Chemical process inference modeling method based on deep adversarial slow feature extraction network

Abstract

The application provides a chemical process inference modeling method based on a deep adversarial slow feature extraction network. The method adopts a variable attention mechanism to adaptively screen input variables at each time step to enhance the prediction performance of the model and inhibit redundancy. At the same time, PSF-Net is introduced to effectively depict the nonlinear and large inertia process characteristics in the chemical process. In order to further improve the robustness of the model and the ability to implicitly extract high-order features, a discriminator is developed, and an adversarial learning framework is designed. In the framework, the discriminator and the PSF-Net perform a minimax game, and the game is iterated until a Nash equilibrium is reached. Finally, the final objective function suitable for APSF-Net is derived, which can effectively update the model parameters to the local optimum, and realizes online estimation of the quality variable, providing a strong basis for subsequent process monitoring, optimization and control operations.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of chemical engineering and complex industrial process modeling and optimization, in particular, but not exclusively, to a deep adversarial slow feature extraction network modeling method for chemical processes. BACKGROUND

[0002] In modern industrial processes, process modeling, as a basic prerequisite for process monitoring, optimization and control, has been increasingly applied by relevant personnel. Reasoning modeling is a practical method of process modeling, which is divided into two typical categories: first principle modeling and data-driven modeling. With the popularity of big data storage technology and the widespread application of distributed control systems, a large amount of process data is saved and can be used for modeling. Therefore, data-driven modeling has attracted attention from academia and industry. Among various data-driven modeling techniques, latent variable models (LVM) have been widely studied because they can handle the collinearity of process variables by establishing a latent space with statistical preference. For example, probabilistic principal component analysis and variational autoencoder, known as static LVM, are widely used in chemical processes to predict quality variables. However, traditional static LVM assumes that latent variables (LV) are independent of each other, which makes them insufficient to explain the dynamic relationship between process variables. In addition, in the field of chemical engineering, it is generally recognized that slower changes in process variables often carry more process information than faster changes because they reflect the inherent inertia and time characteristics of the process. Therefore, incorporating the slow-changing characteristics between continuous LVs can improve modeling performance.

[0003] Slow Feature Analysis (SFA) is a method that explicitly minimizes the time difference between adjacent LVs, which has been widely applied in industrial processes for representing reliable inertia characteristics, such as soft sensing and process monitoring. However, the estimation of parameters by SFA is deterministic, which makes it unsuitable for handling noisy measurements. To address this limitation, the concept of PSFA is introduced. PSFA uses an expectation-maximization algorithm for parameter estimation in a linear Gaussian state-space framework. Based on this theory, researchers have developed a soft-sensing regression algorithm based on PSFA. Considering that probability theory is widely used in engineering and computer science to establish models and learn parameters from data, PSFA and its extensions provide a promising solution. These methods provide more flexible and accurate means for data processing and feature extraction in industrial processes.

[0004] The complexity of chemical processes is due to the complex reaction mechanism and the interdependence between operating units, resulting in strong nonlinearity of process data. This nonlinearity poses a major challenge to traditional linear SFA and PSFA-based models. In addition, industrial process data often exhibit irregularities, including measurement noise, outliers and system disturbances. These irregularities further affect the performance of deep learning (DL) based models. Notably, many DL-based models mainly focus on minimizing the loss function based on first-order statistical patterns, resulting in such methods being sensitive to outliers. To alleviate these problems, adversarial learning has been shown to be effective. By promoting the learning of more general features that are less dependent on specific input changes, adversarial learning can improve the generalization ability of DL-based models to unknown data. In adversarial learning, minimax game theory is an attractive method that has received extensive attention in recent years. This theory provides a promising approach to solving the problem of modeling complex industrial processes. SUMMARY

[0005] To address one or more problems in the prior art, the present application proposes a new deep adversarial slow feature extraction network modeling method based on a deep generative model based on the Bayesian principle, which can identify slow nonlinear patterns in continuous industrial data. Notably, the model introduces a variable attention mechanism, enabling it to adaptively identify input variables related to quality. In addition, an adversarial learning strategy based on minimax game theory further enhances the model's ability to effectively approximate irregular industrial data. The mathematical formula of the model is proposed within a semi-supervised framework, suitable for scenarios with limited labeled data. Finally, the proposed modeling method is explicitly shown to have superior performance in prediction. This innovative approach is expected to play an important role in solving the problem of modeling and predicting complex industrial processes.

