A soft sensor modeling method based on hidden layer enhanced variational adversarial active learning

Abstract

A soft measurement modeling method based on hidden layer enhanced variational adversarial active learning belongs to the field of soft measurement modeling technology. The method includes the following steps: (1) acquiring debutanizer data; (2) debutanizer data preprocessing and data set division; (3) screening representative unlabeled samples and having them annotated by experts; (4) establishing a butane concentration prediction model; and (5) model performance evaluation. The present invention uses a hidden layer enhanced variational adversarial active learning method to manually annotate representative samples in the unlabeled data set, thereby increasing the number of annotated samples and solving the problem of modeling difficulties caused by limited samples. The method can significantly improve the prediction performance of the model with less manual annotation cost and has universality and versatility.

Description

Technical Field

[0001] The present invention relates to a situation where the number of label samples in a soft measurement modeling process is limited, and in particular to a soft measurement modeling method based on hidden layer enhanced variational adversarial active learning. Background Art

[0002] Due to their advantages such as zero latency and low cost, data-driven soft sensing methods are playing an increasingly important role in predicting key quality variables (KVs) of process industry products. However, the accuracy of data-driven modeling approaches is critically dependent on the reliability of the modeling data. Compared to readily available process variable data, KVs are difficult to obtain due to expensive instrumentation and delays in laboratory analysis. Consequently, only a limited number of labeled samples containing both process and quality variables and a large number of unlabeled samples containing only process variables are available. Soft sensing models built solely on limited labeled samples are unreliable and produce poor predictive performance. Active learning (AL) is an attractive approach to addressing this data shortage. This approach selects representative samples from the unlabeled dataset and labels them with experts. These samples are then used to supplement the limited number of labeled samples. The primary goal of active learning is to reduce the labor cost of labeling samples while maintaining high soft sensing model predictive performance.

[0003] Based on how representative unlabeled samples are obtained, active learning can be categorized into membership query active learning, stream-based active learning, and pool-based active learning. Pool-based active learning is currently the most widely studied and applied approach. In pool-based active learning methods, unlabeled samples form a "sample pool," which is then evaluated based on a sample selection strategy. The most valuable unlabeled samples are then selected for expert labeling. The query criteria used in pool-based active learning methods can be categorized into three types: uncertainty, representativeness, and a combination of uncertainty and representativeness. Uncertainty-based criteria select unlabeled samples with the most ambiguous label information as candidate labeled samples. Recently, active learning methods that use the prediction variance of Gaussian process regression (GPR) models as an evaluation metric, which falls within the uncertainty criterion category, have been applied in the field of soft sensor modeling. The variance information provided by GPR methods can provide uncertainty in the prediction results, thereby selecting representative unlabeled samples. Representativeness-based criteria, based on the sample distribution characteristics, select unlabeled samples that increase the diversity of labeled samples. The combined criterion combines uncertainty and representativeness into the same active learning framework, querying for samples that are both uncertain and representative. These active learning methods that can improve the performance of soft sensing models are mostly performed in the original space of the data. However, these methods appear to be ineffective for high-dimensional data affected by the curse of dimensionality.

[0004] Due to the installation of numerous redundant sensors, industrial data exhibits high levels of cross-correlation and redundancy. Active learning strategies based on the raw data space can result in underrepresentation of unlabeled samples without fully exploiting the data's characteristics, further limiting model performance. Therefore, extracting useful features from the data before filtering is essential.

[0005] Deep learning technology is a hot research area in machine learning, aiming to study how to extract multi-layer feature representations from data. This method uses a series of nonlinear transformations to extract features from raw data, from high-level to low-level, and from concrete to abstract. Variational autoencoder (VAE) networks, due to their powerful latent feature learning and data generation capabilities, have been increasingly used in soft sensor modeling in process industries. Therefore, considering the limited number of labeled samples and redundant data features in soft sensor modeling, a latent-enhanced variational adversarial active learning (LVAAL) soft sensor modeling method is proposed. This method minimizes the manual labeling cost while improving the prediction accuracy of the soft sensor model. Summary of the Invention

[0006] To address the difficulty of establishing reliable soft-sensing models for redundant, limited-label samples in industrial processes, this paper proposes a latent-layer enhanced variational adversarial active learning soft-sensing modeling method. This method uses an active learning strategy to select representative unlabeled samples and have them annotated by experts, expanding the initial limited-label sample set. This minimizes the manual annotation cost while maximizing the model's prediction accuracy.

