CN104699991B - Urban heating system year heating load Forecasting Methodology based on gray system theory - Google Patents
Urban heating system year heating load Forecasting Methodology based on gray system theory Download PDFInfo
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Abstract
Urban heating system year heating load Forecasting Methodology based on gray system theory, is related to a kind of urban heating system year heating load Forecasting Methodology, belongs to heating system load prediction technical field.The problem of Forecasting Methodology that the present invention solves existing single heating system cannot be used for urban heating systems organization.Technical key point is：Select initializaing variable, the numerical value over the years of dependent variable；Examine the degree of association of selected initializaing variable and dependent variable；Initializaing variable synteny is examined, and filters out explanatory variable；Build GM (1,1) and GM (1, N+1) model based on gray system theory, solving model parameter；Gray system state equation is set up, the year heating load of project period is predicted.Planned present invention can apply to cities and towns energy resource system or heating system.
Description
Technical field
Managed the present invention relates to a kind of urban heating system year heating load Forecasting Methodology, more particularly to a kind of gray system that is based on
The urban heating system year heating load Forecasting Methodology of opinion, belongs to heating system load prediction technical field.
Background technology
With the raising of China's Development of China's Urbanization and living standards of the people, comfort level to Building Indoor Environment and controllable
Property proposes higher requirement, and China's urban heating area and heating system heating load are continuously increased, nineteen ninety to 2012 years, I
State's Areas benefiting from central heating rise to 51.84 hundred million square metres from 2.13 hundred million square metres, and year heat supply total amount increases to from 2.87 hundred million GJs
29.5 hundred million GJs, heating system energy consumption has turned into the important component of social total energy consumption.But in the energy supply that China is nervous
Under present situation and the background for greatly developing low-carbon economy, need to make rational planning for energy structure, improve energy efficiency.
Urban energy system planning is set up on the basis of to energy demand reasonable prediction, and heat supply planning is broadly divided into two
Class：One class is to be directed to single heating system, based on enlarging scale recent and at a specified future date, in prediction, long-term heating demand, planning system
Extend capacity；Another kind of is to be directed to cities and towns, on the basis of original scattered or central heating, it is considered to the recent and long term planning in cities and towns
The Energy output of whole heating systems and supply in development, prediction heating demand or year heating load, planning cities and towns.At present both at home and abroad
Load prediction for single heating system is often based upon the heating power of objective system and the operational factor of hydraulic regime, outdoor weather
The historical datas such as parameter, it is impossible to which for the prediction of urban heating system loading, and in urban heating systems organization, main use refers to
Budgetary estimate method or Degree Days prediction thermic load or year heating load are marked, estimation basis source is single, it is impossible to reflect economy, the people in cities and towns
The development leveies such as mouth, industry and construction.
Therefore, need one kind badly and can be applied to cities and towns energy resource system or heating system planning, and it is consistent with town planning foundation,
Heat Supply Engineering development level can not only be embodied, can also reflect the confession of the development leveies such as cities and towns economy, population, industry and construction
Hot systems year heating load Forecasting Methodology.
The content of the invention
The purpose of the present invention is to propose to a kind of urban heating system year heating load Forecasting Methodology based on gray system theory,
The problem of to solve to cannot be used for urban heating systems organization for the Forecasting Methodology of single heating system.
The present invention is for the technical scheme that is used of solution above-mentioned technical problem：
Urban heating system year heating load Forecasting Methodology of the present invention based on gray system theory, is according to following
What step was realized：
Step 1: selection initializaing variable, the numerical value over the years of dependent variable：Cities and towns year heating load over the years is counted as dependent variable,
Statistics town planning index of correlation over the years is used as initializaing variable；
Step 2: examining the degree of association of selected initializaing variable and dependent variable：Calculate each first using grey Relational Analysis Method
The grey relational grade of beginning variable and dependent variable, the pass of selected initializaing variable and dependent variable is examined by the grey relational grade calculated
Connection degree, while carrying out preliminary screening to initializaing variable；
Step 3: initializaing variable synteny is examined, and filter out explanatory variable：Examine initial using correlation coefficient matrix
Variable synteny, then by stepwise regression analysis, screening draws explanatory variable；
Step 4: building GM (1,1) and GM (1, N+1) model based on gray system theory, solving model parameter；
Step 5: setting up gray system state equation, the year heating load of project period is predicted.
