A method for predicting oligomer density in a polyester fiber esterification process

Abstract

The present application relates to a kind of oligomer density prediction method of polyester fiber esterification process, first acquisition process variable (esterification kettle outlet temperature, esterification separation water flow, precondensation process liquid level, esterification kettle liquid level and esterification kettle temperature) and quality variable (oligomer density) sensor data, for the data missing problem of process variable and quality variable caused by sensor failure and different sampling rate, obtain the distribution filling sample of missing data by data filling model, obtain its corresponding multiple data filling sample by oversampling strategy, improve the number and quality of complete sample by self-training method, to obtain relatively complete data set, finally different index prediction model is established for different data filling sample of test sample respectively, and the average value of each prediction model output is used as the final result.The method of the present application can simultaneously process the data missing problem of process variable and quality variable, overcome the shortcomings of prior art on high complete sample dependence.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology, and in particular relates to a method for predicting the oligomer density in the esterification process of polyester fibers. Background Technology

[0002] Polyester fiber (PET), as a type of synthetic fiber, possesses numerous advantages such as high strength and good wrinkle resistance, thus gaining wider applications than other synthetic fibers and gradually developing into the synthetic fiber with the highest production volume and most widespread use. The production process of polyester fiber includes four stages: polymerization, melt conveying, spinning, and post-processing. The polymerization process, as the first step, has a direct and significant impact on the quality and performance of the final product. The polymerization process includes three stages: esterification, pre-condensation, and final condensation. Esterification, as the first stage of polymerization, directly affects the degree of reaction in subsequent processes and the quality of the final product. In this process, oligomer density reflects the degree of esterification and condensation reactions, and is crucial for evaluating the production progress of this process and the subsequent capacity of the entire production line. However, due to the multiple equilibrium relationships between the reactants, and the need to consider the properties of the reactants, such as average molecular weight and polymer activity, modeling this process is challenging. Furthermore, the reaction process in this stage is characterized by strong coupling, high time delay, and nonlinearity, posing numerous obstacles to the establishment of data-driven models.

[0003] As polyester fiber production processes gradually shift towards customization and refinement, the production flow faces more diverse challenges and places higher demands on manufacturing techniques. With the continuous development of sensor and data storage technologies, traditional chemical processes are gradually transitioning towards intelligent and automated production. The widespread deployment of various sensors on production lines has generated massive amounts of industrial data, making it crucial to study how to utilize this data to better guide the production process. In polyester fiber production, some key indicators are difficult to obtain directly due to harsh environments, high costs, and other reasons. Therefore, soft measurement technology has emerged. The idea is to construct a predictive model that uses easily measurable process variables as input and difficult-to-measure quality variables as output, thereby indirectly obtaining the predicted results of key indicators and providing necessary reference and guidance for production personnel.

[0004] In the construction of soft sensor models, a large amount of complete labeled data is usually required, and complete process variable data is also needed when making predictions. Reference 1 (Soft Sensor Modeling Method Based on Hybrid Variational Autoencoder Regression Model [J]. Acta Automatica Sinica, 2022, 48(2):398-407.) proposes a soft sensor regression model based on hybrid variational autoencoders. Reference 2 (Parallel Interaction Spatiotemporal Constrained Variational Autoencoder for Soft Sensor Modeling [J]. IEEE Transactions on Industrial Informatics, 2021, 18(8):5190-5198.) proposes a parallel interactive spatiotemporal variational autoencoder soft sensor model and applies it to the polyester fiber polymerization process. However, these models cannot effectively play a role when faced with incomplete data caused by sensor failure or hardware conditions that are prone to occur in actual industrial processes. In actual industrial systems, occasional sensor failures usually lead to partial data loss, and if these missing data are not properly processed, the model will be difficult to train, and the applicability and robustness of the model will also be reduced. Furthermore, due to the high cost of measurement and the harsh measurement environment, the sampling rate of sensors for mass variables is usually lower than that for process variables, resulting in a large amount of unlabeled data. If this data is ignored and only labeled data is used for modeling, the prediction results of the model will inevitably be affected.