[0006] The technical solution for achieving the object of the present application is:

[0007] According to an aspect of the present application, the deep adversarial slow feature extraction network modeling method comprises:

[0008] S1, a variable attention mechanism is used to adaptively filter input variables at each time step to obtain attention-weighted input samples, thereby enhancing the prediction performance of the model and suppressing redundancy;

[0009] S2, a probabilistic slow feature extraction network PSF-Net is used to extract slow features from process information, which can effectively characterize the nonlinear and large inertia process characteristics in chemical processes;

[0010] S3, constructing an adversarial probabilistic slow feature extraction network APSF-Net: let the discriminator and the PSF-Net in the adversarial learning framework constantly game iteration until the Nash equilibrium is reached, so as to improve the robustness of the model and the ability of implicit extraction of high-order features;

[0011] S4, determining the final objective function suitable for the adversarial probabilistic slow feature extraction network APSF-Net, which can effectively update the model parameters to the local optimum, so as to realize online estimation of the quality variable and provide a strong basis for subsequent process monitoring, optimization and control operations.

[0012] Optionally, the specific steps of using the variable attention mechanism in S1 include:

[0013] S1-1, given the input sequence of PSF-Net and the output sequence get the slow feature sequence where T and T' represent the length of the input sequence and the output label sequence respectively, D and d are the dimensions of the input and latent variable space respectively, denotes the set of real numbers;

[0014] S1-2, use the similarity between the current input vector x t and the slow feature z t-1 at the previous moment to measure the correlation of each auxiliary variable to the output variable, the variable attention weight α t at time t is:

[0015] α t =τ VA (z t-1 ,x t ;θ VA )=softmax[V tanh(Qz t-1 +Ax t +b)]

[0016] where t=1,2,...,T, softmax[·] represents the softmax activation function, α t denotes the variable attention weight at time t, θ VA ={V,Q,A,b} is the parameter set of the variable attention network τ VA (·);

[0017] S1-3, the attention weighted input sample at time t is

[0018]

[0019] where x​t denotes the input sample at time t, and denotes element-wise multiplication.

[0020] Optionally, the PSF-Net is used in S2 to extract slow change features, specifically:

[0021] S2-1, PSF-Net inherits the previous assumptions of the probability slow feature analysis PSFA about the latent space, so as to make full use of the slow degree principle:

[0022] z t = Fz t-1 + e z

[0023] Where, t = 1, 2,..., T, F = diag{ω1, ω2,..., ω d}, where diag{·} is a diagonal operator, ω1, ω2,..., ω d denotes a set of parameters, e z denotes Gaussian noise;

[0024] In order to ensure the non-negativity of the elements in the matrix Γ, the state transition coefficient is represented by using the Sigmoid function:

[0025]

[0026] Where, denotes a set of parameters of all sigmoid functions;

[0027] S2-2, the posterior distribution of the initial state z0 is obtained by using the complete input data [x1, x2,..., x T ]:

[0028]

[0029] Where, and denote two gated recurrent unit GRU networks, x 1:T denotes all input data, and denote a set of parameters of the inference network;

[0030] The network learns the conditional relationship between adjacent slow features from the attention weighted input sample :

[0031]

[0032] Where, v μ (·) and v σ (·) denote two GRU networks, denote a set of parameters of the inference network;

[0033] S2-3, using GRU network to establish a nonlinear mapping τ x (·), to generate reconstructed input to enhance the nonlinear approximation ability of the network; construct a linear mapping τ y (·) to fit the regression relationship, in order to reduce the impact of input uncertainty on output data prediction, the model uses z t of the expectation instead of z t . In this way, the process of feature decoding and label regression can be redefined as:

[0034]

[0035]

[0036] where t = 1, 2,..., T, and represent the estimated input and output at time t, is the parameter set of the prior assumption on PSF-Net.

[0037] Optionally, the GRU network in S2-2 is a variant network of recurrent neural network, which is used to alleviate the problem of gradient vanishing and explosion, specifically:

[0038] The GRU network introduces a gating mechanism, which integrates the forgetting gate and the input gate into a unified update gate s, and integrates the storage unit and the hidden layer g into the reset gate r; given the input x t , the update equation of GRU at the t-th time step is formulated as follows:

[0039] r t = δ (W r x t + U r g t-1 + c r )

[0040] s t = δ (W s x t + U s s t-1 + c s )

[0041]

[0042]

[0043] where tanh(·) and δ(·) represent hyperbolic activation function and logistic Sigmoid activation function respectively, ⊙ represents element-wise multiplication, W, U and c represent network parameters, and subscripts s, r, g represent update gate, reset gate and hidden layer respectively.