The beneficial effects of the invention are as follows：
1. the explanatory variable that the present invention chooses is unrelated with heating system operational factor, do not joined by heating system operation in cities and towns
Several limitations, and it is closely related with town development situation, it can reflect that urban heating engineering, economy, population, industry and construction etc. are sent out
Exhibition level, with town planning according to consistent.
2. the present invention is not limited, the year heating load of prediction using cities and towns as heating range by the quantity of heating system in cities and towns
Reflect whole urban heating load, while according to meteorologic parameter, at a temperature of outdoor calculating that year heating load conversion can heat
Thermic load, the foundation planned as cities and towns thermal source.
3. the present invention eliminates correlation between initializaing variable by screening, simplify as some explanatory variables, prediction can be simplified
Model, while ensureing to the explanatory of dependent variable.
4. the present invention is suitable to sample data less cities and towns year heating load based on the state equation that gray system theory is set up
Prediction, while the present invention possesses study, can be updated according to data year by year, explanatory variable and computation model ginseng are screened again
Number, sets up new state equation, it is ensured that the real-time and reliability of prediction.
Brief description of the drawings
Fig. 1 is the flow chart of the inventive method；
Fig. 2 is Harbin City 2003-2012 heating loads statistical value and 2011-2020 heating loads in the embodiment of the present invention
Predicted value schematic diagram.
Embodiment
The embodiment of the present invention is further described with reference to accompanying drawing.
Embodiment one：Illustrate present embodiment with reference to Fig. 1, one kind described in present embodiment is based on grey
The urban heating system year heating load Forecasting Methodology of Systems Theory, it is characterised in that the described method comprises the following steps：
Step 1: selection initializaing variable, the numerical value over the years of dependent variable：Using urban heating system year heating load as prediction pair
As statistics cities and towns year heating load over the years is as dependent variable, because heating system is used as one of northern cities and towns infrastructure construction
Point, in addition to the development level of Heat Supply Engineering itself, also restricted by development leveies such as cities and towns economy, population, industry and construction,
Therefore statistics town planning index of correlation over the years is used as initializaing variable；
The index of correlation is：Heat capacity, area of heat-supply service, heat supply pipeline length, residential estate, public facilities,
Industrial land, city end of the year total population, the total amount in city, regional GDP, city regional GDP, city first per capita
Industry total output value, city secondary industry total output value, city tertiary industry total output value, residential households average per capita disposable receive
Enter, town dweller's per capita consumption expenditure, urban house construction area and urban house building completed floor space, totally 17 it is initial
The statistical value of variable.
Step 2: examining the degree of association of selected initializaing variable and dependent variable：Calculate each first using grey Relational Analysis Method
The grey relational grade of beginning variable and dependent variable, the pass of selected initializaing variable and dependent variable is examined by the grey relational grade calculated
Connection degree, while carrying out preliminary screening to initializaing variable, rejects the relatively low initializaing variable of grey relational grade；
Step 3: initializaing variable synteny is examined, and filter out explanatory variable：Due to that may be present between initializaing variable
Synteny can influence the accuracy of forecast model.Therefore initializaing variable synteny is examined using correlation coefficient matrix, then passed through
Stepwise regression analysis, on the premise of and model accuracy explanatory to dependent variable is taken into account, screening draws explanatory variable；
Step 4: building GM (1,1) and GM (1, N+1) model based on gray system theory, solving model parameter；
Step 5: setting up gray system state equation, the year heating load of project period is predicted.