[0007] The technical solution adopted by the present invention to solve its technical problem is:

[0008] A soft sensor modeling method for hidden layer enhanced variational adversarial active learning includes the following steps:

[0009] (1) Obtain original sample data;

[0010] (2) Preprocessing of original sample data and data set division: The original sample data obtained is divided into a training set and a test set, where the training set includes the initial labeled samples and unlabeled samples; in order to speed up the model convergence and reduce the model training time, the training set data and the test set data are normalized;

[0011] (3) Screening representative unlabeled samples and labeling them by experts: Based on the sample screening strategy of the hidden layer enhanced variational adversarial active learning method, representative samples are screened from the unlabeled samples; then, the unlabeled samples are labeled by experts and combined with the initial labeled samples in the training set to form a new labeled training set;

[0012] (4) Establishing a prediction model: establishing a prediction model and training the established prediction model;

[0013] (5) Model performance evaluation: The root mean square error (RMSE) is introduced to evaluate the model.

[0014] Furthermore, the network structure of the hidden layer enhanced variational adversarial active learning LVAAL sample screening criterion is: a hidden layer enhanced variational autoencoder network and a discriminator network composed of a primary encoder, a decoder and a secondary encoder; the specific process of step (3) is as follows:

[0015] Step 3.1: Learn the hidden feature representations of labeled and unlabeled samples in the training set:

[0016] An effective latent space is learned through a hidden layer enhanced variational autoencoder network, and labeled and unlabeled samples of the training set are mapped into the space to obtain the corresponding latent feature representations;

[0017] Step 3.2: The discriminator distinguishes between labeled samples and unlabeled samples:

[0018] When the hidden layer enhanced variational autoencoder network and the discriminator network are trained to balance, the discriminator can effectively distinguish the labeled samples and unlabeled samples of the training set in the hidden layer space, and then screen out representative unlabeled samples and label them.

[0019] Furthermore, the specific process of step 3.1 is as follows:

[0020] The hidden layer enhanced variational autoencoder maps labeled samples and unlabeled samples to the same latent space, in which the probability distribution of labeled samples is similar to that of unlabeled samples; assuming that the original labeled sample is {X L ,y L}, the unlabeled sample is {X U}; For the hidden layer enhanced variational autoencoder network, {X L} and {X U}After one encoder mapping and decoder reconstruction, we get {X RL} and {X RU The total reconstruction loss function for labeled and unlabeled samples is as follows:

[0021]

[0022] Among them, x represents the sample of the original space, z represents the latent variable, subscripts L and U represent labeled samples and unlabeled samples respectively, and q φ (z|x) and p θ (x|z) are the primary encoder and decoder, respectively, with parameters φ and θ, p θ (z) is the Gaussian prior distribution of latent variables, Indicates expectation, D KL is the KL divergence between probability distributions, and β is a parameter that balances the proportion of reconstruction error and KL divergence in the optimization objective;

[0023] The secondary encoder is used to limit the hidden space from offset, so as to help the hidden layer enhanced variational adversarial active learning LVAAL network learn the optimal hidden space. Its network structure and parameters are the same as those of the primary encoder. The KL divergence is used to measure the distance between the primary encoding features and the secondary encoding features. The expression of KL divergence is:

[0024]

[0025] Where N(·) represents Gaussian distribution, μ and σ 2 are the mean and variance of the Gaussian distribution of the latent variables obtained by the encoder once, and are the mean and variance of the Gaussian distribution of the latent variable obtained by the quadratic encoder, I is the unit matrix, (·) T Indicates transposition, (·) -1 represents the inverse, and tr(·) represents the trace of the matrix; therefore, for labeled and unlabeled samples, the sum of the KL distances between the two hidden layers is:

[0026]

[0027] Where m represents the dimension of the latent variable, m = 1, 2, ..., M, μ Lm and μ Um are the means of the latent variables obtained by the encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the one-time encoder for labeled samples and unlabeled samples, and are the means of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples, respectively.

