Virtual sample generation and soft sensor modeling method based on variational autoencoder and generative adversarial network

Abstract

The present invention discloses a virtual sample generation method and a soft measurement modeling method based on a variational autoencoder and a generative adversarial network. The present invention introduces a supervised virtual sample generation model combining a variational autoencoder and WGANgp, which simultaneously learns the data distribution of input samples and output samples. The generator samples and generates virtual samples with outputs in the final latent space, which can avoid the secondary accumulation of errors. Considering that not all virtual samples can improve the prediction performance of the model, a group of SV‑WGANgp models with diversity are constructed by perturbing the input samples, and the virtual samples generated by each SV‑WGANgp model are evaluated in combination with a Gaussian process regression model, and invalid virtual samples are eliminated; the virtual samples after elimination are secondary selected by using unlabeled samples, which effectively ensures the validity of the final virtual samples; the virtual sample generation model finally constructed and the virtual sample selection method adopted provide an effective way to solve the small sample problem.

Description

Technical Field

[0001] The invention relates to a virtual sample generation and soft measurement modeling method based on a variational autoencoder and a generative adversarial network, and belongs to the field of industrial process control. Background Art

[0002] With the rapid development of monitoring, control and optimization technologies, various process industries such as chemical industry and nonferrous metal processing have begun to widely adopt mature technologies and methods, which have ensured the normal operation of production, improved resource utilization and reduced environmental pollution to a certain extent. In the industrial production process, production quality and efficiency often depend on various variables, many of which are key variables. However, due to the high cost or non-existence of measuring instruments, it may be difficult for ordinary sensors to directly measure some key qualities. In order to solve the above difficulties, variables that are easy to measure are used as the input of the model, and variables that are difficult to measure are used as the output of the model to construct a suitable data-driven soft sensor model. At present, most studies focus on the structure and training methods of the model, and rarely pay attention to the quantity and quality of training data. Generally speaking, sufficient and high-quality training data can improve the prediction accuracy of the model, but due to the existence of factors such as the harsh industrial field environment, the number of high-quality samples collected is small. There have been many achievements in the preprocessing of data sets, such as data dimensionality reduction, data denoising, outlier detection, missing value detection, correlation analysis, etc., but the research on data generation is still limited.

[0003] In addition, it is very difficult to obtain samples with real labels because key quality parameters are difficult to obtain and have a large lag. Secondly, most traditional soft sensor models only use limited labeled samples and directly discard a large number of unlabeled samples that are easy to obtain and contain rich information in industrial processes. Therefore, developing methods that can simultaneously utilize labeled data and a large amount of unlabeled data to improve the prediction performance of the model has received increasing attention.

[0004] Most existing virtual sample generation methods only consider the expansion of input samples, and the corresponding output is predicted by the model built on the labeled samples, which may lead to secondary accumulation of errors. Summary of the invention

[0005] The present invention provides a virtual sample generation method and a soft measurement modeling method based on a variational autoencoder and a generative adversarial network. By taking the sample label as a new input dimension, not only the input of the sample but also the output of the sample is generated to reduce error accumulation. In addition, the information in the unlabeled samples is used to perform secondary selection of virtual samples, which provides a more effective method for increasing the number of high-quality samples in industrial processes.

[0006] The technical solution of the present invention is: a virtual sample generation method based on variational autoencoder and generative adversarial network, comprising:

[0007] Step 1: Obtain industrial process data, determine the process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct the auxiliary variable vector x; where x = [x 1 ,x 2 ,...,x d ], x d represents the dth auxiliary variable;

[0008] Step 2: Screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set;

[0009] Step 3: Normalize the industrial process dataset and divide the normalized labeled dataset into training set D trn , test set D test and validation set D val , the normalized unlabeled dataset is represented as X u ;

[0010] Step 4: By training set D trn The perturbations of the training samples in the training set are used to form multiple training subsets, and a set of diverse supervised virtual sample generation models and virtual samples are generated for the multiple training subsets.

