A small sample quality prediction method for coal-to-ethylene glycol process

Abstract

This invention provides a small-sample quality prediction method for the coal-to-ethylene glycol process, establishing a transferable adversarial slow feature extraction network (TASF-Net). This network combines the slowness principle with Bayesian deep learning, effectively characterizing the large inertia and nonlinearity of the coal-to-ethylene glycol process. Simultaneously, the network employs mini-maximum game theory for adversarial learning, thereby improving the model's robustness and ability to implicitly extract higher-order statistical information. Furthermore, incremental fine-tuning transfer learning is used to transfer knowledge from the pre-trained model to the target domain, and the target model SF-Net is further incrementally fine-tuned using a limited number of labeled data from the target domain, thus improving the small-sample prediction accuracy of the target model. This comprehensive approach effectively solves the modeling difficulties caused by the extreme scarcity of offline laboratory analysis data samples, providing a strong foundation for subsequent process monitoring, optimization, and control operations.

Description

Technical Field

[0001] This invention relates to the fields of chemical engineering, quality prediction and optimization, and specifically, but not limited to, a small-sample quality prediction method for the coal-to-ethylene glycol process. Background Technology

[0002] Ethylene glycol (EG) is an important organic compound with a wide range of industrial applications, including as a basic component of polyesters and coatings, as well as a solvent, antifreeze, and plasticizer. EG production mainly follows two routes: the ethylene route using petroleum, methanol, or ethane as feedstock, and the syngas route using coal, natural gas, or coke oven gas as feedstock. Coal-to-Ethylene Glycol (CTEG) is cost-effective, has shorter processing times, and is more resilient to operational risks. Notably, the dimethyl oxalate synthesis (DMOS) unit plays a crucial role in the CTEG process. A key quality parameter in the DMOS process is the carbon monoxide (CO) concentration in the recovered gas, which significantly impacts stable feed control. Although online analyzers can monitor trends in CO content in the recovered gas, they are susceptible to biases due to measurement environment and instrument accuracy. Furthermore, accurate CO content values ​​are typically obtained through manual sampling and offline laboratory analysis, introducing significant time delays and making real-time monitoring impractical.

[0003] In recent years, there has been an increasing demand for soft sensors in modern chemical processes for estimating key quality variables. Soft sensor modeling can be broadly categorized into first-principles calculations and data-driven modeling. Advances in precision instruments, distributed control systems (DCS), and big data processing technologies have facilitated the measurement and storage of massive amounts of data. Consequently, data-driven methods have been widely applied in real-world industries. Due to factors such as pipeline transportation, raw material chemical reactions, and energy exchange, DMOS processes typically exhibit significant inertia. To effectively capture these process characteristics, a dynamic latent variable model called Slow Feature Analysis (SFA) has been proposed, aiming to extract slowly changing features in the process by minimizing the time differences between adjacent latent variables. However, SFA's parameter estimation is deterministic and susceptible to noise contamination. Probabilistic Slow Feature Analysis (PSFA), as a probabilistic extension, incorporates a linear Gaussian state-space structure and uses the expectation-maximization algorithm for model parameter estimation. Inspired by this theory, SFA-based regression algorithms have been developed for soft sensors, providing a flexible and reliable solution for industrial process modeling.

[0004] The DMOS process is highly complex and strongly coupled, leading to nonlinear process data. This poses a challenge to PSFA-based models with linear structures. To overcome this problem, several methods have emerged that leverage the superior nonlinear fitting capabilities of deep learning. Among these methods, a Bayesian perspective has become a promising strategy for extending deep learning-based nonlinear slow feature extraction methods in various modeling projects.

[0005] Many deep learning-based models primarily focus on minimizing loss functions based on first-order statistical patterns, which can limit their ability to extract complex data irregularities such as measurement noise, outliers, and system perturbations. To address this issue, adversarial learning has proven effective in mitigating these problems by capturing higher-order statistical information and improving the robustness of the model. This, in turn, enhances the generalization ability of deep learning-based models to unknown data. One noteworthy approach within adversarial learning is mini-maximum game theory, which has received considerable attention in recent years.

