Missing Data Filling Method for Industrial Soft Sensing

Abstract

The present invention relates to a method for filling missing data for industrial soft sensing, including determining auxiliary variables of a target variable, generating a first predicted value according to the time correlation of the existing data in the auxiliary variables, and filling the missing data in the auxiliary variables by using the first predicted value; and predicting the target variable based on the spatial dependence relationship between the filled auxiliary variables and the target variable. This application can use the existing data set to predict and fill missing values, ensure the integrity and accuracy of the data while guaranteeing the data generation rate and precision, and at the same time can meet the requirements of high-precision downstream soft sensing and realize customized missing data generation tasks.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor data anomaly processing, and more specifically, to a method for filling missing data for industrial soft measurement. Background Art

[0002] In modern metallurgical industry, especially during the smelting process of nickel flash furnace, real-time monitoring of the smelting process and data analysis are crucial. The nickel flash furnace uses high-temperature and rapid oxidation reaction. Through the precise proportioning of concentrate minerals, fluxes and oxygen-enriched air, the oxidation of concentrate can be completed within a very short time at a temperature range of 1450 to 1550 °C. Subsequently, the melt falls into the sedimentation tank for sedimentation separation, thereby realizing the efficient extraction of nickel. This process not only requires precise control of materials, but also depends on continuous monitoring of the internal conditions of the reaction tower, including key parameters such as temperature, pressure, gas composition, etc., to ensure reaction efficiency and product quality.

[0003] However, traditional sensor monitoring systems face many challenges, especially the reliability problem in extreme working environments. Sensors may fail due to factors such as high temperature, corrosive gases, vibration or wear, resulting in data loss.

[0004] These missing data not only affect the accurate analysis of the actual working conditions of the smelting process, but also hinder the optimization of process parameters based on real-time data, and may thus have a negative impact on production efficiency and product quality. In addition, data loss during the smelting process may also lead to insufficient model training, making data-driven prediction and control strategies unable to exert their maximum potential.

[0005] Therefore, developing a method that can effectively process and fill missing data is of great significance for maintaining the stability and reliability of the smelting process monitoring system and improving the intelligent level of the entire production process. Summary of the Invention

[0006] In view of this, the present invention proposes a method for filling missing data for industrial soft measurement, aiming to solve the problem of data loss caused by sensor failures or system downtime during the monitoring of the nickel flash furnace smelting process.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for filling missing data for industrial soft measurement, comprising:

[0009] Determine the auxiliary variables of the target variable, generate the first predicted value according to the time correlation of the existing data in the auxiliary variables, and use the first predicted value to fill the missing data in the auxiliary variables;

[0010] Predict the target variable based on the spatial dependence between the filled auxiliary variable and the target variable.

[0011] Preferably, extract the temporal correlation of the data in the auxiliary variable through Bi-LSTM.

[0012] Preferably, generate the first predicted value according to the temporal correlation of the existing data in the auxiliary variable, including:

[0013] Forwardly and gradually diffuse and add noise according to the distribution of the existing data;

[0014] Based on the diffusion-added noise data, adopt random-span sampling and reverse denoising considering the temporal correlation to generate the first predicted value.

[0015] Preferably, the data distribution at the nth step of diffusion is:

[0016]

[0017] In the formula, L represents the length of the existing data, t represents the data at the tth moment, and α is defined t = 1 - β t , β t is the noise added at the tth moment. is the variance, and I is the identity matrix.

[0018] Preferably, the steps of adopting random-span sampling and reverse denoising considering the temporal correlation to generate the first predicted value include:

[0019] Fit the noise considering the temporal correlation,

[0020] Remove the fitted noise from the current data and sample with a random span s to obtain the data distribution at the (n - s)th step; and so on, to obtain the overall data distribution after random-span sampling of the diffusion-added noise data;

[0021] Input the overall data distribution into the linear layer to obtain the first predicted value.

[0022] Preferably, the noise-fitted data is:

[0023]

[0024] In the formula, ε and ε θ are the original noise and the fitted noise respectively, n, H t where n is the number of steps and Ht is the temporal correlation; used to enable the model to generate missing data with time orientation.