[0044] Optionally, the specific steps of developing the discriminator in S3 include:

[0045] In order to overcome the difficulty of effectively approximating irregular data, a discriminator is designed, which can play a minimax game with the PSF-Net until a Nash equilibrium is reached.

[0046] The discriminator is used to divide the samples into two categories: real samples (x 1:T′ ,y 1:T′ ), denoted as "true", and generated samples denoted as "false"; accordingly, the sample classification in the discriminator network can be formulated as:

[0047] J=δ(Ω(M;η))

[0048] where M and J represent the input and output of the discriminator respectively, Ω(·) represents a feedforward neural network, and η represents the parameters of the discriminator network.

[0049] Optionally, the specific steps of deriving the final objective function of the APSF-Net in S4 include:

[0050] S4-1, according to the non-negativity of the KL divergence, combined with Bayes' theorem, the marginal log-likelihood function of the observed data is represented as:

[0051]

[0052] where p(·; θ) and q(·; φ) represent the true probability and the approximate probability respectively, θ and φ represent the prior assumption and the inference network parameters respectively, where F = diag{ω1, ω2,..., ω d}, I d represents a d-dimensional identity matrix, D KL (·) represents the KL divergence;

[0053] Using the basic principle of Monte Carlo sampling, the maximization of the right side of the inequality is equivalent to the minimization of the following loss function:

[0054]

[0055] where K is the number of Monte Carlo samples, [z t ] (k) ~ q(z t; φ), where the superscript (k) denotes Monte Carlo sampling;

[0056] S4-2, design an adversarial loss function based on maximum mean difference MMD for PSF-Net aiming at aligning the generated data with the real data, further ensuring the stability of adversarial training, the adversarial loss function is defined as follows:

[0057]

[0058] wherein, is a kind of kernel function and is a reproducing kernel hilbert space, ψ(·) represents a radial basis function, T' represents the number of label outputs, and the superscript ^ represents a predicted value.

[0059] S4-3, in order to facilitate the discriminator network to effectively distinguish samples, the expression formula of the loss function of the discriminator network is as follows:

[0060]

[0061] wherein, represents a predicted value;

[0062] S4-4, according to the minimax game theory, the parameters of PSF-Net are fixed after training, and the gradient of the discriminator network parameters is calculated by maximizing the objective function :

[0063]

[0064] wherein, the superscript * represents a local optimum;

[0065] S4-5, fix the parameters of the discriminator network, and calculate the PSF-Net parameter gradient by minimizing , wherein λ is a balance parameter:

[0066]

[0067] The formula and the above maximum objective function together constitute the final objective function of APSF-Net, and a stochastic gradient descent algorithm is used to optimize it.

[0068] Compared with the prior art, the above technical scheme has the following technical effects:

[0069] The chemical process inference modeling method based on the deep adversarial slow feature extraction network provided by the application can provide real-time estimation of quality variables of a chemical process, and needs to rely on the characteristics of an inference model, and a new deep generation model based on the Bayesian principle is used to realize real-time estimation of quality variables, so that the chemical production process can be optimized, the running state can be adjusted in time, and the reaction efficiency and the capacity utilization rate can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0070] The accompanying drawings are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification, illustrate embodiments of the application, and together with the description serve to explain the principles of the application, and should not be taken as limiting the application. In the drawings:

[0071] Figure 1 A simplified flowchart of the dimethyl oxalate synthesis process of the application.

[0072] Figure 2 A deep adversarial slow feature extraction network architecture diagram of the application.

[0073] Figure 3 A variable attention network diagram of the application.

[0074] Figure 4 A carbon monoxide quality prediction result diagram of an embodiment of the application.

[0075] Figure 5 A model effect comparison diagram of an embodiment of the application. DETAILED DESCRIPTION

[0076] In order to further understand the application, the preferred embodiments of the application are described below in combination with the embodiments, but it should be understood that these descriptions are only for further illustrating the features and advantages of the application, and are not limitations of the claims of the application.

