CN109726474B - Online-correction multi-scale forecasting system for propylene polymerization production process - Google Patents
Online-correction multi-scale forecasting system for propylene polymerization production process Download PDFInfo
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Abstract
The invention discloses an online-corrected multi-scale forecasting system for a propylene polymerization production process, which is used for forecasting a melt index in the propylene polymerization production process and comprises a data preprocessing module, a multi-scale analysis module, a forecasting model module and an online correction module. The invention forecasts the important parameter index melt index in the propylene polymerization production process, overcomes the defects of low measurement precision and weak anti-interference capability of the existing forecasting system, introduces the technical means of online correction and multi-scale analysis, thereby obtaining the online corrected propylene polymerization production process multi-scale forecasting system, and the realized propylene polymerization production process melt index forecasting system can fully utilize the production data in the propylene production process and complete the correction of the forecasting model parameters on line, and has high forecasting precision and anti-interference capability.
Description
Technical Field
The invention relates to an online forecasting system, in particular to an online-corrected multi-scale forecasting system in a propylene polymerization production process.
Background
Polypropylene is a thermoplastic resin, is produced by propylene polymerization, is one of five general-purpose plastics, and is closely related to our daily life. Polypropylene is the most important downstream product of propylene, and 50 percent of the total propylene yield in the world and 65 percent of the propylene yield in China are used for producing the polypropylene. Polypropylene is the fastest growing commodity thermoplastic resin worldwide, second only to polyethylene and polyvinyl chloride. In order to make the polypropylene products in China have market competitiveness, the development of impact-resistant copolymerization products, random copolymerization products, BOPP and CPP film materials, fibers and non-woven fabrics with good balance of rigidity, toughness and fluidity and the application of polypropylene in the fields of automobiles and household appliances are important research subjects in the future.
The melt index is one of the important quality indexes of polypropylene products for determining the grade of the products, and determines different purposes of the products. The measurement of the melt index is an important link of product quality control in polypropylene production, and has very important function and guiding significance for production and scientific research.
However, the online analysis and measurement of the melt index are difficult to achieve at present, on one hand, the lack of the online melt index analyzer is caused, and on the other hand, the existing online analyzer is difficult to use due to the fact that the online melt index analyzer is often blocked and inaccurate in measurement or even cannot be used normally. Therefore, currently, MI measurement in industrial production is mainly obtained by manual sampling and off-line assay analysis, and generally, MI can only be analyzed once every 2-4 hours, so that the time delay is large, which brings difficulty to quality control of propylene polymerization production and becomes a bottleneck problem to be solved urgently in production. The online forecasting system research of the polypropylene melt index becomes a leading edge and a hot spot of academia and industry.
Disclosure of Invention
In order to overcome the defects of low prediction precision and weak anti-interference capability of the existing propylene polymerization production process prediction system, the invention aims to provide the online correction propylene polymerization production process multi-scale prediction system, which can fully utilize data multi-scale information and realize automatic online correction of a model, and has high prediction precision and strong anti-interference capability.
The purpose of the invention is realized by the following technical scheme: an online-corrected multi-scale forecasting system for a propylene polymerization production process is used for forecasting a melt index in the propylene polymerization production process and comprises a data preprocessing module, a multi-scale analysis module, a forecasting model module and an online correction module.
Further, the input of the data preprocessing module is 9 variables of the propylene polymerization production process
Since each variable has different units, in order to prevent different dimensions from causing errors between data magnitudes, all data are normalized, and the normalization formula is as follows:
where mean is the arithmetic mean of the variables and std isThe standard deviation of the variables is the difference between,
the subscript r is the value of the input variable, r is the detection of the r, s is the variable of the s dimension, xrsThe values of the normalized input variables are used as input data. Normalized data is S ═ xr1,xr2,...,xr9}。
Furthermore, the multi-scale analysis module simultaneously observes the frequency and the time axis of the input data through multi-scale analysis, and has better time resolution when the frequency is high and better frequency resolution when the frequency is low so as to acquire data information under multi-scale. Normalizing the data S to { x ═ xr1,xr2,...xr9Performing multi-scale analysis as follows:
(1) representing the corresponding input data at the current scale J as SJAccording to the following formula to SJWavelet decomposition is performed, and the dimension J is reduced by 1:
wherein, J0In order to be the initial scale, the method comprises the following steps,
is the coefficient sequence basis function and psi is the difference sequence basis function.
Is scale J0The next k-th coefficient sequence basis function,
is prepared by reacting with
Corresponding weight coefficient,. psil,kIs the k-th difference sequence basis function at the scale l, dl,kIs equal to psil,kThe corresponding weight coefficients.
