Industrial soft measurement method and system based on nonlinear sparse moment estimation and correlation vector regression

Abstract

The invention discloses an industrial soft measurement method and system based on non-linear sparse moment estimation (NS-GMM) and relevance vector regression (RVR), and aims to solve the problem of key quality variable measurement caused by various variables, excessive redundant variables and non-linear relationship in industrial production. Compared with the traditional generalized moment estimation (GMM) which can only process a linear problem, the GMM model can effectively process a non-linear relationship by introducing a kernel skill, solves a pollution effect in variable selection through a regularization item, and screens out an auxiliary variable which has a remarkable influence on a target variable. Then, variables are selected to be used for training an RVR model, and regression model parameters are accurately estimated through Bayesian inference and sparsity prior; according to the method, NS-GMM and RVR are integrated, a solution which is superior to a traditional technology in the aspects of variable selection, prediction performance and efficiency is provided, and the method is suitable for various industrial application scenes where key quality variables need to be accurately and rapidly predicted.

Description

Technical Field

[0001] The invention relates to the field of industrial process soft measurement, in particular to a method for optimizing industrial process soft measurement by combining a variable selection method based on nonlinear sparse moment estimation with a correlation vector regression model. Background Art

[0002] In the process of industrial process control and optimization, soft measurement is an important technical means. Through computer technology, various parameters and variables in the industrial production process are monitored and predicted in real time to achieve process control and optimization. Soft measurement technology is widely used in chemical, petrochemical, food, pharmaceutical, energy and other industries, which can significantly improve production efficiency, product quality and factory safety. Especially in industrial processes, the application of soft measurement technology is particularly important.

[0003] Industrial process soft sensing is a data-driven modeling method. Traditionally, multiple linear regression models are used for modeling. This method includes multiple input variables and one output variable. It monitors and predicts industrial processes by collecting various measurement data in the process. However, due to the large number of variables in industrial processes, variable selection is a crucial step in the process of establishing soft sensing models. Selecting an optimal set of variables can improve the accuracy and robustness of modeling and reduce the complexity and cost of the model.

[0004] Traditional variable selection methods are usually based on statistical methods, such as stepwise regression analysis, principal component analysis, and Pearson coefficient. Although these methods can solve the variable selection problem to a certain extent, they have limitations in dealing with nonlinear relationships between variables and are prone to overfitting problems. In addition, when dealing with a large number of variables, the amount of calculation is large and the efficiency is low. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes an industrial soft measurement method based on nonlinear sparse moment estimation (NS-GMM) and related vector regression (RVR). By integrating the kernel technique into the GMM model, the nonlinear relationship between variables is effectively processed, and the applicability and accuracy of the model are improved. And by introducing the regularization term, the "contamination effect" in variable selection is solved, which helps to screen out auxiliary variables that have a significant impact on the target variable. Subsequently, the selected variables are used to train the related vector regression model, and the regression model parameters are accurately estimated by combining Bayesian inference and sparsity priors. This method achieves the best industrial process soft measurement by comprehensively using NS-GMM and RVR. The method includes the following steps:

[0006] S1, obtain relevant data in the industrial process, including multiple features and target variables measured by sensors in the industrial process that may affect the target variable and the target variable as well as several sample data collected corresponding to each feature. The set of features that affect the target variable is recorded as Where N represents the number of samples and M represents the number of variable features;

[0007] S2, standardize the sample data corresponding to each variable in X_o to obtain the data set X, and divide the sample data corresponding to the features in the data set X into a training set and a test set;

[0008] S3, for the data set X, the nonlinear sparse moment estimation model NS-GMM is used for variable selection. By defining the nonlinear moment condition and introducing the regularization constraint, the variable selection index is constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test;

[0009] S4, using X_new to train the related vector regression RVR model to obtain the trained RVR model RVR_model;

[0010] S5, use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable value.

