A multi-sampling rate soft sensing method based on progressive transfer learning

Abstract

The present invention relates to a multi-sampling rate soft measurement method based on progressive transfer learning. In the training stage, the training data is first processed in blocks according to the sampling frequency from high to low, and a variational progressive transfer network model is trained; the model is used as a generator of a generative adversarial filling network, and the generative adversarial filling network is trained using the original training data to achieve automatic filling of unsampled data; based on the filled data, the original data is processed in blocks according to the original sampling frequency from high to low again, and a new variational progressive transfer network model is trained as a soft measurement model; in the testing stage, the soft measurement model is used to predict the quality variable, and the prediction result is 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.

Description

Technical Field

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

[0002] In modern industrial processes, quality variables are important indicators for process monitoring and control. It can not only reveal the operating conditions of the production process, ensure its operation according to established standards, but also timely reflect the quality level of products, providing key guidance and decision-making support for enterprises to adjust production strategies. However, due to limitations in measurement technology and economic costs, quality variables are often obtained through off-line analysis, resulting in lagged measurement values and scarce data volume, thus unable to meet the requirements of real-time monitoring, control, alarm, etc. To solve this problem, a soft sensing model establishes a shallow or deep mathematical model between process variables and quality variables, and uses easily measurable process variables to quickly and accurately estimate difficult-to-measure quality variables, solving the deficiencies of off-line 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 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 in the order of seconds to minutes, while the sampling rates of variables such as quality indicators, material consumption, and energy consumption are usually lower or irregular, generally in the order of hours, days, or even weeks. When facing multi-sampling rate data, traditional soft sensing models can only first use up-sampling or down-sampling methods to unify the sampling rates of all variables, and then realize the construction of the model. However, the up-sampling or down-sampling process will lose a large amount of data information and affect the prediction effect of the soft sensing model.

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

[0005] To solve the above problems, the present invention proposes a multi-sampling rate soft sensor method based on progressive transfer learning, which reorganizes data blocks of variables with different sampling rates, fills the data blocks using a generative adversarial model, and finally implements progressive transfer learning between different data blocks to solve the problems of multi-sampling rate data modeling and quality variable prediction.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A multi-sampling rate soft sensor method based on progressive transfer learning, the method comprising the following steps:

[0008] (1) Real-time monitor and record the measured values of process variables in the production process through on-site deployed industrial sensors, and determine the quality variable values by means of laboratory chemical analysis. Integrate these two parts of data into an original data set and perform standardization processing;

[0009] (2) Perform block processing on the original data according to the sampling frequency from high to low;

[0010] (3) Determine the hyperparameters related to the model, randomly initialize all model parameters, and establish a variational progressive transfer network (VPTN) model using the blocked training data;

[0011] (4) Use the model established in step (3) as the generator of the generative adversarial imputation network (GAIN) model, and train the GAIN model using the original data to achieve automatic imputation of un-sampled data;

[0012] (5) Based on the data filled in step (4), perform block processing on the original data again according to the original sampling frequency from high to low;

[0013] (6) Update the VPTN model using the re-blocked training data;

[0014] (7) Online obtain test data, perform standardization processing on it, screen the samples with 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, and finally quantitatively evaluate the prediction results with the help of evaluation indicators.

[0015] Further, the specific process of step (1) is as follows:

[0016] Perform standardization processing on the process variables X and quality variables y in the original data set respectively, so that their average value is 0 and the standard deviation is 1; the standardized training set is denoted as where I represents the number of samples, J represents the number of process variables, and the number of quality variables is 1.

[0017] Furthermore, the specific process of step (2) is as follows: First, construct process variable groups X 1 , X 2 ,…, X K and quality variable groups y K+1 ; If there are K +1 different sampling rates in the training set, where the process variables contain K sampling rates and the quality variables contain 1 sampling rate; The T 1 variables with the highest sampling frequency 1 / J 1 are represented as the process variable group X 1 , and so on. The K variables with the K th sampling frequency 1 / T K ( T 1 represents the minimum sampling period, 1 / T 1 represents the highest sampling frequency, and so on) are represented as the process variable group J K , where X K ; In the actual industrial process, the sampling frequency of the quality variables is often the lowest, and its variable group is represented as K+1 ; Second, construct data blocks for progressive transfer learning based on the above variable groups; The first data block y , only consists of the process variable group 1 , where the superscript “(1)” represents the first data block and the subscript “1” represents the first variable group X 1 X 1 ; And so on, the K th data block is , the K th data block includes the training samples measured on all the process variable groups X 1 to X K ; The K +1th data block covers all process variables and quality variables, and is represented as .