Wherein j is the jth scale,
for the k-th coefficient sequence basis function at the scale j,
is equal to time 2jAnd the t-k related coefficient sequence constant takes the following values:
wherein, t is the time,
is a constant related to t. And defines:
wherein psi0,0(t) is a time-dependent constant,
is equal to the dimension J0-1 k-th difference sequence basis function
The corresponding weight coefficients. Thereby obtaining:
wherein d isj,kIs the k-th difference sequence basis function psi under the scale jj,kThe corresponding weight coefficients. When J is 1, stopping decomposition and obtaining a series of corresponding wavelet analysis coefficients d under the current scale J(l)＝{d1,d2,…dJ-1}。
(2) Updating the time segment T in the current iteration by interpolation(l)If its corresponding wavelet analysis coefficient
The following conditions are met:
the corresponding time segments are combined, where eeGiven a normal number.
(3) If its corresponding wavelet analysis coefficient
The following conditions are met:
further interpolation is performed on the corresponding time segment; so as to obtain a new optimized running time segment T(l +1)In which epsiloniGiven a normal number.
Further, the forecasting model module uses a statistical modeling method to complete the highly nonlinear mapping from the input parameters to the output melt index forecasting values by minimizing an error function, and the topological invariance is kept in the mapping:
where Γ represents an objective function, w represents an inertial weight, ξ represents an error, C represents a penalty factor, u represents a weight coefficient, β represents kernel-function mapping, b represents a bias, x is input data, y is output data, subscript i represents ith data, n is the total number of output variables, and superscript T represents the transpose of the matrix.
Further, the online correction module adopts an online correction strategy to correct the parameters of the prediction model module in real time, and corrects the model error in real time by adding the prediction data with larger prediction error into the training data set as new training data: (1) the online correction module obtains the correction value of the measurement data, so that the correction value meets the material and energy balance relation of the whole device and unit equipment, and the weighted square sum of the difference between the correction value and the measurement value is minimum.
MIp＝MIa+ε (12)
Wherein MI is melt index, MIpFor melt index measurements, MIaIs the true value of the melt index, epsilon is the error vector,
for the correction values, U is the prediction model parameter vector,
and F is a prediction model function vector which represents chemical and physical laws such as material balance, energy balance, chemical reaction metering relation and the like in the propylene polymerization process. The (n × n) order variance-covariance matrix, where Q is MI, can be estimated from the meter accuracy or measurement samples.
(2) Real-time acquisition of on-line calibration module during operationAnalysis value MI at time ta(t) and the predicted value MIp(t) calculating an analysis value MIaAnd predicted value MIpDeviation e ofo(t)：
eo(t)＝|MIa(t)－MIp(t)| (14)
If eo(t) greater than a positive error margin εo：
eo(t)＞εo (15)
The analysis value MI at the time point t is compareda(t) and parameter values x (t) as new training data { x (t), MIaAnd (t) adding the training data set, retraining the parameters of the forecasting model, and performing online correction on the forecasting model. Otherwise, the model parameters are considered to be accurate, and no online correction is required.
(3) Retraining the forecast model parameters, modeling the training process
Wherein E is the square error of the forecast result, ULFor the lower bound of the parameter vector to be estimated, UUIs the upper bound of the parameter vector to be estimated. The model is solved according to the following formula:
wherein ^ E is a Jacobian of E,
is F about
Of the Jacobian, λ is Lagrange multiplier, zLIs bound by the lower bound ULDetermined dual variable, zUIs bound by the beam upper bound UUA determined dual variable, the equation being equivalent to:
(U-UL)zL-μeL＝0 (19)
(UU-U)zU-μeU＝0 (20)
where μ is a barrier parameter, eLIs composed of zLLower bound of decision ULIndicator eUIs composed of zUConstraint upper bound U of decisionUAn indicator. The updating mode of mu is as follows:
wherein the subscript q denotes the loop iteration count, εtolFor a given error margin, the parameter kμ∈(0,1)、θμ∈(1,2)。
The invention has the following beneficial effects: 1. due to the adoption of the technical means of online correction, the frequency and the time axis of input data can be observed simultaneously to acquire data information under multiple scales, and production data in the propylene production process is fully utilized, so that the prediction precision can be improved; 2. due to the adoption of a multi-scale analysis technical means, the forecasting precision of the forecasting model can be monitored in real time, and when the forecasting model is mismatched and the precision is reduced, the parameters of the forecasting model are corrected on line, so that the forecasting anti-jamming capability can be improved.