Embodiment two：Present embodiment from unlike embodiment one：Grey described in step 2 is closed
The calculating process of connection degree is as follows：
Step 2 one, nondimensionalization carried out to dependent variable and each initializaing variable using averaging method：
Wherein, XI, 0、xI, 0The dimensionless number and original value of respectively i-th annual dependent variable, XI, j、xI, jRespectively 1 year
The dimensionless number and original value of j-th of initializaing variable are spent, n is initializaing variable number, and m is the statistics year number of degrees,It is respectively
Dependent variable and the average in j-th of initializaing variable m year；
Step 2 two, using dimensionless dependent variable as auxiliary sequence X0=(X1,0, X2,0..., XM, 0)T, with dimensionless initializaing variable
For subsequence Xj=(X1, j, X2, j..., XM, j)T, calculate each annual auxiliary sequence X0With each subsequence XjAbsolute difference δI, j, and take
Maximum δ thereinmaxWith minimum value δmin：
δI, j=| XI, 0-XI, j| (2)
δmax=max { δI, j；I=1,2 ..., m；J=1,2 ..., n } (3)
δmin=min { δI, j；I=1,2 ..., m；J=1,2 ..., n } (4)
Step 2 three, each annual auxiliary sequence X of calculating0With each subsequence XjGrey incidence coefficient lI, j：
Wherein, ζ is resolution ratio, and its value is 0.5；
The grey relational grade of step 2 four, each initializaing variable and dependent variable is：
Embodiment three：Present embodiment from unlike embodiment one or two：
The process for carrying out preliminary screening to initializaing variable described in step 2 is as follows：
As grey relational grade LjJudge limit value L more than grey relational grade*When, judge the pass of j-th of initializaing variable and dependent variable
Lian Dugao, otherwise rejects the initializaing variable, completes preliminary screening, wherein L*Value is 0.6~0.8.
Embodiment four：Unlike one of present embodiment and embodiment one to three：Described in step 3
Initializaing variable synteny examine detailed process it is as follows：
Calculate the relative coefficient between initializaing variable：
Wherein, ruvFor the relative coefficient between u-th and v-th of initializaing variable, Var (Xu)、Var(Xv) it is respectively sub- sequence
Arrange Xu、XvVariance, Cov (Xu, Xv) it is subsequence Xu、XvCovariance；
Relative coefficient between all initializaing variables constitutes symmetrical correlation coefficient matrix r, and diagonal entry value is
1, matrix r diagonal is designated as with the element absolute value of up or down row or column | rpq|, when it is more than correlation prediction limit value r*When,
Judge that u-th of initializaing variable and v-th of initializaing variable correlation are strong, when between at least one initializaing variable and other initializaing variables
When having strong correlation, judge there is multicollinearity between initializaing variable, then initializaing variable is eliminated using Stepwise Regression Method
Between synteny, while filtering out explanatory variable, otherwise all initializaing variables are explanatory variable, wherein r*Value 0.8.
Embodiment five：Unlike one of present embodiment and embodiment one to four：Described in step 3
The detailed process for filtering out explanatory variable it is as follows：
Initializaing variable is screened using Stepwise Regression Method：The horizontal α of specification test, if parameter is estimated in regression model
The corresponding probable value p of t test statistics of evaluation is less than insolation level α, then retains the initializaing variable, otherwise deletes the initial change
Amount, the t for completing all initializaing variables according to forward or a backward stepwise regression analysis order is examined, and the initializaing variable finally retained is i.e.
To screen obtained explanatory variable, z is designated as1, z2..., zN, wherein α values are 5%~10%.
Embodiment six：Unlike one of present embodiment and embodiment one to five：Described in step 4
GM (1, the 1) model of structure based on gray system theory, the detailed process of solving model parameter is：
Statistics is pre-processed first, the original sequence that the calendar year statistics value of dependent variable and each explanatory variable is constituted
Row are designated asWithWherein k=1,2 ..., N, carry out it is cumulative after obtain dependent variable and
The one-accumulate formation sequence of each explanatory variable, is designated asWith
Then it is rightGM (1,1) model is set up respectively, obtains GM (1,1) model of each explanatory variable：
Wherein, akk、ckFor the parameter of k-th of explanatory variable GM (1,1) model, k=1,2 ..., N, τ is the time；
Discrete differential equation, obtaining matrix equation is：
Yk=BkAk (11)
Wherein,
GM (1,1) model parameter of k-th of explanatory variable is solved according to least square method：
Wherein,For Ak、akk、ckEstimate, k=1,2 ..., N.