[0005] Currently, scholars have adopted different methods to try to solve the above problems. For the problem of missing process data caused by factors such as sensor failure, some scholars have constructed estimation models for missing values ​​through various means such as mean imputation, forward imputation, and regression imputation. Reference 3 (Auret L. Variational autoencoders for missing data imputation with application to a simulated milling circuit[J].IFAC-PapersOnLine,2018,51(21):141-146.) proposes a missing value imputation model based on variational autoencoders and verifies it in a simulated milling circuit system. Reference 4 (Deep generative modelling and imputation of incomplete data sets[C] / / International conference on machine learning.PMLR,2019:4413-4423.) proposes a data imputation framework based on importance-weighted variational autoencoders and uses it for the imputation task of incomplete data. To address the issue of significant missing labeled data due to different sampling rates for process and quality variables, some researchers have constructed various semi-supervised models to utilize unlabeled samples. For example, reference 5 (Anovel self-training semi-supervised deep learning approach for machineryfault diagnosis[J]. International Journal of Production Research, 2022:1-14.) proposes a semi-supervised deep learning method based on self-training and applies it to fault diagnosis tasks. Reference 6 (Shen B, Yao L, Ge Z. Predictive modeling with multiresolution pyramid VAE and industrial soft sensor applications[J]. IEEE Transactions on Cybernetics, 2022.) combines variational autoencoders and feature pyramids to propose a semi-supervised soft sensor framework to address the multi-sampling rate problem. However, these models still have some issues that need to be addressed. Since some sensor faults do not occur at a single moment but persist for a certain period of time, traditional imputation models are difficult to apply in this case.Furthermore, traditional semi-supervised models typically only estimate a single point for missing labels and do not consider the problem of missing data in the input data. When the estimation is inappropriate or the input data is incomplete, it will reduce the prediction accuracy of the model and introduce a certain degree of instability.

[0006] Therefore, it is necessary to consider both the random and continuous missing process variables and the periodic missing quality variables, and to construct a missing data imputation and key indicator prediction model applicable to the above problems, so as to make reasonable predictions of oligomer density in the polyester fiber esterification process and provide guidance for production and operation personnel. Summary of the Invention

[0007] To address the problems in existing technologies, this invention proposes a method that can simultaneously fill in missing data and predict key indicators in the current polyester fiber esterification process, thereby enhancing the model's anti-interference ability, improving the applicability and generalization of the prediction model, maintaining the efficient and stable operation of the production process, and improving the performance and quality of the final fiber.

[0008] This invention provides a method for predicting oligomer density during the esterification process of polyester fibers. First, sensor data of process variables and mass variables are collected. To address the problem of missing process and mass variable data due to sensor malfunctions and different sampling rates, a data imputation model is used to obtain distribution-filled samples of the missing data. An oversampling strategy is used to obtain multiple corresponding data imputation samples. A self-training method is used to improve the quantity and quality of complete samples, thereby obtaining a relatively complete dataset. Finally, different index prediction models are established for different data imputation samples of the test samples, and the average value of the output of each prediction model is used as the final oligomer density prediction result.

[0009] To achieve the above objectives, the present invention adopts the following solution:

[0010] A method for predicting oligomer density during the esterification process of polyester fibers includes the following steps:

[0011] (1) The collected process variable and quality variable sensor data are used as sample datasets, and the sample datasets are divided into training datasets and validation datasets.

[0012] (2) Use the complete samples in the training dataset to train the data imputation model, and then input the samples with missing values ​​in the training dataset into the trained data imputation model to imput them, so as to obtain the distribution imputation samples of missing data (the distribution imputation samples are samples that replace the missing values ​​in the form of a distribution, which is described by the corresponding mean and variance).

[0013] (3) Sort the distribution imputation samples of missing data according to the variance of the distribution of quality variable, select the distribution imputation samples with smaller variances of a specified proportion, and use an oversampling strategy to sample from the distribution of these distribution imputation samples (oversampling the sample set to reduce the adverse effects of larger variances to a greater extent) to obtain the data imputation samples of missing data (data imputation samples are samples that replace missing values ​​with a certain number), and regard them as new complete samples.

[0014] (4) Based on the self-training method, a relatively complete dataset is obtained after the data is expanded based on the imputation samples and a data imputation model trained on the dataset. The self-training (ST) method is a mature solution to semi-supervised problems. It can gradually improve the quantity and quality of complete data in a cyclical and iterative manner, thereby obtaining a relatively complete dataset and providing necessary guidance for the subsequent modeling process.

[0015] (5) Collect process variable data in real time and input it into the data imputation model trained with complete samples in the training dataset to imput the missing data. Then, use an oversampling strategy to sample multiple data imputation samples of the missing data from the distribution of the distribution imputation samples, thereby expanding to obtain multiple complete samples.

