A multi-condition distributed output process compensation migration modeling method

Abstract

The present invention discloses a multi-condition distributed output process compensation migration modeling method. By transforming in the label space, the characteristics of the label space of a small amount of known target domain data are migrated to the label space of the source domain data, so as to better reduce the difference in the label space distribution of the distributed output process data between different conditions. The deviation compensation migration method based on the Gaussian process regression model proposed by the present invention effectively handles the multi-condition and large-noise characteristics in the styrene radical polymerization reaction, and enhances the robustness and accuracy of the prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of process industry prediction modeling, and particularly relates to a multi-condition distributed output process compensation migration modeling method. Background Art

[0002] In the chemical industry process, with the development of advanced instruments and data-driven modeling techniques, the measured system feedback signal is often not a single value but the probability density function (PDF) of the system output with respect to the input characteristics. The output processes of such products are collectively referred to as distributed output processes. Typical examples include: the molecular weight distribution (MWD) in the polymerization process, the crystal size distribution (CSD) in the crystallization process, the particle size distribution (PSD) in the powder industry, the pulp fiber length distribution and the flame gray level distribution in the paper industry, etc. In the polymerization process, MWD is similar to the fingerprint of the polymer. In the simplest case, assuming no heterogeneous factors, two linear homopolymers with the same MWD will completely have the same mechanical strength, melt rheology, density, and other physical and chemical properties, and will exhibit the same performance under the same processing and use conditions. In the crystallization process, CSD is crucial for determining the efficiency of filtration and washing operations and for producing high-quality products.

[0003] Under the background of the highly competitive chemical industry process market, the demand for product diversification is increasing day by day, and the working conditions of CSD change from time to time. This process is called a multi-condition process. And multi-condition migration control essentially belongs to a dynamic optimization problem. In recent years, the dynamic optimization problem of complex processes has gradually become a research hotspot in the field of process systems engineering. In order to model the product quality of the distributed output process, most researchers study the aggregate value of the quality variables of this process. However, recent studies have shown that adjusting the overall distribution shape of the distributed output process can effectively improve the efficiency of the product quality prediction process and thus improve economic benefits. To solve the problem of distributed output process modeling, many research experts, professors, and scholars have conducted in-depth research and discussion on this process and proposed diverse modeling methods, which are mainly divided into two categories: mechanism modeling methods and data-driven modeling methods. Mechanism modeling methods can be further subdivided into partial differential equation modeling methods and "inverse formula" modeling methods. Data-driven modeling methods can be divided into neural network modeling methods, statistical learning modeling methods, and deep learning modeling methods.

[0004] The above two major modeling methods have achieved good results in the field of chemical engineering modeling. However, the above methods are often only applicable to single or stable operating conditions for kinetic analysis modeling or data-driven modeling of processes, and cannot solve the modeling problem of multi-operating-condition distributed output processes at the same time. At the same time, the mechanism modeling method usually assumes the prior distribution of the PDF of data, tracks and predicts the PDF of the target data, and fully studies the kinetic properties of the distributed output process. However, for new data after changing production and experimental conditions, a large amount of kinetic analysis is often required, and the computational complexity is relatively high. The neural network modeling method, statistical learning modeling method, and deep learning modeling method can only establish data-driven models for each operating condition of the multi-operating-condition distributed output process separately. Due to the differences in operating conditions, they cannot fully learn the information of operating condition changes from historical data, and still cannot establish effective data-driven models.