[0077] The description in this part is only for a few typical embodiments, and the application is not limited to the scope described in the embodiments. Combination of different embodiments, mutual replacement of some technical features in different embodiments, and mutual replacement of the same or similar prior art means and some technical features in the embodiments are also within the description and protection scope of the application.

[0078] Taking the dimethyl oxalate synthesis (DMOS) process in the CtEG process as an example, the carbon monoxide quality in the recovered gas is predicted, and a simplified flowchart of the DMOS process is as follows: Figure 1The Dimethyl Oxalate (DMO) reactor uses carbon monoxide feed from recycle gas and fresh carbon monoxide. To ensure the stability of the feed, it is essential to monitor the carbon monoxide content in the recycle gas and maintain it at an appropriate level. Therefore, we propose a data-driven inference model that can estimate the carbon monoxide content in the recycle gas in real time. Using the deep adversarial slow feature extraction network APSF-Net of the technical solution, the carbon monoxide mass of carbon monoxide in the recycle gas during the DMOS process is estimated online, as shown in Figure 2 The specific steps include:

[0079] S1, combining Figure 3 The attention network given by the variable attention mechanism is used to obtain input samples with weighted attention at each time iteration;

[0080] S1-1, given the input sequence and output sequence The slow feature sequence where T and T' represent the length of the input sequence and the output label sequence respectively, D and d are the dimensions of the input and latent variable space respectively, denotes the set of real numbers;

[0081] S1-2, using the similarity between the current input vector x t and the slow feature z t-1 at the previous moment to measure the relevance of each auxiliary variable to the output variable, the variable attention weight α t at time t is:

[0082] α t =τ VA (z t-1 , x t ; θ VA )=softmax[V tanh(Qz t-1 +Ax t +b)]

[0083] where t=1,2,...,T, softmax[·] denotes the softmax activation function, α t denotes the variable attention weight at time t, θ VA ={V,Q,A,b} is the parameter set of the variable attention network τ VA (·);

[0084] S1-3, the attention weighted input sample at time t is :

[0085]

[0086] where x t denotes the input sample at time t, and denotes element-wise multiplication.

[0087] In S2, the PSF-Net is used to extract the slowly varying features, which is specifically:

[0088] S2-1, PSF-Net inherits the previous assumption of the probability slow feature analysis PSFA about latent space, so as to make full use of the slow degree principle:

[0089] z t = Fz t-1 + e z

[0090] where t = 1, 2,..., T, F = diag{ω1, ω2,..., ω d}, where diag{·} is a diagonal operator, ω1, ω2,..., ω d denote the parameter set, e z denotes Gaussian noise;

[0091] In order to ensure the non-negativity of the elements in the matrix Γ, the state transition coefficient is represented by a Sigmoid function:

[0092]

[0093] where denotes the parameter set of all sigmoid functions;

[0094] S2-2, the posterior distribution of the initial state z0 is obtained by using the complete input data [x1, x2,..., x T ]:

[0095]

[0096] where and denote two gated recurrent unit GRU networks, x 1:T denotes all input data, and denote the parameter set of the inference network;

[0097] The network learns the conditional relationship between adjacent slow features from the attention weighted input sample :

[0098]

[0099] where v μ (·) and v σ(·) denotes two GRU networks, denotes the parameter set of the inference network;

[0100] S2-3, using GRU networks to establish a nonlinear mapping τ x (·), generating reconstructed input to enhance the nonlinear approximation ability of the network; constructing a linear mapping τ y (·) to fit the regression relationship, in order to reduce the impact of input uncertainty on output data prediction, the model uses z t expectation instead of z t . In this way, the process of feature decoding and label regression can be redefined as follows:

[0101]

[0102]

[0103] where t = 1, 2,..., T, and denote the estimated input and output at time t, is the parameter set of the prior assumption on the PSF-Net.

[0104] GRU network is a variant of recurrent neural network, which is used to alleviate the problem of gradient vanishing and explosion, specifically:

[0105] GRU network introduces a gating mechanism, which integrates the forget gate and the input gate into a unified update gate s, and integrates the storage unit and the hidden layer g into the reset gate r; given the input x t , the update equation of GRU at the t-th time step is formulated as follows:

[0106] r t = δ (W r x t + U r g t-1 + c r )

[0107] s t = δ (W s x t + U s s t-1 + c s )

[0108]

[0109]

[0110] where tanh(·) and δ(·) represent hyperbolic activation function and logistic Sigmoid activation function respectively, ⊙ represents element-wise multiplication, W, U and c represent network parameters, and subscripts s, r, g represent update gate, reset gate and hidden layer respectively.

