Multi-sampling-rate soft measurement method based on progressive transfer learning

Abstract

The invention relates to a multi-sampling-rate soft measurement method based on progressive transfer learning, and the method comprises the steps: carrying out the partitioning of training data from high to low according to the sampling frequency at a training stage, and training a variational progressive transfer network model; taking the model as a generator of a generative adversarial filling network, training the generative adversarial filling network by using original training data, and realizing automatic filling of unsampled data; based on the filled data, performing block processing on the original data again according to the original sampling frequency from high to low, and training a new variational progressive migration network model as a soft measurement model; in the test stage, the soft measurement model is used for predicting quality variables, and a prediction result is quantitatively evaluated. According to the method, the generation model is fully utilized to fill up the unsampled data in the soft measurement modeling stage, so that the soft measurement model extracts more valuable data information, and the prediction performance of the soft measurement model can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of soft measurement, and in particular relates to a multi-sampling rate soft measurement method based on progressive transfer learning. Background Art

[0002] In modern industrial processes, quality variables are important indicators for process monitoring and control. They can not only reveal the operating status of the production process and ensure that it operates according to established standards, but also reflect the quality level of the product in a timely manner, providing key guidance and decision-making support for enterprises to adjust their production strategies. However, due to the limitations of measurement technology and economic costs, quality variables are often obtained through offline analysis, resulting in delayed measurement values ​​and scarce data, and therefore cannot meet the needs of real-time monitoring, control, and alarm. In order to solve this problem, the soft measurement model establishes a shallow or deep mathematical model between process variables and quality variables, and uses easy-to-measure process variables to quickly and accurately estimate difficult-to-measure quality variables, solving the shortcomings of offline analysis and showing great application value and development potential in actual industrial scenarios.

[0003] With the rapid development of technologies such as Industry 4.0, Industrial Internet of Things, and Artificial Intelligence, the operation and management of process industries presents multi-level and multi-scale characteristics, resulting in differences in the sampling rates of different variables. For example, the sampling rates of variables such as temperature, pressure, and flow are from seconds to minutes, while the sampling rates of variables such as quality indicators, material consumption, and energy consumption are usually lower or irregular, generally at the hourly, daily, or even weekly levels. When faced with multi-sampling rate data, traditional soft sensor models can only use upsampling or downsampling methods to unify the sampling rates of all variables, and then realize model construction. However, the upsampling or downsampling process will lose a lot of data information, affecting the prediction effect of the soft sensor model.

[0004] In response to the above problems, some scholars have proposed a semi-supervised soft measurement modeling method. When there is limited labeled data, unlabeled data is used to improve the performance of the model, which effectively solves the modeling problem when the sampling rates of process variables and quality variables are different. Typical semi-supervised soft measurement models include semi-supervised Gaussian process regression, semi-supervised support vector regression, and semi-supervised deep neural networks. However, such methods can only process data with two sampling rates. When there are differences in sampling rates between different process variables, it will be difficult for the semi-supervised modeling method to use all the collected data to achieve soft measurement modeling. Therefore, it is necessary to propose a multi-sampling rate data modeling method to make full use of the existing data foundation, realize feature extraction and fusion of data with different sampling rates, and improve the prediction accuracy and generalization performance of the soft measurement model. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a multi-sampling rate soft measurement method based on progressive transfer learning, which reorganizes the variables of different sampling rates into data blocks, and uses a generative adversarial model to fill the data blocks. Finally, progressive transfer learning is implemented between different data blocks to solve the difficult problems of multi-sampling rate data modeling and quality variable prediction.

[0006] The technical solution adopted by the present invention is: A multi-sampling rate soft sensing method based on progressive transfer learning, the method comprising the following steps: (1) Use industrial sensors deployed on-site to monitor and record the measured values ​​of process variables in the production process in real time, and use laboratory analysis methods to determine the values ​​of quality variables. These two parts of data are integrated into the original data set and standardized; (2) Process the original data in blocks according to the sampling frequency from high to low; (3) Determine the model-related hyperparameters, randomly initialize all model parameters, and use the block training data to establish a variational progressive transfer network (VPTN) model; (4) Using the model established in step (3) as the generator of the Generative Adversarial Infilling Network (GAIN) model, and using the original data to train the GAIN model to achieve automatic filling of unsampled data; (5) Based on the data filled in step (4), the original data is re-divided into blocks from high to low according to the original sampling frequency; (6) Update the VPTN model using the re-blocked training data; (7) Acquire test data online, standardize it, select samples of full sampling of process variables to construct a test data set, and use the VPTN model obtained in step (6) to predict the quality variables. Finally, use the evaluation indicators to quantitatively evaluate the prediction results.