[0005] In recent years, domestic and foreign research scholars have conducted a large number of studies on chemical process data modeling. Aiming at two difficult problems in chemical processes: one is the multi-operating-condition problem, and the other is the data-driven modeling problem under the condition of less data, a new machine learning paradigm, that is, the transfer learning method, has been proposed. The main purpose of transfer learning is to extract knowledge and experience from one or more source tasks and then apply them to a relevant target field. Traditional machine learning aims to find a model with the minimum expected risk for test data by minimizing the regularized empirical risk on training data. However, this model assumes that the training data and test data share a similar joint probability distribution. When there are differences in the data distributions between the source domain task and the target task, the effect of the prediction learner may be greatly reduced. This method helps to solve the modeling problem of less data volume in the target field by reducing the data distribution differences between different operating conditions and learning information from related fields. Therefore, the transfer learning method has become an effective way to solve the multi-operating-condition distributed output process in chemical engineering. Summary of the Invention

[0006] Aiming at the multi-operating-condition distributed output process with large differences in the label space, the purpose of the present invention is to provide a compensation transfer modeling method based on the multi-operating-condition distributed output process. By transforming the label space, the characteristics of the label space of a small amount of known target domain data are migrated to the label space of the source domain data, so as to better reduce the differences in the data label space distribution of the distributed output process between different operating conditions, and compare with traditional methods, reflecting the effectiveness of the proposed method.

[0007] The specific technical solution is as follows:

[0008] A compensation transfer modeling method based on the multi-operating-condition distributed output process, comprising the following steps:

[0009] 1) Acquisition and integration of data

[0010] Divide the dataset into a source domain working condition dataset, a small amount of target domain label dataset, and a target domain test dataset. Use the source domain working condition dataset as the training set and the small amount of target domain label dataset as the test set. Obtain the predicted data of the target domain label dataset through the Gaussian process regression model. From the formula Obtain the displacement deviation between the source domain working condition data and the small amount of target domain label data, and reconstruct it into a new dataset, that is, the domain deviation dataset. Where Represents the displacement deviation, Represents the target domain label data, Represents the input variable of the new dataset, y te Represents the label of the new dataset;

[0011] 2) Obtain a new source domain working condition compensation dataset

[0012] Use the domain deviation dataset as the training set and the source domain working condition dataset as the test set. Obtain the predicted displacement deviation data of the source domain working condition through the Gaussian process regression model. From the formula Obtain the new dataset after the source domain working condition data is reconstructed in the label space through the deviation compensation mechanism, that is, the new source domain working condition compensation dataset {X tr , y new}, where y new Represents the new source domain working condition data, y tr Represents the source domain working condition dataset, X tr Represents the input variable of the source domain;

[0013] 3) Modeling and training

[0014] Use the new source domain working condition compensation dataset as the training set and the target domain test dataset as the test set. Obtain the final prediction effect of the target domain test dataset through the Gaussian process regression model to complete the prediction;

[0015] 4) Model testing

[0016] Use the molecular weight distribution dataset of the compound free radical polymerization process to verify the effectiveness of the proposed method.

[0017] The specific process of step 1) is as follows:

[0018] Construct a Gaussian process regression from the source domain working condition data {X tr , y tr} and predict the in the known small amount of label data of the target domain working condition . Calculate the source domain working condition offset through . The formula is as follows: The formula is as follows:

[0019]

[0020] According to the posterior probability distribution The offset is calculated by Gaussian process regression for the mean and variance:

[0021]

[0022]

[0023] where λ is the regularization parameter, I is the identity matrix, X tr represents the input variables of the source domain working condition dataset, y tr represents the label data of the source domain working condition dataset, N represents the two-dimensional normal distribution, represents the covariance of X tr and ; represents the variance of X tr ; represents variance, μ S represents the mean of the offset Σ S represents the variance of the offset ;

[0024] Construct a Gaussian process regression from the newly formed dataset and predict X in the source domain working condition data {X tr , y tr}, according to tr obtain the offset of the source domain working condition Thus, the label value y after deviation compensation of the source domain working condition data is obtained new and the mean and variance of the offset are as follows:

[0025]

[0026]

[0027]

[0028] where μ 0 represents the mean of the label value y after deviation compensation of the source domain working condition data new and the offset Σ 0 represents the variance of the label value y after deviation compensation of the source domain working condition data new and the offset ;

[0029] 3) The new data set after the deviation compensation mechanism Use the model to process the unlabeled data in the target domain to obtain predicted data