[0028] Furthermore, the specific process of step 3.2 is as follows:

[0029] The hidden layer enhanced variational autoencoder and the discriminator are trained with a minimax game; the hidden layer enhanced variational autoencoder deceives the discriminator into identifying all samples in the hidden space as labeled samples, while the discriminator strives to distinguish labeled samples from unlabeled samples; through iterative training of the hidden layer enhanced variational autoencoder and the discriminator network, after the network training is completed, the discriminator can screen out representative unlabeled samples; according to the probability value, b unlabeled samples {X SU} are selected and sent to experts for annotation; the annotated samples are added to the original training set to obtain a new training set {X SU ,y SU}∪{X L ,y L}.

[0030] Furthermore, the specific process of training the hidden layer enhanced variational autoencoder and the discriminator using the minimax game is as follows:

[0031] The hidden layer enhanced variational autoencoder not only learns an effective latent space, but also conducts adversarial training with the discriminator, that is, it is hoped that the discriminator will discriminate all samples in the hidden layer as labeled samples; 1 represents labeled samples and 0 represents unlabeled samples, then the objective function is:

[0032]

[0033] Where D(·) is the discriminator;

[0034] Therefore, the total loss function of the hidden layer enhanced variational autoencoder part in the LVAAL network is expressed as:

[0035]

[0036] Among them, λ1 and λ2 are hyperparameters, which respectively determine the proportion of the quadratic encoder part and the adversarial network part in learning effective feature space representation;

[0037] The goal of the discriminator is to effectively distinguish labeled samples from unlabeled samples; the objective function of the discriminator is as follows:

[0038]

[0039] The closer the probability of the discriminator's judgment is to 0, the more likely the sample is from an unlabeled sample.

[0040] Furthermore, the specific process of step (4) is as follows:

[0041] Establish a GPR prediction model to provide the variance information of the prediction results to evaluate the uncertainty of the prediction. Use the expanded labeled data set as the training set to train the GPR prediction model.

[0042] The beneficial effects of the present invention are mainly manifested in:

[0043] The present invention proposes a soft measurement modeling method based on hidden layer enhanced variational adversarial active learning. By screening representative unlabeled samples and having them labeled by experts, the original limited labeled samples are expanded, which solves the problem of unreliable soft measurement model establishment due to limited samples. While minimizing the number of manually labeled samples, the prediction accuracy of the model is maximized. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a network flow chart of sample screening criteria for the method of the present invention;

[0045] Figure 2 This is a flow chart of the active learning soft measurement method of the present invention;

[0046] Figure 3 RMSE curves of the method of the present invention under different learning steps; DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0048] On the contrary, the present invention covers any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention as defined by the claims. Furthermore, to facilitate a better understanding of the present invention, certain specific details are described in detail below in the detailed description of the present invention. Those skilled in the art will be able to fully understand the present invention without these details.

[0049] Reference Figures 1 to 3 A soft sensor modeling method based on hidden layer enhanced variational adversarial active learning is proposed. Taking the construction of a butane concentration prediction model in a debutanizer as an example, the method includes the following steps:

[0050] (1) Obtain debutanizer data

[0051] The debutanizer is a key component of the desulfurization and naphtha separation unit. Its primary purpose is to minimize the butane content in crude gasoline. Because traditional methods of measuring butane content using chromatographs have a delay, developing a real-time soft-sensor model to predict butane content using other readily measurable process variables has become an alternative. These seven readily measurable process variables are: top temperature, top pressure, reflux flow rate, flow rate to the next stage, baffle VI temperature, bottom temperature A, and bottom temperature B.

[0052] (2) Debutanizer data preprocessing and data set division

[0053] The collected debutanizer data is divided into a training set and a test set. A small portion of the training set samples are initial labeled samples, while the majority are unlabeled samples. Next, to accelerate model convergence and reduce model training time, the training and test data are normalized.