[0007] Furthermore, the specific process of step (1) is as follows: For the process variables in the original data set X and quality variables y Standardization is performed respectively to make the mean value 0 and the standard deviation 1; the standardized training set is expressed as ,in I represents the number of samples, J Represents the number of process variables, the number of quality variables is 1.

[0008] Furthermore, the specific process of step (2) is as follows: First, construct the process variable grouping X 1, X 2, ..., X K and quality variable groupingy K+1 ; If there is K +1 different sampling rate, where process variables include K sampling rates, the quality variable contains 1 sampling rate; with the highest sampling frequency 1 / T 1 of J 1 variable represents the process variable grouping X 1, and so on, with K Sampling frequency 1 / T K ( T 1 represents the minimum sampling period, 1 / T 1 represents the highest sampling frequency, and so on) J K Variables are represented as process variables group X K ,in, ; In actual industrial processes, the sampling frequency of quality variables is often the lowest, and its variable grouping is expressed as y K+1 ; Secondly, build the data block of progressive transfer learning based on the above variable grouping; the first data block , grouped only by process variables X 1, where the superscript "(1)" represents the first data block and the subscript "1" represents the first variable grouping. X 1; and so on, K The data blocks are , No. K The data blocks contain process variables grouped X 1 to X K The average number of training samples measured on K +1 data block covers all process variables and quality variables, represented as .

[0009] Furthermore, the specific process of step (3) is as follows: VPTN is a semi-supervised variational autoencoder (SSVAE) based on progressive transfer learning, which consists of an encoder, a decoder and a regressor.

[0010] Before model training, set the hyperparameters of SSVAE, including the number of model layers, number of hidden layer nodes, batch size, learning rate, and number of iterations. At the same time, randomly initialize all weights and biases in the SSVAE model, and select the corresponding activation function. In the model training phase, we first use Training a Variational Autoencoder (VAE) model in an unsupervised manner (1) , its loss function for: ; in, yes D (1) The reconstruction error of the process variables in yes D (1) The KL divergence between the true distribution and the prior distribution of the latent variable corresponding to the process variable in the process variable, the coefficient β KL Used to adjust the proportion of different losses in the loss function; Secondly, VAE (1) The model parameters are passed to VAE (2) , and use D (2) Training the VAE (2) , and so on, until we get VAE (K) ; Based on VAE (K) The model parameters are further utilized using a data block containing both process variables and quality variables D (K+1) Perform supervised training to obtain the VPTN model, and its loss function for: ; in, yes D (K+1) The reconstruction error of the process variables in yes D (K+1) The KL divergence between the true distribution and the prior distribution of the latent variable corresponding to the process variable in , yes D (K+1) The prediction error of the quality variable in β KL and β RG Used to adjust the proportion of different losses in the loss function.

[0011] Furthermore, the specific process of step (4) is as follows: When constructing the data block in step (2), some samples cannot be included in the corresponding data block due to missing variables, resulting in the VPTN model lacking sufficient sample support during the training process and being unable to fully capture the data features. Figure 1 For example, when building a data block D (3) When , the 4th and 10th samples are v 5 ~ v 7 Missing measurements will not be included inD (3) As a result, the data information in such samples cannot be fully mined and utilized in the model training stage. Therefore, it is necessary to use the GAIN model to fill the unsampled parts so that it can help the VPTN model training. The specific steps include: (a) Use the VPTN model trained in step (3) as the initial generator of GAIN G , and using random noise Z Padding multi-rate data X The unsampled part of the matrix is ​​obtained by X’ : ; in, M It is multi-rate data X The corresponding mask matrix; generator G Will X’ and M As input, the output matrix for: ; For the part of the original data with measured values, its true value is retained; for the part of the original data that has not been sampled, the output of the generator is used to fill the missing part, and the complete data matrix after filling The specific calculation method is: ; (b) The complete data matrix after filling and the prompt matrix H Input GAIN's discriminator D , output probability matrix P for: ; in, , B is a random matrix, B Each element of is randomly sampled from {0,1}; (c) Training the generator and discriminator, the loss function of the generator for: ; in M(i, j) Represents the mask matrix M Middle i Sample No. j The value corresponding to the variable, P(i, j) Represents the probability matrix P Middle i Sample No. j The value corresponding to the variable, Indicates the first i Sample No. j The value corresponding to the variable, the coefficient α Used to adjust the proportion of different losses in the generator loss function; Loss function of the discriminator L D (M,P) for: ; GAIN trains by alternately optimizing the loss functions of the generator and discriminator until the data filled in the unsampled part of the generator is as close to the real data as possible.

