CN110210000A - The identification of industrial process efficiency and diagnostic method based on Multiple Non Linear Regression - Google Patents
The identification of industrial process efficiency and diagnostic method based on Multiple Non Linear Regression Download PDFInfo
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- 238000004519 manufacturing process Methods 0.000 title claims abstract description 31
- 238000012417 linear regression Methods 0.000 title claims abstract description 20
- 238000002405 diagnostic procedure Methods 0.000 title claims abstract description 15
- 239000002994 raw material Substances 0.000 claims abstract description 52
- 230000001419 dependent effect Effects 0.000 claims abstract description 28
- 238000004458 analytical method Methods 0.000 claims abstract description 10
- 238000009776 industrial production Methods 0.000 claims abstract description 6
- 238000006467 substitution reaction Methods 0.000 claims abstract description 6
- 238000004364 calculation method Methods 0.000 claims description 32
- 238000009826 distribution Methods 0.000 claims description 7
- 230000000694 effects Effects 0.000 claims description 4
- 239000011159 matrix material Substances 0.000 claims description 3
- VGGSQFUCUMXWEO-UHFFFAOYSA-N Ethene Chemical compound C=C VGGSQFUCUMXWEO-UHFFFAOYSA-N 0.000 abstract description 47
- 239000005977 Ethylene Substances 0.000 abstract description 47
- 238000000034 method Methods 0.000 abstract description 17
- 239000000463 material Substances 0.000 abstract description 10
- 239000000126 substance Substances 0.000 description 10
- 239000000446 fuel Substances 0.000 description 8
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 8
- 239000010779 crude oil Substances 0.000 description 7
- 230000005611 electricity Effects 0.000 description 6
- 230000008569 process Effects 0.000 description 6
- 238000005265 energy consumption Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 238000000611 regression analysis Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 239000003921 oil Substances 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- -1 steam Substances 0.000 description 2
- 150000001336 alkenes Chemical class 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000007621 cluster analysis Methods 0.000 description 1
- 230000001149 cognitive effect Effects 0.000 description 1
- 238000002485 combustion reaction Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000007405 data analysis Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000003745 diagnosis Methods 0.000 description 1
- 239000003814 drug Substances 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 229930195733 hydrocarbon Natural products 0.000 description 1
- 150000002430 hydrocarbons Chemical class 0.000 description 1
- 230000003455 independent Effects 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012544 monitoring process Methods 0.000 description 1
- 238000000491 multivariate analysis Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000000513 principal component analysis Methods 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Abstract
The industrial process efficiency based on Multiple Non Linear Regression that the invention discloses a kind of identifies and diagnostic method, it include: product output data and each raw material data obtained among industrial production data, product output data and raw material data are carried out unitization, so that product output data are as dependent variable, raw material data is as independent variable, curve estimation is carried out respectively to dependent variable and each independent variable, substitution is fitted respectively to each raw material data, raw material data after replacing to product output data and fitting carries out linear regression analysis, obtain efficiency identification and diagnostic model.The objective mathematical relationship presented between product output and each production raw material of technical solution provided by the invention, realizes and puts into the method for obtaining optimal product output by adjusting different raw material.Therefore, the present invention adjusts the material rate of ethylene producing device by above-mentioned mathematical relationship, improves energy efficiency, reduces wastage of material.
Description
Technical field
The present invention relates to the technical field of Industrial Process Monitoring more particularly to a kind of industry based on Multiple Non Linear Regression
The identification of process efficiency and diagnostic method.
Background technique
Industrial process is the important production process for being related to Chinese national economy and social development, especially complicated chemical industry
Process.Ethylene is one of most important chemicals in chemical industry, and production process accounts for the 30% of chemical industry production process.
2017,1.69 hundred million tons of global ethylene production capacity increased by 7,250,000 tons than last year, and 1.54 hundred million tons of same period ethylene consumption figure increases than last year
Long 4.2%.2017, China's ethylene aggregated capacity increased to 23,210,000 tons, and the consumption increase rate of same period ethylene is up to 10% or more, second
The demand of alkene is in a short time by sustainable growth.2017, Sinopec reinforced raw material structure adjustment, realized input-output efficiency
It maximizes, carries out dynamic optimization.For optimizing raw material quality, oil company adjusts lighter hydrocarbons and naphtha ratio.However, high energy consumption is
One of the significant challenge that complicated chemical industry faces, ethylene production are one of the processes that complicated chemical most consumes energy in the process.