[0018] Furthermore, the specific process of step (3) is as follows:

[0019] VPTN is a semi-supervised variational autoencoder (SSVAE) based on progressive transfer learning, consisting of an encoder, a decoder, and a regressor.

[0020] Before model training, set the hyperparameters of SSVAE, including the number of model layers, the number of hidden layer nodes, the batch size, the learning rate, and the number of iterations. At the same time, randomly initialize all weights and biases in the SSVAE model and select the corresponding activation functions;

[0021] In the model training stage, first use Train the variational autoencoder (VAE) model VAE in an unsupervised manner (1) , whose loss function is:

[0022] ;

[0023] Among them, is D (1) the reconstruction error of the process variables in is D (1) the KL divergence between the true distribution and the prior distribution of the latent variables corresponding to the process variables in β KL The coefficient

[0024] is used to adjust the proportion of different losses in the loss function; (1) Next, transfer the model parameters of VAE (2) to VAE D (2) and use (2) to train VAE (K) ; and so on until VAE

[0025] Based on the model parameters of VAE (K) , further use the data block D (K+1) that contains both process variables and quality variables for supervised training to obtain the VPTN model, whose loss function is:

[0026] ;

[0027] Among them, is D (K+1) the reconstruction error of the process variables in is D (K+1) the KL divergence between the true distribution and the prior distribution of the latent variables corresponding to the process variables in is D(K+1) Prediction error of quality variables in , coefficient β KL and β RG Used to adjust the proportion of different losses in the loss function.

[0028] Furthermore, the specific process of step (4) is:

[0029] 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) , the 4th and 10th samples are due to v 5 ~ v 7 Missing measurements will not be included in D (3) , which results in the data information in such samples not being fully mined and utilized during the model training phase. Therefore, it is necessary to use the GAIN model to fill in the unsampled parts so that it can help the VPTN model training. The specific steps include:

[0030] (a) Use the VPTN model trained in step (3) as the initial generator of GAIN G , and using random noise Z Padding multi-sampling rate data X The unsampled part of gets the complete input matrix X’ :

[0031] ;

[0032] Among them, M is multi-sampling rate data X Corresponding mask matrix; generator G Will X’ and M As input, output matrix is:

[0033] ;

[0034] For the part of the original data with measured values, retain its true value; for the part of the original data that has not been sampled, use the output of the generator to fill the missing part, and the complete data matrix after filling The specific calculation method is:

[0035] ; ​

[0036] (b) The complete data matrix after filling and the hint matrix H are input into the discriminator of GAIN D , and the probability matrix is output P as follows:

[0037] ;

[0038] Among them, , B is a random matrix, B and each element of it is randomly sampled from {0, 1};

[0039] (c) Train the generator and the discriminator. The loss function of the generator is as follows:

[0040] ;

[0041] Among them M(i, j) represents the value corresponding to the M th variable of the i th sample in the mask matrix j , P(i, j) represents the value corresponding to the P th variable of the i th sample in the probability matrix j , represents the value corresponding to the i th variable of the j th sample in the complete data matrix after filling. The coefficient α is used to adjust the proportion of different losses in the generator loss function;

[0042] The loss function of the discriminator L D (M, P) is as follows:

[0043] ;

[0044] GAIN is trained by alternately optimizing the loss functions of the above generator and discriminator until the data filled by the generator in the unsampled part is as close as possible to the real data.

[0045] Further, the specific process of step (5) is as follows:

[0046] Using the original multi-sampling rate data and the unsampled data filled by GAIN, the training dataset is updated to . Based on this dataset and the data chunking method of the multi-sampling rate data in step (2), re-chunk the data. Taking Figure 1 as an example, in step (2), when constructing the data chunk D(3) At this time, for the 4th and 10th samples, due to v 5 ~ v 7 the missing measurement values, they cannot be included in D (3) However, in the updated dataset, GAIN fills in the missing values, so the above two samples can be added to D (3) which effectively increases the useful information in the data block.

[0047] Furthermore, the specific process of step (6) is as follows:

[0048] Based on the new data chunks, gradually perform information migration between data chunks according to step (3) to train a new VPTN model.

[0049] Furthermore, the specific process of step (7) is as follows:

[0050] Online collect test data, perform standardization processing on it, and screen out the samples with full sampling of process variables to form a test dataset; input each sample in the test dataset into the VPTN model trained in step (6) to obtain the predicted values of quality variables y pre , and evaluate the performance of the VPTN model in the present invention through root mean square error (RMSE) and mean absolute error (MAE); their specific formula definitions are:

[0051] ;

[0052] where and are the true value and predicted value of the quality variable respectively, is the number of test samples.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] (1) The present invention pre-trains the generator of GAIN using multi-sampling rate data, enabling the generator to learn to capture complex features of the data distribution in advance when the number of fully sampled samples is limited, so that it can generate higher-quality data to effectively fill the unsampled part.