[0011] Each training subset is used to build a variety of supervised virtual sample generation models and the process of generating virtual samples is as follows:

[0012] From the training set D trn Collect a fixed number of samples n in , repeat M times, and get M training subsets. Where D m represents the mth training subset, x m,i represents the i-th sample of the m-th training set, y i For x m,i The corresponding key variable value, that is, the true label value;

[0013] The virtual samples are generated after training the supervised virtual sample generation model using the training subset.

[0014] The supervised virtual sample generation model includes a variational autoencoder and a generative adversarial network. The decoder in the variational autoencoder is used as a generator of the generative adversarial network to form a supervised virtual sample generation model.

[0015] According to another aspect of an embodiment of the present invention, a virtual sample generation system based on a variational autoencoder and a generative adversarial network is provided, comprising:

[0016] A construction module is used to obtain industrial process data, determine process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct an auxiliary variable vector x; wherein x = [x 1 ,x 2 ,...,x d ], x d represents the dth auxiliary variable;

[0017] An acquisition module is used to screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set;

[0018] The partitioning module is used to normalize the industrial process data set and divide the normalized labeled data set into the training set D trn , test set D test and validation set D val , the normalized unlabeled dataset is represented as X u ;

[0019] The generation module is used to generate trn The perturbations of the training samples in the training set are used to form multiple training subsets, and a set of diverse supervised virtual sample generation models and virtual samples are generated for the multiple training subsets.

[0020] According to another aspect of an embodiment of the present invention, a soft measurement modeling method based on a variational autoencoder and a generative adversarial network is provided, including any one of the virtual sample generation methods described above, and further including:

[0021] Step 5: Use the training subset before expansion and the virtual sample to expand to the corresponding training subset as the training set of Gaussian process regression model GPR to train the Gaussian process regression model GPR; compare the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it;

[0022] Step 6: Utilize unlabeled samples X u Select the virtual samples retained in step 5; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ;

[0023] Step 7: On the final training set D real+virtualThe Gaussian process regression model GPR is constructed on the test set D test Finally, the offline estimation of key variables is realized.

[0024] The selection process is: using unlabeled samples X u Calculate the Euclidean distance with the virtual samples; arrange the virtual samples in order of Euclidean distance from small to large; take the first Q non-repeated virtual samples and add them to the original training set D trn ; constitute the final training set D real+virtual .

[0025] According to another aspect of an embodiment of the present invention, a soft measurement modeling system based on a variational autoencoder and a generative adversarial network is provided, including a virtual sample generation system based on a variational autoencoder and a generative adversarial network, and further comprising:

[0026] The comparison module is used to use the training subset before expansion and the virtual sample to expand the corresponding training subset as the training set of the Gaussian process regression model GPR to train the Gaussian process regression model GPR; compare the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it;

[0027] Selection module, used to utilize unlabeled samples X u Select the virtual samples retained in the comparison module; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ;

[0028] The test module is used to test the final training set D real+virtual The Gaussian process regression model GPR is constructed on the test set D test Finally, the offline estimation of key variables is realized.

[0029] According to another aspect of an embodiment of the present invention, a method for predicting penicillin concentration is provided, which is performed using the soft measurement modeling method based on variational autoencoder and generative adversarial network described above.