[0006] The development of soft sensors is also hampered by the severe lack of accurate measurements of quality variables, leading to the problem of few-shot learning, where traditional deep learning-based models may suffer from overfitting or underfitting. This problem is particularly prominent in CTEG (Chemical Technology for Engineering and Technology) because obtaining accurate quality variables through offline laboratory analysis is expensive, time-consuming, and labor-intensive, resulting in an extremely limited number of samples for model development. As a popular paradigm for few-shot quality prediction, Deep Transfer Learning (DTL) provides the ability to leverage knowledge acquired from the source domain to improve performance in the target domain. Although data distributions may differ across domains, transferring shared underlying patterns or features from the source domain to the target domain has proven effective. In the field of chemical processes, DTL methods have gained significant appeal and widespread application. Summary of the Invention

[0007] To address the problems in existing technologies, this invention proposes a small-sample quality prediction method for the coal-to-ethylene glycol process. A transferable adversarial slow feature extraction network (TASF-Net) is established for small-sample quality prediction in the coal-to-ethylene glycol process. TASF-Net incorporates the slowness principle into a deep Bayesian framework to capture process nonlinearity and inertia. The model adaptively identifies quality-related input variables using a variable attention mechanism. Adversarial learning using a mini-maximum game enhances the model's ability to approximate irregular industrial data. An incremental fine-tuning transfer learning framework is designed to improve small-sample prediction performance. The proposed method is validated using a real coal-to-ethylene glycol dataset and compared with existing methods, demonstrating its effectiveness and superiority.

[0008] The technical solution to achieve the purpose of this invention is as follows:

[0009] According to one aspect of the present invention, a small-sample quality prediction method for a coal-to-ethylene glycol process is provided, comprising constructing a transferable adversarial slow feature extraction network TASF-Net, and obtaining quality prediction results after inputting the sample to be tested into TASF-Net; the construction of TASF-Net includes the following steps:

[0010] S1. Combine the DCS data at the corresponding sampling time with the online analyzer data to construct the source domain dataset D. S ={X S Y S}, where X S It's DCS data, Y S This involves online analyzer data; similarly, combining the DCS data at the corresponding sampling time with offline laboratory analysis data to construct the target domain dataset D. T ={X T Y T}, where XT It's DCS data, Y T It is offline laboratory analysis data;

[0011] S2. Construct the slow feature extraction network SF-Net to describe the inertial and nonlinear characteristics of the coal-to-ethylene glycol process;

[0012] S3. Construct an adversarial slow feature extraction network ASF-Net, and use the discriminator to engage in a minimax game with SF-Net until a Nash equilibrium is reached, thereby improving the robustness of the model and its ability to implicitly extract higher-order statistical information.

[0013] S4. Design an incremental fine-tuning transfer learning (IRTL) framework to transfer knowledge from the pre-trained model ASF-Net to the target domain, and further incrementally fine-tune the target model SF-Net using rare labeled data in the target domain to obtain a transferable adversarial slow feature extraction network TASF-Net; thereby improving the prediction accuracy of TASF-Net on small sample data in the target domain.

[0014] Optionally, the slow feature extraction network structure in S2 is as follows:

[0015] S2-1. Given an input sequence in the source domain. Tag sequence Slow feature sequences are represented as Where L and L′ represent the lengths of the input sequence and label sequence, respectively, D and d correspond to the dimensions of the input and latent variable spaces, and the superscript (S) denotes the source domain. The set of real numbers;

[0016] S2-2. Using a variable attention mechanism, measure the correlation between input variables and quality variables, utilizing the current input vector. The slow characteristics of the previous moment t-1 The similarity between the input variables is used to assess the importance of each input variable to the quality variable. The variable attention weights at time t are expressed as:

[0017]

[0018] Where softmax[·] is the softmax activation function. This is the parameter set of the variable attention network in the source model ASF-Net; the attention-weighted input is represented as follows:

[0019]

[0020] Where ⊙ represents element-wise multiplication.