[0011] Furthermore, the specific implementation of the standardization process in step S2 is as follows:

[0012] Standardization processing includes normalizing the standard deviation of the sample data corresponding to each feature in the data set. Standard deviation normalization converts the sample data corresponding to the feature in the data set into a data distribution centered on 0. The specific formula is as follows:

[0013] x=(x_o-min(x_o)) / (max(x_o)-min(x_o))

[0014] Among them, x_o is the original value of the data sample corresponding to a numerical feature in the data set, x is the value of the data sample corresponding to the feature after the standard deviation is normalized, min(x_o) is the minimum value in the data sample corresponding to the feature, and max(x_o) is the maximum value in the data sample corresponding to the feature, and the standardized data set X is obtained.

[0015] Furthermore, the specific implementation of step S3 is as follows:

[0016] (3.1) The normalized data is mapped to a high-dimensional space through the kernel function K, where K(X) represents the high-dimensional space mapping of the normalized data set under the kernel function, which can be expressed as follows:

[0017]

[0018] Where y is the target variable, X is the input auxiliary variable, that is, the standardized data set. is the parameter vector, and u is the error term. This transformation ensures that the k-th moment condition of the error term u still holds in the transformed space, thereby more accurately simulating the true distribution of the data.

[0019] According to the defined moment condition, the nonlinear moment condition is expressed as:

[0020]

[0021] Where E represents the expected value, represents the model prediction value after the kernel function conversion, and g represents a prediction function of the model. This condition ensures that the error term The k-th moment of is 0 under the condition of given X, thus maintaining the nonlinear relationship of data in high-dimensional space;

[0022] (3.2) According to the defined moment condition, the sample moment condition is constructed using sample data. The sample moment condition is expressed as:

[0023]

[0024] Where n represents the number of samples in the data set X;

[0025] (3.3) Construct the objective function. NS-GMM has the following advantages in the objective function: L1 and L2 regularization terms are added, and the specific expression is:

[0026]

[0027] Where W represents the weight matrix, λ and β are regularization parameters, ||||1 represents the L1 norm, ||||2 represents the L2 norm, and θ is the model parameter in NS-GMM;

[0028] (3.4) Similar to the traditional generalized moment estimation method, the objective function with regularization constraints is minimized through optimization algorithm Get parameter estimates

[0029]

[0030] It represents the relationship between different variables in X and y. The absolute value of is used as an indicator to evaluate the importance of the variable. The larger the value, the greater the influence of the variable on the model. Thus, a group of key variables X_new that have a significant impact on the target variable are selected.

[0031] Furthermore, the kernel function is a polynomial kernel, a radial basis kernel, or a Gaussian kernel.

[0032] Furthermore, the specific implementation of step S4 is as follows:

[0033] (4.1) The RVR model is expressed as:

[0034] y=f(X_new,w)+∈

[0035] Among them, y is the target variable, X_new is the set of input variables, w is the model parameter in RVR, f(X_new,w) represents the regression function determined by the kernel function, and ∈ is the noise term;

[0036] (4.2) By combining the prior distribution and observed data, the posterior distribution of the model parameters is estimated through the Bayesian inference method:

[0037] p(w|y,X_new)∝p(y|X_new,w)p(w)

[0038] Here, p(y|X_new,w) is the likelihood function of the target variable y under X_new and model parameters w; p(w) is the prior distribution of model parameters w, and p(w|y,X_new) is the posterior distribution of model parameters w. ∝ means proportional or proportional to;

[0039] (4.3) By maximizing the posterior distribution and optimizing the model parameters, we can obtain a regression model RVR_model with strong sparsity:

[0040]

[0041] in are the optimal model parameters.

[0042] Furthermore, in step S5, the trained model RVR_model is used to predict X_new_test to obtain the corresponding target variable. The specific implementation method is:

[0043]

[0044] Among them, f represents the trained model RVR_model, ∈ is the noise term.

[0045] Furthermore, the method further includes step S6 of evaluating the generalization ability of the trained RVR model, specifically evaluating the performance of the RVR model using mean square error (MSE) and determination coefficient.