[0030] The beneficial effects of the present invention are as follows: the virtual sample generation soft measurement modeling method based on supervised variational autoencoder and generative adversarial network proposed by the present invention takes into account the problem that the traditional virtual sample generation model only generates virtual input, while the accurate output is difficult to obtain and a large amount of unlabeled data is not effectively utilized, and introduces a supervised virtual sample generation model combining variational autoencoder and WGANgp. The model simultaneously learns the data distribution of input samples and output samples, and the generator samples and generates virtual samples with output in the final latent space, which can avoid the secondary accumulation of errors. Considering that not all virtual samples can improve the prediction performance of the model, a group of SV-WGANgp models with diversity are constructed by perturbing the input samples, and the virtual samples generated by each SV-WGANgp model are evaluated in combination with the Gaussian process regression model, and invalid virtual samples are eliminated. By using unlabeled samples to perform secondary selection on the virtual samples after elimination, the validity of the final virtual samples is effectively guaranteed. The virtual sample generation model finally constructed and the virtual sample selection method adopted provide an effective way to solve the small sample problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of a virtual sample generation and soft measurement modeling method based on a supervised variational autoencoder and a generative adversarial network in the present invention;

[0032] Figure 2 It is a curve chart of the predicted value and the true value of the traditional Gaussian process regression model;

[0033] Figure 3 It is a curve graph of predicted values ​​and true values ​​in the penicillin fermentation process case of the virtual sample generation and soft measurement modeling method based on the supervised variational autoencoder and the generative adversarial network in the present invention. DETAILED DESCRIPTION

[0034] The invention is further described below in conjunction with the accompanying drawings and embodiments, but the content of the invention is not limited to the scope of the embodiments.

[0035] Example 1: Figure 1-3 As shown, a virtual sample generation method based on variational autoencoder and generative adversarial network includes:

[0036] Step 1: Obtain industrial process data, determine the process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct the auxiliary variable vector x; where x = [x 1 ,x 2 ,...,x d ], x d represents the dth auxiliary variable;

[0037] Specifically, industrial process data is collected through a distributed control system or offline detection method, and process variables closely related to the key variable y are determined as auxiliary variables using feature selection methods (such as PCA, SAE, etc.), and an auxiliary variable vector x is constructed;

[0038] Step 2: Screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set;

[0039] Step 3: Normalize the industrial process dataset and divide the normalized labeled dataset into training set D trn , test set D test and validation set D val , the normalized unlabeled dataset is represented as X u ;

[0040] Specifically, the Z-Score method is used to normalize the data set, converting data of different magnitudes into the same magnitude to ensure comparability between data.

[0041] Step 4: By training set D trn The perturbation of the training samples in the training set forms multiple training subsets, and a set of diverse supervised virtual sample generation models and virtual samples are constructed for the multiple training subsets. That is, it is used to generate different virtual samples on different training subsets.

[0042] Optionally, each training subset is used to construct a diverse supervised virtual sample generation model and the process of generating virtual samples is:

[0043] Using the Bootstrap method from the training set D trn Collect a fixed number of samples n in , repeat M times, and get M training subsets. Where D m represents the mth training subset, x m,i represents the i-th sample of the m-th training set, y i For x m,i The corresponding key variable value, that is, the true label value;

[0044] The virtual samples are generated after training the supervised virtual sample generation model using the training subset.

[0045] Optionally, the supervised virtual sample generation model includes a variational autoencoder and a generative adversarial network, and the decoder in the variational autoencoder is used as the generator of the generative adversarial network to form a supervised virtual sample generation model. The first half of the model learns the data distribution under the constraint of the reconstruction error, and the second half of the model is judged by the discriminator to make the virtual samples generated by the generator closer to the real samples. After the training is completed, the input of the generator is obtained by random sampling from the standard distribution, and then the virtual sample is output.

[0046] Specifically, the specific construction process of the supervised virtual sample generation model is as follows:

[0047] ① Variational autoencoder VAE, which maps the complex observation space x to a relatively simple latent space z, has a marginal likelihood of:

[0048] p θ (x) = ∫p θ (z)p θ (x|z)dz (1)

[0049] The true posterior is shown in (2):

[0050]

[0051] Since the latent space z and the generation model parameters θ are uncertain, q θ As an approximation to the intractable true posterior, the marginal log-likelihood (z|x) can be written as:

[0052]

[0053] Among them, the first term on the right side of the formula is the KL divergence between the approximation and the true posterior, and the second term is the lower bound of the marginal likelihood evidence of the input x, which can be expressed as:

[0054]

[0055] Among them, the parameters θ and It is learned jointly by back-propagation of neural networks.