[0025] Preferably, the formula for inputting the overall data distribution into the linear layer is expressed as:

[0026] x t ′ +1 =Linear(X t ′ +1 )+bias

[0027] In the formula, X t ′ +1 represents the overall data distribution, and bias represents the deviation rate.

[0028] Preferably, based on the spatial dependence relationship between the filled auxiliary variable and the target variable, the target variable is predicted; including:

[0029] Construct a relationship topology graph based on the auxiliary variable and the target variable, and construct an adjacency matrix based on the correlation degree between different variables;

[0030] Use the symmetric normalized Laplace matrix to perform eigen-decomposition on the adjacency matrix to obtain an eigenvector matrix;

[0031] Predict the target variable based on the eigenvector matrix through graph convolution.

[0032] Preferably, the process of performing graph convolution operation on the eigenvector matrix to obtain the second predicted value includes:

[0033] Perform Fourier transforms on the convolution kernel h and the eigenvector V of graph convolution respectively, and then multiply them to obtain a new feature representation X t , and the formula is:

[0034]

[0035] U represents the Fourier transform of the graph, and U t h, U t V respectively represent the results after performing Fourier transforms on the convolution kernel h and V;

[0036] Perform graph convolution operation on the feature X t to obtain the second predicted value; the formula representation is:

[0037]

[0038] In the formula, y t ′ +1 represents the second predicted value, X t is the auxiliary variable input at the t-th moment, A represents the adjacency matrix, W t represents the GCN network parameter, and σ is the activation function.

[0039] Preferably, the adjacency matrix is constructed according to the following formula based on the correlation degree between variables;

[0040]

[0041] In the formula, e ij represents the correlation degree between variables and is calculated by KL divergence; μ represents the correlation threshold, and a ij ∈A represents an element in the adjacency matrix, and i and j respectively represent the types of auxiliary variables.

[0042] Preferably, when the losses of generating the first predicted value and predicting the target variable are respectively reduced to half of their respective initial losses, the total loss of the prediction process is introduced;

[0043] The loss function for generating the first predicted value is:

[0044]

[0045] The loss function for predicting the target variable is:

[0046]

[0047] In the formula, loss noise represents the noise fitting error, and loss FGCDM represents the total loss of the prediction process, x′ t+1 is the first predicted value, x t+1 represents the target value corresponding to the first predicted value, y′ t+1 represents the predicted value of the target variable, and y t+1 represents the target value corresponding to the predicted value of the target variable.

[0048] Preferably, the total loss loss FGCDM of the prediction process is:

[0049]

[0050] Preferably, the Isolation Forest algorithm is first used to detect the data, determine the data missing positions and the amount of missing data, and fill in the data according to the missing positions and the amount of missing data.

[0051] Through the above technical solutions, the present invention discloses a method for filling missing data for industrial soft sensing, which uses an intelligent algorithm and a model to predict and fill in missing values by using the existing and complete data set; compared with the prior art, the present application has the following technical effects:

[0052] (1) FCDM not only has high-precision data generation performance, but also has a fast calculation process, which can effectively reduce the model calculation complexity. At the same time, it also shows good prediction performance in the soft sensing model based on GCN;

[0053] (2) The mild loss feedback strategy proposed by the present invention enables the soft measurement model of the target variable to have high precision, and at the same time, achieves the goal of more reasonable prediction;

[0054] (3) The present invention can ensure the integrity and accuracy of data, thereby providing solid data support for the optimization of the production process and the improvement of product quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the provided drawings.

[0056] Figure 1 It is a flowchart of the method for filling missing data for industrial soft measurement of the present invention;

[0057] Figure 2 It is a data processing flowchart of the fast conditional diffusion model (FCDM) of the present invention;

[0058] Figure 3 It is a flowchart of extracting time-related information by Bi-LSTM of the present invention;

[0059] Figure 4 It is a schematic diagram of the data diffusion process in the fast conditional diffusion model of the present invention;

[0060] Figure 5 It is a structure diagram of the one-dimensional convolutional neural network of the present invention;

[0061] Figure 6 It is a data processing flowchart of the graph convolution (GCN) of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0063] The embodiment of the present invention discloses a method for filling missing data for industrial soft measurement, referring to Figure 1 , which mainly includes two parts, namely

[0064] Determine the auxiliary variable of the target variable, generate the first prediction value according to the time correlation of the existing data in the auxiliary variable, and use the first prediction value to fill the missing data in the auxiliary variable;

[0065] Predict the target variable based on the spatial dependence relationship between the filled auxiliary variable and the target variable.