[0046] Furthermore, the formula for the mean square error MSE is:

[0047]

[0048] Where y i is the actual value, y ipre is the predicted value, n represents the number of samples, Represents the mean value of the target variable.

[0049] Furthermore, the coefficient of determination R 2 The formula is:

[0050]

[0051] Where y i is the actual value, y ipre is the predicted value, n represents the number of samples, Represents the mean value of the target variable.

[0052] The present invention also provides an industrial soft measurement system based on nonlinear sparse moment estimation and correlation vector regression, comprising the following modules:

[0053] The data acquisition module is used to obtain relevant data in the industrial process, including multiple features and target variables measured by sensors in the industrial process that may affect the target variable and the target variable, as well as several sample data collected corresponding to each feature. The set of features that affect the target variable is recorded as Where N represents the number of samples and M represents the number of variable features;

[0054] The data preprocessing module is used to standardize the sample data corresponding to each variable in X_o to obtain the data set X, and divide the sample data corresponding to the features in the data set X into a training set and a test set;

[0055] The variable selection module is used to select variables for the data set X using the nonlinear sparse moment estimation model NS-GMM. By defining nonlinear moment conditions and introducing regularization constraints, variable selection indicators are constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test.

[0056] The model training module is used to train the relevant vector regression RVR model using X_new to obtain the trained RVR model RVR_model;

[0057] The prediction execution module is used to use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable value.

[0058] Compared with the prior art, the above technical solution conceived by the present invention can achieve the following beneficial effects:

[0059] (1) This paper proposes a new variable selection method, namely NS-GMM. This method effectively solves the limitation of the traditional GMM model mainly for linear problems by integrating the kernel technique into the GMM variable model, significantly enhances the ability of the soft sensor model to handle nonlinear relationships, and thus improves the adaptability and accuracy of the model.

[0060] (2) The present invention introduces a regularization term in the variable selection process to improve the accuracy of variable selection and reduce the "contamination effect" in the selection process. This innovation can more accurately screen out auxiliary variables that have an important impact on the predicted target variable and optimize the performance and stability of the soft sensor model.

[0061] (3) The present invention combines the variable selection of NS-GMM with the modeling capability of RVR, further improving the accuracy and efficiency of soft sensing. The method performs well in numerical simulation and actual production process applications, demonstrating its practicality and effectiveness in complex industrial processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of an industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression provided by an embodiment of the present invention;

[0063] Figure 2 is an example diagram of a penicillin fermentation process provided by an embodiment of the present invention;

[0064] Figure 3 Schematic diagram of contributions of different variables provided by an embodiment of the present invention;

[0065] Figure 4 A schematic diagram showing a comparison between a predicted value and an actual value provided by an embodiment of the present invention; DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0068] In order to solve the problem of difficulty in measuring key quality variables due to numerous variables, too many redundant variables and nonlinear relationships between variables in industrial production processes, the present invention proposes an industrial soft measurement method based on nonlinear sparse moment estimation (NS-GMM) and related vector regression (RVR). This method effectively handles the nonlinear relationship between variables by integrating kernel techniques into the generalized moment estimation (GMM) model, significantly improving the applicability and prediction accuracy of the model. In addition, in order to solve the "contamination effect" in variable selection, the present invention introduces a regularization term into the model to screen out auxiliary variables that have a significant impact on the target variable. The selected variables are then used to train the related vector regression model, which combines Bayesian inference and sparsity priors to accurately estimate the regression model parameters. By comprehensively using NS-GMM and RVR, the present invention is superior to traditional methods in terms of variable selection, prediction performance and computational efficiency, and is suitable for various industrial application scenarios that require accurate and rapid prediction of key quality variables. Figure 1 The method flow of the present invention is demonstrated, and the following are specific embodiments.