[0021] The prior assumptions of S2-3 and SF-Net regarding the latent space are expressed as follows: in Indicates Gaussian noise; Let Γ be a matrix with a mean of 0 and a covariance matrix of 0. (S) Multidimensional normal distribution; F (S) Represents the hidden state transition matrix; initial state The posterior distribution is obtained using the complete input data. The result is as follows:

[0022]

[0023] in ε is often used in reparameterization techniques to ensure that the expected estimate is differentiable in Monte Carlo sampling. Let I represent a matrix with a mean of 0 and a covariance matrix of size I. d The multidimensional normal distribution, where I d It is a d-dimensional identity matrix; and These represent two gated recurrent unit (GRU) networks that generate the mean and standard deviation of the initial state using the complete input sequence, respectively. and This represents the parameters of the inference network in the source model ASF-Net; from the weighted input The conditional relationships between adjacent slow features learned in the middle are as follows:

[0024]

[0025] Where t = 1, 2, ..., L; v μ (·) and v σ (·) represents two gated cyclic unit (GRU) networks, which represent the mean and standard deviation of the conditional distribution, respectively.

[0026] Optionally, to further improve the nonlinear approximation capability of the network, the slow feature extraction network structure in S2 also includes: S2-4, establishing a nonlinear mapping τ x (·) is used to generate a reconstructed input for a gated recurrent unit (GRU) network, and a linear mapping τ is constructed through a feedforward neural network. y (·) is used to fit the regression relationship.

[0027] Optionally, to mitigate the impact of input uncertainty on output data prediction, the model uses The expected value rather than Feature decoding and label regression are expressed as follows:

[0028]

[0029]

[0030] In the formula, t = 1, 2, 3, ..., L, and Let represent the input and output of the estimate at time t, respectively; It is the set of parameters pre-assumed on the source model, v μ (·) represents the average value of the conditional distribution; This represents the parameters of the inference network in the source model ASF-Net.

[0031] Optional, the adversarial slow feature extraction network architecture in S3 is as follows:

[0032] S3-1. Introduce a discriminator network to perform a minimum-maximum game with SF-Net;

[0033] S3-2. The discriminator network divides samples into two classes: real samples are represented as "true," and generated samples are represented as "false." The sample classification in the discriminator network can be represented as:

[0034] O (S) =δ(Ω(Z) (S) η (S) ))

[0035] Z (S) Z is the input to the discriminator network, where Z (S) It consists of both real and generated samples, Ω(·) is a feedforward neural network, δ(·) represents the logistic sigmoid activation function, and η (S) For the training parameters of the discriminator in the source model ASF-Net, O (S) This represents the output of the discriminator network. Based on the output of the entire discriminator, the entire ASF-Net is iteratively updated.

[0036] S3-3. Based on the nonnegativity of the KL divergence and combined with Bayes' theorem, the marginal log-likelihood function of the observed data can be expressed as the inequality:

[0037]

[0038] in p θ (·) and q φ (·) represent the actual probability and the approximate probability, respectively; Represents a real sample. Let represent the slow feature sequence, and θ and φ represent the prior hypothesis and the parameters of the inference network, respectively. Indicates about The expectation operator on; D KL (·) represents the KL divergence;

[0039] Maximizing the right side of the inequality is equivalent to minimizing the following loss function using Monte Carlo sampling:

[0040]

[0041] Where K is the number of Monte Carlo samples, and

[0042] S3-4. An adversarial loss function based on Maximum Mean Difference (MMD) is proposed to enhance the stability of adversarial training and ensure that the generated data maintains consistency with the statistical characteristics of real data. The adversarial loss function is defined as follows:

[0043]

[0044] It is a kernel function One type, It is a regenerated Hilbert space, and ψ(·) is a radial basis function;

[0045] S3-5. In order for the discriminator network to accurately distinguish samples, the loss function of the discriminator network is expressed as:

[0046]

[0047] S3-6. According to mini-maximum game theory, the parameters of SF-Net are fixed after training, and the gradient of the discriminator network parameters is obtained by maximizing the objective function. To calculate:

[0048]

[0049] The parameters of the discriminator network were then fixed and minimized. The gradient of the SF-Net parameters is iteratively calculated, where λ is a balancing parameter;

[0050]

[0051] The superscript * indicates that the corresponding parameters have been updated during training; based on the minimum and maximum objective functions mentioned above. and Together, they constitute the final objective function of ASF-Net, and the ASF-Net is optimized using the stochastic gradient descent (SGD) algorithm.

[0052] Optionally, the construction steps of the incremental fine-tuning transfer learning IRTL framework in S4 are as follows:

[0053] S4-1. Provide the attention weights for the variables and the attention-weighted representation of the input samples in the target model SF-Net.

[0054]

[0055]

[0056] Parameter set in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network The migration is used for initialization; the pre-trained model ASF-Net network is obtained by extracting adversarial slow features in the source domain using ASF-Net.