[0066] In an exemplary embodiment,

[0067] The first part, refer to Figure 2 ;

[0068] In this embodiment, Bi-LSTM is used to extract the time correlation of the existing data in the auxiliary variable, and the first prediction value is generated based on the Fast Conditional Diffusion Model (FCDM);

[0069] Specifically, the structure of Bi-LSTM is as Figure 3 shown, including an input layer, a forward layer, a backward layer and an output layer. The process of extracting the time correlation according to the existing data is prior art and will not be repeated here. It should be noted that in this application, the existing data is dynamically obtained through a moving window.

[0070] After obtaining the time correlation H t , further input it together with the data of the moving window into the FCDM to generate the first prediction value; assuming the length of the moving window is L, the local data within the window is X t-L:t ={x t-L ,x t-L+1 ,x t-L+2 ,L,x t-1 ,x t};

[0071] In this application, through the training and parameter optimization of the Bi-LSTM network, the latent variable H t at time t contains the historical information of the local data, and finally the time dependence relationship at time t + 1 is obtained. By obtaining the latent variable H t , it provides guiding information for the FCDM to achieve the task of generating missing data with time orientation.

[0072] Refer to Figure 4 , set the total number of diffusion steps of the FCDM to N, n is the current diffusion step, and the data processing process is as follows:

[0073] First, gradually diffuse and add noise forward according to the distribution of the existing data in the auxiliary variable; among them, when predicting and filling the time correlation of the missing data at time t + 1, the data distribution at the nth step of diffusion can be calculated from the initial data distribution within the moving window, and the calculation formula is:

[0074]

[0075] In the formula, L represents the length of the existing data, t represents the data at the t-th moment, and α is defined t = 1 - β t , where β t is the noise added at the t-th moment. is the variance, and I is the identity matrix.

[0076] Secondly, based on the forward diffusion noisy data, random-span sampling is adopted, and the first predicted value is reversely generated considering the time correlation; in this application, the random span means that the step size is a random value s and is not fixed, so that the network samples at the n - s diffusion step, which can effectively reduce the computational amount and training time in the reverse process, accelerate the model training speed and reduce the computational complexity, thereby realizing fast missing data generation.

[0077] In the training stage of the reverse process, time-related information H at the (t + 1)-th moment is introduced into the FCDM t as additional information, enabling the model to perform time-oriented missing data generation, including:

[0078] Considering the time correlation to fit the noise. In this embodiment, a one-dimensional convolutional neural network is used to fit the noise, and its structure is as Figure 5 shown, including an input layer, a convolutional layer, a pooling layer, and an output layer; and the fitted noise data is:

[0079]

[0080] In the formula, ε and ε θ are the original noise and the fitted noise respectively. n, H t where n is the number of steps and Ht is the time correlation; enabling the model to perform time-oriented missing data generation.

[0081] Then, the fitted noise is removed from the current data , and sampling is performed with a random span s to obtain the data distribution at the n - s step, that is And so on, the overall data distribution after random-span sampling of the diffusion noisy data is obtained;

[0082] Finally, the overall data distribution is input into the linear layer to obtain the first predicted value, that is

[0083] x t ′ +1 = Linear(X t ′ +1 ) + bias

[0084] In the formula, X t ′ +1It represents the overall data distribution, and bias represents the deviation rate.

[0085] In this embodiment, when the moving window is on the existing data sequence, FCDM uses the actual next moment data as the label and optimizes the parameters, and the obtained data is the predicted data of the model under the guidance of the time-dependent information of the latent variable. When the moving window reaches the missing area, the trained FCDM is used to generate the time correlation of the missing data. Subsequently, the prediction result is used to fill the missing value.

[0086] The second part,

[0087] Based on the spatial dependence relationship between the filled auxiliary variable and the target variable, the target variable is predicted; in this embodiment, as Figure 6 shown, it includes:

[0088] (1) Construct a relationship topology graph based on the auxiliary variable and the target variable, and construct an adjacency matrix based on the correlation degree between different variables; that is, use the data matrix F composed of the auxiliary variables in the window and the target variable data Y = {y t-L , y t-L+1 , L, y t} to construct the adjacency matrix A and obtain the spatial dependence relationship between nodes (variables).