Currently, the energy consumption of ethylene production accounts for 15% or more (including fuel and material etc.) in all chemical products.Therefore, it is necessary to
Mathematical relationship between ethylene production capacity and raw material is identified and diagnosed.
Summary of the invention
A kind of industry based on Multiple Non Linear Regression is provided to solve limitation and defect, the present invention of the existing technology
The identification of process efficiency and diagnostic method, comprising:
Obtain the product output data among industrial production data and each raw material data；
It is unitization to the product output data and raw material data progress, so that the product output data conduct
Dependent variable, the raw material data is as independent variable；
Curve estimation is carried out respectively to the dependent variable and each independent variable, the calculation formula of multiple linear equation is such as
Under:
yi=β0+β1x1+β2x2+...+βmxm+δiδi~N (0, δ2)
Wherein, yiIt is dependent variable, x1..., xmIt is dependent variable, β0It is constant, β1... βmIt is coefficient, δiExpression is each adopted
The deviation of sampling point and straight line, δiMutually indepedent and Normal Distribution；
Substitution is fitted respectively to each raw material data, the calculation formula of multilinear fitting equation is as follows:
yi=b0+b1xi1+b2xi2+...+bmxim+ δ, i=1,2..., n
Wherein, b0It is the intercept of fit equation, b1..., bmIt is the slope of fit equation；
Raw material data after replacing to the product output data and fitting carries out linear regression analysis, obtains efficiency
Identification and diagnostic model, the calculation formula of Cubic regression model are as follows:
Y=b0+b1x+b2x2+b3x3
Alternatively, the calculation formula of regression model is as follows twice:
Y=b0+b1x+b2x2。
Optionally, the calculation formula of linear equation in two unknowns is as follows:
Wherein, yiIt is dependent variable, xiIt is dependent variable, β0It is constant, β1It is coefficient, δiIndicate the inclined of each sampled point and straight line
Difference, δiMutually indepedent and Normal Distribution；
The calculation formula of binary linearity fit equation is as follows:
Wherein, b0It is the intercept of fit equation, b1It is the slope of fit equation
Residual sum of squares (RSS) calculation formula is as follows:
It is as follows that calculation formula is obtained according to above three formula:
Wherein,WithIt is sample mean.
Optionally, further includes:
Use R2Value indicates fitting effect, R2The calculation formula of value is as follows:
Optionally, further includes:
Matrix expression is carried out to the multilinear fitting equation, calculation formula is as follows:
Y=X β+δ
Wherein, the value of β, δ, Y and X are expressed as follows:
The value of β is expressed as follows:
β=(XTX)-1XTY。
Optionally, further includes:
Non-rectilinear equation is converted into linear equation by variable replacement, calculation formula is as follows:
The present invention have it is following the utility model has the advantages that
The identification of industrial process efficiency and diagnostic method provided by the invention based on Multiple Non Linear Regression, comprising: obtain
Product output data and each raw material data among industrial production data, to the product output data and the raw material
Data progress is unitization, so that the product output data are as dependent variable, the raw material data is as independent variable, to described
Dependent variable and each independent variable carry out curve estimation respectively, are fitted substitution respectively to each raw material data,
Raw material data after replacing to the product output data and fitting carries out linear regression analysis, obtains efficiency identification and examines
Disconnected model.The objective mathematical relationship presented between product output and each production raw material of technical solution provided by the invention,
It realizes and puts into the method for obtaining optimal product output by adjusting different raw material.Therefore, technical solution provided by the invention
The objective mathematical relationship between ethylene production capacity and various raw material energy consumptions can be identified, so as to adjust the original of ethylene producing device
Material ratio improves energy efficiency, reduces wastage of material.
Detailed description of the invention
Fig. 1 is the ethylene data modeling flow chart that the embodiment of the present invention one provides.
Fig. 2 is the curve matching figure of the ethylene yield that the embodiment of the present invention one provides and crude oil amount.
Fig. 3 is the curve matching figure of ethylene yield and fuel quantity that the embodiment of the present invention one provides.
Fig. 4 is the curve matching figure of ethylene yield and quantity of steam that the embodiment of the present invention one provides.
Fig. 5 is the curve matching figure of the ethylene yield provided of the embodiment of the present invention one and water.
Fig. 6 is the curve matching figure of ethylene yield and electricity that the embodiment of the present invention one provides.
Fig. 7 is the linear fit schematic diagram of prediction ethylene yield and practical ethylene yield that the embodiment of the present invention one provides.
Fig. 8 is the predicted value for the ethylene yield that the embodiment of the present invention one provides and the comparison schematic diagram of actual value.
