CN111863151A - Prediction method of polymer molecular weight distribution based on Gaussian process regression - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 146
- 229920000642 polymer Polymers 0.000 title claims abstract description 106
- 238000006116 polymerization reaction Methods 0.000 claims abstract description 62
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- 238000012549 training Methods 0.000 claims abstract description 23
- 238000010606 normalization Methods 0.000 claims abstract description 20
- 238000006243 chemical reaction Methods 0.000 claims abstract description 15
- 238000000746 purification Methods 0.000 claims abstract description 4
- 239000003999 initiator Substances 0.000 claims description 12
- 239000000178 monomer Substances 0.000 claims description 10
- 239000002904 solvent Substances 0.000 claims description 10
- 239000011159 matrix material Substances 0.000 claims description 9
- 238000012360 testing method Methods 0.000 claims description 7
- 238000002474 experimental method Methods 0.000 claims description 6
- 239000012295 chemical reaction liquid Substances 0.000 claims description 5
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- 230000035484 reaction time Effects 0.000 claims description 5
- 238000012544 monitoring process Methods 0.000 claims description 3
- 238000010998 test method Methods 0.000 claims description 3
- PPBRXRYQALVLMV-UHFFFAOYSA-N Styrene Chemical compound C=CC1=CC=CC=C1 PPBRXRYQALVLMV-UHFFFAOYSA-N 0.000 description 4
- OZAIFHULBGXAKX-UHFFFAOYSA-N 2-(2-cyanopropan-2-yldiazenyl)-2-methylpropanenitrile Chemical group N#CC(C)(C)N=NC(C)(C)C#N OZAIFHULBGXAKX-UHFFFAOYSA-N 0.000 description 3
- 239000000047 product Substances 0.000 description 3
- RTZKZFJDLAIYFH-UHFFFAOYSA-N Diethyl ether Chemical compound CCOCC RTZKZFJDLAIYFH-UHFFFAOYSA-N 0.000 description 2
- 238000012854 evaluation process Methods 0.000 description 2
- OZAIFHULBGXAKX-VAWYXSNFSA-N AIBN Substances N#CC(C)(C)\N=N\C(C)(C)C#N OZAIFHULBGXAKX-VAWYXSNFSA-N 0.000 description 1
- 239000002202 Polyethylene glycol Substances 0.000 description 1
- 239000004353 Polyethylene glycol 8000 Substances 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000012467 final product Substances 0.000 description 1
- 239000003208 petroleum Substances 0.000 description 1
- 229920001223 polyethylene glycol Polymers 0.000 description 1
- 229940068918 polyethylene glycol 400 Drugs 0.000 description 1
- 229940085678 polyethylene glycol 8000 Drugs 0.000 description 1
- 235000019446 polyethylene glycol 8000 Nutrition 0.000 description 1
- 239000002994 raw material Substances 0.000 description 1
- 238000012216 screening Methods 0.000 description 1
- 238000010517 secondary reaction Methods 0.000 description 1
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Abstract
The invention discloses a prediction method of polymer molecular weight distribution based on Gaussian process regression, which comprises the steps of obtaining all process parameters in the polymerization reaction process, recording historical data of corresponding polymer molecular weight concentration distribution, carrying out purification treatment, carrying out normalization treatment on all the process parameters, the purified polymer molecular weight distribution and the concentration distribution thereof, introducing the normalized data into a training model, training and simulating data of the corresponding polymer molecular weight concentration distribution under all known process parameters in the polymerization reaction process through a Gaussian process distribution model, and building the prediction model. The invention relates to a processing mode of polymer molecular weight distribution data and application of a Gaussian process regression model in polymerization reaction, and the analysis of the existing polymer molecular weight distribution data and the good prediction of the polymer molecular weight distribution under unknown reaction conditions can be carried out through the combination of the two.
Description
Technical Field
The invention relates to a prediction method of polymer molecular weight distribution based on Gaussian process regression.