[0055] (2) The present invention combines the original data and the data generated by GAIN, overcomes the limitation that the traditional VPTN model cannot fully utilize all original samples for modeling in the process of multi-sampling rate data modeling, improves the utilization efficiency of the original data, enables the model to extract more valuable data information, and thus significantly improves the prediction accuracy and generalization ability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a schematic diagram of multi-sampling rate data;

[0057] Figure 2 is a flowchart of the multi-sampling rate soft sensor method based on progressive transfer learning of the present invention;

[0058] Figure 3 is a schematic diagram of the fitting effect between the predicted value and the true value provided by the embodiment of the present invention. Detailed implementation manners

[0059] Aiming at the problem that the traditional VPTN model cannot utilize all original samples for modeling in the process of multi-sampling rate data modeling, the present invention proposes a multi-sampling rate soft sensor method based on progressive transfer learning. The present invention will be described in detail below in combination with industrial examples. Taking the pre-decarbonization unit of a synthetic ammonia process as an example, the method architectures of generator pre-training, GAIN modeling, filling of unsampled data, and VPTN modeling are applied to the prediction of the residual concentration of CO 2 gas.

[0060] Referring to Figure 2 , a multi-sampling rate soft sensor method based on progressive transfer learning includes the following steps:

[0061] (1) Collecting the original data set and preprocessing the data set: Through the industrial sensors deployed on site, the measured values of the process variables in the production process are monitored and recorded in real time by using the distributed control system, and the quality variable values are measured by means of laboratory chemical analysis. These two parts of data are integrated into the original data set and standardized;

[0062] For the process variables X and quality variables y in the original data set, standardization processing is respectively performed to make their average value 0 and standard deviation 1; the standardized training set is denoted as , where I represents the number of samples, J represents the number of process variables, and the number of quality variables is 1.

[0063] (2) Data block construction: The original data is processed in blocks according to the sampling frequency from high to low; it is assumed that there are K +1 different sampling rates in the training set, where the process variables include K sampling rates, and the quality variables include 1 sampling rate. The T 1 with the highest sampling frequency 1 / J 1 variables are represented as the process variable group X 1 , and so on, with theK A sampling frequency of 1 / T K of J K variables are represented as process variable groups X K , where . In actual industrial processes, the sampling frequency of quality variables is often the lowest, and its variable grouping is represented as y K+1 . Secondly, based on the above variable grouping, data blocks for progressive transfer learning are constructed; the first data block , which consists only of the process variable group X 1 , where the superscript “(1)” represents the first data block and the subscript “1” represents the first variable group X 1 ; and so on, the K th data block is , the K th data block includes the training samples measured on all of the process variable groups X 1 to X K ; the K +1th data block covers all process variables and quality variables, represented as .

[0064] (3) Pre-training of the VPTN model:

[0065] Before model training, the hyperparameters of SSVAE are set in advance, including the number of model layers, the number of hidden layer nodes, the batch size, the learning rate, the number of iterations, etc. At the same time, all weights and biases in the SSVAE model are randomly initialized (model parameter initialization), and the corresponding activation function is selected;

[0066] In the model training stage (training the VPTN model), first use to train the variational autoencoder (VAE) model VAE (1) in an unsupervised manner, and its loss function is:

[0067] ;

[0068] where is D (1) the reconstruction error, is D (1) the KL divergence between the true distribution and the prior distribution of the corresponding latent variables, and the coefficient β KLUsed to adjust the proportion of different losses in the loss function;

[0069] Secondly, transfer the model parameters of VAE (1) to VAE (2) , and use D (2) to train VAE (2) , and so on until VAE (K) is obtained;

[0070] Based on the model parameters of VAE (K) , further use the data block D (K+1) that simultaneously contains process variables and quality variables for supervised training to obtain the VPTN model, and its loss function is:

[0071] ;

[0072] Among them, is D (K+1) the reconstruction error of the process variables in is D (K+1) the KL divergence between the true distribution and the prior distribution of the latent variables corresponding to the process variables in is D (K+1) the prediction error of the quality variables in β KL and β RG are used to adjust the proportion of different losses in the loss function.