[0089] In this application, the auxiliary variable sensors X = {X1, X2, L, X k} are regarded as the nodes of the graph, and the spatial coupling relationship between the sensors is regarded as the edge of the graph; and the KL divergence is used to calculate the correlation degree e ij between variables, and the adjacency matrix is constructed according to the following formula based on the correlation degree between the auxiliary variables;

[0090]

[0091] In the formula, e ij represents the correlation degree between the auxiliary variables, which is calculated by the KL divergence; μ represents the correlation threshold, and a ij ∈ A represents the element in the adjacency matrix, and i and j respectively represent the types of the auxiliary variables.

[0092] When e ij > μ, it means that there is a strong correlation between the i-th auxiliary variable and the j-th auxiliary variable and there is an edge connection. When e ij < μ, it means that the correlation is weak and there is no edge connection.

[0093] (2) Use the symmetric normalized Laplace matrix to perform eigenvalue decomposition on the adjacency matrix to obtain the eigenvector matrix;

[0094] The decomposition process is:

[0095]

[0096] Where: L represents the Laplace matrix, I is the identity matrix, D is the degree matrix, is the eigenvector matrix.

[0097] (3) Based on the eigenvector matrix, perform graph convolution to predict the target variable; the process includes:

[0098] Perform Fourier transforms on the convolution kernel h and the eigenvector V of the graph convolution respectively, and then multiply them to obtain a new feature representation X t , the formula is:

[0099]

[0100] U represents the Fourier transform of the graph, U t h, U t V respectively represent the results after performing Fourier transforms on the convolution kernel h and V;

[0101] Perform graph convolution operation on the feature X t to obtain the predicted value of the target variable; the formula representation is:

[0102]

[0103] In the formula, y t ′ +1 represents the second predicted value, X t is the input of the auxiliary variable at the t-th moment, A represents the adjacency matrix, W t represents the GCN network parameter, and σ is the activation function.

[0104] In this application, through Fourier transform, the convolution operation can be converted into a dot product operation, thereby simplifying the calculation process and improving the calculation efficiency. At the same time, the Fourier transform also helps to better understand the structure and features of the graph, thereby improving the performance of the model.

[0105] This application can achieve the GCN soft measurement space-related prediction of the target variable y t ′ +1 by learning the graph structure and optimizing the network parameters.

[0106] Through the first part and the second part, a missing data prediction model for industrial soft measurement can be obtained, denoted as FGCDM.

[0107] In a preferred embodiment, a gentle loss feedback mechanism of the FCDM and GCN modules is constructed to improve the accuracy of customized missing data generation on the basis of downstream soft sensing tasks. Specifically, the total loss in the FGCDM prediction process is introduced into the GCN and FCDM modules respectively, so that the overall model can achieve relatively gentle data generation and soft sensing modeling. That is, the FCDM receives the feedback from the downstream GCN module and fine-tunes its own parameters to realize data generation for specific soft sensing tasks. The GCN receives the information from the upstream FCDM and can realize soft sensing prediction related to time and space.

[0108] Among them, the predicted value of FCDM is x t ′ +1 , and the prediction error

[0109] The predicted value of GCN is y t ′ +1 , and the prediction error

[0110] Therefore, the loss of FGCDM is expressed as loss FGCDM , as follows:

[0111]

[0112] When loss FGCDM is introduced into the GCN and FCDM respectively to participate in and guide the module optimization process, the loss improvement of the two modules is as follows:

[0113]

[0114]

[0115] In the formula, loss noise represents the noise fitting error, loss FGCDM represents the total loss in the prediction process, x′ t+1 is the first predicted value, x t+1 represents the target value corresponding to the first predicted value, y′ t+1 represents the predicted value of the target variable, and y t+1 represents the target value corresponding to the predicted value of the target variable.

[0116] The improved loss of FCDM consists of the noise fitting error loss noise , the prediction deviation and the prediction error loss FGCDM of GCN. The loss of GCN consists of the prediction error and the prediction error loss FGCDM of FCDM.