Background
In the polymerization reaction of polymer monomers in a solvent in the presence of an initiator, the molecular weight of a polymer of a reaction output product is not a single value, but a distribution range of the chain length and the molecular weight of the polymer, and the output of the polymer is difficult to accurately predict. While the Molecular Weight Distribution (MWD) directly affects many end-use properties of the product, such as thermal properties, stress-strain properties, impact resistance, strength and hardness. For example, polyethylene glycol 400, polyethylene glycol 2000, and polyethylene glycol 8000 have totally different uses.
In addition, in the process of polymerization reaction, the involved reaction process parameters are often complex and changeable, and the process parameters influencing the molecular weight distribution of the final product are usually: reaction temperature, reaction time, polymer monomer concentration, initiator concentration, and the like. The time and space costs of first principle (physicochemical formula derivation) modeling of complex reaction process parameters are too large and imperfect. Some data-driven modeling methods do not explain it well and predict with low accuracy.
Disclosure of Invention
In order to solve the above technical problems in the prior art, the present invention aims to provide a method for predicting a polymer molecular weight distribution based on gaussian process regression. Wherein, in the polymerization reaction of the polymer monomer in the solvent in the presence of the initiator, the molecular weight distribution of the polymer which is the output product of the reaction corresponds to the concentration distribution of the molecular weight of the polymer one by one.
The invention provides a potential model suitable for the field of polymer molecular weight distribution prediction, provides a nonparametric Bayesian modeling method of Gaussian process regression aiming at the defects of insufficient interpretability and poor prediction performance effect of the existing distributed prediction, provides probability prediction information by using the prediction uncertainty given by the model, and can well explain the model, and the model can also specify different kernel functions, such as: linear kernels, polynomial kernels, gaussian kernels, exponential kernels, etc., and applying corresponding kernel functions to different experimental data will result in higher accuracy predicted values.
For a given modeling task, the determination of network topology and the generalization capability of neural networks remain unresolved. And the Gaussian process regression is greatly superior to the traditional method in both the result and the interpretability of the generalization error.
The prediction method of the polymer molecular weight distribution based on the Gaussian process regression is characterized in that a polymer monomer is subjected to polymerization reaction in a solvent in the presence of an initiator, and the prediction method of the polymer molecular weight distribution in a reaction liquid in the polymerization reaction process comprises the following steps:
1) data acquisition: acquiring all process parameters in the polymerization reaction process by adopting an orthogonal test method, grouping the process parameters according to types, recording corresponding historical data about the molecular weight concentration distribution of polymers in reaction liquid under all the process parameters, and establishing a historical process data sequence library;
2) And (3) data purification: purifying historical data about the molecular weight concentration distribution of the polymer recorded in a historical process data sequence library, namely extracting concentration data of one polymer molecular weight according to the difference between every two polymerization degrees, and removing the data of the rest polymer molecular weight concentrations to finally obtain a corresponding purified historical process data sequence library;
3) data processing: all process parameters, the molecular weight distribution and the concentration distribution of the purified polymer in the historical process data sequence library are normalized, and finally, the historical process data sequence library after corresponding data processing is obtained;
4) establishing a polymer molecular weight distribution prediction model: in a historical process data sequence library after data processing, each group of process parameters after normalization processing is used as input characteristics, data of polymer molecular weight concentration distribution after normalization processing is used as output characteristics, the input characteristics and the output characteristics are imported into a training model, the data of the polymer molecular weight concentration distribution corresponding to all known process parameters in the polymerization reaction process are trained and simulated through a Gaussian process distribution model, a prediction model is built, and finally the corresponding relation between unknown process parameters and the polymer molecular weight concentration distribution is obtained.
The prediction method of the polymer molecular weight distribution based on the Gaussian process regression is characterized in that in the step 2), the numerical value of the difference between the polymerization degrees is 30.
The prediction method of the polymer molecular weight distribution based on the Gaussian process regression is characterized in that in the step 1), the grouping types of the process parameters comprise 4 groups, namely reaction temperature, reaction time, concentration of a polymer monomer in a solvent and concentration of an initiator in the solvent.