[0057] S4-2. The inference network of the target model SF-Net is based on a slow feature extraction network, as shown in the following formula:

[0058]

[0059]

[0060] Parameters in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network Migrate over and initialize;

[0061] S4-3, Based on Formula The decoding network of the target model SF-Net is represented as follows: Parameters in the target domain Using the corresponding parameters transferred from the pre-trained ASF-Net model initialization;

[0062] S4-4. The parameters corresponding to the regression layer for quality variables are randomly initialized, as follows:

[0063]

[0064] Where parameters Initialize in the target domain;

[0065] S4-5 and TASF-Net employ an incremental fine-tuning strategy to merge a limited amount of offline laboratory analysis data and update the established model to adapt to specific target tasks.

[0066] Optionally, in S4-5, the incremental fine-tuning strategy includes updating model parameters using the target domain data via the SGD algorithm, as described below:

[0067]

[0068] Attached Figure Description

[0069] The accompanying drawings are provided to further illustrate the invention and, together with the description, serve to explain embodiments of the invention, but do not constitute a limitation thereof. In the drawings:

[0070] Figure 1 This provides the overall framework for quality prediction methods.

[0071] Figure 2 This section explains the multi-source sampling data used in the CTEG process.

[0072] Figure 3 The proposed architecture of the ASF network.

[0073] Figure 4 The structure of a variable attention network.

[0074] Figure 5 This is a simplified diagram of the DMOS process.

[0075] Figure 6 The results are the predictions. (a) SF-Net. (b) ASF-Net. (c) TSF-Net. (d) TASF-Net. Detailed Implementation

[0076] To further understand the present invention, preferred embodiments of the present invention are described below in conjunction with examples. However, it should be understood that these descriptions are only for further illustrating the features and advantages of the present invention, and not for limiting the scope of the claims of the present invention.

[0077] The description in this section pertains to only a few typical embodiments, and the present invention is not limited to the scope of the embodiments described. Combinations of different embodiments, substitution of some technical features in different embodiments, and substitution of similar or identical prior art with some technical features in the embodiments are also within the scope of the description and protection of the present invention.

[0078] Taking the monitoring and control system of coal-to-ethylene glycol (CTEG) process as an example, this paper uses the transferable anti-slow feature extraction network (TASF-Net) of this technical solution to estimate the CO mass in the circulating gas online during the synthesis of dimethyl oxalate. Figure 1 As shown, the overall framework for predicting the CO mass in the circulating gas during the DMOS process is constructed. Figure 5This provides an example of a DMOS process where CO from an external pipeline is mixed with gas recovered from the compressor, preheated, and then fed into the DMO reactor to produce DMO and NO, while generating impurities such as dimethyl carbonate (DMC). The waste gas enters a gas separator, where DMO and DMC are absorbed by methanol (ME), condensed, and recycled back to the top. The uncondensed gas follows two paths: one part mixes with oxygen and enters the methyl nitrite (MN) regeneration tower, and the other part enters the nitric acid reduction tower. The bottom ME is fed to the DMO flash tower, while the top gas mixes with oxygen and is introduced into the MN regeneration tower to generate MN and water. Gas from the nitric acid reduction tower is absorbed by ME, and the waste gas is sent to the MN recovery tower, where the recovered gas flows to the DMO reactor compressor. In the MN recovery tower, ME absorbs water; part of the liquid is cooled and recycled back to the MN regeneration tower, and the other part enters the nitric acid reduction tower, where nitric acid reacts with the gas to produce MN. Specific steps include:

[0079] S1. Combine the Distributed Control Systems (DCS) data at the corresponding sampling time with the online analyzer data to construct the source domain dataset D. S ={X S Y S}, where X s It's DCS data, Y S This involves online analyzer data; similarly, combining the DCS data at the corresponding sampling time with offline laboratory analysis data to construct the target domain dataset D. T ={X T Y T}, where X T It's DCS data, Y T It is offline laboratory analysis data; such as Figure 2 As shown, the data obtained using online analyzers have large deviations, and the values ​​obtained using manual sampling and offline laboratory analysis have a significant delay. Combining the two methods yields multi-source sampling data.