[0111] The specific steps of developing the discriminator in S3 include:

[0112] In order to overcome the difficulty of effectively approximating irregular data, a discriminator is designed, which can play a minimax game with the PSF-Net until a Nash equilibrium is reached.

[0113] The discriminator is used to classify samples into two categories: real samples (x 1:T′ ,y 1:T′ ), denoted as "true", and generated samples denoted as "false"; accordingly, the sample classification in the discriminator network can be formulated as:

[0114] J = δ (Ω (M; η))

[0115] where M and J represent the input and output of the discriminator respectively, Ω(·) represents a feedforward neural network, and η represents the parameters of the discriminator network.

[0116] The specific steps of deriving the final objective function of APSF-Net in S4 include:

[0117] S4-1, according to the non-negativity of KL divergence, combined with Bayes theorem, the marginal log-likelihood function of the observed data is represented as:

[0118]

[0119] where p(·; θ) and q(·; φ) represent the true probability and the approximate probability respectively, θ and φ represent the prior assumption and the inference network parameters respectively, where F = diag{ω1, ω2,..., ω d}, I d represents a d-dimensional identity matrix, D KL (·) represents the KL divergence;

[0120] Using the basic principle of Monte Carlo sampling, the maximization of the right side of the inequality is equivalent to the minimization of the following loss function:

[0121]

[0122] where K is the number of Monte Carlo samples, [z t ] (k) ~ q(z t; φ), where the superscript (k) denotes Monte Carlo samples;

[0123] S4-2, a maximum mean discrepancy (MMD) based adversarial loss function is designed for PSF-Net to align the generated data with the real data and further guarantee the stability of adversarial training is defined as follows:

[0124]

[0125] where, is a class of kernel functions and is a reproducing kernel Hilbert space, ψ(·) represents a radial basis function, T' represents the number of label outputs, and the superscript ^ represents the predicted value.

[0126] S4-3, in order to facilitate the discriminator network to effectively distinguish samples, the expression of the loss function of the discriminator network is as follows:

[0127]

[0128] where, represents the predicted value;

[0129] S4-4, according to the minimax game theory, the parameters of PSF-Net are fixed after training, and the gradient of the discriminator network parameters is calculated by maximizing the objective function :

[0130]

[0131] where the superscript * represents a local optimum;

[0132] S4-5, the parameters of the discriminator network are fixed, and the PSF-Net parameter gradient is calculated by minimizing , where λ is a balance parameter:

[0133]

[0134] The formula and the above-mentioned maximum objective function together constitute the final objective function of APSF-Net, and a stochastic gradient descent algorithm is used to optimize it.

[0135] S4-6, according to the established deep adversarial slow feature extraction network, the mass of carbon monoxide in the recovered gas in the CtEG process can be estimated in real time, and the results are shown in Figure 4 .

[0136]

[0137]

[0138] α L = softmax[V * tanh(Q * z L-1 +A * z L +b * )]

[0139] where K is the number of Monte Carlo samples, [z t ] (k) ~ q(z t ; φ).

[0140] The root mean square error (RMSE) and R 2 are used to quantitatively evaluate the model:

[0141]

[0142]

[0143] where y i and are the actual and predicted labels at time i, respectively, is the mean of the test output samples, and N is the number of test samples.

[0144] Compared with APSF-Net and PSF-Net, VA-APSF-Net and VA-PSF-Net, which integrate the variable attention mechanism, improve the R 2 by 23.53% and 53.54%, respectively. These findings indicate that the attention mechanism effectively improves the predictive ability of the model by adaptively selecting input variables related to quality. In addition, compared with VA-PSF-Net and PSF-Net, VA-APSF-Net and APSF-Net, which integrate the minimax game theory adversarial learning, improve the R 2 by 133.61% and 215.59%, respectively, as shown in Figure 5 . These results verify the effectiveness of adversarial learning in improving the prediction accuracy of the model on actual industrial data, as it can improve the robustness of the model and the ability to capture high-order statistical information.