[0054] Step 2.1: Divide the dataset

[0055] The 600 butane data sets collected were divided into two parts: 300 samples for the training set and the remaining 300 samples for the test set. To simulate the situation of limited labeled samples, 10 samples were uniformly selected from the 300 training set samples as the initial labeled samples, and the remaining 290 samples were unlabeled samples, that is, these samples only contained process variables and no key quality variables.

[0056] Step 2.2: Data normalization

[0057] In order to speed up the convergence of the model and reduce the training time, the data is normalized. The formula is as follows:

[0058]

[0059] In the formula, x is the normalized data; a is the collected original data; a min is the minimum value in the original data; a max is the maximum value in the original data.

[0060] (3) Screening representative unlabeled samples and having them labeled by experts

[0061] A sample screening strategy based on hidden layer enhanced variational adversarial active learning method is used to select representative samples from unlabeled samples. Subsequently, the unlabeled samples are annotated by experts and combined with the initial limited labeled samples to form a new labeled training set.

[0062] Step 3.1: Map the labeled and unlabeled samples of the training set to the same latent space

[0063] The network structure of the LVAAL sample screening criterion is: a hidden layer enhanced variational autoencoder network and a discriminator network composed of a primary encoder, a decoder and a secondary encoder. The network flow chart is as follows: Figure 1As shown in Figure 2, the hidden layer augmented variational autoencoder and discriminator in the network are trained using a minimax game. Specifically, the hidden layer augmented variational autoencoder maps labeled and unlabeled samples into the same latent space, where the probability distribution of labeled samples is similar to that of unlabeled samples, thereby tricking the discriminator into identifying all samples as labeled. The quadratic encoder is used to prevent the latent space from shifting, helping the LVAAL network learn the optimal latent space.

[0064] Assume that the original labeled sample is {X L ,y L}, the unlabeled sample is {X U For the hidden layer enhanced variational autoencoder network, {X L} and {X U}After one encoder mapping and decoder reconstruction, we get {X RL} and {X RU The total reconstruction loss function for labeled and unlabeled samples is as follows:

[0065]

[0066] Among them, x represents the sample of the original space, z represents the latent variable, subscripts L and U represent labeled samples and unlabeled samples respectively, and q φ (z|x) and p θ (x|z) are the primary encoder and decoder, respectively, with parameters φ and θ, p θ (z) is the Gaussian prior distribution of latent variables, Indicates expectation, D KL is the KL (Kullback-Leibler) divergence between probability distributions, and β is a parameter that balances the proportion of reconstruction error and KL divergence in the optimization objective.

[0067] The secondary encoder is used to ensure that the learned latent space is sufficiently reliable. Its network structure and parameters are the same as those of the primary encoder. The KL divergence is used to measure the distance between the primary and secondary encoding features. The expression of KL divergence is:

[0068]

[0069] Among them, μ and σ 2 are the mean and variance of the latent variables obtained by one encoder, and are the mean and variance of the latent variables obtained by the secondary encoder, I is the unit matrix, (·) T Indicates transposition, (·) -1=Tr(·) represents the inverse, and tr(·) represents the trace of the matrix. Therefore, for labeled and unlabeled samples, the sum of the KL distances between the two hidden layers is:

[0070]

[0071] Where m represents the dimension of the latent variable, m = 1, 2, ..., M, μ Lm and μ Um are the means of the latent variables obtained by the encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the one-time encoder for labeled samples and unlabeled samples, and are the means of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples, respectively.

[0072] Step 3.2: The discriminator distinguishes between labeled samples and unlabeled samples

[0073] The discriminator in the LVAAL network maps the latent representations of labeled and unlabeled samples into binary labels, where 1 represents a labeled sample and 0 represents an unlabeled sample. The hidden layer augmented variational autoencoder not only learns an effective latent space but also trains adversarially against the discriminator, hoping that the discriminator will classify all samples in the hidden layer as labeled. The objective function is:

[0074]

[0075] Among them, D(·) is the discriminator.

[0076] Therefore, the total loss function of the hidden layer enhanced variational autoencoder part in the LVAAL network is expressed as:

[0077]

[0078] Among them, λ1 and λ2 are hyperparameters, which respectively determine the proportion of the quadratic encoder part and the adversarial network part in learning effective feature space representation.