[0016] (6) Based on the similarity between each sample in the multiple complete samples obtained in step (5) of KL divergence calculation and all samples in the relatively complete dataset, for any sample X in the multiple complete samples, select a specified number of samples with the highest similarity to the sample from the relatively complete dataset, use the process variables in the selected samples as input and the quality variables as output to train an indicator prediction model, and use the trained indicator prediction model to predict sample X to obtain the prediction result of sample X;

[0017] (7) The average of the prediction results of each sample in the multiple complete samples is the predicted quality variable data.

[0018] The process variables are the esterification reactor outlet temperature, esterification separation water flow rate, prepolymerization process liquid level, esterification reactor liquid level and esterification reactor temperature, and the mass variable is the oligomer density during the esterification process.

[0019] The data imputation model is a variational autoencoder (IVAE) model with uncertainty, which replaces the output of the variational autoencoder (VAE) model with data points in the form of a data distribution; the index prediction model is a Gaussian process regression model.

[0020] As a preferred technical solution:

[0021] In the oligomer density prediction method of the polyester fiber esterification process described above, the ratio of the training dataset to the validation dataset in step (1) is 8:2.

[0022] The oligomer density prediction method for the polyester fiber esterification process described above requires a total sample size of no less than 2000 in the sample dataset.

[0023] As described above, in the method for predicting the oligomer density of a polyester fiber esterification process, the specified proportion in step (3) refers to the first 20%, and this percentage threshold is a hyperparameter that is artificially set in advance.

[0024] As described above, the method for predicting oligomer density in the esterification process of polyester fibers includes the following steps: Steps (2) to (3) are repeated until the stopping condition is met. The stopping condition is that the prediction error of the validation dataset in the current cycle is greater than that in the previous cycle or the maximum number of cycles has been reached. (If the current prediction error is greater than that in the previous cycle, the expanded relatively complete dataset and the data imputation model trained on the dataset in this cycle will not be retained. Instead, the relatively complete dataset and the data imputation model obtained in the previous cycle will remain unchanged and the cycle will end.) When the cycle ends, the relatively complete dataset expanded based on the imputation sample and the data imputation model trained on the dataset corresponding to the minimum prediction error or the maximum number of cycles will be obtained.

[0025] The method for predicting oligomer density during the esterification process of polyester fibers, as described above, has a maximum number of cycles of 10, and the root mean square error is selected as the prediction error index.

[0026] As described above, in the method for predicting oligomer density during the esterification process of polyester fibers, the number of samples specified in step (6) shall not exceed the number of samples in the training dataset and shall not be less than the number of complete samples in the training dataset. To ensure the real-time performance and speed of the prediction, it is recommended that the number of samples selected shall not exceed 500. At the same time, to ensure the accuracy and precision of the index prediction model, it is recommended that the number of samples selected shall not be less than 300.

[0027] As described above, in the method for predicting oligomer density during the esterification process of polyester fibers, step (6) uses KL divergence, which is a way to measure the distance between two distributions. For two normal distributions... and The KL divergence between them is defined as follows:

[0028]

[0029] Among them, μ1, μ2、 Here, J represents the mean and variance of two normal distributions, respectively, and J represents the number of samples in the normal distribution. The smaller the KL divergence, the closer the distributions are, which means that the two samples are more similar.

[0030] The variational lower bound of the variational autoencoder model with uncertainty in the polyester fiber esterification process, as described above, is given by the following method for predicting oligomer density during the polyester fiber esterification process:

[0031]

[0032] in, This is the variational lower bound for the variational autoencoder model with uncertainty. and p θ (x|z) represent the encoder and decoder of the variational autoencoder model with uncertainty, respectively. θ and θ represent their corresponding parameters, z represents the latent variable of the variational autoencoder model with uncertainty, and μ(z) and σ(z) represent the mean and standard deviation of z, respectively.

[0033] Beneficial effects

[0034] (1) The oligomer density prediction method of the polyester fiber esterification process of the present invention can simultaneously handle the missing problems caused by sensor failure in the process variables and the missing data of quality variables caused by different sampling rates. It overcomes the shortcomings of traditional modeling methods that rely on high complete samples, helps to improve the quality of polymers and fiber properties, has strong applicability, and has good effects in practice.