[0080] S2. Construct the slow feature extraction network SF-Net to describe the inertial and nonlinear characteristics of the coal-to-ethylene glycol process;

[0081] S2-1. Given an input sequence in the source domain. Tag sequence Slow feature sequences are represented as Where L and L′ represent the lengths of the input sequence and label sequence, respectively, D and d correspond to the dimensions of the input and latent variable spaces, and the superscript (S) denotes the source domain. The set of real numbers;

[0082] S2-2. Using a variable attention mechanism, measure the correlation between input variables and quality variables, utilizing the current input vector. The slow characteristics of the previous moment t-1 The similarity between the two variables is used to assess the importance of each input variable to the quality variable. (Combined) Figure 4 The attention weights of the variables at time t are expressed as:

[0083]

[0084] Where softmax[·] is the softmax activation function. It is the parameter set of the variable attention network in the source model ASF-Net;

[0085] 1) Attention-weighted input can be represented as follows:

[0086]

[0087] Where ⊙ represents element-wise multiplication.

[0088] The prior assumptions of S2-3 and SF-Net regarding the latent space are expressed as follows: in Indicates Gaussian noise; Let Γ be a matrix with a mean of 0 and a covariance matrix of 0. (S) Multidimensional normal distribution; Γ (S) It is the covariance matrix of a normal distribution, F (S) Represents the hidden state transition matrix; initial state The posterior distribution is obtained using the complete input data. The result is as follows:

[0089]

[0090] in ε is often used in reparameterization techniques to ensure that the expected estimate is differentiable in Monte Carlo sampling. Let I represent a matrix with a mean of 0 and a covariance matrix of size I. d The multidimensional normal distribution, where I d It is a d-dimensional identity matrix; and These represent two gated recurrent unit (GRU) networks that generate the mean and standard deviation of the initial state using the complete input sequence, respectively. and This represents the parameters of the inference network in the source model ASF-Net; from the weighted input The conditional relationships between adjacent slow features learned in the middle are as follows:

[0091]

[0092] Where t = 1, 2, ..., L; vμ (·) and v σ (·) represents two gated cyclic unit (GRU) networks, which represent the mean and standard deviation of the conditional distribution, respectively.

[0093] 1) To further improve the nonlinear approximation capability of the network, the slow feature extraction network structure in S2 also includes: S2-4, establishing a nonlinear mapping τ x (·) is used to generate a reconstructed input for a gated recurrent unit (GRU) network, and a linear mapping τ is constructed through a feedforward neural network. y (·) is used to fit the regression relationship.

[0094] 2) To mitigate the impact of input uncertainty on output data prediction, this model uses... The expected value rather than Feature decoding and label regression are expressed as follows:

[0095]

[0096]

[0097] In the formula, t = 1, 2, 3, ..., L, and Let represent the input and output of the estimate at time t, respectively; It is the set of parameters pre-assumed on the source model, v μ (·) represents the average value of the conditional distribution; This represents the parameters of the inference network in the source model ASF-Net.

[0098] S3, such as Figure 3 As shown, the architecture of the adversarial slow feature extraction network (ASF-Net) is constructed. The discriminator engages in a mini-maximum game with SF-Net until a Nash equilibrium is reached, thereby improving the model's robustness and its ability to implicitly extract higher-order statistical information.

[0099] S3-1. Introduce a discriminator network to perform a minimum-maximum game with SF-Net;

[0100] S3-2. The discriminator network divides samples into two classes: real samples are represented as "true," and generated samples are represented as "false." The sample classification in the discriminator network can be represented as:

[0101] O (S) =δ(Ω(Z) (S) η (S) ))

[0102] Z (S) Z is the input to the discriminator network, where Z (S)It consists of both real and generated samples, Ω(·) is a feedforward neural network, δ(·) represents the logistic sigmoid activation function, and η (S) For the training parameters of the discriminator in the source model ASF-Net, O (S) This represents the output of the discriminator network. Based on the output of the entire discriminator, the entire ASF-Net is iteratively updated.