[0012] Furthermore, the specific process of step (5) is as follows: Using the original multi-rate data and the unsampled data filled with GAIN, the training dataset is updated to Based on this data set and the multi-sampling rate data partitioning method in step (2), the data is partitioned again. Figure 1 For example, step (2) is to build a data block D (3) When , the 4th and 10th samples are v 5 ~ v 7 Missing measurements will not be included in D (3) In the updated data set, GAIN fills the missing value, so the above two samples can be added D (3) , effectively increasing the useful information in the data block.

[0013] Furthermore, the specific process of step (6) is as follows: Based on the new data blocks, information migration between data blocks is gradually performed according to step (3) to train a new VPTN model.

[0014] Furthermore, the specific process of step (7) is as follows: Collect test data online, standardize it, and select samples that fully sample the process variables to form a test data set; input each sample in the test data set into the VPTN model trained in step (6) to obtain the predicted value of the quality variable y pre , the performance of the VPTN model in the present invention is evaluated by the root mean square error (RMSE) and the mean absolute error (MAE); its specific formula is defined as: ; in, and are the true value and predicted value of the quality variable, is the number of test samples.

[0015] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention uses multi-sampling rate data to pre-train the GAIN generator, so that the generator can learn to capture the complex characteristics of data distribution in advance when the complete sampling samples are limited, and thus can generate higher quality data to effectively fill the unsampled parts.

[0016] (2) The present invention combines the original data and the data generated by GAIN, overcoming the limitation of the traditional VPTN model that it cannot fully utilize all the original samples for modeling in the multi-sampling rate data modeling process, improving the efficiency of the use of original data, and enabling the model to extract more valuable data information, thereby significantly improving the prediction accuracy and generalization ability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of multi-sampling rate data; Figure 2 It is a flow chart of a multi-sampling rate soft sensing method based on progressive transfer learning of the present invention; Figure 3 It is a schematic diagram of the fitting effect of the predicted value and the true value provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention aims at the problem that the traditional VPTN model cannot use all the original samples for modeling in the process of multi-sampling rate data modeling, and proposes a multi-sampling rate soft sensing method based on progressive transfer learning. The present invention is described in detail below with reference to an industrial example. Taking a pre-decarbonization unit of a synthetic ammonia process as an example, the method architecture of generator pre-training and GAIN modeling, unsampled data filling, and VPTN modeling is applied to the prediction of CO2 gas residual concentration.

[0019] Reference Figure 2 , a multi-sampling rate soft sensing method based on progressive transfer learning, comprising the following steps: (1) Collecting and preprocessing raw data sets: Using industrial sensors deployed on site and distributed control systems to monitor and record the measured values ​​of process variables in the production process in real time, and using laboratory analysis methods to determine the values ​​of quality variables, these two parts of data are integrated into the raw data set and standardized; For the process variables in the original data set X and quality variables y Standardization is performed respectively to make the mean value 0 and the standard deviation 1; the standardized training set is expressed as ,in I represents the number of samples, J Represents the number of process variables, the number of quality variables is 1.