Drawings
FIG. 1 is a schematic diagram of the basic structure of an on-line corrected multi-scale forecasting system for propylene polymerization production process;
fig. 2 is a schematic structural diagram of an online-corrected multi-scale forecasting system.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
Referring to fig. 2, an online-corrected multi-scale prediction system for propylene polymerization production process is used for performing melt index prediction on a propylene polymerization process 1, and comprises a data preprocessing module 7, a multi-scale analysis module 8, a prediction model module 9 and an online correction module 10.
Further, the input of the data preprocessing module 7 is 9 variables of the propylene polymerization production process 1
Since each variable has different units, in order to prevent different dimensions from causing errors between data magnitudes, all data are normalized, and the normalization formula is as follows:
wherein mean is the arithmetic mean of each variable, std is the standard deviation of each variable,
the subscript r is the value of the input variable, r is the detection of the r, s is the variable of the s dimension, xrsThe values of the normalized input variables are used as input data. Normalized data is S ═ xr1,xr2,...,xr9}。
Further, the multi-scale analysis module 8 observes the frequency and the time axis of the input data through multi-scale analysis, and has a better time resolution when the frequency is high and a better frequency resolution when the frequency is low, so as to obtain data information under multi-scale. Normalizing the data S to { x ═ xr1,xr2,...xr9Performing multi-scale analysis as follows:
(1) representing the corresponding input data at the current scale J as SJAccording to the following formula to SJWavelet decomposition is performed, and the dimension J is reduced by 1:
wherein, J0In order to be the initial scale, the method comprises the following steps,
is the coefficient sequence basis function and psi is the difference sequence basis function.
Is scale J0The next k-th coefficient sequence basis function,
is prepared by reacting with
Corresponding weight coefficient,. psil,kIs the k-th difference sequence basis function at the scale l, dl,kIs equal to psil,kThe corresponding weight coefficients.
Wherein j is the jth scale,
for the k-th coefficient sequence basis function at the scale j,
is equal to time 2jAnd the t-k related coefficient sequence constant takes the following values:
wherein, t is the time,
is a constant related to t. And defines:
wherein psi0,0(t) is a time-dependent constant,
is equal to the dimension J0-1 k-th difference sequence basis function
The corresponding weight coefficients. Thereby obtaining:
wherein d isj,kIs the k-th difference sequence basis function psi under the scale jj,kThe corresponding weight coefficients. When J is 1, stopping decomposition and obtaining a series of corresponding wavelet analysis coefficients d under the current scale J(l)＝{d1,d2,…dJ-1}。
(2) Updating the time segment T in the current iteration by interpolation(l)If its corresponding wavelet analysis coefficient
The following conditions are met:
the corresponding time segments are combined, where eeGiven a normal number.
(3) If its corresponding wavelet analysis coefficient
The following conditions are met:
further interpolation is performed on the corresponding time segment; so as to obtain a new optimized running time segment T(l +1)In which epsiloniGiven a normal number.
Further, the prediction model module 9 uses a statistical modeling method to perform a highly nonlinear mapping from the input parameters to the output melt index prediction values by minimizing an error function, and the mapping maintains a topological invariance:
where Γ represents an objective function, w represents an inertial weight, ξ represents an error, C represents a penalty factor, u represents a weight coefficient, β represents kernel-function mapping, b represents a bias, x is input data, y is output data, subscript i represents ith data, n is the total number of output variables, and superscript T represents the transpose of the matrix.
Further, the online correction module 10 performs real-time correction on the parameters of the predictive model module 9 by using an online correction strategy, and adds the predictive data with a large predictive error as new training data into the training data set to correct the model error in real time:
(1) the online calibration module 10 obtains a calibration value of the measurement data so that it satisfies the material and energy balance relationship of the whole apparatus and unit equipment, while minimizing the weighted sum of squares of the difference between the measurement value and the calibration value.
MIp＝MIa+ε (12)
Wherein MI is melt index, MIpFor melt index measurements, MIaIs the true value of the melt index, epsilon is the error vector,
for the correction values, U is the prediction model parameter vector,
and F is a prediction model function vector which represents chemical and physical laws such as material balance, energy balance, chemical reaction metering relation and the like in the propylene polymerization process. The (n × n) order variance-covariance matrix, where Q is MI, can be estimated from the meter accuracy or measurement samples.