Specific embodiment
To make those skilled in the art more fully understand technical solution of the present invention, the present invention is mentioned with reference to the accompanying drawing
The industrial process efficiency identification based on Multiple Non Linear Regression supplied is described in detail with diagnostic method.
Embodiment one
Due to the multidimensional of complicated chemical data, close coupling and noise characteristic, it is difficult to accurately identify and predict complicated chemistry
The Relationship with Yield of process.The analysis of multivariate statistics data can be divided into two major classes, and wherein cognitive approach includes principal component analysis and cluster
Analysis, modeling method includes regression analysis and discriminant analysis.Regression analysis mainly by data analysis find out dependent variable with
Functional relation between independent variable, for establishing prediction model.In mathematical modeling, regression analysis can be determined between variable
Quantitative relationship, to obtain prediction result.Regression analysis has been used for food, medicine and chemical analysis.With Multiple Non Linear Regression
Method can establish objective mathematical model, obtain the non-linear relation between multiple independents variable and dependent variable.Therefore, this implementation
Example proposes a kind of identification of efficiency and diagnostic method, and raw material disappears during analyzing complicated chemical using multiple nonlinear regression method
Objective mathematical relationship between consumption and corresponding product output.
The present embodiment propose it is a kind of based on nonlinear regression complex industrial process efficiency identification and diagnostic method, the party
Method uses degree of fitting to raw material variable to each raw material and product output data progress curve estimation in industrial process respectively
Higher curvilinear equation is calculated and is replaced, and the variable after finally replacing to product output and each raw material is linearly returned
Return analysis, identifies the objective mathematical relationship in industrial process between product output and each raw material material energy consumption.
The present embodiment obtains product output data and each raw material data in industrial production data, produces to the product
Data and the raw material data carry out unitization out, using product output data as dependent variable, each raw material data conduct
Independent variable carries out curve estimation to dependent variable and each independent variable respectively.What the present embodiment was related to is that can be replaced by variable
Change the curve for being converted into linear relationship.The calculation formula of linear equation in two unknowns provided in this embodiment is as follows:
Wherein, yiIt is dependent variable, xiIt is dependent variable, β0It is constant, β1It is coefficient, δiIndicate the inclined of each sampled point and straight line
Difference, δiMutually indepedent and Normal Distribution.
The calculation formula of binary linearity fit equation provided in this embodiment is as follows:
Wherein, b0It is the intercept of fit equation, b1It is the slope of fit equation.
Residual sum of squares (RSS) calculation formula provided in this embodiment is as follows:
The present embodiment is as follows according to above three formula acquisition calculation formula:
Wherein,WithIt is sample mean.
R provided in this embodiment2Value is used to indicate fitting effect, wherein R2Value closer to 1, indicate that fitting effect is better.
R2The calculation formula of value is as follows:
The present embodiment carries out curve estimation, the meter of multiple linear equation to the dependent variable and each independent variable respectively
It is as follows to calculate formula:
yi=β0+β1x1+β2x2+...+βmxm+δiδ x~N (0, δ2)
Wherein, yiIt is dependent variable, x1..., xmIt is dependent variable, β0It is constant, β1... βmIt is coefficient, δiExpression is each adopted
The deviation of sampling point and straight line, δiMutually indepedent and Normal Distribution.
The present embodiment is fitted substitution to each raw material data respectively, and the calculating of multilinear fitting equation is public
Formula is as follows:
yi=b0+b1xi1+b2xi2+...+bmxim+ δ, i=1,2..., n
Wherein, b0It is the intercept of fit equation, b1..., bmIt is the slope of fit equation.
The present embodiment carries out matrix expression to the multilinear fitting equation, and calculation formula is as follows:
Y=X β+δ
Wherein, the value of β, δ, Y and X are expressed as follows:
The value of β is expressed as follows:
β=(XTX)-1XTY
Non-rectilinear equation is converted to linear equation by variable replacement by the present embodiment, and calculation formula is as follows:
Cubic fit homing method provided in this embodiment and Quadratic Regression Fitting method are similar to simple linear.Residual error is flat
Square and smaller, the degree of fitting of regression equation is higher.The value of regression coefficient can be determined by calculating partial derivative.The present embodiment mentions
The calculation formula of the Cubic regression model of confession is as follows:
Y=b0+b1x+b2x2+b3x3
The calculation formula of regression model twice provided in this embodiment is as follows:
Y=b0+b1x+b2x2
Below with the actual industrial data instance of ethylene producing device, to efficiency provided in this embodiment identification and diagnosis side
The specific implementation details and mode of method are illustrated.