[0035] (2) The present invention provides a method for predicting the oligomer density of polyester fiber esterification process. It adopts a self-training learning framework and an improved variational autoencoder model with uncertainty. This method can simultaneously obtain the uncertainty of the missing data, overcome the disadvantage that the original missing data model can only be filled with a single value. Through the oversampling strategy, a more reasonable missing value filling result can be obtained.

[0036] (3) The purpose of existing technologies in processing missing values ​​is mostly to make better use of the information in the missing data to build models, but complete process variable data are still required in the testing stage. The oligomer density prediction method of the polyester fiber esterification process of the present invention can predict key quality indicators even in the case of missing data in the prediction stage, and has higher feasibility in practical application. Attached Figure Description

[0037] Figure 1 This is a process flow diagram of polyester fiber esterification and esterification vapor separation.

[0038] Figure 2This is a diagram illustrating the framework structure of the self-training method.

[0039] Figure 3 The structure diagram of the variational autoencoder model for uncertainty;

[0040] Figure 4 This is a schematic diagram of an oversampling strategy;

[0041] Figure 5 The graph shows the prediction results of the simulation data;

[0042] Figure 6 This is a graph showing the prediction error of actual data. Detailed Implementation

[0043] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0044] The density of oligomers reflects the degree of esterification and polycondensation reactions, ultimately determining the properties and yield of the final product. The polyester polymerization process comprises five stages: slurry formulation, esterification, oligomer delivery and additive injection, pre-polymerization, and final polycondensation. Esterification, as the second stage, includes two steps: esterification and esterification vapor separation. Figure 1 As shown, the process can be described in detail as follows: Materials prepared according to the specified proportions are fed into the esterification reactor via a transfer pipeline, and the flow rate is controlled by a material pump. In the esterification reactor, the mixture undergoes an esterification reaction to generate the desired oligomer. Due to the high temperature in the esterification reactor, esterification vapor is generated during the reaction. This vapor mainly consists of ethylene glycol and water, byproducts of the esterification reaction. Ethylene glycol can be recovered and reused, so an esterification separation tower is needed to separate the esterification vapor. The oligomer generated in the esterification reactor is transported to the next stage of the polymerization process via a pipeline. After being cooled by a heat exchanger, the remaining EG is returned to the upstream esterification separation tower for reuse, and the wastewater is discharged through a water reflux device. The esterification separation water is then converted into condensate by a steam treatment device and discharged from the production unit.

[0045] The density of oligomers can be predicted through production processes, multiple equilibrium relationships between reactants during preparation, and the properties of reactants (such as average molecular weight and polymer activity). However, in actual industrial systems, occasional sensor malfunctions often lead to partial data loss. High measurement costs and harsh measurement environments, coupled with the fact that the sampling rate of mass variables is usually lower than that of process variables, all affect the predicted density of oligomers. Therefore, this invention aims to solve the problem of data loss caused by sensor malfunctions and different sampling rates. The random, continuous loss of process variables due to sensor malfunctions and the periodic loss of mass variables due to different sampling rates can be mathematically described as follows: For a multi-input single-output system, the data can be described as D = {X, Y} ∈ R. n×(d+1) , where X∈R n×d Y = {y1, y2, ..., y} n} represent the input and output data of the system, respectively; for any i∈{1,2,...,n}, Let be a sample in X, where n is the number of samples and d represents the dimension of the input data. Data gaps caused by sensor failures and different sampling rates between process variables and quality variables can be described as non-periodic continuous gaps in the input data and periodic gaps in the output data, respectively.

[0046] Continuous, non-uniform missing values ​​in a process variable can be understood as meaning that the location of the missing values ​​cannot be predicted in advance; they can occur at any location and at any time step. Furthermore, missing values ​​do not only occur at a single time point but also exist in several subsequent time periods. Assuming a missing rate of α, then we have... There are missing samples, among which This represents the integer part number. For a single sample, the number of missing values ​​*m* satisfies... Assume the maximum step size for consecutive missing values ​​is β, and that there are missing values ​​at time step p and dimension q, where p∈{1,2,...,n}, q∈{1,2,...,d}, n is the number of samples, and d represents the dimension of the input data. Then, for any step size less than β, l∈{0,1,2,...,(β-1)}, It is also defined as a missing value.

[0047] Uniform missing values ​​in the output data mean that the occurrence of missing values ​​follows a fixed step size. Assuming the sampling step size is γ, then for any parameter... y k Defined as an observation, while {y} k+1 ,y k+2 ,...,y k+γ-1} is then defined as a missing value.