[0145] The above formula can be used to predict the mass of carbon monoxide in the recovered gas during the CtEG process. The proposed network is based on the slowness principle and deep Bayesian learning, which provides a method for capturing the complex process dynamics that exhibit nonlinear and inertial behavior, while addressing the problem of randomly missing labels. In addition, the model incorporates a variable attention mechanism that dynamically assigns weights to input variables based on their relevance to mass prediction. During the training phase, the robustness and ability to implicitly extract high-order features are improved using adversarial learning. The feasibility and effectiveness of the proposed model are demonstrated through evaluation of real CtEG processes under two scenarios. Compared with the traditional PSFA, the R 2 indicator is improved by more than 15.89%. These results show that the model has superior performance in dealing with actual industrial processes with complex dynamic characteristics, providing a powerful tool for quality prediction in chemical processes.

[0146] The description and application of the present application herein are illustrative, and are not intended to limit the scope of the present application to the embodiments described above. The effects or advantages related descriptions involved in the specification may not be embodied in actual experimental examples due to the uncertainty of specific conditions parameters or other factors, and the effects or advantages related descriptions are not used to limit the scope of the present application. Variations and changes of the embodiments disclosed herein are possible, and the alternatives and equivalent components of the embodiments are known to those skilled in the art. It should be clear to those skilled in the art that the present application can be realized in other forms, structures, arrangements, proportions, and with other components, materials and parts without departing from the spirit or essential characteristics of the present application. Other variations and changes of the embodiments disclosed herein can be made without departing from the scope and spirit of the present application.

Claims

1. A chemical process inference modeling method based on deep adversarial slow feature extraction network, characterized in that, An adversarial probabilistic slow feature extraction network APSF-Net is constructed, and slow features are recognized in continuous industrial data by using the APSF-Net after the input of the sample to be tested; the construction of the APSF-Net comprises the following steps: S1, a variable attention mechanism is used to adaptively filter input variables at each time step, and attention weighted input samples are obtained, so as to enhance the prediction performance of the model and suppress redundancy; in S1, the variable attention mechanism is used to adaptively filter input variables at each time step, so as to obtain attention weighted input samples, specifically: S1-1, given a PSF-Net input sequence and output sequence obtain a slow feature sequence where T and T ′ denote the length of the input sequence and output label sequence, respectively, and D and d are the dimension of the input and latent variable space, respectively, denote the set of real numbers; S1-2, measure the relevance of each auxiliary variable to the output variable using the similarity between the current input vector x t and the slow feature z t-1 at the previous time step, the variable attention weight a t at time t is: alpha t = tau VA (z t-1 , x t ; theta VA ) = softmax[V tanh(Qz t-1 + Ax t + b)] where t = 1, 2,..., T, softmax[·] denotes a softmax activation function, a t denotes the variable attention weight at time t, θ VA = {V, Q, A, b} is the parameter set of the variable attention network τ VA (·). S1-3, attention-weighted input sample at time t is: where x t denotes the input sample at time t, and denotes element-wise multiplication. S2, a probabilistic slow feature extraction network PSF-Net is used to extract slow features in process information, which can effectively depict the nonlinear and large inertia process characteristics in the chemical process; S3, an adversarial probabilistic slow feature extraction network APSF-Net is constructed: the discriminator and the PSF-Net are subjected to a minimum-maximum game in an adversarial learning framework, and the game is iterated until a Nash equilibrium is reached, so as to improve the robustness of the model and the ability to implicitly extract high-order features; S4, the final objective function suitable for the adversarial probabilistic slow feature extraction network APSF-Net is determined, which can effectively update the model parameters to a local optimum, so as to realize online estimation of the quality variable and provide a strong basis for subsequent process monitoring, optimization and control operations. 2.The chemical process inferential modeling method based on deep adversarial slow feature extraction network according to claim 1, characterized in that, In S2, the PSF-Net is used to extract slow features, specifically: S2-1, the PSF-Net inherits the previous assumption of the probabilistic slow feature analysis PSFA about the latent space, so as to make full use of the slowness principle: z t = Fz t-1 + e z where t = 1, 2,..., T, F = diag{ω1, ω2,..., ω d}, where diag{·} is a diagonal operator, ω1, ω2,..., ω d denote a set of parameters, e z denotes a Gaussian noise; In order to ensure the non-negativity of the elements in the matrix Γ, the Sigmoid function is used to represent the state transition coefficient: wherein, denotes a parameter set for all sigmoid functions; S2-2, obtain the posterior distribution of the initial state z0 using the complete input data [x1, x2,..., x T ]: wherein, and denote two gated recurrent unit, GRU, networks, x 1:T denotes all input data, with denotes a set of parameters of the inference network; The network learns conditional relationships between neighboring slow features from attention-weighted input samples from attention-weighted input samples where v μ (·) and v σ (·) represent two GRU networks, denotes a parameter set of the inference network; S2-3, using GRU network to establish a nonlinear mapping τ x (·) to generate reconstructed input to enhance the nonlinear approximation ability of the network; construct a linear mapping τ y (·) to fit the regression relationship, in order to reduce the impact of input uncertainty on output data prediction, this model uses z t of the expectation , not z t ; in this way, the process of feature decoding and label regression is redefined: where t = 1, 2,..., T, and denote the estimated input and output at time t, respectively, is the set of parameters of the prior assumption on PSF-Net.