The prediction method of the polymer molecular weight distribution based on the Gaussian process regression is characterized in that in the step 3), all process parameters, the purified polymer molecular weight distribution and the concentration distribution are subjected to normalization treatment, and the normalization treatment formula is as follows:
wherein:
expressing the result of normalization processing of a certain parameter;
x represents a numerical value of a certain parameter before normalization processing;
xminrepresents the minimum value of a certain parameter;
xmaxrepresents the maximum value of a certain parameter;
after normalization, the numerical values of all process parameters, polymer molecular weight distribution and concentration distribution are floating point numbers between [0, 1).
The prediction method of the polymer molecular weight distribution based on Gaussian process regression is characterized in that in the step 4), a formula for establishing a prediction model based on a Gaussian process regression model is as follows:
y～N(μ(X),K(X,X))
Wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
k represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
n denotes a normal distribution (mathematical concept).
The prediction method of the polymer molecular weight distribution based on the Gaussian process regression is characterized by also comprising an evaluation process of monitoring a model result: according to the prediction model established in the step 4), by inputting unknown process parameters to be detected, comparing the fitting condition of the prediction result of the polymer molecular weight concentration distribution based on the prediction model and the detection result of the polymer molecular weight concentration distribution based on the real polymerization reaction experiment to judge the accuracy of the prediction model established in the step 4);
the prediction formula of the polymer molecular weight concentration distribution based on the prediction model is as follows:
wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
X*data representing sets of process parameters for performing the polymerization reaction in the test data;
f*The concentration distribution value of the molecular weight of the polymer detected and output in a real polymerization reaction experiment is represented;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
μ(X*) Data mean values representing the sets of process parameters for polymerization reactions in the test data;
k represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
σnvariance values of the data representing the sets of process parameters for carrying out the polymerization reaction;
t denotes the transpose of the matrix.
N denotes a normal distribution (mathematical concept).
Compared with the prior art, the invention has the following beneficial effects:
the invention relates to a processing mode of polymer molecular weight distribution data and application of a Gaussian process regression model in polymerization reaction, and the analysis of the existing polymer molecular weight distribution data and the prediction of the polymer molecular weight distribution under unknown reaction conditions can be carried out through the combination of the two modes. The invention considers that the influence of some secondary reaction conditions on the model is slight, so that the molecular weight distribution of the polymer can be predicted more accurately after screening is removed. Can provide a new reference idea for the prediction of the molecular weight distribution of the polymer in industrial engineering.
Drawings
FIG. 1 is a graph of the results of predicting the molecular weight concentration distribution of a polymer using a prediction model established in the present application;
FIG. 2 is a graph showing the results of actually measuring the molecular weight concentration distribution of a polymer.
Detailed Description
The present invention is further illustrated by the following examples, which should not be construed as limiting the scope of the invention.
Example (b):
the polymer monomer is subjected to polymerization reaction in a solvent in the presence of an initiator, and the prediction method of the polymer molecular weight distribution based on Gaussian process regression in the polymerization reaction process comprises the following steps:
1) data acquisition: all process parameters in the polymerization reaction process are obtained by adopting an orthogonal test method, and are grouped according to types, wherein if the process parameters mainly influencing the reaction result are four types, namely temperature T, reaction time T, polymer monomer concentration c1 and initiator concentration c2, the process parameters are divided into a group of temperature data, a group of reaction time data, a polymer monomer concentration data and an initiator concentration data. Recording corresponding historical data about the molecular weight concentration distribution of the polymer in the reaction solution under all process parameters, and establishing a historical process data sequence library;
2) And (3) data purification: and (3) purifying historical data about the molecular weight concentration distribution of the polymer recorded in the historical process data sequence library, namely extracting the concentration data of one polymer molecular weight according to the difference of every two polymerization degrees being 30, and rejecting the data of the rest polymer molecular weight concentrations. For example, 3000 total points with a polymerization degree of 1, 2, 3.. and 3000 are purified, 100 total points with a polymerization degree of 30, 60, 90.. and 3000 are selected, and data of the rest points are removed, so that the data processing process is simplified. Finally obtaining a corresponding purified historical process data sequence library;
3) data processing: all process parameters, the molecular weight distribution and the concentration distribution of the purified polymer in the historical process data sequence library are normalized, and finally, the historical process data sequence library after corresponding data processing is obtained;
all the technological parameters, the molecular weight distribution and the concentration distribution of the purified polymer are normalized, and the formula of the normalization treatment is as follows:
wherein:
expressing the result of normalization processing of a certain parameter;
x represents a numerical value of a certain parameter before normalization processing;
xminRepresents the minimum value of a certain parameter;
xmaxrepresents the maximum value of a certain parameter;
after normalization, the numerical values of all process parameters, polymer molecular weight distribution and concentration distribution are floating point numbers between [0, 1).