[0048] In the method of this invention, a distribution of missing data imputation samples is obtained through a data imputation model, and multiple data imputation samples of missing data are obtained by using an oversampling strategy to improve the reliability of data imputation. In order to improve the quantity and quality of samples and obtain a relatively complete dataset, a self-training method is combined, and finally, index prediction models for different data imputation samples are established and the average value of the output of each prediction model is used as the final result.

[0049] Among them, such as Figure 2 As shown, the working process of the self-training method used in this method can be mainly described as follows:

[0050] (1) Use the existing labeled data to train the data to fill the model, and use the model to obtain the pseudo-label distribution of unlabeled samples to replace the original missing data;

[0051] (2) The numbers at specified positions of the pseudo-label variance sorted from smallest to largest are set as confidence levels to filter the pseudo-label sample set and select high-quality pseudo-label sample sets from them.

[0052] (3) Combine the high-quality pseudo-label sample set mentioned above with the original labeled data to retrain a new data imputation model;

[0053] (4) Repeat process (1) to (3). When the loop ends, that is, when the new data imputation model cannot improve the accuracy of the indicator prediction model on the validation set or the maximum number of loops has been reached, the optimal data imputation model is obtained.

[0054] In this invention, the data imputation model is a variational autoencoder (VAE) model with uncertainty. It is a data imputation model based on the traditional VAE model that can describe data uncertainty. The traditional VAE model is a widely used nonlinear feature extraction and generation model that combines Bayesian inference and deep neural networks. A VAE model typically includes an encoder and a decoder, also known as an inference network and a generator network. The inference network seeks a mapping from input data x to latent variable z, where z represents a continuous arbitrary variable. The generator network aims to reconstruct the input data from z. Assuming p(z) is the distribution function of z, then data x can be generated from the following marginal likelihood function:

[0055] p θ (x)=∫p θ (z)p θ (x|z)dz;

[0056] Where θ represents the encoder parameters, a probability distribution is introduced. Its input is x, and its output is the probability distribution of the latent variable z given x. Then p θ The logarithmic function of (x) can be described as:

[0057]

[0058] in The KL (Kullback-Leibler) divergence represents... and p θ The magnitude of the difference between (z|x). To represent the variational lower bound, it can also be rewritten as:

[0059]

[0060] The first term in the above formula represents Minimizing the KL divergence between and means making the approximate posterior Tendency towards prior p θ (z); The second term is based on the known encoder output. Based on log(p) θ Maximizing the expectation of (x|z) means minimizing the reconstruction error of the VAE. Typically, p θ (x|z) will be considered to be a normal distribution, that is:

[0061] p θ (x|z)~N(μ(z),σ 2 (z));

[0062]

[0063] Where μ(z) and σ 2 (z) is the output of the decoder. In VAE, σ 2 (z) will be fixed as σ 2 This means:

[0064]

[0065] in Represents the reconstructed value of the input data, ||x-μ(z)|| 2 Also known as MSE loss, This is then considered a coefficient and is usually ignored. Based on the above, the reconstruction error can be replaced by the MSE loss, and the VAE model can be trained by maximizing the variational lower bound, thus obtaining a standard data imputation model. The aforementioned VAE model with uncertainty, p θThe variance of (x|z) is treated as a variable, not a fixed value. This means that each output sample has a separate variance. In other words, each original output sample point can be replaced by a unique normal distribution. This operation of replacing points with distributions introduces uncertainty, hence it is called an indeterminate VAE (IVAE), such as... Figure 3 As shown. Therefore, the variational lower bound of the traditional variational autoencoder model. It can be redescribed as:

[0066]

[0067] in, This is the variational lower bound for the variational autoencoder model with uncertainty. and p θ (x|z) represent the encoder and decoder of the variational autoencoder model with uncertainty, respectively. θ and θ represent their corresponding parameters, z represents the latent variable of the variational autoencoder model with uncertainty, and μ(z) and σ(z) represent the mean and standard deviation of z, respectively.

[0068] Through the above improvements, we can obtain the mean and variance for each sample generated by IVAE. By feeding both process and quality variables into the input layer of the IVAE model, we can simultaneously generate the distributions corresponding to the missing values ​​of both. Furthermore, the variance of the generated samples can also be seen as the uncertainty of the generation quality. Larger uncertainty corresponds to larger variance. Therefore, this uncertainty can be used as the confidence level in the self-training method, thus combining it with the self-training approach.