[0030] Furthermore, the evaluation criteria for the model in step 4) are as follows:

[0031] Take the root mean square error and the coefficient of determination as the evaluation criteria

[0032] The root mean square error is expressed as

[0033]

[0034] where m is the number of samples, y i is the sample label value is the predicted value of the sample label

[0035] The coefficient of determination R 2 is expressed as

[0036]

[0037] where is the mean value of the sample label values

[0038] The beneficial effects of the present invention are mainly manifested in that by transforming the label space, the characteristics of the label space of a small amount of known target domain data are migrated to the label space of the source domain data, so as to better reduce the difference in the label space distribution of the distributed output process data between different working conditions BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the flowchart of the deviation compensation migration model based on GPR of the present invention;

[0040] Figure 2 is the structural diagram of the deviation compensation mechanism of the present invention;

[0041] Figure 3 is the comparison scheme of offset-GPR migration modeling and GPR traditional modeling of the present invention;

[0042] Figure 4 is the visualization diagram of the target domain label space deviation of the training results of the two GPR models when the source domain data of 5 batches in working condition 3 is migrated to working condition 1 of the present invention;

[0043] Figure 5 is the visualization diagram of the compensated and reconstructed source domain data of the training results of the two GPR models when the source domain data of 5 batches in working condition 3 is migrated to working condition 1 of the present invention;

[0044] Figure 6It is the prediction visualization diagram of the prediction results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 5 batches;

[0045] Figure 7 It is the prediction evaluation results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 5 batches;

[0046] Figure 8 It is the visualization diagram of the target domain label space deviation of the training results of two GPR models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 14 batches;

[0047] Figure 9 It is the visualization diagram of the source domain data after compensation and reconstruction of the training results of two GPR models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 14 batches;

[0048] Figure 10 It is the prediction visualization diagram of the prediction results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 14 batches;

[0049] Figure 11 It is the prediction evaluation results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 1 in 14 batches;

[0050] Figure 12 It is the visualization diagram of the target domain label space deviation of the training results of two GPR models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 2 in 14 batches;

[0051] Figure 13 It is the visualization diagram of the source domain data after compensation and reconstruction of the training results of two GPR models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 2 in 14 batches;

[0052] Figure 14 It is the prediction visualization diagram of the prediction results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 2 in 14 batches;

[0053] Figure 15 It is the prediction evaluation results of four soft sensor models when the source domain data of the present invention is migrated from operating condition 3 to operating condition 2 in 14 batches. Detailed implementation manners

[0054] The present invention will be further described below in conjunction with the accompanying drawings of the specification and embodiments, but the protection scope of the present invention is not limited thereto.

[0055] Refer to Figure 1 and Figure 2 , a multi-condition distributed output process compensation migration modeling method, includes the following steps:

[0056] (1) Acquisition and integration of data

[0057] First, the data set can be divided into a source domain working condition data set, a small number of target domain label data sets, and a target domain test data set. The source domain working condition data set is used as the training set, and a small number of target domain label data sets are used as the test set. The target domain label data set prediction data is obtained through the GPR model. By formula ( represents the displacement deviation, Represents the target domain label data) to obtain the displacement deviation between the source domain working condition data and a small amount of target domain label data, and reconstruct it into a new dataset, namely the domain deviation dataset in Represents the input variable of the new data set, y te Represents the labels of the new dataset.

[0058] The specific process of step 1) is as follows:

[0059] From the source domain operating data {X tr ,y tr}Build a GPR with a small amount of labeled data for the target domain conditions In Make predictions through To calculate the source domain condition offset The formula is as follows:

[0060]

[0061] According to the posterior probability distribution The offset can be calculated using GPR The mean and variance of (where λ is the regularization parameter, I is the identity matrix, Represents X tr and The covariance of Represents X tr Variance of ):

[0062]

[0063]

[0064] Reconstructed dataset Construct a GPR and perform the source domain operation data {X tr ,y tr X in} tr Make predictions based on The offset of the source domain condition can be obtained Thus, the label value y after source domain working condition data deviation compensation is obtained new and the offset The mean and variance, where λ is the regularization parameter, and the formula is as follows:

[0065]

[0066]

[0067]

[0068] The new data set after the bias compensation mechanism Use the model for the unlabeled data in the target domain Make predictions to obtain predicted data

[0069] (2) Obtain the new source domain working condition compensation data set

[0070] Use the domain bias data set as the training set and the source domain working condition data set as the test set. Through the GPR model, obtain the displacement deviation prediction data of the source domain working condition From the formula (y new represents the new source domain working condition data, y tr represents the source domain working condition data set), obtain the new data set after the bias compensation mechanism reconstructs the source domain working condition data in the label space, that is, the new source domain working condition compensation data set {X tr ,y new}, where X tr represents the input variable of the source domain.

[0071] (3) Modeling and training

[0072] Use the new source domain working condition compensation data set as the training set and the target domain test data set as the test set. Through the GPR model, obtain the final prediction effect of the target domain test data set to complete the prediction.

[0073] Embodiment

[0074] 1) Obtain the styrene radical polymerization process data set, and the process is as follows:

[0075] Step 1.1: Obtain the process data generated by the MWD simulation of the styrene radical polymerization process under 30 different experimental operating conditions, and record them as working condition 1, working condition 2, and working condition 3. Each experimental operating condition has 100 sample label data. Working condition 1 has 5 experimental operating condition data, working condition 2 has 11 experimental operating condition data, and working condition 3 has 14 experimental operating condition data.

[0076] Step 1.2: Use working condition 3 with relatively more label data and the lowest degree of non-linearity as the source domain training data, and the data of the other two working conditions as the target domain working condition data.

[0077] Step 1.3: Apply medium noise (5% Gaussian noise) to the data in the styrene radical polymerization MWD experiment.

[0078] 2) Conduct Gaussian process regression model training

[0079] Step 2.1: Take operating condition 3 as the source domain operating condition (5 batches), operating condition 1 as the target domain test operating condition (4 batches), and a small amount of known label operating condition data in the target domain (1 batch). The two GPR model training results of migrating operating condition 3 to operating condition 1 when the source domain training operating condition data is 5 batches are shown in Figure 4 and Figure 5 , Figure 4 The left figure in shows the new training data sets of the source domain and the target domain after adding 5% Gaussian noise, and the right figure shows the prediction results of the target domain after training with the new training set using the GPR model. Figure 5 The left figure in shows the true label data of the source domain and the new label data of the compensated source domain, and the right figure shows the prediction results using one batch of source domain data prediction and one batch of new label data of the compensated source domain, and compares with the target domain operating condition data. The prediction results of four soft-sensing models when migrating operating condition 3 to operating condition 1 with 5 batches of source domain training operating condition data are shown in Figure 6 and Figure 7 , Figure 6 The upper left figure in shows the comparison chart of the four-batch prediction results of the four models migrating from operating condition 3 to operating condition 1, the upper right figure shows the comparison chart of the four-model predictions of one batch in the target domain after source domain compensation, the lower left figure shows the comparison chart of the absolute errors of the four-batch predictions of the four models migrating from operating condition 3 to operating condition 1, and the lower right figure shows the comparison chart of the absolute errors of the four-model predictions of one batch in the target domain after source domain compensation. It can be seen that the GPR model effectively improves the prediction accuracy by using the compensated and reconstructed source domain data.