Embodiment seven：Unlike one of present embodiment and embodiment one to six：Described in step 4
GM (1, the N+1) model of structure based on gray system theory, the detailed process of solving model parameter is：
To the one-accumulate formation sequence of dependent variableSet up the GM on N number of explanatory variable one-accumulate formation sequence
(1, N+1) model, obtains GM (1, N+1) model of dependent variable：
GM (1, N+1) model reflects the influence of N number of explanatory variable and dependent variable for dependent variable first derivative in itself.Its is micro-
Point equation form is：
Wherein, a00、a0kFor the parameter of GM (1, N+1) model, k=1,2 ..., N；
Discrete differential equation, obtaining matrix equation is：
Y0=B0A0 (14)
Wherein,
GM (1, N+1) model parameter is solved according to least square method：
Wherein,For A0、a00、a0kEstimate, k=1,2 ..., N.
Embodiment eight：Unlike one of present embodiment and embodiment one to seven：Described in step 5
Set up gray system state equation, predict project period year heating load detailed process be：
GM (1,1) model (formula (10)) of the N number of explanatory variable of simultaneous, GM (1, N+1) model (formula of dependent variable
(13)), formula (12) and formula (15) are substituted into formula (10) and formula (13) respectively, the state equation of gray system is obtained
For：
The calendar year statistics value of dependent variable and explanatory variable is initial value, setting number of degrees project period year, using Runge-Kutta methods
Solving state equation obtains the one-accumulate formation sequence of dependent variableThe predicted value that regressive reduction obtains dependent variable is carried out again
Wherein, M is statistics and total year number of degrees of project period.
The embodiment of the present invention is as follows：
Further elucidated below in conjunction with Harbin City year heating load prediction.
To verify the precision of Forecasting Methodology of the present invention, 2003~2010 years statistics are taken to predict 2011~the year two thousand twenty
Year heating load, wherein heating load predicted value in 2011 and 2012 is contrasted with statistical value, calculate predicated error.
Step 1: selection initializaing variable, the numerical value over the years of dependent variable.
According to《Chinese town and country construction database》Take passages Harbin City 2003-2012 heating loads (x0) united as dependent variable
Evaluation, is shown in Table 1.
The Harbin City 2003-2012 heating load statistical values of table 1
According to《Urban Construction in China statistical yearbook》、《Regional economic statistics yearbook》With《Chinese town and country construction data
Storehouse》Take passages Harbin City 2003-2010 heat capacities (x1), area of heat-supply service (x2), heat supply pipeline length (x3), residential estate
(x4), public facilities (x5), industrial land (x6), city end of the year total population (x7), the total amount (x in city8), area production it is total
It is worth (x9), city regional GDP (x per capita10), city primary industry total output value (x11), city secondary industry total output value
(x12), city tertiary industry total output value (x13), residential households per capita disposable income (x14), town dweller's pre-capita consumption branch
Go out (x15), urban house construction area (x16) and urban house building completed floor space (x17) etc. 17 initializaing variables system
Evaluation, is shown in Table 2.
The Harbin City 2003-2010 initializaing variable statistical values of table 2
Step 2: examining the degree of association of selected initializaing variable and dependent variable.
Using averaging method to dependent variable x0With initializaing variable x1~x17Nondimensionalization is carried out, auxiliary sequence X is constituted0With subsequence
Xj, the absolute difference of 2003~2010 annual each subsequences and auxiliary sequence is calculated, its maximum δ is obtainedmax=0.40862, it is minimum
Value δmin=0.00146.
Resolution ratio ζ takes 0.5, calculates 2003~2010 annual auxiliary sequence X0With each subsequence XjGrey incidence coefficient
lI, j, obtain each initializaing variable and the grey relational grade L of dependent variablej, it is shown in Table 3.
