对其进行预测。This model can reflect the influence of n related factors on the change rate of one of them. We mainly look for the relationship between a certain variable in energy supply and demand and other factors among n related factors. This influencing factor is proposed in the process of factor analysis. n principal components of , and predict them.

步骤(12)对能源的供和需中经因子分析后有n个影响系统的变量，每个变量有n个时刻的资料

其中相应的一次累加生成序列为

即：Step (12) In the supply and demand of energy, there are n variables that affect the system after factor analysis, and each variable has n time data

The corresponding one-time accumulation generation sequence is

Right now:

${X x}_{i i}^{((11))} ((k k)) = = {Σ Σ}_{j j = = 11}^{k k} {X x}_{i i}^{((00))} ((k k))$

式中：i＝1,2,…,N。In the formula: i=1,2,...,N.

步骤(13)建立MGM(1，n)模型；Step (13) establishes MGM (1, n) model;

MGM(1，n)模型就是对此生成序列建立n元一阶常微分方程组：The MGM(1,n) model is to establish an n-ary first-order ordinary differential equation system for this generated sequence:

$\{\begin{matrix} \frac{{dX wxya}_{11}^{((11))}}{dt dt} = = {a a}_{1111} {X x}_{11}^{((11))} + + {a a}_{1212} {X x}_{22}^{((11))} + + \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; + + {a a}_{11 n no} {X x}_{n no}^{((11))} + + {b b}_{11} \\ \frac{{dX wxya}_{22}^{((11))}}{dt dt} = = {a a}_{21 twenty one} {X x}_{11}^{((11))} + + {a a}_{22 twenty two} {X x}_{22}^{((11))} + + \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; + + {a a}_{22 n no} {X x}_{n no}^{((11))} + + {b b}_{22} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \frac{{dX wxya}_{n no}^{((11))}}{dt dt} = = {a a}_{n no 11} {X x}_{11}^{((11))} + + {a a}_{n no 22} {X x}_{22}^{((11))} + + \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot + + {a a}_{nn n} {X x}_{n no}^{((11))} + + {b b}_{n no} \end{matrix}$

令：make:

${X x}^{((00))} ((k k)) = = {[[{X x}_{11}^{((00))} ((k k)),, {X x}_{22}^{((00))} ((k k)),, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot;,, {X x}_{n no}^{((00))} ((k k))]]}^{T T}$

${X x}^{((11))} ((k k)) = = {[[{X x}_{11}^{((11))} ((k k)),, {X x}_{22}^{((11))} ((k k)),, \cdot \cdot \cdot \cdot \cdot \cdot,, {X x}_{n no}^{((11))} ((k k))]]}^{T T}$

$A A = = [\begin{matrix} {a a}_{1111} & {a a}_{1212} & \cdot \cdot \cdot \cdot \cdot \cdot & {a a}_{11 n no} \\ {a a}_{21 twenty one} & {a a}_{22 twenty two} & \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; & {a a}_{22 n no} \\ \cdot \cdot & \cdot &Center Dot; & \cdot \cdot & \cdot \cdot \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {a a}_{n no 11} & {a a}_{n no 22} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {a a}_{nn n} \end{matrix}]$

$B B = = [\begin{matrix} {b b}_{11} \\ {b b}_{22} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {b b}_{n no} \end{matrix}]$

式中：A、B——称为辨识参数。In the formula: A, B - called identification parameters.

步骤(14)根据MGM模型，写成矩阵形式有：Step (14) is written in matrix form according to the MGM model:

$\frac{{dX wxya}^{((11))}}{dt dt} {AX AX}^{((11))} + + B B$

步骤(15)用MATLAB，求解矩阵方程；Step (15) solves the matrix equation with MATLAB;

步骤(16)对方程的解，作累减还原，即求得系统中各因素的拟合值和预测值；Step (16) is to the solution of equation, carries out cumulative reduction reduction, namely obtains the fitted value and the predicted value of each factor in the system;

步骤(17)对计算结果进行分析，如不满意，或未达到顶期目标，可根据各系数的灰色区间，对系数矩阵进行适当调整或控制，再作仿真计算。这样反复协调，直到求得满意结果为止。Step (17) analyze the calculation result, if it is not satisfied, or the peak target is not reached, the coefficient matrix can be adjusted or controlled appropriately according to the gray interval of each coefficient, and then the simulation calculation can be performed. This coordination is repeated until a satisfactory result is obtained.

4.对预测的能源供需指标各个指标分别建立GM(1，1)残差修正模型4. Establish a GM(1, 1) residual correction model for each index of the predicted energy supply and demand index

步骤(18)对预测后的能源供需量建立残差序列；Step (18) establishes a residual sequence to the predicted energy supply and demand;

步骤(19)对残差序列的要求；Step (19) is to the requirement of residual sequence;

①非负：e≥0；①Non-negative: e≥0;

②单调升：e(K+1)≥e(K)；②Monotonically rising: e(K+1)≥e(K);

③如果残差序列中有e(h)<0，则应在残差上加一个适当的正数，使其中最小值变为0，得到新的残差序列。③ If there is e(h)<0 in the residual sequence, an appropriate positive number should be added to the residual to make the minimum value become 0 to obtain a new residual sequence.

步骤(20)建立残差GM(1，1)模型；Step (20) establishes residual GM (1,1) model;

步骤(21)得到

求出

Step (21) gets

find out

步骤(22)与实际值相比较得出新的残差，可验证其预测精度有所提高。Step (22) compares with the actual value to obtain a new residual error, which can verify that the prediction accuracy has been improved.

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变形，这些改进和变形也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.

Claims

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.