[0056] The variational autoencoder assumes a prior distribution p θ (z) is the standard multivariate Gaussian distribution N(z; 0, I), the true posterior p θ (z|x) is also a multivariate Gaussian distribution. Let μ k , σ k Represent the k-th mean and standard deviation respectively, then:

[0057]

[0058] In summary, the approximate result of this model at any input x is:

[0059]

[0060] Where j represents the number of samples, z (j) =μ+σ⊙∈ (j) ,∈ (j) ~N(0,I), ⊙ represents element-wise multiplication.

[0061] ② The variational autoencoder used in the present invention takes the real label of the sample as an additional dimension of input based on the above ①, uses the encoder to construct the latent space z, and then uses the decoder to sample from the latent space z to reconstruct the sample and its corresponding label. The encoder and decoder symmetrically use a fully connected neural network with multiple hidden layers. Under the assumptions in 1), the KL divergence between the approximate posterior and prior is:

[0062]

[0063] Among them, μ xy and logσ xy 2 It is learned by the encoder.

[0064] From N(z;μ xy ,logσ xy 2 ) is used as the decoder input to reconstruct the sample and its corresponding label. Using the reparameterization method, z~q θ (z|x,y) is reparameterized to z = μ xy +σ xy ⊙∈,∈~N(0,I). The final evidence lower bound is:

[0065]

[0066] ③ The decoder of the variational autoencoder is used as the generator of WGANgp, and the discriminator is also a fully connected neural network with multiple hidden layers. According to 2), the loss function (evidence lower bound) of the supervised variational autoencoder is:

[0067]

[0068] Moreover, the loss function of WGANgp can be given by formula (10):

[0069]

[0070] Among them, p r 、p g and p hThey represent the real sample distribution, generated sample distribution and latent space distribution respectively, x represents the real sample, represents the fake samples generated by the decoder, x p Represents the reconstructed sample obtained by decoding the latent space z by the decoder, which can be obtained by interpolating from real samples and fake samples using random numbers λ represents the gradient penalty coefficient.

[0071] Combining formula (9) and formula (10), the loss function of SV-WGANgp, i.e., the optimization objective, is defined as:

[0072] J SV-WGANgp =J SVAE +η JWGANgp (11)

[0073] Among them, η is the scaling factor used to balance the SVAE loss and WGANgp loss.

[0074] Set λ=10, η=20, training iterations epoch=200, training batch batch=30, generator learning rate α 1 =0.001, discriminator learning rate α 2 = 0.001, train the SV-WGANgp model on each training subset, and finally obtain M SV-WGANgp models. Using the trained model, randomly sample and generate F virtual samples in the latent space, repeat M times, and obtain a set of virtual samples represents the f-th virtual sample generated by the m-th SV-WGANgp model, The virtual label generated for it.

[0075] A soft measurement modeling method based on variational autoencoder and generative adversarial network, including any one of the above-mentioned virtual sample generation methods, and further comprising:

[0076] Step 5: Use the training subset before expansion and the virtual sample to expand to the corresponding training subset as the training set of Gaussian process regression model GPR to train the Gaussian process regression model GPR; compare the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it;

[0077] Specifically, because the industrial process data exhibits nonlinearity and time-varying properties, the Gaussian process regression model GPR is selected as the base model. The present invention uses the selected Gaussian process regression model GPR as the base model for the validation set D val Verify the validity of the virtual samples generated in step 4 and retain the virtual samples that do not deteriorate the performance.