The initializaing variable x of table 31~x17With dependent variable x0Grey relational grade L1~L17
| Grey relational grade | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 |
| Numerical value | 0.9437 | 0.9519 | 0.8997 | 0.8357 | 0.8087 | 0.8072 | 0.7274 | 0.7657 | 0.8301 |
| Grey relational grade | L10 | L11 | L12 | L13 | L14 | L15 | L16 | L17 | |
| Numerical value | 0.8456 | 0.9170 | 0.8280 | 0.7896 | 0.9013 | 0.8931 | 0.6089 | 0.6762 |
Grey relational grade judges limit value L*Take 0.6, the degree of association L of each initializaing variable and dependent variablej0.6 is above, illustrates institute
Select 17 initializaing variables high with the dependent variable degree of association.
Step 3: initializaing variable synteny is examined, and filter out explanatory variable.
Relative coefficient between initializaing variable is calculated, correlation coefficient matrix r is constituted, is shown in Table 4.
The correlation coefficient matrix r of the initializaing variable of table 4
Correlation prediction limit value r*Take 0.8, it is known that x16And x17Correlation with other each initializaing variables is weaker, but other
Have between initializaing variable between stronger correlation, initializaing variable and there is multicollinearity, it is necessary to using stepwise regression analysis side
Method eliminates synteny.
Initializaing variable is screened using forward stepwire regression analytic approach.It is initial relative to each that dependent variable is set up respectively
The regression model of variable, calculates the t test statistics and corresponding probable value p of estimates of parameters in each regression model, by t
The order of test statistics (or probable value p is from small to large) from big to small arranges each initializaing variable.Sequentially add t test statistics
The initializaing variable of (or probable value p is small) carries out successive Regression greatly.Insolation level α takes 5%, when probable value p is less than 5%, retains
The initializaing variable, is otherwise deleted.Said process is repeated, is examined until all initializaing variables are added regression model and complete t.Most
After obtain 2 explanatory variables：Urban house building completed floor space (is designated as z1=x17) and heat capacity (be designated as z2=x1)。
Step 4: building GM (1,1) and GM (1,3) model based on gray system theory, solving model parameter.
Statistics is pre-processed first, the one-accumulate formation sequence of dependent variable and two explanatory variables is calculated With
Then to explanatory variableWithGM (1,1) model is set up respectively：
According to least square method, above-mentioned two GM (1,1) model parameter is solved：
Again to dependent variableSet up on explanatory variableWithGM (1,3) model：
According to least square method, GM (1,3) model parameter is solved：
Step 5: setting up gray system state equation, the year heating load of project period is predicted.
GM (1, the 1) models of two explanatory variables of simultaneous and GM (1,3) model of dependent variable, substitute into what is solved in step 4
Model parameter, builds gray system state equation as follows：
Using Runge-Kutta method solving state equations.If project period is 2011~the year two thousand twenty, pass through regressive reducing condition
Non trivial solution, obtains each annual heating load project period：
Harbin City 2003-2012 heating loads statistical value and 2011-2020 heating load predicted values are as shown in Figure 2.
Using predicted value and the error ε evaluation and foreca precision of statistical value：
Wherein,X is respectively predicted value and statistical value.
The Harbin City heating system year predicted value of heating load and the error of statistical value of 2011 and 2012 be respectively
1.82%th, 8.24%, less than acceptable error limit value 10%, precision of prediction is subjected to.