(2) When the online correction module 10 works, the analysis value MI at the moment t is obtained in real timea(t) and the predicted value MIp(t) calculating an analysis value MIaAnd predicted value MIpDeviation e ofo(t)：
eo(t)＝|MIa(t)－MIp(t)| (14)
If eo(t) greater than a positive error margin εo：
eo(t)＞εo (15)
The analysis value MI at the time point t is compareda(t) and parameter values x (t) as new training data { x (t), MIa(t) adding the training data set, and retraining the parameters of the forecasting model module 9 to perform online correction of the forecasting model. Otherwise, the model parameters are considered to be accurate, and no online correction is required.
(3) Retraining the parameters of the predictive model module 9, modeling the training process
Wherein E is the square error of the forecast result, ULFor the lower bound of the parameter vector to be estimated, UUIs to be treatedThe upper bound of the parameter vector is estimated. The model is solved according to the following formula:
wherein ^ E is a Jacobian of E,
is F about
Of the Jacobian, λ is Lagrange multiplier, zLIs bound by the lower bound ULDetermined dual variable, zUIs bound by the beam upper bound UUA determined dual variable, the equation being equivalent to:
(U-UL)zL-μeL＝0 (19)
(UU-U)zU-μeU＝0 (20)
where μ is a barrier parameter, eLIs composed of zLLower bound of decision ULIndicator eUIs composed of zUConstraint upper bound U of decisionUAn indicator. The updating mode of mu is as follows:
wherein the subscript q denotes the loop iteration count, εtolFor a given error margin, the parameter kμ∈(0,1)、θμ∈(1,2)。
Referring to fig. 1, an on-site intelligent instrument 2 and a control station 3 are connected to a propylene polymerization production process 1 and to a database 4; the online correction multi-scale forecasting system 5 is connected with the database 4 and the forecasting result display instrument 6. The on-site intelligent instrument 2 measures the easily-measured variable of the propylene polymerization production process 1 and transmits the easily-measured variable to the database 4; the control station 3 controls the manipulated variables of the propylene polymerization production process 1, and transmits the manipulated variables to the database 4. The variable data recorded in the database 4 is used as the input of the online corrected multi-scale forecasting system 5, and the forecasting result display instrument 6 is used for displaying the output of the online corrected multi-scale forecasting system 5, namely the forecasting result.
According to the reaction mechanism and the process analysis, in consideration of various factors influencing the melt index in the production process of polypropylene, nine commonly used operation variables and easily-measured variables in the actual production process are taken as model input variables, including: three propylene feed flow rates, main catalyst flow rate, auxiliary catalyst flow rate, temperature, pressure, liquid level in the kettle, hydrogen volume concentration in the kettle, and the like.
TABLE 1 Online corrected input variables of model required by multiscale prediction system 5
Table 1 lists 9 model input variables, namely, the temperature in the kettle (T), the pressure in the kettle (p), the liquid level in the kettle (L) and the volume concentration of hydrogen in the kettle (X), which are input by the multi-scale forecasting system 5 for online correctionv) 3 propylene feed flow rates (first propylene feed flow rate f1, second propylene feed flow rate f2, third propylene feed flow rate f3), 2 catalyst feed flow rates (main catalyst flow rate f4, cocatalyst flow rate f 5). The polymerization reaction in the reaction kettle is carried out after reaction materials are repeatedly mixed, so that the process variable of the model input variable related to the materials adopts the average value of a plurality of previous moments. The data in this example were averaged over the previous hour. The melt index off-line test value is obtained by manual sampling and off-line test analysis, and is analyzed and collected every 4 hours.
The examples are intended to illustrate the invention, but not to limit the invention, and any modifications and variations of the invention within the spirit and scope of the claims are intended to fall within the scope of the invention.