[0079] The goal of the discriminator is to effectively distinguish between labeled samples and unlabeled samples. The objective function of the discriminator is:

[0080]

[0081] It is worth noting that the closer the probability of the discriminator is to 0, the more likely the sample is from an unlabeled sample. By iteratively training the hidden layer enhanced variational autoencoder and the discriminator network, representative unlabeled samples can be screened. According to the probability value, b unlabeled samples {X SU} are selected and sent to experts for annotation. Once the samples are annotated, they are added to the original training set to obtain a new training set {X SU ,y SU}∪{X L ,y L}.

[0082] (4) Establishing a butane concentration prediction model

[0083] A GPR model was developed to predict butane concentration. GPR, a model based on a probability kernel function, provides information about the variance of predictions to assess uncertainty, a property that distinguishes GPR from other deterministic modeling methods. The expanded labeled butane dataset was used as the training set to train the GPR butane concentration prediction model. Figure 2 Flowchart of the LVAAL active learning soft sensing method.

[0084] (5) Model performance evaluation

[0085] The root mean square error is defined as follows:

[0086]

[0087] Where: Represents the test data y i The predicted value of , r is the total number of test set samples. The smaller the RMSE, the better the prediction performance of the regression model.

[0088] The proposed LVAAL active learning method is compared with four methods: random sampling, variance-based GPR active learning method (VAL), kernel partial least squares regression hidden layer variable variance-based GPR active learning method (KPLS-VAL), and variational adversarial active learning (VAAL). In each learning process, 5 representative samples are selected from the debutanizer unlabeled samples, manually annotated and added to the original limited label dataset, and then the GPR model is constructed based on the new training set. As the number of learning times increases, Figure 3The following table shows the RMSE values ​​of the five methods on the test set. The experimental results show that the LVAAL method has a lower RMSE value than the other four methods, especially in the initial stages of the learning process. This indicates that the LVAAL method outperforms the other four methods in predicting performance on the test set. This is primarily because the LVAAL method can better exploit the characteristics of redundant data, remove the influence of redundant features on the active learning process, and select more representative unlabeled samples in the latent space, thereby significantly improving the model's predictive performance.

[0089] The method proposed in this paper uses a hidden-layer augmented variational adversarial active learning method to manually label representative samples in an unlabeled dataset, thereby increasing the number of labeled samples. This method can significantly improve the model's predictive performance with less manual labeling cost and is universal and applicable.