Fig. 1 is the ethylene data modeling flow chart that the embodiment of the present invention one provides.As shown in Figure 1, dependent variable is ethylene production
Measure (E), crude oil (Co), fuel (F1), steam (Sm), water (Wr), electric (Ey) total flow be independent variable.Ethylene yield and original
Oil with ton (t) be unit metering, fuel, steam, water, electricity measurement unit be converted into GJ.To (including the combustion of ethylene yield and raw material
Material, crude oil, steam, water and electricity) between carry out curve estimation respectively.This host uses the calculated result of the higher equation of degree of fitting
Instead of the variable of raw material, linear regression analysis then is carried out to the raw material after ethylene yield and substitution.R2Value is as shown in table 1:
The corresponding R of fit equation between 1 ethylene yield of table and raw material2Value
In the present embodiment, the final regression curve equation of ethylene yield and crude oil is as follows:
E=exp (11.64-118819.68/Co)
Wherein, R2Value is 0.985.
Fig. 2 is the curve matching figure of the ethylene yield that the embodiment of the present invention one provides and crude oil amount.As shown in Fig. 2, showing
The curvilinear equation has very high fitness and applicability.
In the present embodiment, the final regression curve equation between ethylene yield and fuel quantity is as follows:
E=-173403.74+19191.80*Fl-18.42*Fl3
Wherein, R2Value is 0.983.
Fig. 3 is the curve matching figure of ethylene yield and fuel quantity that the embodiment of the present invention one provides.Shown in Fig. 3, illustrate song
Line equation has very high fitness and applicability.
In the present embodiment, the final regression curve equation between ethylene yield and steam is as follows:
E=63653.03+1347.31*Sm-1385.40*Sm2+108.96*Sm3
Wherein, R2Value is 0.969.
Fig. 4 is the curve matching figure of ethylene yield and quantity of steam that the embodiment of the present invention one provides.As shown in figure 4, explanation
Curvilinear equation has very high fitness and applicability.
In the present embodiment, the final regression curve equation between ethylene yield and water is as follows:
E=100306.07-25582.53*Wr+491.88*Wr3
Wherein, R2Value is 0.980.
Fig. 5 is the curve matching figure of the ethylene yield provided of the embodiment of the present invention one and water.As shown in figure 5, showing song
Line equation has very high fitness and applicability.
In the present embodiment, the final regression curve equation between ethylene yield and electricity is as follows:
E=62997.29+28356.77*Ey-32157.34*Ey2
Wherein, R2Value is 0.948.
Fig. 6 is the curve matching figure of ethylene yield and electricity that the embodiment of the present invention one provides.As shown in fig. 6, illustrating song
Line equation has very high fitness and applicability.
Pass through the calculating to actual production data, crude oil variable (Cov), fuel variable (Flv), steam variable (Smv), water
Variable (Wrv) and electric variable (Eyv) are replaced using the calculated result of ethylene variable among above-mentioned five formula respectively.Select ethylene
Variable is dependent variable, and Cov, Flv, Smv, Wrv and Eyv are independent variable, after carrying out variable conversion, ethylene yield and each change certainly
There are linear relationship between amount, calculation formula is as follows:
E=-1041.28+0.33*Cov+0.42*Flv
+0.05*Smv+0.003*Ww+0.22*Eyv
Wherein, R2Value is 0.991, illustrates linear model fitness with higher and applicability.The present embodiment provides
Technical solution it is objective present product output and it is each production raw material between mathematical relationship, realize by adjusting different
Raw material put into the method for obtaining optimal product output.R2Value is as shown in table 1:
The corresponding R of 2 linear model of table2Value
It is as follows that the present embodiment according to above-mentioned six formula obtains final numerical relationship model:
E=-1041.28+0.33*exp (11.64-118819.68Co)
+0.42*(-173403.74+19191.80*Fl-18.42*Fl3)
+0.05*(63653.03+1347.31*Sm-1385.40*Sm2
+108.96*Sm3)+0.003*(100306.07-25582.53*Wr
+491.88*Wr3)+0.22*(62997.29+28356.77*Ey
-32157.34*Ey2)
The data of ethylene unit are brought into the ethylene yield value that above-mentioned formula is predicted by the present embodiment.Fig. 7 is the present invention
The linear fit schematic diagram of prediction ethylene yield and practical ethylene yield that embodiment one provides, Fig. 8 are the embodiment of the present invention one
The predicted value of the ethylene yield of offer and the comparison schematic diagram of actual value.According to Fig. 7 and Fig. 8 it is found that energy provided in this embodiment
Source efficiency identifying and diagnosing model fitness with higher and applicability.Meanwhile based on this model to crude oil, fuel, steam,
The raw material such as water, electricity carry out reasonable distribution, and energy efficiency can be improved, and reduce waste of raw materials.