[0117] By introducing the downstream GCN prediction loss into the upstream FCDM, FCDM can achieve the goal of customized missing data generation based on downstream tasks. Introducing the time-related prediction loss of FCDM into GCN can also enable GCN to consider the spatio-temporal dependence characteristics of data, achieving the purpose of soft sensor prediction based on spatio-temporal correlation.

[0118] To further optimize the above technical solution, when the losses of FCDM and GCN are reduced to half of their respective initial loss values, loss FGCDM ;

[0119] In an actual industrial process, sensors are independent detection individuals, and their detection results objectively exist and are not affected by the detection results of other sensors. If the prediction of the target variable overly relies on the prediction results of other variables, it does not conform to the actual industrial process. Therefore, try to avoid the prediction results of downstream applications having a negative impact on the optimization of the upstream model.

[0120] For example, when and it indicates that the generated data of FCDM has a small deviation from the original data, while the prediction error of GCN is large. If the GCN prediction error is introduced into FCDM at this time and used to guide its optimization process, it will cause a greater deviation in the generated data and reduce the filling accuracy of missing data.

[0121] In the initial training stage, two modules are set for separate optimization, rather than directly adding another loss to the model. Assume that the network starts training at time t0, and after time t n the generation loss of FCDM is that is, it is reduced to half of the initial loss . Similarly, the GCN loss is also reduced to half of the initial loss . When the above conditions are satisfied simultaneously, loss FGCDM is introduced into FCDM and GCN respectively to avoid introducing large errors into the GCN and FCDM modules, thereby having a negative impact on module optimization and further improving the soft sensor prediction accuracy.

[0122] In another embodiment, the Isolation Forest Algorithm (IIF) is preferably used to detect data to determine the data missing positions and the amount of missing data, and data filling is performed for the missing positions and the amount of missing data.

[0123] The data filling method of the present application is verified through examples below.

[0124] All the data in this invention come from the sensor monitoring data of a nickel smelting plant in China and the sensor monitoring data of a gas turbine in a power plant in the northwestern region of Turkey in the UCI public library. By analyzing the nickel flash smelting process, four auxiliary variables with the highest correlation with the furnace temperature are selected, namely concentrate humidity (CH), concentrate particle size (CPS), sulfur dioxide content (SDC) of sulfur-containing flue gas, and water content (WC) of sulfur-containing flue gas, for the soft measurement modeling of the furnace temperature (T). Four variables, namely ambient temperature (AT), atmospheric pressure (AP), relative humidity (RH), and exhaust pressure (V), are selected as auxiliary variables for soft measurement to model the full-load output electric power (PE) of the equipment.

[0125] The variables in different datasets are shown in Table 1;

[0126] Table 1

[0127]

[0128]

[0129] The missing area information in different datasets is shown in Table 2;

[0130] Table 2

[0131]

[0132] The time consumption of different comparison methods on different datasets is shown in Table 3;

[0133] Table 3

[0134]

[0135] From the calculation times of the four different methods recorded in the two datasets,

[0136] FGCDM and its three extended methods all use a moving window for iterative generation of missing data. In FGCDM-2, the acceleration structure is cancelled, that is, this method uses an ordinary DDPM for data generation, and a structure with a step size span of 1 is adopted in the reverse process. It can be seen that FGCDM-2 has the longest calculation time consumption and the highest calculation complexity.

[0137] While FGCDM, FGCDM-1, and FGCDM-3 all adopt the acceleration structure proposed in this invention, that is, a sampling strategy with a random step size span is adopted in the reverse process, which takes less time than FGCDM-2. Therefore, by recording the running times of each model, it indirectly shows that the FGCDM method proposed in this invention can effectively reduce the model calculation complexity and reduce the calculation time consumption.

[0138] The MSE and R of the missing data generated under different methods 2As shown in Table 4;

[0139] Table 4

[0140]

[0141] According to the MSE and R of the missing data generated under different methods and the original data 2 Error. It can be seen that even under different datasets, different missing positions, and different amounts of missing data, the three models FGCDM-1, FGCDM-2, and FGCDM have lower MSE and R of the generated missing data than the other six models. 2 The error is lower.