[0069] (1) Data processing and feature selection

[0070] (1.1) Obtain relevant data in the industrial process, including multiple variable features and target variables that affect target measurement values ​​measured by sensors in the industrial process, and several pieces of sample data collected corresponding to each feature, specifically:

[0071] Obtain industrial process data, and the features that affect the target variable constitute the original data set Where N represents the number of samples and M represents the number of variable features;

[0072] (1.2) Standardize the sample data corresponding to each feature in the data set X_o to obtain the standardized data set X, and divide the sample data in the data set X into a training set and a test set. Specifically:

[0073] (1.2.1) The data standardization calculation method is:

[0074] Standardization processing includes normalizing the standard deviation of each data in the data set. Similar to mean normalization, standard deviation normalization converts the data samples corresponding to the features in the data set into a data distribution centered on 0, but it uses a standardized method. The specific formula is as follows:

[0075] x=(x_o-min(x_o)) / (max(x_o)-min(x_o))

[0076] Among them, x_o is the original value of the data sample corresponding to a numerical feature in the data set, x is the value of the data sample corresponding to the feature after the standard deviation is normalized, min(x_o) is the minimum value in the data sample corresponding to the feature, and max(x_o) is the maximum value in the data sample corresponding to the feature, and the standardized data set X is obtained.

[0077] (1.2.2) Split the standardized data set X into a training set and a test set at a ratio of 7 to 3.

[0078] (1.3) Nonlinear sparse moment estimation model (NS-GMM) is used for variable selection. By defining nonlinear moment conditions and introducing regularization constraints, variable selection indicators are constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test; specifically:

[0079] (1.3.1) Through the kernel function K, such as polynomial kernel, radial basis kernel, Gaussian kernel, etc., the training set of the standardized data X is mapped to a high-dimensional space to enhance the model's ability to model nonlinear relationships, where K(X) represents the high-dimensional space mapping of the standardized data set X under the action of the kernel function. After the kernel function is introduced, the model function is:

[0080]

[0081] Where y is the target variable, X is the input auxiliary variable, that is, the standardized data set. is the parameter vector, and u is the error term. This transformation ensures the k-th moment condition of the error term u (E[u k |X] = 0 for all k ≥ 1, E represents the expectation) still holds in the transformed space, thereby more accurately simulating the true distribution of the data.

[0082] According to the defined moment conditions, the nonlinear moment conditions can be expressed as:

[0083]

[0084] in, represents the model prediction value after the kernel function conversion, and g represents a prediction function of the model. This condition ensures that the error term The k-th moment of is 0 given X, thus maintaining the nonlinear relationship of the data in high-dimensional space.

[0085] (1.3.2) According to the defined moment condition, the sample moment condition is constructed using the sample data. The sample moment condition can be expressed as:

[0086]

[0087] Here, n represents the number of samples in the dataset X.

[0088] (1.3.3) Construct the objective function. In order to increase the generalization ability of the model and reduce the risk of overfitting, NS-GMM adds L1 and L2 regularization terms to the objective function. The specific expression is:

[0089]

[0090] Where W represents the weight matrix, λ and β are regularization parameters, ||||1 represents the L1 norm, ||||2 represents the L2 norm, and θ is the model parameter in NS-GMM. L1 regularization (Lasso regularization) tends to produce some effects with zero weights. L2 regularization (Ridge) helps reduce model complexity and ensure model stability by uniformly reducing the weights of all parameters.

[0091] (1.3.4) Similar to the traditional generalized moment estimation method, the objective function with regularization constraints is minimized through optimization algorithm Get parameter estimates

[0092]

[0093] It represents the relationship between different variables in X and y. The absolute value of is used as an indicator to evaluate the importance of the variable. The larger the value, the greater the impact of the variable on the model.

[0094] (1.4) Use X_new to train the relevant vector regression (RVR) model, specifically:

[0095] (1.4.1) The RVR model can be expressed as:

[0096] y=f(X_new,w)+∈

[0097] Among them, y is the target variable, X_new is the set of input variables, w is the model parameter, f(X_new,w) represents the regression function determined by the kernel function, and ∈ is the noise term.