For example, the temperature range of the polymerization reaction is 100-.
For example, the molecular weight of the polymer ranges from 100-.
4) Establishing a polymer molecular weight distribution prediction model: in a historical process data sequence library after data processing, each group of process parameters after normalization processing is used as input characteristics, data of polymer molecular weight concentration distribution after normalization processing is used as output characteristics, the input characteristics and the output characteristics are imported into a training model, the data of the polymer molecular weight concentration distribution corresponding to all known process parameters in the polymerization reaction process are trained and simulated through a Gaussian process distribution model, a prediction model is built, and finally the corresponding relation between unknown process parameters and the polymer molecular weight concentration distribution is obtained.
The formula for establishing the prediction model based on the Gaussian process regression model is as follows:
y～N(μ(X),K(X,X))
wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
k represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
n represents a normal distribution (mathematical concept);
5) monitoring the evaluation process of the model result, and comparing the predicted result of the polymer molecular weight concentration distribution based on the predicted model with the fitting condition of the detection result of the polymer molecular weight concentration distribution based on the real polymerization reaction experiment according to the predicted model established in the step 4) by inputting unknown process parameters to be detected so as to judge the accuracy of the predicted model established in the step 4);
the prediction formula of the polymer molecular weight concentration distribution based on the prediction model is as follows:
wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
X*data representing sets of process parameters for performing the polymerization reaction in the test data;
f*A concentration distribution value representing the molecular weight of the polymer output by the detection of the polymerization reaction in the test data;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
μ(X*) Data mean values representing the sets of process parameters for polymerization reactions in the test data;
k represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
σnvariance values of the data representing the sets of process parameters for carrying out the polymerization reaction;
n represents a normal distribution (mathematical concept);
t denotes the transpose of the matrix.
Example 1:
styrene is used as a reaction raw material, petroleum ether is used as a solvent, an initiator is azobisisobutyronitrile AIBN, for example, the initial concentration of styrene in a reaction liquid is 9.16mol/L and the initial concentration of the initiator is 5.98mol/L under the experimental condition temperature of 20 ℃, and after continuous reaction for 4 hours, the molecular weight concentration distribution of a polymer in the reaction liquid is tested.
Using the above formula
f*This is the result of predicting the molecular weight concentration distribution of the resulting polymer, as shown in FIG. 1.
By directly detecting the reaction solution, the obtained result of the molecular weight concentration distribution of the polymer can be directly and truly detected, as shown in fig. 2.
Comparing fig. 1 and fig. 2, it can be seen that the degree of fitting between the prediction result of the polymer molecular weight concentration distribution based on the prediction model and the detection result of the polymer molecular weight concentration distribution based on the real polymerization reaction experiment is good, the feasibility of the gaussian regression model for predicting the molecular weight distribution in the polymerization process is verified, and a new reference idea can be provided for the prediction of the polymer molecular weight distribution in industrial engineering.
The statements in this specification merely set forth a list of implementations of the inventive concept and the scope of the present invention should not be construed as limited to the particular forms set forth in the examples.