[0078] The process of verifying the validity of the virtual sample is as follows:

[0079] For the dataset D m For each sample x in m,i Prediction output in Gaussian process regression model Obey Gaussian distribution:

[0080]

[0081] Wherein, E(.) and Var(.) represent the mean and variance operators respectively. Then, the Gaussian process regression model can be described as:

[0082]

[0083] In the formula, k m,i =[C(x i ,x m,1 ),…,C(x i ,x m,N ))] T , C is an NxN-order symmetric positive definite matrix consisting of the covariances of each sample in X with each other, and are the predicted mean and variance of the model, respectively.

[0084] The virtual samples generated by the SV-WGANgp model are added to the corresponding training subset as the training set of GPR, and the validation set D is used. val To verify, D val ={X val ,y val}, the predicted value corresponding to the true label in the validation set is Calculate the validation error RMSE val :

[0085]

[0086] Repeat M times and calculate the corresponding model improvement rate, retain the virtual samples with improvement rate greater than 0, and remove the virtual samples with improvement rate less than 0, that is,

[0087] Step 6: Utilize unlabeled samples X u Select the virtual samples retained in step 5; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ;

[0088] Step 7: On the final training set D real+virtual The Gaussian process regression model GPR is constructed on the test set Dtest Finally, the offline estimation of key variables is realized.

[0089] The selection process is: using unlabeled samples X u Calculate the Euclidean distance with the virtual samples; arrange the virtual samples in order of Euclidean distance from small to large; take the first Q small non-repeated virtual samples and add them to the original training set D trn ; constitute the final training set D real+virtual .

[0090] Specifically, in step 6, the unlabeled sample X is used u right The steps to implement the selection are as follows:

[0091] ① Calculate the unlabeled sample X u With virtual samples Euclidean distance between features:

[0092]

[0093] Among them, s represents the sth feature of the sample.

[0094] ② Arrange the virtual samples in order of Euclidean distance from small to large.

[0095] ③ Take the first Q virtual samples and add them to the original training set D to form the final training set D real+virtual .

[0096] Step 7 is performed on the training set D real+virtual The Gaussian process regression model GPR is constructed on the test set D test The specific process of testing is as follows:

[0097] Using the training data set D after adding virtual samples real+virtual To train the Gaussian process regression model GPR, and use the test set D test Test, D test ={X test ,y test}, test set label matrix y test The corresponding prediction result is The test error is RMSE test :

[0098]

[0099] Among them, y i Represents the true label on the corresponding test set.

[0100] According to another aspect of the embodiment of the present invention, a method for predicting penicillin concentration is provided, which is performed by using the soft sensor modeling method based on variational autoencoder and generative adversarial network described above. An optional implementation case of the present invention is described in detail below.

[0101] The above method is suitable for monitoring various industrial process quality variable parameters. This embodiment verifies the effectiveness of the present invention in combination with the implementation of the penicillin fermentation process case. The penicillin fermentation process includes two typical time periods: the cell culture stage and the penicillin fed-batch fermentation stage. A large number of bacteria will be produced in the cell culture stage, and then the product synthesis will be promoted by continuously supplementing nutrients. This is the penicillin growth stage. In order to improve the efficiency of penicillin production and increase output, it is necessary to monitor the penicillin concentration during the culture process in real time. Penicillin concentration is used as the dominant variable, and 14 process variables that are highly correlated with the dominant variable are used as input variables, as shown in Table 1.

[0102] Table 1 Description of input variables of penicillin fermentation process

[0103] Serial number Variable Description (Unit) 1 Fermentation time (h) 2 Aeration value (L / h) 3 Stirring power(W) 4 Substrate feed rate (L / h) 5 Substrate feed temperature (K) 6 Dissolved oxygen concentration (g / L) 7 Fermentation volume (L) 8 Carbon dioxide concentration (g / L) 9 pH 10 Fermentation tank temperature (K) 11 Heat generated (kcal) 12 Acid flow rate (L / h) 13 Substrate flow rate (L / h) 14 Cooling water flow rate (L / h)

[0104] A total of 12 batches of data were collected under default operating conditions, of which 5 batches of data were used for model training, 2 batches of data were used for model validation, and 5 batches of data were used for model testing.