[0069] In the process of combining the data imputation model (IVAE model) with the self-training method, an oversampling strategy is adopted to reasonably evaluate and replace the variance corresponding to different generated samples in order to better utilize the uncertainty of label information. For samples with high uncertainty, the mean alone is insufficient to directly describe the label distribution, so more substitute data is needed to describe and characterize the label distribution information; conversely, for samples with high confidence, i.e., low variance, the mean is sufficient to replace the label distribution information, and no extra samples are needed. Guided by the above ideas, the oversampling strategy is introduced, defining a value that depends on the variance of the generated samples. The sampling rate is r m This can be obtained through MinMax normalization, i.e.:

[0070]

[0071] Where σ2 This represents the set of variances of the variables corresponding to the given data point in the generated data. For each missing data point, t samples are required, where r is the variance of the variable. m This represents the sampling probability in each sampling process. For i = {1, 2, ..., t}, random sampling is performed from a uniform distribution between 0 and 1, i.e.:

[0072] r i ~U(0,1);

[0073] If r i <r m Then, a new sample will be sampled from the normal distribution of the missing data based on the corresponding mean and variance. Therefore, for data points with smaller variances, they correspond to smaller sampling probabilities, resulting in a smaller final number of samples collected. This allows for effective utilization of the variance information of the samples from each iteration in the self-training framework, such as... Figure 4 As shown.

[0074] In the framework combining the data imputation model (IVAE model) with a self-training method (also known as ST-IVAE), the training phase refers to the process of training a relatively complete dataset and a better-performing data imputation model using initial labeled and unlabeled samples. First, the IVAE data imputation model is trained on the existing complete dataset to impute missing data, resulting in distributed imputation samples for different missing data. Based on this, the variance of the quality variables in the distributed imputation samples is used as the criterion for the confidence level of the imputed data, and the 20% of samples with the lowest variance are selected as the sample set with higher confidence. Oversampling is then performed on this sample set to further reduce the adverse effects of large variance. The oversampled sample set is then combined with the original complete dataset, and the IVAE data imputation model is retrained. This process is iterated continuously within the above framework until a stopping condition is met. That is, the model terminates when the number of iterations exceeds the set maximum number of iterations or when adding the currently selected sample set no longer improves the model's prediction accuracy, resulting in a relatively complete dataset with a large sample size and an IVAE data imputation model trained on that dataset.

[0075] The testing phase refers to the process of using the relatively complete dataset obtained in the training phase and a high-performing data imputation model to fill in missing values ​​for each test sample and construct an indicator prediction model to obtain the prediction results for the corresponding key indicators. For each test sample, firstly, the missing values ​​in the sample are filled in based on the aforementioned data imputation model, resulting in its corresponding distribution-filled sample. Then, an oversampling strategy is used to oversample this distribution, resulting in multiple equivalent alternative data imputed samples. For each alternative sample, a different indicator prediction model is constructed. The training samples required for training each indicator prediction model are obtained by calculating the KL divergence between the complete dataset and the current sample. The indicator prediction model is trained by selecting a subset of samples with the smallest KL divergence and then predicting for that sample. Finally, the average of the prediction results of all alternative samples is taken as the final prediction result for the test sample.

[0076] Based on the above-mentioned inventive concept, the specific method of the present invention is as follows:

[0077] A method for predicting oligomer density during the esterification process of polyester fibers includes the following steps:

[0078] (1) Collect process variables (esterification kettle outlet temperature, esterification separation water flow rate, prepolymerization process liquid level, esterification kettle liquid level and esterification kettle temperature) and mass variables (oligomer density of esterification process) sensor data as sample datasets. The total number of samples in the sample dataset is not less than 2000. The sample dataset is divided into training dataset and validation dataset in an 8:2 ratio.

[0079] (2) Use the complete samples in the training dataset to train the data imputation model (IVAE model), and then input the samples with missing values ​​in the training dataset into the trained data imputation model to imput them, so as to obtain the distribution imputation samples of missing data.

[0080] (3) Sort the distribution imputation samples of missing data according to the variance of the quality variable distribution, select the top 20% of distribution imputation samples with smaller variance, and use an oversampling strategy to sample from the distribution of these distribution imputation samples to obtain the data imputation samples of missing data, which are regarded as new complete samples.