[0090] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A soft sensor modeling method based on hidden layer enhanced variational adversarial active learning, characterized in that: The following steps are involved: (1) Obtain original sample data; (2) Preprocessing of original sample data and data set division: The original sample data obtained is divided into a training set and a test set, where the training set includes the initial labeled samples and unlabeled samples; in order to speed up the model convergence and reduce the model training time, the training set data and the test set data are normalized; (3) Screening representative unlabeled samples and labeling them by experts: Based on the sample screening strategy of the hidden layer enhanced variational adversarial active learning method, representative samples are screened from the unlabeled samples; then, the unlabeled samples are labeled by experts and combined with the initial labeled samples in the training set to form a new labeled training set; (4) Establishing a prediction model: establishing a prediction model and training the established prediction model; (5) Model performance evaluation: The evaluation index root mean square error (RMSE) is introduced to evaluate the model; The network structure of the hidden layer enhanced variational adversarial active learning LVAAL sample screening criterion is: a hidden layer enhanced variational autoencoder network and a discriminator network composed of a primary encoder, a decoder and a secondary encoder; the specific process of step (3) is as follows: Step 3.1: Learn the hidden feature representations of labeled and unlabeled samples in the training set: An effective latent space is learned through a hidden layer enhanced variational autoencoder network, and labeled and unlabeled samples of the training set are mapped into this space to obtain the corresponding latent feature representations. The specific process is as follows: Hidden layer enhanced variational autoencoder maps labeled samples and unlabeled samples to the same latent space; assuming that the original labeled sample is {X L ,y L }, the unlabeled sample is {X U }; For the hidden layer enhanced variational autoencoder network, {X L } and {X U }After one encoder mapping and decoder reconstruction, we get {X RL } and {X RU The total reconstruction loss function for labeled and unlabeled samples is as follows: Among them, x represents the sample of the original space, z represents the latent variable, subscripts L and U represent labeled samples and unlabeled samples respectively, and q φ (z|x) and p θ (x|z) are the primary encoder and decoder, respectively, with parameters φ and θ, p θ (z) is the Gaussian prior distribution of the latent variable, E[represents the expectation, D KL is the KL divergence between probability distributions, and β is a parameter that balances the proportion of reconstruction error and KL divergence in the optimization objective; The secondary encoder is used to limit the hidden space from offset, so as to help the hidden layer enhanced variational adversarial active learning LVAAL network learn the optimal hidden space. Its network structure and parameters are the same as those of the primary encoder. The KL divergence is used to measure the distance between the primary encoding features and the secondary encoding features. The expression of KL divergence is: Where N(·) represents Gaussian distribution, μ and σ 2 are the mean and variance of the Gaussian distribution of the latent variables obtained by the encoder once, and are the mean and variance of the Gaussian distribution of the latent variable obtained by the quadratic encoder, I is the unit matrix, (·) T Indicates transposition, (·) -1 represents the inverse, and tr(·) represents the trace of the matrix; therefore, for labeled and unlabeled samples, the sum of the KL distances between the two hidden layers is: Where m represents the dimension of the latent variable, m = 1, 2, ..., M, μ Lm and μ Um are the means of the latent variables obtained by the encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the one-time encoder for labeled samples and unlabeled samples, and are the means of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples, and are the variances of the latent variables obtained by the secondary encoder for labeled samples and unlabeled samples respectively; Step 3.2: The discriminator distinguishes between labeled samples and unlabeled samples: When the hidden layer enhanced variational autoencoder network and the discriminator network are trained to balance, the discriminator can effectively distinguish the labeled samples and unlabeled samples of the training set in the hidden layer space, and then screen out representative unlabeled samples and label them; the specific process is as follows: The hidden layer enhanced variational autoencoder and the discriminator are trained with a minimax game; the hidden layer enhanced variational autoencoder deceives the discriminator into identifying all samples in the hidden space as labeled samples, while the discriminator strives to distinguish labeled samples from unlabeled samples; through iterative training of the hidden layer enhanced variational autoencoder and the discriminator network, after the network training is completed, the discriminator can screen out representative unlabeled samples; according to the probability value, b unlabeled samples {X SU } are selected and sent to experts for annotation; the annotated samples are added to the original training set to obtain a new training set {X SU ,y SU }∪{X L ,y L }.

2. The soft sensor modeling method for hidden layer enhanced variational adversarial active learning according to claim 1, characterized in that: The specific process of training the hidden layer enhanced variational autoencoder and the discriminator using the minimax game is as follows: The hidden layer enhanced variational autoencoder not only learns an effective latent space, but also conducts adversarial training with the discriminator, that is, it is hoped that the discriminator will discriminate all samples in the hidden layer as labeled samples; 1 represents labeled samples and 0 represents unlabeled samples, then the objective function is: Where D(·) is the discriminator; Therefore, the total loss function of the hidden layer enhanced variational autoencoder part in the LVAAL network is expressed as: Among them, λ1 and λ2 are hyperparameters, which respectively determine the proportion of the quadratic encoder part and the adversarial network part in learning effective feature space representation; The goal of the discriminator is to effectively distinguish labeled samples from unlabeled samples; the objective function of the discriminator is as follows: L D =-E[log(D(q φ (z L |x L )))]-E[log(1-D(q φ (z U |x U )))] The closer the probability of the discriminator's judgment is to 0, the more likely the sample is from an unlabeled sample.

3. A soft sensor modeling method for hidden layer enhanced variational adversarial active learning according to claim 1 or 2, characterized in that: The specific process of step (4) is as follows: A GPR prediction model is established to provide variance information of the prediction results to evaluate the uncertainty of the prediction. The expanded labeled dataset is used as the training set to train the GPR prediction model.

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