Claims (1)
1. An on-line corrected multi-scale forecasting system for propylene polymerization production process, which is used for forecasting melt index of the propylene polymerization production process, and is characterized in that: the system comprises a data preprocessing module, a multi-scale analysis module, a forecasting model module and an online correction module;
the input of the data preprocessing module is 9 variables of the propylene polymerization production process
Since each variable has different units, in order to prevent different dimensions from causing errors between data magnitudes, all data are normalized, and the normalization formula is as follows:
wherein mean is the arithmetic mean of each variable, std is the standard deviation of each variable,
the subscript r is the value of the input variable, r is the detection of the r, s is the variable of the s dimension, xrsTaking the value of the input variable after standardization as input data; normalized data is S ═ xr1,xr2,...,xr9}；
The multi-scale analysis module simultaneously observes the frequency and the time axis of input data through multi-scale analysis, and has better time resolution when the frequency is high and better frequency resolution when the frequency is low so as to acquire data information under multi-scale; normalizing the data S to { x ═ xr1,xr2,...xr9Performing multi-scale analysis as follows:
(1) representing the corresponding input data at the current scale J as SJAccording to the following formula to SJWavelet decomposition is performed, and the dimension J is reduced by 1:
wherein, J0In order to be the initial scale, the method comprises the following steps,
is a coefficient sequence basis function and psi is a difference sequence basis function;
is scale J0The next k-th coefficient sequence basis function,
is prepared by reacting with
Corresponding weight coefficient,. psil,kIs the k-th difference sequence basis function at the scale l, dl,kIs equal to psil,kA corresponding weight coefficient;
wherein j is the jth scale,
for the k-th coefficient sequence basis function at the scale j,
is equal to time 2jAnd the t-k related coefficient sequence constant takes the following values:
wherein, t is the time,
is a constant related to t; and defines:
wherein psi0,0(t) is a time-dependent constant,
is equal to the dimension J0-1 k-th difference sequence basis function
A corresponding weight coefficient; thereby obtaining:
wherein d isj,kIs the k-th difference sequence basis function psi under the scale jj,kA corresponding weight coefficient; when J is 1, stopping decomposition and obtaining a series of corresponding wavelet analysis coefficients d under the current scale J(l)＝{d1,d2,…dJ-1}；
(2) Updating the time segment T in the current iteration by interpolation(l)If its corresponding wavelet analysis coefficient
The following conditions are met:
the corresponding time segments are combined, where eeIs a given normal number;
(3) if its corresponding wavelet analysis coefficient
The following conditions are met:
further interpolation is performed on the corresponding time segment; so as to obtain a new optimized running time segment T(l+1)In which epsiloniIs a given normal number;
the forecasting model module uses a statistical modeling method to complete the highly nonlinear mapping from input parameters to output melt index forecasting values through error function minimization, and the mapping keeps topology invariance:
wherein Γ represents an objective function, w represents an inertial weight, ξ represents an error, C represents a penalty factor, u represents a weight coefficient, β represents kernel function mapping, b represents bias, x is input data, y is output data, subscript i represents ith data, n is the total number of output variables, and superscript T represents the transpose of a matrix;
the online correction module adopts an online correction strategy to correct the parameters of the prediction model module in real time, and corrects the model error in real time by adding the prediction data with larger prediction error into a training data set as new training data:
(1) the online correction module acquires a correction value of the measurement data, so that the correction value meets the material and energy balance relation of the whole device and unit equipment, and the weighted square sum of the difference between the correction value and the measurement value is minimum;
MIp＝MIa+ε (12)
wherein MI is melt index, MIpFor melt index measurements, MIaIs the true value of the melt index, epsilon is the error vector,
for the correction values, U is the prediction model parameter vector,
the vector is a parameter vector to be estimated, F is a forecasting model function vector and represents the relationship among material balance, energy balance and chemical reaction metering in the propylene polymerization process; an (nxn) order variance-covariance matrix with Q MI, which can be estimated from the meter accuracy or measurement samples;
(2) when the on-line correction module works, the analysis value MI at the moment t is obtained in real timea(t) and the predicted value MIp(t) calculating an analysis value MIaAnd predicted value MIpDeviation e ofo(t)：
eo(t)＝|MIa(t)－MIp(t)| (14)
If eo(t) greater than a positive error margin εo：
eo(t)＞εo (15)
The analysis value MI at the time point t is compareda(t) and parameter values x (t) as new training data { x (t), MIa(t) adding to the training dataset and retraining the forecast model parametersPerforming online correction of the forecasting model; otherwise, the model parameters are considered to be accurate, and online correction is not needed;
(3) retraining the forecast model parameters, modeling the training process
Wherein E is the square error of the forecast result, ULFor the lower bound of the parameter vector to be estimated, UUThe parameter vector to be estimated is an upper bound; the model is solved according to the following formula:
wherein the content of the first and second substances,
a jacobian matrix of E is the,
is F about
Of the Jacobian, λ is Lagrange multiplier, zLIs bound by the lower bound ULDetermined dual variable, zUIs bound by the beam upper bound UUA determined dual variable, the equation being equivalent to:
(U-UL)zL-μeL＝0 (19)
(UU-U)zU-μeU＝0 (20)
wherein μ is a disorder parameter，eLIs composed of zLLower bound of decision ULIndicator eUIs composed of zUConstraint upper bound U of decisionUAn indicator; the updating mode of mu is as follows:
wherein the subscript q denotes the loop iteration count, εtolFor a given error margin, the parameter kμ∈(0,1)、θμ∈(1,2)。
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