[0081] (4) Repeat steps (2) to (3) until the stopping condition is met. The stopping condition is that the prediction error (root mean square error) of the validation dataset in the current loop is greater than that of the previous loop or the maximum number of loops has been reached (the maximum number of loops is 10). When the loop ends, the relatively complete dataset after the expansion based on the imputation sample and the data imputation model trained on the dataset will be obtained when the prediction error is the smallest or the maximum number of loops is reached.

[0082] (5) Collect process variable data in real time and input it into the data imputation model trained with complete samples in the training dataset to imput the missing data. Then, use an oversampling strategy to sample multiple data imputation samples of the missing data from the distribution of the distribution imputation samples, thereby expanding to obtain multiple complete samples.

[0083] (6) Based on the similarity between each sample in the multiple complete samples obtained in step (5) of the KL divergence calculation and all samples in the relatively complete dataset, for any sample X in the multiple complete samples, select a specified number of samples with the highest similarity to the sample from the relatively complete dataset (the specified number of samples shall not exceed the number of samples in the training dataset and shall not be less than the number of complete samples in the training dataset, preferably 300 to 500), use the process variables in the selected samples as input and the quality variables as output, train an index prediction model (Gaussian process regression model), and use the trained index prediction model to predict sample X to obtain the prediction result of sample X;

[0084] KL divergence is a way to measure the distance between two distributions. For two normal distributions... and The KL divergence between them is defined as follows:

[0085]

[0086] Among them, μ1, μ2、 Let J represent the mean and variance of the two normal distributions, respectively, and J represent the number of samples in the normal distribution.

[0087] (7) The average of the prediction results of each of the multiple complete samples is the predicted quality variable data, namely the oligomer density.

[0088] To better demonstrate the technical effects of the present invention, the present invention is described through the following specific embodiments:

[0089] Example 1

[0090] This embodiment conducts experiments on a simulation dataset, generating time series data following a nonlinear Gaussian process, with a total of 2000 samples:

[0091] z = (z1, z2) T

[0092] x = A T z+ξ x ,A∈R 2×4

[0093] ξx ~N(0,0.1)

[0094]

[0095] Where z represents the set of latent variables, z1 and z2 are the latent variables within it, x represents the input data, A is a 2×4 real matrix, and ξ x Let x represent the noise corresponding to x, which follows a normal distribution with a mean of 0 and a variance of 0.1, and y represent the output data.

[0096] The entire dataset was divided into training and validation sets in an 8:2 ratio. Different missing rates α = {5%, 10%, 15%, 20%}, maximum missing step size β = {1, 2, 3}, and sampling step size γ = {2, 3, 4} were selected for experiments. The specified number of samples for each indicator prediction model was 400. The number of neurons per layer of the data imputation model was [5, 20, 20, 5, 20, 20, 5]. The batch size during the training process of the data imputation model was 32. The training epochs of the data imputation model were 200. The number of samples t in the oversampling strategy of the ST-IVAE model was set to 6. The stopping condition was that the validation dataset had been tested 10 times in the current loop.

[0097] The method of this invention is compared with a comparative method, which uses only IVAE and standard VAE models under the same missing parameters. The comparison results are as follows. Figure 5 As shown in Table 1, the traditional VAE model uses a single-point prediction and imputation method, which does not bring significant improvement in accuracy when the imputation is inaccurate. However, IVAE takes into account the uncertainty of the imputation data, and the prediction results are significantly improved. ST-IVAE (i.e. the method of this invention) further improves the rationality, accuracy and generalization of the model by introducing a self-training method.

[0098] Table 1 Comparison of prediction results for each model based on simulation data.

[0099]

[0100] Example 2

[0101] In the modeling of the polyester fiber esterification process, the sampling interval of the process variable sensor is 1 minute. Based on expert knowledge, features related to oligomer density are selected. The esterification kettle outlet temperature, esterification separation water flow rate, prepolymerization process liquid level, esterification kettle liquid level, and esterification kettle temperature are selected as input variables, and the oligomer density is selected as the output variable. After normalizing the data, 2400 samples were selected. The entire dataset was divided into training and validation sets in an 8:2 ratio. Different missing rates α = {5%, 10%, 15%, 20%}, maximum missing step size β = {1, 2, 3}, and sampling step size γ = {2, 3, 4} were selected for experiments. The specified number of samples for each indicator prediction model was 400. The number of neurons per layer of the data imputation model was [5, 20, 20, 5, 20, 20, 5]. The batch size during the training of the data imputation model was 32, the training epochs of the data imputation model were 200, the number of samples t in the oversampling strategy of the ST-IVAE model was set to 6, and the stopping condition was that the validation dataset had been tested 10 times in the current loop.