[0103] S3-3. Based on the nonnegativity of the KL divergence and combined with Bayes' theorem, the marginal log-likelihood function of the observed data can be expressed as the inequality:

[0104]

[0105] in p θ (·) and q φ (·) represent the actual probability and the approximate probability, respectively; Represents a real sample. Let represent the slow feature sequence, and θ and φ represent the prior hypothesis and the parameters of the inference network, respectively. Indicates about The expectation operator on; D KL (·) represents the KL divergence;

[0106] Maximizing the right side of the inequality is equivalent to minimizing the following loss function using Monte Carlo sampling:

[0107]

[0108] Where K is the number of Monte Carlo samples, and

[0109] S3-4. An adversarial loss function based on Maximum Mean Difference (MMD) is proposed to enhance the stability of adversarial training and ensure that the generated data maintains consistency with the statistical characteristics of real data. The adversarial loss function is defined as follows:

[0110]

[0111] It is a kernel function One type, It is a regenerated Hilbert space, and ψ(·) is a radial basis function;

[0112] S3-5. In order for the discriminator network to accurately distinguish samples, the loss function of the discriminator network is expressed as:

[0113]

[0114] S3-6. According to mini-maximum game theory, the parameters of SF-Net are fixed after training, and the gradient of the discriminator network parameters is obtained by maximizing the objective function. To calculate:

[0115]

[0116] The parameters of the discriminator network were then fixed and minimized. The gradient of the SF-Net parameters is iteratively calculated, where λ is a balancing parameter;

[0117]

[0118] Where the superscript * indicates that the corresponding parameters have been updated during training; from the above minimum and maximum objective functions and Together, they constitute the final objective function of ASF-Net, and the ASF-Net is optimized using the stochastic gradient descent (SGD) algorithm.

[0119] S4. Design an incremental fine-tuning transfer learning (IRTL) framework to transfer knowledge from the pre-trained model ASF-Net to the target domain, and further incrementally fine-tune the target model SF-Net using rare labeled data in the target domain to obtain a transferable adversarial slow feature extraction network TASF-Net; thereby improving the prediction accuracy of TASF-Net on small sample data in the target domain.

[0120] S4-1. Provide the attention weights for the variables and the attention-weighted representation of the input samples in the target model SF-Net.

[0121]

[0122]

[0123] Parameter set in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network The migration is used for initialization; the pre-trained model ASF-Net network is obtained by extracting adversarial slow features in the source domain using ASF-Net.

[0124] S4-2. The inference network of the target model SF-Net is based on a slow feature extraction network, as shown in the following formula:

[0125]

[0126]

[0127] Parameters in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network Migrate over and initialize;

[0128] S4-3, Based on Formula The decoding network of the target model SF-Net is represented as follows: Parameters in the target domain Using the corresponding parameters transferred from the pre-trained ASF-Net model initialization;

[0129] S4-4. The parameters corresponding to the regression layer for quality variables are randomly initialized, as follows:

[0130]

[0131] Where parameters Initialize in the target domain;

[0132] S4-5 and TASF-Net employ an incremental fine-tuning strategy to analyze a limited amount of offline laboratory analysis data and update the established model to adapt to specific target tasks.

[0133] 1) In S4-5, the incremental fine-tuning strategy includes updating model parameters using target domain data via the SGD algorithm, as described below:

[0134]

[0135]

[0136] The aforementioned research proposes a novel TASF-Net specifically for small-sample quality prediction in the coal-to-ethylene glycol process. The proposed network is built upon deep Bayesian learning to enhance nonlinear fitting capabilities and effectively models large inertia characteristics using the slowness principle. Furthermore, the model incorporates minimax game theory adversarial learning to enhance its robustness and ability to implicitly extract higher-order statistical information. Additionally, the proposed network utilizes IRTL to address the challenge posed by the limited sample size of online analyzer data. The feasibility and effectiveness of the proposed model were evaluated using a real CTEG factory dataset, yielding prediction results as shown below. Figure 6As shown, compared to ASF-Net and SF-Net, TASF-Net and TSF-Net reduced RMSE by 29.30% and 17.81%, respectively. These findings demonstrate that IRTL can leverage pre-trained models on the source domain dataset, avoiding model retraining and improving model performance in the target domain. Furthermore, compared to TSF-Net and SF-Net, TASF-Net and ASF-Net reduced RMSE by 26.49% and 14.53%, respectively. These results validate that adversarial learning can improve model robustness and the ability to capture higher-order statistical information, thereby improving the model's prediction accuracy. This indicates that the proposed scheme has excellent performance for small-sample quality prediction problems.