[0080] Step 2.2: Take operating condition 3 as the source domain operating condition (all 14 batches), operating condition 1 as the target domain test operating condition (4 batches), and a small amount of known label operating condition in the target domain (1 batch). The two GPR model training results of migrating operating condition 3 to operating condition 1 when the source domain training operating condition data is 14 batches are shown in Figure 8 and Figure 9 , Figure 8 The left figure in shows the prediction results of the four models for 14 batches of the source domain and the target domain migrating from operating condition 3 to operating condition 1, and the right figure shows the visualization diagram of the label space deviation of the four models for one batch in the target domain after source domain compensation. Figure 9 The left figure shows the visualization comparison of the 14-batch source domain label data and the compensated and reconstructed labels of the four models migrating from operating condition 3 to operating condition 1 after compensation and reconstruction, and the right figure shows the visualization diagram of the prediction using only the source domain prediction and the prediction after source domain compensation. The prediction results of four soft-sensing models when migrating operating condition 3 to operating condition 1 with 14 batches of source domain training operating condition data are shown inFigure 10 and Figure 11 , Figure 10 The upper left figure in the middle shows the comparison chart of the prediction results of 14 batches of four models migrated from working condition 3 to working condition 1, and the upper right figure shows the comparison chart of the prediction results of four models in one batch after source domain compensation; the lower left figure shows the comparison chart of the absolute errors of the 14 batches of predictions of the four models migrated from working condition 3 to working condition 1, and the lower right figure shows the comparison chart of the absolute errors of the predictions of the four models in one batch after source domain compensation. It can be seen that the proposed offset-GPR model has the highest accuracy, followed by GPR(S+T), and GPR(T) has the worst prediction effect.

[0081] Step 2.3: Take working condition 3 as the source domain working condition (all 14 batches), working condition 2 as the target domain test working condition (4 batches), and a small amount of known label working conditions in the target domain (1 batch). The training results of the two GPR models when migrating working condition 3 to working condition 2 with 14 batches of source domain training working condition data are shown in Figure 12 and Figure 13 , Figure 12 The left figure shows the prediction results of the four models in 14 batches of the source domain and the target domain migrated from working condition 3 to working condition 2, and the right figure shows the visualization diagram of the label space deviation of the four models in one batch of the target domain after source domain compensation; Figure 13 The upper left figure in the middle shows the comparison chart of the prediction results of 14 batches of four models migrated from working condition 3 to working condition 2. The right figure shows the visualization comparison of the 14 batches of source domain label data and the compensated and reconstructed labels of the four models migrated from working condition 3 to working condition 2 after compensation and reconstruction. The right figure shows the visualization diagram of the prediction using only the source domain prediction and the prediction after source domain compensation. The prediction results of the four soft-sensing models when migrating working condition 3 to working condition 2 with 14 batches of source domain training working condition data are shown in Figure 14 and Figure 15 , Figure 14 The upper left figure in the middle shows the comparison chart of the prediction results of 14 batches of four models migrated from working condition 3 to working condition 2, and the upper right figure shows the comparison chart of the prediction results of four models in one batch after source domain compensation. The lower left figure shows the comparison chart of the absolute errors of the 14 batches of predictions of the four models migrated from working condition 3 to working condition 2, and the lower right figure shows the comparison chart of the absolute errors of the predictions of the four models in one batch after source domain compensation. It can be seen that the prediction effect of offset-GPR is still the best among the four models.

[0082] 3) Comparison of the prediction performance of the four soft-sensing models

[0083] The four soft-sensing models are as Figure 3 shown. GPR(S) represents prediction using only source domain data, GPR(T) represents prediction using only target domain data, and GPR(S+T) represents prediction using a small amount of source domain label data and target domain label data.

[0084] This model uses the root mean square error (RMSE) and the coefficient of determination (R2 ) As an evaluation criterion, RMSE is expressed as:

[0085]

[0086] where m is the number of samples, y i is the sample label value, is the predicted value of the sample label.

[0087] R 2 is expressed as:

[0088]

[0089] where y i is the sample label value, is the predicted value of the sample label, is the mean value of the sample label values.