Claims (8)
1. a kind of urban heating system year heating load Forecasting Methodology based on gray system theory, it is characterised in that methods described bag
Include following steps：
Step 1: selection initializaing variable, the numerical value over the years of dependent variable：Cities and towns year heating load over the years is counted as dependent variable, statistics
Town planning index of correlation over the years is used as initializaing variable；
Step 2: examining the degree of association of selected initializaing variable and dependent variable：Each initial change is calculated using grey Relational Analysis Method
Amount and the grey relational grade of dependent variable, associating for selected initializaing variable and dependent variable is examined by the grey relational grade calculated
Degree, while carrying out preliminary screening to initializaing variable；
Step 3: initializaing variable synteny is examined, and filter out explanatory variable：Initializaing variable is examined using correlation coefficient matrix
Synteny, then by stepwise regression analysis, screening draws explanatory variable；
Step 4: building GM (1,1) model of each explanatory variable, GM (1, N+ is built jointly with all explanatory variables and dependent variable
1) model, solving model parameter；
Step 5: setting up gray system state equation, the year heating load of project period is predicted.
2. the urban heating system year heating load Forecasting Methodology according to claim 1 based on gray system theory, it is special
Levy and be that the calculating process of the grey relational grade described in step 2 is as follows：
Step 2 one, nondimensionalization carried out to dependent variable and each initializaing variable using averaging method：
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Wherein, Xi,0、xi,0The dimensionless number and original value of respectively i-th annual dependent variable, Xi,j、xi,jRespectively i-th annual jth
The dimensionless number and original value of individual initializaing variable, n are initializaing variable number, and m is the statistics year number of degrees,It is dependent variable respectively
With the average in j-th of initializaing variable m year；
Step 2 two, using dimensionless dependent variable as auxiliary sequence X0=(X1,0,X2,0,…,Xm,0)T, using dimensionless initializaing variable as son
Sequence Xj=(X1,j,X2,j,…,Xm,j)T, calculate each annual auxiliary sequence X0With each subsequence XjAbsolute difference δi,j, and take wherein
Maximum δmaxWith minimum value δmin：
δi,j=| Xi,0-Xi,j| (2)
δmax=max { δi,j；I=1,2 ..., m；J=1,2 ..., n } (3)
δmin=min { δi,j；I=1,2 ..., m；J=1,2 ..., n } (4)
Step 2 three, each annual auxiliary sequence X of calculating0With each subsequence XjGrey incidence coefficient li,j：
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The grey relational grade of step 2 four, each initializaing variable and dependent variable is：
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3. the urban heating system year heating load Forecasting Methodology according to claim 2 based on gray system theory, it is special
Levy and be that the process for carrying out preliminary screening to initializaing variable described in step 2 is as follows：
As grey relational grade LjJudge limit value L more than grey relational grade*When, judge the degree of association of j-th of initializaing variable and dependent variable
Height, otherwise rejects the initializaing variable, completes preliminary screening, wherein L*Value is 0.6~0.8.
4. the urban heating system year heating load Forecasting Methodology according to claim 3 based on gray system theory, it is special
Levy and be that the detailed process that the initializaing variable synteny described in step 3 is examined is as follows：
Calculate the relative coefficient between initializaing variable：
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<mi>a</mi>
<mi>r</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>X</mi>
<mi>v</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
</mrow>
</mfrac>
<mo>,</mo>
<mi>u</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>n</mi>
<mo>;</mo>
<mi>v</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, ruvFor the relative coefficient between u-th and v-th of initializaing variable, Var (Xu)、Var(Xv) it is respectively subsequence Xu、
XvVariance, Cov (Xu,Xv) it is subsequence Xu、XvCovariance；
Relative coefficient between all initializaing variables constitutes symmetrical correlation coefficient matrix r, and diagonal entry value is 1, square
Battle array r diagonal are designated as with the element absolute value of up or down row or column | rpq|, when it is more than correlation prediction limit value r*When, judge
U-th of initializaing variable and v-th of initializaing variable correlation are strong, strong when having between at least one initializaing variable and other initializaing variables
During correlation, judge there is multicollinearity between initializaing variable, then using between Stepwise Regression Method elimination initializaing variable
Synteny, while filtering out explanatory variable, otherwise all initializaing variables are explanatory variable.