[0137] The description and application of the present invention herein are illustrative and not intended to limit the scope of the invention to the embodiments described above. The effects or advantages described in the specification may not be apparent in actual experimental cases due to uncertainties in specific conditions or other factors, and such descriptions are not intended to limit the scope of the invention. Variations and modifications to the embodiments disclosed herein are possible, and various substitutions and equivalents of the components in the embodiments are well known to those skilled in the art. It should be understood by those skilled in the art that the invention can be implemented in other forms, structures, arrangements, proportions, and with other components, materials, and parts without departing from the spirit or essential characteristics of the invention. Other variations and modifications can be made to the embodiments disclosed herein without departing from the scope and spirit of the invention.

Claims

1. A small-sample quality prediction method for the coal-to-ethylene glycol process, characterized in that, A transferable adversarial slow feature extraction network (TASF-Net) is constructed. The quality prediction results are obtained after the test samples are input into TASF-Net. The construction of TASF-Net includes the following steps: S1. Combine the distributed control system (DCS) data at the corresponding sampling time with the online analyzer data to construct the source domain dataset D. S ={X S ,Y S }, where X S It's DCS data, Y S This involves online analyzer data; similarly, combining the DCS data at the corresponding sampling time with offline laboratory analysis data to construct the target domain dataset D. T ={X T ,Y T }, where X T It's DCS data, Y T It is offline laboratory analysis data; S2. Construct the slow feature extraction network SF-Net to describe the inertial and nonlinear characteristics of the coal-to-ethylene glycol process; S3. Construct an adversarial slow feature extraction network ASF-Net and use the discriminator to engage in a minimax game with SF-Net until a Nash equilibrium is reached, thereby improving the robustness of the model and its ability to implicitly extract higher-order statistical information. S4. Design an incremental fine-tuning transfer learning (IRTL) framework to transfer knowledge from the pre-trained model ASF-Net to the target domain, and further incrementally fine-tune the target model SF-Net using rare labeled data in the target domain to obtain a transferable adversarial slow feature extraction network TASF-Net; thereby improving the prediction accuracy of TASF-Net on small sample data in the target domain.

2. The method for small-sample quality prediction in the coal-to-ethylene glycol process according to claim 1, characterized in that, The slow feature extraction network structure in S2 is as follows: S2-1. Given an input sequence in the source domain. Label output sequence Slow feature sequences are represented as Where L and L ′ Let represent the lengths of the input sequence and the label sequence, respectively. D and d correspond to the dimensions of the input and latent variable spaces, respectively. The superscript (S) denotes the source domain. The set of real numbers; S2-2. Using a variable attention mechanism, measure the correlation between input variables and quality variables, utilizing the current input vector. The slow characteristics of the previous moment t-1 The similarity between the variables is used to assess the importance of each input variable to the quality variable; the variable attention weights at time t are expressed as: Where softmax[·] is the softmax activation function. This is the parameter set of the variable attention network in the source model ASF-Net; the attention-weighted input is represented as follows: in Indicates input In the weighted attention representation at time t, ⊙ represents element-wise multiplication; The prior assumptions of S2-3 and SF-Net regarding the latent space are expressed as follows: in Indicates Gaussian noise; Let Γ be a matrix with a mean of 0 and a covariance matrix of 0. (S) Multidimensional normal distribution; Γ (S) It is the covariance matrix of a normal distribution, F (S) Represents the hidden state transition matrix; initial state The posterior distribution is obtained using the complete input data. The result is as follows: in ε is often used in reparameterization techniques to ensure that the expected estimate is differentiable in Monte Carlo sampling. Let I represent a matrix with a mean of 0 and a covariance matrix of size I. d The multidimensional normal distribution, where I d It is a d-dimensional identity matrix; and These represent two gated recurrent unit (GRU) networks that generate the mean and standard deviation of the initial state using the complete input sequence, respectively. and This represents the parameters of the inference network in the source model ASF-Net; from the weighted input The conditional relationship between adjacent slow features learned in the middle is: Where t = 1, 2, ..., L; v μ (·) and v σ (·) represents two gated cyclic unit (GRU) networks, which represent the mean and standard deviation of the conditional distribution, respectively.

3. The method according to claim 2, characterized in that, To further improve the nonlinear approximation capability of the network, the slow feature extraction network structure in S2 also includes: S2-4, establishing a nonlinear mapping τ x (·) is used to generate a reconstructed input for a gated recurrent unit (GRU) network, and a linear mapping τ is constructed through a feedforward neural network. y (·) is used to fit the regression relationship.