[0090] According to the RMSE and R in Table 1 2 it can be seen that for the GPR model trained only with source domain label data established when the number of source domain working condition training samples is 5 batches, i.e., the GPR(S) model, the prediction effect is the worst; at the same time, as the number of source domain working condition training samples increases to 14 batches, the prediction accuracy of the proposed offset compensation transfer model (offset-GPR) model increases by 12.5%, while for the GPR model trained with source domain and a small amount of target domain working condition label data, i.e., GPR(S+T), it increases by 9.2%. The improvement amplitude of the proposed model is greater and the advantage is more obvious; when the difference between the source domain and the target domain working conditions is reduced, all models have good prediction accuracy, and the offset-GPR model is still the optimal model. Finally, it shows that the proposed offset-GPR model can solve the problem of predicting the MWD of styrene free radical polymerization with multi-working condition characteristics.

[0091] Table 1 Comparison of the prediction performance of four soft sensor models for the MWD of styrene free radical polymerization

[0092]

[0093] The offset compensation transfer method based on the Gaussian process regression model proposed by the present invention has been fully verified on the MWD dataset of styrene free radical polymerization, improving the prediction accuracy and having universality and generality.

[0094] The content described in the embodiments of this specification is only an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms stated in the embodiments, and the protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art according to the inventive concept.

Claims

1. A multi-condition distributed output process compensation migration modeling method, characterized in that it includes the following steps: 1) Acquisition and integration of data The dataset is divided into a source domain working condition dataset, a small amount of target domain label dataset, and a target domain test dataset. The source domain working condition dataset is used as the training set, and the small amount of target domain label dataset is used as the test set. The predicted data of the target domain label dataset is obtained through the Gaussian process regression model , and the displacement deviation between the source domain working condition data and the small amount of target domain label data is obtained by the formula , and is reconstructed into a new dataset, that is, the domain deviation dataset , where represents the displacement deviation, represents the target domain label data, represents the input variable of the new dataset, represents the label of the new dataset; 2) Acquisition of a new source domain condition compensation data set Taking the domain deviation dataset as the training set and the source domain working condition dataset as the test set, the displacement deviation prediction data of the source domain working condition is obtained through the Gaussian process regression model , and from the formula a new dataset after the deviation compensation mechanism reconstructs the source domain working condition data in the label space is obtained, that is, the new source domain working condition compensation dataset , where represents the new source domain working condition data, represents the source domain working condition dataset, represents the input variable of the source domain; 3) Modeling and training Using the new source domain condition compensation data set as the training set and the target domain test data set as the test set, the final prediction effect of the target domain test data set is obtained through the Gaussian process regression model to complete the prediction; 4) Model testing Using the molecular weight distribution data set of the compound free radical polymerization process to verify the effectiveness of the proposed method; The specific process of step 1) is: 1) From the source domain operating condition data Construct a Gaussian process regression and predict the small amount of labeled data of the target domain operating condition in and calculate the source domain operating condition offset through The formula is as follows: The formula is as follows: （1） 2) According to the posterior probability distribution Calculate the offset using Gaussian process regression for the mean and variance: （2） （3） wherein is the regularization parameter, is the identity matrix, represents the input variables of the source domain operating condition dataset, represents the label data of the source domain operating condition dataset, N represents the two-dimensional normal distribution, represents and the covariance of, represents the variance of, represents the variance of, μ S represents the offset the mean of, represents the offset the variance of; From the newly constructed dataset Construct a Gaussian process regression and predict the source domain working condition data in According to , obtain the offset of the source domain working condition , and thus obtain the labeled values after deviation compensation of the source domain working condition data and the offset The mean and variance are as follows: （4） （5） （6） where μ 0 represents the labeled value after the deviation compensation of the source domain operating condition data and the mean value of the offset , represents the labeled value after the deviation compensation of the source domain operating condition data and the variance of the offset ; 3) The new data set after the deviation compensation mechanism , use the model to process the unlabeled data in the target domain to obtain predicted data .

2. A multi-condition distributed output process compensation migration modeling method according to claim 1, characterized in that the evaluation criteria for the model in step 4) are as follows: Taking the root mean square error and the coefficient of determination as the evaluation criteria, The root mean square error is expressed as （7） wherein is the number of samples, is the sample label value, is the predicted value of the sample label Coefficient of determination R 2 Expressed as （8） where is the mean of the sample label values.

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