[0073] (4) GAIN model training and filling in the unsampled data; specifically including the following steps:

[0074] (a) Use the VPTN model trained in step (3) as the initial generator of GAIN G , and use random noise Z to fill in the unsampled part of the multi-sampling rate data X to obtain the complete input matrix X’ :

[0075] ;

[0076] Among them, M is the mask matrix corresponding to the multi-sampling rate data X ; the generator G takes X’ and M as inputs, and the output matrix is:

[0077] ;

[0078] For the part of the original data with measured values, retain its true value; for the part of the original data that is not sampled, use the output of the generator to fill in the missing part, and the complete data matrix after filling The specific calculation method is as follows:

[0079] ;

[0080] (b) Input the complete data matrix after filling and the hint matrix H into the discriminator of GAIN D , and the output probability matrix is:

[0081] ;

[0082] Among them, , B is a random matrix, and each element B(i, j) is randomly sampled from {0, 1};

[0083] (c) Train the generator and the discriminator. The loss function of the generator is:

[0084] ;

[0085] Among them M(i, j) represents the value corresponding to the M th sample and the i th variable in the mask matrix j , P(i, j) represents the value corresponding to the P th sample and the i th variable in the probability matrix j , represents the value corresponding to the th sample and the i th variable in the complete data matrix after filling j . The coefficient α is used to adjust the proportion of different losses in the generator loss function;

[0086] The loss function of the discriminator L D (M, P) is:

[0087] ;

[0088] GAIN is trained by alternately optimizing the loss functions of the above-mentioned generator and discriminator until the data filled with missing values by the generator is as close as possible to the real data.

[0089] (5) Using the original multi-sampling rate data and the unsampled data filled by GAIN, the training dataset is updated to ; Based on this dataset and the method of dividing the multi-sampling rate data in step (2), data chunking is performed again (construction of new data chunks). Taking Figure 1 as an example, in step (2) when constructing the data chunk D (3) the 4th and 10th samples cannot be included in v 5 ~ v 7 due to missing measurement values, while in the updated dataset, GAIN fills the missing values, so the above two samples can be added to D (3) effectively increasing the useful information in the data chunk. D (3)

[0090] (6) Perform information migration on the new data chunks according to the steps in step (3) to establish a new VPTN model (retrain the VPTN model).

[0091] (7) Online collect (acquire) test data, perform standardization processing on it (data preprocessing), and input the samples with full sampling of process variables into the trained VPTN model to obtain the predicted values of quality variables y pre (make predictions using the VPTN model), and evaluate the performance of the VPTN model through root mean square error (RMSE) and mean absolute error (MAE) (quantitative evaluation of model performance):

[0092] ;

[0093] where and are the true value and predicted value of the quality variable respectively, is the number of test data.

[0094] In the training stage of the present invention, first, the training data is divided into blocks according to the sampling frequency from high to low, and the variational progressive transfer network model is trained; this model is used as the generator of the generative adversarial imputation network, and the generative adversarial imputation network is trained using the original training data to realize the automatic imputation of unsampled data; based on the imputed data, the original data is re-divided into blocks according to the original sampling frequency from high to low, and a new variational progressive transfer network model is trained as the soft sensor model; in the testing stage, the soft sensor model is used to predict the quality variables, and the prediction results are quantitatively evaluated. The present invention makes full use of the generative model to impute unsampled data in the soft sensor modeling stage, enabling the soft sensor model to extract more valuable data information and effectively improving the prediction performance of the soft sensor model.

[0095] The present invention is applied to the pre-decarbonization unit of the ammonia synthesis process in a chemical plant to predict the residual CO 2 concentration in the gas. First, 9000 multi-sampling rate samples are collected to form a training set. Among them, 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. Among them, U1-U20 are process variables and U21 is the quality variable. Then, the VPTN model is pre-trained using this training set and used as the initial generator of GAIN. Furthermore, the GAIN model is trained using the training set, and the unsampled variables are imputed. Based on the original data and the imputed data, the multi-sampled data blocks are re-divided and a new VPTN model is trained. Finally, 4000 samples are collected as the test data set and input into the VPTN model. The predicted values output by this model are compared with the true values of the quality variables. The comparison results are as Figure 3 . As Figure 3 can be seen, the model proposed by the present invention is relatively accurate in predicting most of the data, indicating that the present invention can effectively solve the problems of multi-sampling rate data modeling and prediction in the actual industrial process.

[0096] To demonstrate the importance of unsampled data imputation and progressive transfer learning in the present invention, next, the soft sensor model (GAIN-VPTN) of the present invention is respectively compared with the original VPTN model without data imputation and the soft sensor model (GAIN-SVAE) with data imputation but without progressive transfer learning in terms of prediction performance. The comparison results are shown in Table 1.

[0097] Table 1: Comparison of prediction performance of different soft sensor models

[0098]

[0099] As can be seen from Table 1, 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.

[0100] 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 there are many variations. 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 from high to low according to the sampling frequency; the specific process is as follows: First, construct process variable groups 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 ; (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; the specific process 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; (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 (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 it, 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) 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, X(i,j) Represents multi-rate data X 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.

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 (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.

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 (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.

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 (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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