Claims (6)
1. The prediction method of the polymer molecular weight distribution based on Gaussian process regression is characterized in that a polymer monomer is subjected to polymerization reaction in a solvent in the presence of an initiator, and the prediction method of the polymer molecular weight distribution in a reaction solution in the polymerization reaction process comprises the following steps:
1) data acquisition: acquiring all process parameters in the polymerization reaction process by adopting an orthogonal test method, grouping the process parameters according to types, recording corresponding historical data about the molecular weight concentration distribution of polymers in reaction liquid under all the process parameters, and establishing a historical process data sequence library;
2) and (3) data purification: purifying historical data about the molecular weight concentration distribution of the polymer recorded in a historical process data sequence library, namely extracting concentration data of one polymer molecular weight according to the difference between every two polymerization degrees, and removing the data of the rest polymer molecular weight concentrations to finally obtain a corresponding purified historical process data sequence library;
3) Data processing: all process parameters, the molecular weight distribution and the concentration distribution of the purified polymer in the historical process data sequence library are normalized, and finally, the historical process data sequence library after corresponding data processing is obtained;
4) establishing a polymer molecular weight distribution prediction model: in a historical process data sequence library after data processing, each group of process parameters after normalization processing is used as input characteristics, data of polymer molecular weight concentration distribution after normalization processing is used as output characteristics, the input characteristics and the output characteristics are imported into a training model, the data of the polymer molecular weight concentration distribution corresponding to all known process parameters in the polymerization reaction process are trained and simulated through a Gaussian process distribution model, a prediction model is built, and finally the corresponding relation between unknown process parameters and the polymer molecular weight concentration distribution is obtained.
2. The method for predicting the molecular weight distribution of a polymer based on gaussian process regression as set forth in claim 1, wherein the value of the difference between the degrees of polymerization in step 2) is 30.
3. The method for predicting the molecular weight distribution of a polymer based on gaussian process regression as claimed in claim 1, wherein the grouping types of the process parameters in the step 1) include 4 groups, which are reaction temperature, reaction time, concentration of the polymer monomer in the solvent and concentration of the initiator in the solvent.
4. The method for predicting the molecular weight distribution of a polymer based on the gaussian process regression as claimed in claim 1, wherein in the step 3), all the process parameters, the molecular weight distribution of the purified polymer and the concentration distribution thereof are normalized, and the formula of the normalization is as follows:
wherein:
expressing the result of normalization processing of a certain parameter;
x represents a numerical value of a certain parameter before normalization processing;
xminrepresents the minimum value of a certain parameter;
xmaxrepresents the maximum value of a certain parameter;
after normalization, the numerical values of all process parameters, polymer molecular weight distribution and concentration distribution are floating point numbers between [0, 1).
5. The method for predicting the molecular weight distribution of a polymer based on gaussian process regression as claimed in claim 1, wherein the formula for establishing the prediction model based on the gaussian process regression model in the step 4) is as follows:
y～N(μ(X),K(X,X))
wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
k represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
And N represents a normal distribution.
6. The method of claim 1, further comprising monitoring the process of estimating the model results by: according to the prediction model established in the step 4), by inputting unknown process parameters to be detected, comparing the fitting condition of the prediction result of the polymer molecular weight concentration distribution based on the prediction model and the detection result of the polymer molecular weight concentration distribution based on the real polymerization reaction experiment to judge the accuracy of the prediction model established in the step 4);
the prediction formula of the polymer molecular weight concentration distribution based on the prediction model is as follows:
wherein y represents the concentration distribution value of the polymer molecular weight output in the training data;
x represents the data of each set of process parameters for carrying out the polymerization reaction in the training data;
X*data representing sets of process parameters for performing the polymerization reaction in the test data;
f*the concentration distribution value of the molecular weight of the polymer detected and output in a real polymerization reaction experiment is represented;
mu (X) represents the data mean value of each group of process parameters for polymerization reaction in the training data;
μ(X*) Data mean values representing the sets of process parameters for polymerization reactions in the test data;
K represents a covariance matrix of data of each set of process parameters for carrying out the polymerization reaction;
σnvariance values of the data representing the sets of process parameters for carrying out the polymerization reaction;
t represents the transpose of the matrix;
and N represents a normal distribution.
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