[0105] The present invention implements the case to select the root mean square error RMSE and the determination coefficient R 2 To evaluate the effectiveness of the final virtual sample, as shown below:

[0106]

[0107]

[0108] Where N test , y test , They represent the total number of test samples, the predicted value of the test samples, the true value of the test samples, and the mean of the true value of the test samples. The smaller the RMSE value, the smaller the error and the better the model prediction performance. 2 The larger the value, the higher the degree of fit of the model and the better the prediction performance of the model. The following Table 2 shows the prediction performance of penicillin concentration by different methods.

[0109] Table 2 Prediction performance of different methods in penicillin fermentation process

[0110]

[0111] From the analysis of Table 2, we can see that compared with the traditional Gaussian process regression model GPR, the small sample soft measurement modeling method based on supervised variational autoencoder and WGANgp proposed in this invention has better prediction performance. This method not only expands the labeled samples under the condition of small samples and reduces the cumulative error caused by the secondary prediction labels, but also uses the information of unlabeled samples to perform secondary selection on the generated virtual samples, effectively improving the confidence of the virtual samples. Figure 2 , Figure 3 The comparison results show that the virtual sample generation and soft measurement modeling method based on supervised variational autoencoder and generative adversarial network in the penicillin fermentation process case has a higher degree of fit between the curve of predicted value and true value than the curve of predicted value and true value of the traditional Gaussian process regression model ( Figure 2 , 3 The horizontal axis represents the number of test samples in the test set, the vertical axis represents the value of the key variable, the actual value represents the true value, and the prediction value represents the predicted value).

[0112] The above cases are used to illustrate that the present invention has certain feasibility and effectiveness. The focus of the present invention is to introduce variational autoencoders and WGANgp as virtual sample generation models SV-WGANgp, taking into account the generation of input and output, eliminating invalid virtual samples by improving the model performance, and using unlabeled samples to perform secondary selection of virtual samples. Any modification or improvement of the present invention that is not made within the spirit and scope of protection of the claims will be limited by the scope of protection of the present invention.

[0113] Embodiment 2: According to another aspect of the embodiments of the present invention, a virtual sample generation system based on a variational autoencoder and a generative adversarial network is provided, comprising:

[0114] A construction module is used to obtain industrial process data, determine process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct an auxiliary variable vector x; wherein x = [x 1 ,x 2 ,...,x d ], x d represents the dth auxiliary variable;

[0115] An acquisition module is used to screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set;

[0116] The partitioning module is used to normalize the industrial process data set and divide the normalized labeled data set into the training set D trn , test set D test and validation set Dval , the normalized unlabeled dataset is represented as X u ;

[0117] The generation module is used to generate trn The perturbations of the training samples in the training set are used to form multiple training subsets, and a set of diverse supervised virtual sample generation models and virtual samples are generated for the multiple training subsets.

[0118] Embodiment 3: According to another aspect of the embodiment of the present invention, a soft measurement modeling system based on a variational autoencoder and a generative adversarial network is provided, including a virtual sample generation system based on a variational autoencoder and a generative adversarial network, that is, including (a construction module, an acquisition module, a division module, a generation module), and also including:

[0119] The comparison module is used to use the training subset before expansion and the virtual sample to expand the corresponding training subset as the training set of the Gaussian process regression model GPR to train the Gaussian process regression model GPR; compare the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it;

[0120] Selection module, used to utilize unlabeled samples X u Select the virtual samples retained in the comparison module; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ;

[0121] The test module is used to test the final training set D real+virtual The Gaussian process regression model GPR is constructed on the test set D test Finally, the offline estimation of key variables is realized.