[0098] (1.4.2) By combining the prior distribution and observed data, the posterior distribution of the model parameters is estimated using the Bayesian inference method:

[0099] p(w|y,X_new)∝p(y|X_new,w)p(w)

[0100] Here, p(y|X_new,w) is the likelihood function of the target variable y given X_new and model parameters w; p(w) is the prior distribution of model parameters w, and p(w|y,X_new) is the posterior distribution of model parameters w. "∝" means "proportional" or "directly proportional to". Specifically, this means that in the formula, the posterior distribution p(w|y,X_new) is proportional to the expression on the right p(y|X_new,w)p(w), and "∝" is used to indicate that the posterior distribution is proportional to the product of these two terms.

[0101] (1.4.3) By maximizing the posterior distribution and optimizing the model parameters, we can obtain a regression model RVR_model with strong sparsity:

[0102]

[0103] in are the optimal model parameters.

[0104] (1.5) Use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable. Specifically:

[0105]

[0106] Among them, f represents the trained RVR_model model.

[0107] (1.6) Evaluate the generalization ability of the trained RVR_model. Specifically:

[0108] The performance of the RVR_model model is evaluated using evaluation indicators such as mean square error (MSE) and determination coefficient.

[0109] (1.6.1)The mean square error (MSE) formula is:

[0110]

[0111] (1.6.2) Coefficient of determination R 2 The formula is:

[0112]

[0113] Where y i is the actual value, y ipre is the model prediction value, n represents the number of samples, Represents the mean value of the target variable.

[0114] The embodiment of the present invention uses a variable selection method based on nonlinear sparse moment estimation to quickly and accurately select the best variable combination, which can effectively improve the accuracy and stability of the soft sensor model. By using RVR for modeling, it can better adapt to the nonlinear relationship in the soft measurement of industrial processes and improve the accuracy and performance of the soft sensor model.

[0115] The beneficial effects that can be achieved by the present invention are further explained below in conjunction with specific application scenarios.

[0116] In the following application scenario, the above industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression is verified through the penicillin fermentation process.

[0117] The mechanism of penicillin fermentation is relatively complex, involving multiple biological and chemical reactions. For the penicillin fermentation process, Penicillium needs to be provided with appropriate nutrients and growth conditions in the fermentation tank, such as carbon source, nitrogen source, phosphorus source, etc., in order to grow and produce penicillin. During the fermentation process, factors such as pH value, temperature and oxygen content will also affect the production of penicillin. Figure 2 shown.

[0118] The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression can establish an accurate model to predict the yield of penicillin and the state of the production process by monitoring and analyzing these variables. In the present invention, penicillin concentration is used as the target variable, and 16 variables such as bacterial concentration, carbon dioxide concentration, pH value, etc. are used as auxiliary feature variables, and the specific description is summarized in Table 1.

[0119] Table 1 Penicillin fermentation process variables

[0120]

[0121]

[0122] In this case, samples are collected every 0.5 hours, and a total of 400 hours of data is collected, with a total of 800 sample data. The first 560 sample data are taken as the training set, and the last 240 sample data are taken as the test set.

[0123] The nonlinear sparse moment estimation method is used for variable selection, and the variable contribution diagram obtained is as follows: Figure 3 , the selection results are shown in Table 2;

[0124] Table 2 Variable selection results using nonlinear sparse moment estimation method

[0125] Serial number variable 1 Substrate feed rate 2 Substrate concentration 3 Biomass concentration 4 Temperature 5 Generated heat 6 Base flow rate 7 Cooling water flow rate

[0126] The RVR model is trained using the optimal variable subset selected above, and the performance of the model is evaluated using test data. The comparison between the actual value and the predicted value is shown in the figure below: Figure 4 , from which it can be seen that the error between the true value and the predicted value is very small, which also shows that the soft measurement accuracy of the present invention is very high and has good use value. The error result data is shown in Table 3, which shows that the error rate of the algorithm proposed by the present invention is extremely low.