3. The method for modeling deep adversarial slow feature extraction network for chemical processes as claimed in claim 2 wherein, In S2-2, the GRU network is a variant network of the recurrent neural network, which is used to alleviate the problems of gradient disappearance and explosion, specifically: The GRU network introduces a gating mechanism that integrates the forget gate and the input gate into a unified update gate s, while combining the storage unit and the hidden layer g into a reset gate r; given the input x t The update equation of the GRU at the t-th time step is formulated as follows: r t = δ(W r x t + U r g t-1 + c r ) s t = δ(W s x t + U s s t-1 + c s ) Wherein, tanh(·) and δ(·) respectively represent the hyperbolic activation function and the logical Sigmoid activation function, ⊙ represents element-wise multiplication, W, U and c represent network parameters, and the subscripts s, r and g represent update gate, reset gate and hidden layer respectively. 4.The chemical process inferential modeling method based on deep adversarial slow feature extraction network according to claim 1, characterized in that, S3 In order to overcome the difficulty of not being able to effectively approximate irregular data, a discriminator is designed, which can perform a minimum-maximum game with the PSF-Net until a Nash equilibrium is reached; The discriminator is used to classify samples into two classes: real samples (x 1:T′ ,y 1:T′ ), denoted as "true", and generated samples denoted as "false"; correspondingly, the classification of samples in the discriminator network can be formulated as: J = δ (Ω (M; η)) Wherein, M and J represent the input and output of the discriminator respectively, Ω(·) represents a feedforward neural network, and η represents the parameters of the discriminator network. 5.The chemical process inferential modeling method based on deep adversarial slow feature extraction network according to claim 1, characterized in that, In S4, the variational inference, Monte Carlo sampling and minimax game theory techniques are used to derive the final objective function of the APSF-Net. 6.The chemical process inferential modeling method based on deep adversarial slow feature extraction network according to claim 1, characterized in that, The specific steps of derivation are as follows: S4-1, according to the non-negativity of the KL divergence, combined with the Bayes theorem, the marginal log-likelihood function of the observed data is expressed as: where p(·; θ) and q(·; φ) represent the true and approximate probabilities, respectively, and θ and φ represent the parameters of the prior assumption and the inference network, respectively, where F = diag{ω1, ω2,..., ω d} and I d denotes the d-dimensional identity matrix, D KL (·) represents the KL divergence; Using the basic principle of Monte Carlo sampling, the maximization of the right side of the inequality is equivalent to the minimization of the following loss function: where K is the number of Monte Carlo samples, [z t ] (k) ~q(z t ; φ), with the superscript (k) denoting the Monte Carlo sample; S4-2, design an adversarial loss function based on maximum mean discrepancy MMD for PSF-Net aiming to align the generated data with the real data, further guarantee the stability of adversarial training, and the adversarial loss function is defined as follows: wherein, is a kernel function and is a reproducing kernel Hilbert space, ψ(·) represents a radial basis function, T ′ denotes the number of label outputs, the superscript ^ denotes a predicted value; S4-3, in order to facilitate the discriminator network to effectively distinguish samples, the loss function of the discriminator network is expressed as follows: wherein represents a predicted value; S4-4、According to the minimax game theory, the parameters of the PSF-Net are fixed after training, and the gradient of the discriminator network parameters is calculated by maximizing the objective function : Wherein, the superscript * represents a local optimum; S4-5, fix the parameters of the discriminator network, and minimize iteratively compute the gradient of the PSF-Net parameters, where λ is a balancing parameter: The formula and the maximum objective function constitute the final objective function of APSF-Net, and is optimized using a stochastic gradient descent algorithm.

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