[0142] From this result, it can be shown that compared with the method that regards missing data generation and soft sensor prediction as two independent tasks, the missing data with downstream task customization has lower bias and higher generation accuracy. Therefore, the data generation strategy for specific requirements proposed in the present invention for downstream tasks in actual industrial processes is reasonable, effective, and superior.

[0143] In addition, it can be seen from Table 4 that FGCDM and FGCDM-2 have lower data generation errors and higher generation accuracies than FGCDM-1. Therefore, the mild feedback strategy proposed in the present invention is more reasonable and superior.

[0144] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is the difference from other embodiments. The same and similar parts among the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0145] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for filling missing data for industrial soft sensing, characterized in that determine the auxiliary variables of the target variable, generate the first prediction value according to the time correlation of the existing data in the auxiliary variables, and use the first prediction value to fill the missing data in the auxiliary variables; including: consider the time correlation to fit the noise, From the current data Remove the fitting noise, sample with a random span s to obtain the data distribution at the n - s step; and so on, to obtain the overall data distribution after random span sampling of the diffusion - noise - added data. input the overall data distribution into the linear layer to obtain the first prediction value; predict the target variable based on the spatial dependence relationship between the filled auxiliary variable and the target variable; when the losses of generating the first prediction value and predicting the target variable are respectively reduced to half of their respective initial losses, introduce the total loss of the prediction process; In the initial training stage, two processes are set for separate optimization instead of directly adding the total loss of the prediction process. Assume that the network starts training at time t0, and after time t n the loss generated by FCDM is which is reduced to half of the initial loss Similarly, the loss of GCN is also reduced to half of the initial loss When the above conditions are met simultaneously, loss FGCDM is introduced into FCDM and GCN respectively to avoid introducing large errors into the GCN and FCDM modules, thereby having a negative impact on the module optimization and further improving the soft-sensor prediction accuracy.

2. The missing data filling method for industrial soft measurement according to claim 1, characterized in that extract the time correlation of the data in the auxiliary variable through Bi-LSTM.

3. A method for filling missing data for industrial soft measurement according to claim 1, characterized in that Generate the first prediction value according to the time correlation of the existing data in the auxiliary variable, including: gradually diffuse and add noise forward according to the distribution of the existing data; Based on the diffusion-added noise data, adopt random span sampling and consider time correlation to denoise backward to generate the first prediction value.

4. A method for filling missing data for industrial soft measurement according to claim 3, characterized in that The data distribution at the nth step of diffusion is: where L represents the length of the existing data, t represents the data at the t-th moment, and α is defined as t = 1 - β t , β t is the noise added at the t-th moment, is the variance, and I is the identity matrix.

5. A method for filling missing data for industrial soft sensors according to claim 1, characterized in that, Predict the target variable based on the spatial dependence relationship between the filled auxiliary variable and the target variable; including: construct a relationship topology graph based on the auxiliary variable and the target variable, and construct an adjacency matrix based on the correlation degree between different variables; perform eigenvalue decomposition on the adjacency matrix using the symmetric normalized Laplace matrix to obtain the eigenvector matrix; predict the target variable based on the eigenvector matrix using graph convolution.

6. A method for filling missing data for industrial soft sensing according to claim 5, characterized in that Construct the adjacency matrix according to the correlation degree between variables according to the following formula; where, e ij represents the correlation degree between variables, which is calculated by KL divergence; μ represents the correlation threshold, a ij ∈A represents an element in the adjacency matrix, and i and j respectively represent the types of auxiliary variables.

7. The method for filling missing data for industrial soft sensing according to claim 1, characterized in that The loss function for generating the first prediction value is: The loss function for predicting the target variable is: where loss noise represents the noise fitting error, and loss FGCDM represents the total loss of the prediction process, x t ′ +1 is the first predicted value, and x t+1 represents the target value corresponding to the first predicted value, y t ′ +1 represents the predicted value of the target variable, and y t+1 represents the target value corresponding to the predicted value of the target variable.

8. A method for filling missing data for industrial soft measurement according to claim 7, characterized in that The total loss of the prediction process FGCDM is as follows:

9. A method for filling missing data for industrial soft measurement according to claim 1, characterized in that, Preferably, use the isolation forest algorithm to detect the data, determine the data missing position and the amount of missing data, and fill the data for the missing position and the amount of missing data.

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