[0122] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A soft sensor modeling method based on variational autoencoder and generative adversarial network, characterized by: Used for penicillin concentration prediction, including: Step 1: Obtain industrial process data, determine the process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct the auxiliary variable vector x; where x = [x1, x2, ..., x d ], x d represents the dth auxiliary variable; Step 2: Screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set; Step 3: Normalize the industrial process dataset and divide the normalized labeled dataset into training set D trn , test set D test and validation set D val , the normalized unlabeled dataset is represented as X u ; Step 4: By training set D trn Perturb the training samples in the training set to form multiple training subsets, and construct a set of diverse supervised virtual sample generation models and generate virtual samples for the multiple training subsets; Step 5: Use the training subset before expansion and the virtual sample to expand to the corresponding training subset as the training set of Gaussian process regression model GPR to train the Gaussian process regression model GPR; compare the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it; Step 6: Using unlabeled samples X u Select the virtual samples retained in step 5; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ; Step 7: On the final training set D real+virtual The Gaussian process regression model GPR is constructed on the test set D test Test on the network and finally achieve offline estimation of key variables; The supervised virtual sample generation model includes a variational autoencoder and a generative adversarial network, and the decoder in the variational autoencoder is used as a generator of the generative adversarial network to form a supervised virtual sample generation model; The selection process is: using unlabeled samples X u Calculate the Euclidean distance with the virtual samples; arrange the virtual samples in order of Euclidean distance from small to large; take the first Q non-repeated virtual samples and add them to the original training set D trn ; constitute the final training set D real+virtual .

2. The soft sensor modeling method based on variational autoencoder and generative adversarial network according to claim 1, characterized in that: Each training subset is used to build a variety of supervised virtual sample generation models and the process of generating virtual samples is as follows: From the training set D trn Collect a fixed number of samples n in , repeat M times, and get M training subsets. Where D m represents the mth training subset, x m,i represents the i-th sample of the m-th training set, y i For x m,i The corresponding key variable value, that is, the true label value; The virtual samples are generated after training the supervised virtual sample generation model using the training subset.

3. A soft sensor modeling system based on variational autoencoder and generative adversarial network, characterized by: Used for penicillin concentration prediction, including: A construction module is used to obtain industrial process data, determine process variables closely related to the key variable y of the industrial process data as auxiliary variables, and construct an auxiliary variable vector x; wherein x=[x1,x2,...,x d ], x d represents the dth auxiliary variable; An acquisition module is used to screen the industrial process data according to the key variable y and the auxiliary variable vector x to obtain an industrial process data set; wherein the industrial process data set includes a labeled data set and an unlabeled data set; The partitioning module is used to normalize the industrial process data set and divide the normalized labeled data set into the training set D trn , test set D test and validation set D val , the normalized unlabeled dataset is represented as X u ; The generation module is used to generate trn Perturb the training samples in the training set to form multiple training subsets, and construct a set of diverse supervised virtual sample generation models and generate virtual samples for the multiple training subsets; The comparison module uses the training subset before expansion and the virtual sample to expand the corresponding training subset as the training set of the Gaussian process regression model GPR to train the Gaussian process regression model GPR; compares the Gaussian process regression model GPR trained before and after expansion on the validation set D val Prediction performance on: if the performance improves, keep the virtual sample; otherwise, remove it; Selection module, used to utilize unlabeled samples X u Select the virtual samples retained in the comparison module; use the selected virtual samples to expand the original training set D trn ; constitute the final training set D real+virtual ; The test module is used to test the final training set D real+virtual The Gaussian process regression model GPR is constructed on the test set D test Test on the network and finally achieve offline estimation of key variables; The supervised virtual sample generation model includes a variational autoencoder and a generative adversarial network, and the decoder in the variational autoencoder is used as a generator of the generative adversarial network to form a supervised virtual sample generation model; The selection process is: using unlabeled samples X u Calculate the Euclidean distance with the virtual samples; arrange the virtual samples in order of Euclidean distance from small to large; take the first Q non-repeated virtual samples and add them to the original training set D trn ; constitute the final training set D real+virtual .

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