[0102] The method of this invention is compared with a comparative method, which uses only IVAE and standard VAE models. Under the same missing parameters, the error comparison results of the different models are as follows: Figure 6 As shown in Table 2, it can be observed that the prediction error of the method proposed in this invention is significantly reduced compared to other methods.

[0103] Table 2 Comparison of prediction results for each model based on actual data.

[0104]

Claims

1. A method for predicting oligomer density during the esterification process of polyester fibers, characterized in that... Includes the following steps: (1) The collected process variable and quality variable sensor data are used as sample datasets, and the sample datasets are divided into training datasets and validation datasets. (2) Use the complete samples in the training dataset to train the data imputation model, and then input the samples with missing values ​​in the training dataset into the trained data imputation model to imput them, so as to obtain the distribution imputation samples of missing data. (3) Sort the distribution imputation samples of missing data according to the variance of the quality variable distribution, select the distribution imputation samples with smaller variances of a specified proportion, and use an oversampling strategy to sample from the distributions of these distribution imputation samples to obtain the data imputation samples of missing data, which are regarded as new complete samples. (4) Based on the self-training method, iteratively obtain a relatively complete dataset after being expanded with the imputed samples and a data imputation model trained on the relatively complete dataset; (5) Collect process variable data in real time and input it into the data imputation model trained with complete samples in the training dataset to imput the missing data. Then, use an oversampling strategy to sample multiple data imputation samples of the missing data from the distribution of the distribution imputation samples, thereby expanding to obtain multiple complete samples. (6) Based on the similarity between each sample in the multiple complete samples obtained in step (5) of KL divergence calculation and all samples in the relatively complete dataset, for any sample X in the multiple complete samples, select a specified number of samples with high similarity to the sample from the relatively complete dataset, use the process variables in the selected samples as input and the quality variables as output, train an indicator prediction model, and use the trained indicator prediction model to predict sample X to obtain the prediction result of sample X; For two normal distributions and The KL divergence between them is defined as follows: Among them, μ1, μ2、 Let J represent the mean and variance of the two normal distributions, respectively, and J represent the number of samples in the normal distribution. (7) The average of the prediction results of each sample in the multiple complete samples is the predicted quality variable data. The process variables are the esterification reactor outlet temperature, esterification separation water flow rate, prepolymerization process liquid level, esterification reactor liquid level and esterification reactor temperature, and the mass variable is the oligomer density during the esterification process. The data imputation model is a variational autoencoder model with uncertainty, which replaces the output of the variational autoencoder model with data points in the form of a data distribution; the index prediction model is a Gaussian process regression model. The variational lower bound of the variational autoencoder model with uncertainty is described as follows: in, This is the variational lower bound for the variational autoencoder model with uncertainty. and p θ (x|z) represent the encoder and decoder of the variational autoencoder model with uncertainty, respectively. θ and θ represent their corresponding parameters, z represents the latent variable of the variational autoencoder model with uncertainty, and μ(z) and σ(z) represent the mean and standard deviation of z, respectively.

2. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 1, characterized in that, In step (1), the ratio of the training dataset to the validation dataset is 8:

2.

3. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 2, characterized in that, The total number of samples in the sample dataset is no less than 2000.

4. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 1, characterized in that, The specified percentage in step (3) refers to the top 20%.

5. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 1, characterized in that, The specific process of step (4) is as follows: repeat steps (2) to (3) until the stopping condition is met. The stopping condition is that the prediction error of the verification dataset in the current loop is greater than that of the previous loop or the maximum number of loops has been reached. When the loop ends, the relatively complete dataset after the expansion based on the imputation sample and the data imputation model trained on the dataset will be obtained when the prediction error is the smallest or the maximum number of loops has been reached.

6. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 5, characterized in that, The maximum number of iterations is 10, and the root mean square error is selected as the prediction error metric.

7. The method for predicting oligomer density during the esterification process of polyester fibers according to claim 1, characterized in that, The number of samples specified in step (6) shall not exceed the number of samples in the training dataset, and shall not be less than the number of complete samples in the training dataset.

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