5. the urban heating system year heating load Forecasting Methodology according to claim 4 based on gray system theory, it is special
Levy and be that the detailed process for filtering out explanatory variable described in step 3 is as follows：
Initializaing variable is screened using Stepwise Regression Method：The horizontal α of specification test, if estimates of parameters in regression model
The corresponding probable value p of t test statistics be less than insolation level α, then retain the initializaing variable, otherwise delete the initializaing variable,
The t for completing all initializaing variables according to forward or a backward stepwise regression analysis order is examined, and the initializaing variable finally retained is
Obtained explanatory variable is screened, z is designated as1,z2,…,zN, wherein α values are 5%~10%.
6. the urban heating system year heating load Forecasting Methodology according to claim 5 based on gray system theory, it is special
Levy and be GM (1, the 1) model of the structure described in step 4 based on gray system theory, the detailed process of solving model parameter is：
The original series that the calendar year statistics value of dependent variable and each explanatory variable is constituted are designated asWithWherein k=1,2 ..., N, obtained after adding up the one-accumulate life of dependent variable and each explanatory variable
Into sequence, it is designated asWith
<mrow>
<msubsup>
<mi>x</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
</msub>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</munderover>
<msub>
<mi>x</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</munderover>
<msub>
<mi>x</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>x</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>z</mi>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>z</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</munderover>
<msub>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>i</mi>
</munderover>
<msub>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>z</mi>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mi>k</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
Then it is rightGM (1,1) model is set up respectively, obtains GM (1,1) model of each explanatory variable：
<mrow>
<mfrac>
<mrow>
<msubsup>
<mi>dz</mi>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
<mrow>
<mi>d</mi>
<mi>&tau;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>a</mi>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>z</mi>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msub>
<mi>c</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, akk、ckFor the parameter of k-th of explanatory variable GM (1,1) model, k=1,2 ..., N, τ is the time；
Discrete differential equation, obtaining matrix equation is：
Yk=BkAk (11)
Wherein,
GM (1,1) model parameter of k-th of explanatory variable is solved according to least square method：
<mrow>
<msub>
<mover>
<mi>A</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mi>a</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>c</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>B</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>B</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msubsup>
<mi>B</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>Y</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,For Ak、akk、ckEstimate, k=1,2 ..., N.
7. the urban heating system year heating load Forecasting Methodology according to claim 6 based on gray system theory, it is special
Levy and be GM (1, the N+1) model of the structure described in step 4 based on gray system theory, the detailed process of solving model parameter
For：
To the one-accumulate formation sequence of dependent variableSet up the GM (1, N+ on N number of explanatory variable one-accumulate formation sequence
1) model, obtains GM (1, N+1) model of dependent variable：
The differential equation form of GM (1, N+1) model is：
<mrow>
<mfrac>
<mrow>
<msubsup>
<mi>dx</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
<mrow>
<mi>d</mi>
<mi>&tau;</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>00</mn>
</msub>
<msubsup>
<mi>x</mi>
<mn>0</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>a</mi>
<mrow>
<mn>0</mn>
<mi>k</mi>
</mrow>
</msub>
<msubsup>
<mi>z</mi>
<mi>k</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, a00、a0kFor the parameter of GM (1, N+1) model, k=1,2 ..., N；
Discrete differential equation, obtaining matrix equation is：
Y0=B0A0 (14)
Wherein,
<mrow>
<msub>
<mi>Y</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>x</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>x</mi>
<mrow>
<mn>3</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>x</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msub>
<mi>B</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mrow>
<mn>3</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mn>3</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mn>3</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mrow></mrow>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>&lsqb;</mo>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
<mtd>
<mn>...</mn>
</mtd>
<mtd>
<msubsup>
<mi>z</mi>
<mrow>
<mi>m</mi>
<mo>,</mo>
<mi>N</mi>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>00</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mn>01</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>a</mi>
<mrow>
<mn>0</mn>
<mi>N</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
GM (1, N+1) model parameter is solved according to least square method：
<mrow>
<msub>
<mover>
<mi>A</mi>
<mo>^</mo>
</mover>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mover>
<mi>a</mi>
<mo>^</mo>
</mover>
<mn>00</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>a</mi>
<mo>^</mo>
</mover>
<mn>01</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>a</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>0</mn>
<mi>N</mi>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>B</mi>
<mn>0</mn>
<mi>T</mi>
</msubsup>
<msub>
<mi>B</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msubsup>
<mi>B</mi>
<mn>0</mn>
<mi>T</mi>
</msubsup>
<msub>
<mi>Y</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,For A0、a00、a0kEstimate, k=1,2 ..., N.