The identification of industrial process efficiency and diagnostic method provided in this embodiment based on Multiple Non Linear Regression, comprising: obtain
The product output data among industrial production data and each raw material data are obtained, to the product output data and the former material
It is unitization to expect that data carry out, so that the product output data are as dependent variable, the raw material data is as independent variable, to institute
It states dependent variable and each independent variable carries out curve estimation respectively, each raw material data is fitted respectively and is taken
Generation, the raw material data after replacing to the product output data and fitting carry out linear regression analysis, obtain efficiency identification
With diagnostic model.The objective mathematics presented between product output and each production raw material of technical solution provided in this embodiment
Relationship is realized and puts into the method for obtaining optimal product output by adjusting different raw material.Technical side provided in this embodiment
Case can identify the objective mathematical relationship between ethylene production capacity and various raw material energy consumptions, so as to adjust ethylene producing device
Material rate improves energy efficiency, reduces wastage of material.
It is understood that the principle that embodiment of above is intended to be merely illustrative of the present and the exemplary implementation that uses
Mode, however the present invention is not limited thereto.For those skilled in the art, essence of the invention is not being departed from
In the case where mind and essence, various changes and modifications can be made therein, these variations and modifications are also considered as protection scope of the present invention.
Claims (5)
1. a kind of identification of industrial process efficiency and diagnostic method based on Multiple Non Linear Regression characterized by comprising
Obtain the product output data among industrial production data and each raw material data；
It is unitization to the product output data and raw material data progress, so that the product output data are used as because becoming
Amount, the raw material data is as independent variable；
Curve estimation is carried out respectively to the dependent variable and each independent variable, the calculation formula of multiple linear equation is as follows:
yi=β0+β1x1+β2x2+...+βmxm+δi δi~N (0, δ2)
Wherein, yiIt is dependent variable, x1,…,xmIt is dependent variable, β0It is constant, β1,...βmIt is coefficient, δiIndicate each sampled point and
The deviation of straight line, δiMutually indepedent and Normal Distribution；
Substitution is fitted respectively to each raw material data, the calculation formula of multilinear fitting equation is as follows:
yi=b0+b1xi1+b2xi2+...+bmxim+ δ, i=1,2..., n
Wherein, b0It is the intercept of fit equation, b1,…,bmIt is the slope of fit equation；
Raw material data after replacing to the product output data and fitting carries out linear regression analysis, obtains efficiency identification
It is as follows with the calculation formula of diagnostic model, Cubic regression model:
Y=b0+b1x+b2x2+b3x3
Alternatively, the calculation formula of regression model is as follows twice:
Y=b0+b1x+b2x2。
2. the identification of industrial process efficiency and diagnostic method according to claim 1 based on Multiple Non Linear Regression, special
Sign is that the calculation formula of linear equation in two unknowns is as follows:
Wherein, yiIt is dependent variable, xiIt is dependent variable, β0It is constant, β1It is coefficient, δiIndicate the deviation of each sampled point and straight line,
δiMutually indepedent and Normal Distribution；
The calculation formula of binary linearity fit equation is as follows:
Wherein, b0It is the intercept of fit equation, b1It is the slope of fit equation；
Residual sum of squares (RSS) calculation formula is as follows:
It is as follows that calculation formula is obtained according to above three formula:
Wherein,WithIt is sample mean.
3. the identification of industrial process efficiency and diagnostic method according to claim 1 based on Multiple Non Linear Regression, special
Sign is, further includes:
Use R2Value indicates fitting effect, R2The calculation formula of value is as follows:
4. the identification of industrial process efficiency and diagnostic method according to claim 1 based on Multiple Non Linear Regression, special
Sign is, further includes:
Matrix expression is carried out to the multilinear fitting equation, calculation formula is as follows:
Y=X β+δ
Wherein, the value of β, δ, Y and X are expressed as follows:
The value of β is expressed as follows:
β=(XTX)-1XTY。
5. the identification of industrial process efficiency and diagnostic method according to claim 1 based on Multiple Non Linear Regression, special
Sign is, further includes:
Non-rectilinear equation is converted into linear equation by variable replacement, calculation formula is as follows:
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