4. The method according to claim 3, characterized in that, To mitigate the impact of input uncertainty on output data prediction, this model uses The expected value rather than Feature decoding and label regression are expressed as follows: In the formula, t = 1, 2, 3, ..., L. and Let represent the input and output of the estimate at time t, respectively; It is the set of parameters pre-assumed on the source model, υ μ (·) represents the average value of the conditional distribution; This represents the parameters of the inference network in the source model ASF-Net.

5. The method for small-sample quality prediction in the coal-to-ethylene glycol process according to claim 1, characterized in that, The adversarial slow feature extraction network architecture in S3 is as follows: S3-1. Introduce a discriminator network to perform a minimum-maximum game with SF-Net; S3-2. The discriminator network divides samples into two classes: real samples are represented as "true" and generated samples are represented as "false". The sample classification in the discriminator network can be represented as: The (S) =δ(Ω(Z (S) ;or (S) )) Z (S) Z is the input to the discriminator network, where Z (S) It consists of both real and generated samples, Ω(·) is a feedforward neural network, δ(·) represents the logistic sigmoid activation function, and η (S) For the training parameters of the discriminator in the source model ASF-Net, O (S) This represents the output of the discriminator network. Based on the output of the entire discriminator, the entire ASF-Net is iteratively updated. S3-3. Based on the nonnegativity of the KL divergence and combined with Bayes' theorem, the marginal log-likelihood function of the observed data can be expressed as the inequality: in p θ (·) and q φ (·) represent the actual probability and the approximate probability, respectively; Represents a real sample. Let represent the slow feature sequence, and θ and φ represent the prior hypothesis and the parameters of the inference network, respectively. Indicates about The expectation operator on; D KL (·) represents the KL divergence; Maximizing the right side of the inequality is equivalent to minimizing the following loss function using Monte Carlo sampling: Where K is the number of Monte Carlo samples, and S3-4. An adversarial loss function based on Maximum Mean Difference (MMD) is proposed to enhance the stability of adversarial training and ensure that the generated data maintains consistency with the statistical characteristics of real data. The adversarial loss function is defined as follows: It is a kernel function One type, It is a regenerated Hilbert space, and ψ(·) is a radial basis function; S3-5. To enable the discriminator network to accurately distinguish samples, the loss function of the discriminator network is expressed as: S3-6. According to mini-maximum game theory, the parameters of SF-Net are fixed after training, and the gradient of the discriminator network parameters is obtained by maximizing the objective function. To calculate: The parameters of the discriminator network were then fixed and minimized. The gradient of the SF-Net parameters is calculated iteratively, where λ is a balancing parameter; the superscript * indicates that the corresponding parameter has been updated during training. From the above maximum objective function and minimum objective function Together, they constitute the final objective function of ASF-Net.

6. The method according to claim 5, characterized in that, ASF-Net was optimized using the stochastic gradient descent (SGD) algorithm.

7. The method according to claim 1, characterized in that, The construction steps of the incremental fine-tuning transfer learning IRTL framework in S4 are as follows: S4-1. Provide the attention weights of the variables and the attention-weighted representation of the input samples of the target model SF-Net. Parameter set in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network The migration is used for initialization; the pre-trained model ASF-Net network is obtained by extracting adversarial slow features in the source domain using ASF-Net. S4-2. The inference network of the target model SF-Net is based on a slow feature extraction network, as shown in the following formula: Parameters in the target domain Using the parameter set of the corresponding pre-trained model ASF-Net network Migrate over and initialize; S4-3, Based on Formula The decoding network of the target model SF-Ne is represented as follows: Parameters in the target domain Using the corresponding parameters transferred from the pre-trained ASF-Net model initialization; S4-4. The parameters corresponding to the regression layer for quality variables are randomly initialized, as follows: Where parameters Initialize in the target domain; S4-5 and TASF-Net employ an incremental fine-tuning strategy to analyze a limited amount of offline laboratory analysis data and update the established model to adapt to specific target tasks.

8. The method according to claim 7, characterized in that, In S4-5, the incremental fine-tuning strategy includes updating model parameters using target domain data through the SGD algorithm, as described below:

Images