[0020] (2) Data block construction: The original data is divided into blocks according to the sampling frequency from high to low; assuming that there are K +1 different sampling rate, where process variables include K sampling rates, the quality variable contains 1 sampling rate. The highest sampling frequency is 1 / T 1 of J 1 variable represents the process variable grouping X 1, and so on, with K Sampling frequency 1 / T K of J K Variables are represented as process variables group X K ,in, In actual industrial processes, the sampling frequency of quality variables is often the lowest, and its variable grouping is expressed as y K+1 Secondly, we construct the data blocks for progressive transfer learning based on the above variable groupings; the first data block , grouped only by process variables X 1, where the superscript "(1)" represents the first data block and the subscript "1" represents the first variable grouping. X 1; and so on, K The data blocks are , No. K The data blocks contain process variables grouped X 1 to X K The average number of training samples measured on K +1 data block covers all process variables and quality variables, represented as .

[0021] (3) VPTN model pre-training: Before model training, set the hyperparameters of SSVAE in advance, including the number of model layers, number of hidden layer nodes, batch size, learning rate, number of iterations, etc. At the same time, randomly initialize all weights and biases in the SSVAE model (model parameter initialization) and select the corresponding activation function; In the model training phase (training the VPTN model), first use Training a Variational Autoencoder (VAE) model in an unsupervised manner (1) , its loss function for: ; in, yes D (1) The reconstruction error, yes D (1) The KL divergence between the corresponding latent variable true distribution and prior distribution, coefficient β KL Used to adjust the proportion of different losses in the loss function; Secondly, VAE (1) The model parameters are passed to VAE (2) , and use D (2) Training the VAE (2) , and so on, until we get VAE (K) ; Based on VAE (K) The model parameters are further utilized using a data block containing both process variables and quality variables D (K+1) Perform supervised training to obtain the VPTN model, and its loss function for: ; in, yes D (K+1) The reconstruction error of the process variables in yes D (K+1) The KL divergence between the true distribution and the prior distribution of the latent variable corresponding to the process variable in , yes D (K+1) The prediction error of the quality variable in β KL and β RG Used to adjust the proportion of different losses in the loss function.

[0022] (4) GAIN model training and filling in unsampled data; specifically including the following steps: (a) Use the VPTN model trained in step (3) as the initial generator of GAIN G , and using random noise Z Padding multi-rate data X The unsampled part of the matrix is ​​obtained by X’ : ; in, M It is multi-rate data X The corresponding mask matrix; generatorG Will X’ and M As input, the output matrix for: ; For the part of the original data with measured values, its true value is retained; for the part of the original data that has not been sampled, the output of the generator is used to fill the missing part, and the complete data matrix after filling The specific calculation method is: ; (b) The complete data matrix after filling and the prompt matrix H Input GAIN's discriminator D , the output probability matrix is: ; in, , B is a random matrix, where each element B(i, j) Randomly sample from {0,1}; (c) Training the generator and discriminator, the loss function of the generator for: ; in M(i, j) Represents the mask matrix M Middle i Sample No. j The value corresponding to the variable, P(i, j) Represents the probability matrix P Middle i Sample No. j The value corresponding to the variable, Represents the complete data matrix after filling Middle i Sample No. j The value corresponding to the variable, the coefficient α Used to adjust the proportion of different losses in the generator loss function; Loss function of the discriminator L D (M,P) for: ; GAIN trains by alternately optimizing the loss functions of the generator and discriminator until the generator is as close to the real data as possible when the missing value is filled.

[0023] (5) Using the original multi-rate data and the unsampled data filled by GAIN, the training data set is updated to ; Based on the data set and the block division method of multi-sampling rate data in step (2), re-block the data (construct new data blocks). Figure 1 For example, step (2) is to build a data block D (3) When , the 4th and 10th samples are v 5 ~ v 7 Missing measurements will not be included in D (3) In the updated data set, GAIN fills the missing value, so the above two samples can be added D (3) , effectively increasing the useful information in the data block.

[0024] (6) Follow the steps in step (3) to migrate the information of the new data block and establish a new VPTN model (retrain the VPTN model).

[0025] (7) Collect (acquire) test data online, standardize it (data preprocessing), and input the samples of all process variables into the trained VPTN model to obtain the predicted value of the quality variable. y pre (Using the VPTN model for prediction), the performance of the VPTN model is evaluated by the root mean square error (RMSE) and the mean absolute error (MAE) (quantitative evaluation of model performance): ; in, and are the true value and predicted value of the quality variable, is the number of test data.