8. the urban heating system year heating load Forecasting Methodology according to claim 7 based on gray system theory, it is special
Levy and be to set up gray system state equation described in step 5, predict project period year heating load detailed process be：
GM (1,1) model of the N number of explanatory variable of simultaneous, GM (1, N+1) model of dependent variable, by formula (12) and formula (15) point
Dai Ru not be in formula (10) and formula (13), the state equation for obtaining gray system is：
The calendar year statistics value of dependent variable and explanatory variable is initial value, and setting number of degrees project period year are solved using Runge-Kutta methods
State equation obtains the one-accumulate formation sequence of dependent variableThe predicted value that regressive reduction obtains dependent variable is carried out again
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mn>0</mn>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>M</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>s</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>M</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<msubsup>
<mover>
<mi>x</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mo>,</mo>
<mn>0</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, M is statistics and total year number of degrees of project period.
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| CN108646688B (en) * | 2018-05-31 | 2019-05-07 | 成都天衡智造科技有限公司 | A kind of process parameter optimizing analysis method based on recurrence learning |
| CN110309944B (en) * | 2019-04-23 | 2023-09-01 | 上海发电设备成套设计研究院有限责任公司 | Regional energy supply cold and hot load prediction method |
| CN110097403A (en) * | 2019-05-08 | 2019-08-06 | 国网冀北电力有限公司秦皇岛供电公司 | A kind of prediction technique and forecasting system of heating demands |
| CN111476439B (en) * | 2020-05-18 | 2023-08-04 | 瑞纳智能设备股份有限公司 | Heating valve adjusting method, system and equipment based on gray time sequence |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1892205A (en) * | 2005-07-07 | 2007-01-10 | 日本油漆株式会社 | Heat amount prediction method, heat amount prediction system, and recording medium having heat amount prediction program |
| CN103363585A (en) * | 2013-08-08 | 2013-10-23 | 天津海天方圆节能技术有限公司 | Regulating method of center heating system in urban area |
| CN103649852A (en) * | 2011-05-11 | 2014-03-19 | 原子能及能源替代委员会 | Method of predicting the energy consumption of a building |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW200933517A (en) * | 2008-01-22 | 2009-08-01 | Univ Nat Pingtung Sci & Tech | Calculating method of systematic risk |
| WO2013071414A1 (en) * | 2011-11-14 | 2013-05-23 | Energent Incorporated | System, method and computer program for forecasting energy price |
-
2015
- 2015-03-30 CN CN201510144306.9A patent/CN104699991B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1892205A (en) * | 2005-07-07 | 2007-01-10 | 日本油漆株式会社 | Heat amount prediction method, heat amount prediction system, and recording medium having heat amount prediction program |
| CN103649852A (en) * | 2011-05-11 | 2014-03-19 | 原子能及能源替代委员会 | Method of predicting the energy consumption of a building |
| CN103363585A (en) * | 2013-08-08 | 2013-10-23 | 天津海天方圆节能技术有限公司 | Regulating method of center heating system in urban area |
Non-Patent Citations (3)
| Title |
|---|
| 基于灰色模型和最小二乘支持向量机的电力短期负荷组合预测;唐杰明 等;《电网技术》;20090228;第33卷(第3期);第63-68页 * |
| 民用建筑供热负荷的神经网络法预测;杜进荣 等;《煤气与热力》;20010215;第21卷(第1期);第16-19页 * |
| 集中供热系统运行调节优化及热负荷预测方法研究;王庆峰;《中国优秀硕士学位论文全文数据库工程科技Ⅱ辑》;20100815;第1-75页 * |
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