[0026] In the training stage, the present invention first divides the training data into blocks according to the sampling frequency from high to low, and trains the variational progressive migration network model; the model is used as the generator of the generative adversarial filling network, and the generative adversarial filling network is trained using the original training data to realize the automatic filling of unsampled data; based on the filled data, the original data is again divided into blocks according to the original sampling frequency from high to low, and a new variational progressive migration network model is trained as a soft measurement model; in the testing stage, the soft measurement model is used to predict the quality variables, and the prediction results are quantitatively evaluated. The present invention makes full use of the generation model to fill the unsampled data in the soft measurement modeling stage, so that the soft measurement model extracts more valuable data information, and can effectively improve the prediction performance of the soft measurement model.

[0027] The present invention is applied to the pre-decarbonization unit of the ammonia synthesis process of a chemical plant to predict the residual CO2 concentration in the gas. First, 9000 multi-sampling rate samples are collected to form a training set, wherein the sampling interval of variables labeled U1-U8 is 1 minute, the sampling interval of variables labeled U9-U13 is 3 minutes, and the sampling interval of variables labeled U14-U21 is 5 minutes, wherein U1-U20 are process variables, and U21 is a quality variable. Then, the VPTN model is pre-trained using the training set and used as the initial generator of GAIN, and then the GAIN model is trained using the training set, and the unsampled variables are filled. Based on the original data and the filled data, the multi-sampling data blocks are re-divided and the new VPTN model is trained. Finally, 4000 samples are collected as a test data set, which are input into the VPTN model, and the predicted value output by the model is compared with the true value of the quality variable. The comparison effect is shown as follows. Figure 3 .Depend on Figure 3 It can be seen that the model proposed in the present invention is relatively accurate in predicting most of the data, indicating that the present invention can effectively solve the problem of multi-sampling rate data modeling and prediction in actual industrial processes.

[0028] In order to reflect the importance of unsampled data filling and progressive transfer learning in the present invention, the prediction performance of the soft sensor model (GAIN-VPTN) of the present invention is compared with the original VPTN model without data filling and the soft sensor model (GAIN-SVAE) with data filling but without progressive transfer learning. The comparison results are shown in Table 1.

[0029] Table 1: Comparison of prediction performance of different soft sensor models

[0030] It can be seen from Table 1 that although GAIN-SVAE uses data filling, the quality of the filled data is uneven, and the effect is much worse than that of no filling (VPTN); compared with other soft sensor models, the soft sensor model trained by the present invention has the lowest RMSE and MAE, which verifies the effectiveness of unsampled data filling, progressive transfer learning and soft sensor modeling in the present invention.

[0031] Finally, it should be noted that the above examples are only specific embodiments of the present invention. Obviously, the present invention is not limited to the above examples, and many variations are possible. All variations that can be directly derived or associated with the content disclosed by a person skilled in the art should be considered as the protection scope of the present invention.

Claims

1. A multi-sampling rate soft sensing method based on progressive transfer learning, characterized in that The steps include: (1) Use industrial sensors deployed on site to monitor and record the measured values ​​of process variables in the production process in real time, and use laboratory analysis methods to determine the values ​​of quality variables. These two parts of data are integrated into the original data set and standardized; (2) Process the original data in blocks according to the sampling frequency from high to low; (3) Determine the model-related hyperparameters, randomly initialize all model parameters, and use the block training data to establish a variational progressive transfer network model, namely the VPTN model; (4) The VPTN model established in step (3) is used as the generator of the generative adversarial data filling network model, i.e., the GAIN model, and the original data is used to train the GAIN model to achieve automatic filling of unsampled data; (5) Based on the data filled in step (4), the original data is re-divided into blocks from high to low according to the original sampling frequency; (6) Update the VPTN model using the re-blocked training data; (7) Acquire test data online, standardize it, select samples of full sampling of process variables to construct a test data set, and use the VPTN model obtained in step (6) to predict the quality variables. Finally, use the evaluation indicators to quantitatively evaluate the prediction results.

2. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 1, characterized in that: The specific process of step (1) is as follows: X and quality variables y Standardization is performed respectively to make the mean value 0 and the standard deviation 1; the standardized training set is expressed as ,in I represents the number of samples, J Represents the number of process variables, the number of quality variables is 1.

3. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 2, characterized in that: The specific process of step (2) is as follows: First, construct process variable grouping X 1, X 2, ..., X K and quality variable grouping y K+1 ; If there is K +1 different sampling rate, where process variables include K sampling rates, the quality variable contains 1 sampling rate; with the highest sampling frequency 1 / T 1 of J 1 variable represents the process variable grouping X 1. With the K Sampling frequency 1 / T K of J K Variables are represented as process variables group X K ,in, ; The quality variables are grouped as y K+1 ; Secondly, build the data blocks for progressive transfer learning based on the above variable grouping; the first data block , grouped only by process variables X 1, where the superscript (1) represents the first data block and the subscript 1 represents the first variable grouping X 1; No. K The data blocks are , No. K The data blocks contain process variables grouped X 1 to X K The average number of training samples measured on K +1 data block covers all process variables and quality variables, represented as .

4. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 3 is characterized in that: The specific process of step (3) is as follows: Before model training, set the hyperparameters of the semi-supervised variational autoencoder SSVAE, including the number of model layers, number of hidden layer nodes, batch size, learning rate, and number of iterations. At the same time, randomly initialize all weights and biases in the SSVAE model, and select the corresponding activation function. In the model training phase, we first use Training a variational autoencoder (VAE) model in an unsupervised manner (1) , its loss function for: ； in, yes D (1) The reconstruction error, yes D (1) The KL divergence between the corresponding latent variable true distribution and prior distribution, coefficient β KL Used to adjust the proportion of different losses in the loss function; Secondly, VAE (1) The model parameters are passed to VAE (2) , and use D (2) Training the VAE (2) , and so on, until we get VAE (K) ; Based on VAE (K) The model parameters are further utilized using a data block containing both process variables and quality variables D (K+1) Perform supervised training to obtain the VPTN model, and its loss function for: ； in, yes D (K+1) The reconstruction error of the process variables in yes D (K+1) The KL divergence between the true distribution and the prior distribution of the latent variable corresponding to the process variable in , yes D (K+1) The prediction error of the quality variable in β KL and β RG Used to adjust the proportion of different losses in the loss function.

5. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 4 is characterized in that: The specific process of step (4) is as follows: (a) Use the VPTN model trained in step (3) as the initial generator of GAIN G , and using random noise Z Padding multi-rate data X The unsampled part of the matrix is ​​obtained by X’ : ； in, M It is multi-rate data X The corresponding mask matrix; generator G Will X’ and M As input, the output matrix for: ； For the part of the original data with measured values, its true value is retained; for the part of the original data that has not been sampled, the output of the generator is used to fill the missing part, and the complete data matrix after filling for: ； (b) The complete data matrix after filling and the prompt matrix H Input GAIN's discriminator D , output probability matrix P for: ； in, , B is a random matrix, B Each element of is randomly sampled from {0,1}; (c) Train the generator and discriminator, the loss function of the generator is for: ； in M(i, j) Represents the mask matrix M Middle i Sample No. j The value corresponding to the variable, P(i, j) Represents the probability matrix P Middle i Sample No. j The value corresponding to the variable, Represents the complete data matrix after filling Middle i Sample No. j The value corresponding to the variable, the coefficient α Used to adjust the proportion of different losses in the generator loss function; Loss function of the discriminator L D (M,P) for: ； GAIN trains by alternately optimizing the loss functions of the generator and discriminator until the generator is as close to the real data as possible when the missing value is filled.

6. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 5, characterized in that: The specific process of step (5) is as follows: using the original multi-sampling rate data and the unsampled data filled with GAIN, the training data set is updated to Based on the data set and the multi-sampling rate data partitioning method in step (2), the data is partitioned again.

7. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 6, characterized in that: The specific process of step (6) is as follows: based on the new data blocks, information migration between data blocks is gradually performed according to step (3) to establish a new VPTN model.

8. The multi-sampling rate soft sensing method based on progressive transfer learning according to claim 7, characterized in that: The specific process of step (7) is as follows: Collect test data online, standardize it, and select samples that fully sample the process variables to form a test data set; input each sample in the test data set into the VPTN model trained in step (6) to obtain the predicted value of the quality variable y pre , the performance of the VPTN model is evaluated by the root mean square error RMSE and the mean absolute error MAE: ； in, and are the true value and predicted value of the quality variable, is the number of test data.

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