[0127] Table 3 Error result data

[0128] algorithm MSE R2 Random Forest + Mallow's Cp + SVR 0.0132±0.0011 0.977±0.0019

[0129] In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the scope of protection of the present invention.

[0130] An industrial soft-sensing system based on nonlinear sparse moment estimation and correlation vector regression includes the following modules:

[0131] The data acquisition module is used to obtain relevant data in the industrial process, including multiple features and target variables measured by sensors in the industrial process that may affect the target variable and the target variable, as well as several sample data collected corresponding to each feature. The set of features that affect the target variable is recorded as Where N represents the number of samples and M represents the number of variable features;

[0132] The data preprocessing module is used to standardize the sample data corresponding to each variable in X_o to obtain the data set X, and divide the sample data corresponding to the features in the data set X into a training set and a test set;

[0133] The variable selection module is used to select variables for the data set X using the nonlinear sparse moment estimation model NS-GMM. By defining nonlinear moment conditions and introducing regularization constraints, variable selection indicators are constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test.

[0134] The model training module is used to train the relevant vector regression RVR model using X_new to obtain the trained RVR model RVR_model;

[0135] The prediction execution module is used to use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable value.

[0136] The specific implementation method of each module corresponds to each step and is not described in detail in the present invention.

[0137] A computer-readable storage medium includes a stored computer program. When the computer program is executed by a processor, the device where the computer-readable storage medium is located is controlled to execute the industrial soft measurement method based on nonlinear sparse moment estimation and correlation vector regression provided by the above embodiment.

[0138] The above description is only a preferred specific implementation manner of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the scope of protection of the invention.

Claims

1. An industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression, characterized in that: The following steps are involved: S1, obtain relevant data in the industrial process, including multiple features and target variables measured by sensors in the industrial process that may affect the target variable and the target variable as well as several sample data collected corresponding to each feature. The set of features that affect the target variable is recorded as Where N represents the number of samples and M represents the number of variable features; S2, standardize the sample data corresponding to each variable in X_o to obtain the data set X, and divide the sample data corresponding to the features in the data set X into a training set and a test set; S3, for the data set X, the nonlinear sparse moment estimation model NS-GMM is used for variable selection. By defining the nonlinear moment condition and introducing the regularization constraint, the variable selection index is constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test; S4, using X_new to train the relevant vector regression RVR model to obtain the trained RVR model RVR_model; S5, use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable value.

2. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 1, characterized in that: The specific implementation of the standardization process in step S2 is as follows: Standardization processing includes normalizing the standard deviation of the sample data corresponding to each feature in the data set. Standard deviation normalization converts the sample data corresponding to the feature in the data set into a data distribution centered on 0. The specific formula is as follows: x=(x_o-min(x_o)) / (max(x_o)-min(x_o)) Among them, x_o is the original value of the data sample corresponding to a numerical feature in the data set, x is the value of the data sample corresponding to the feature after the standard deviation is normalized, min(x_o) is the minimum value in the data sample corresponding to the feature, and max(x_o) is the maximum value in the data sample corresponding to the feature, and the standardized data set X is obtained.

3. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 1, characterized in that: The specific implementation of step S3 is as follows: (3.1) The normalized data is mapped to a high-dimensional space through the kernel function K, where K(X) represents the high-dimensional space mapping of the normalized data set under the kernel function, which can be expressed as follows: Where y is the target variable, X is the input auxiliary variable, that is, the standardized data set. is the parameter vector, and u is the error term. This transformation ensures that the k-th moment condition of the error term u still holds in the transformed space, thereby more accurately simulating the true distribution of the data. According to the defined moment condition, the nonlinear moment condition is expressed as: Where E represents the expected value, represents the model prediction value after the kernel function conversion, and g represents a prediction function of the model. This condition ensures that the error term The k-th moment of is 0 under the condition of given X, thus maintaining the nonlinear relationship of data in high-dimensional space; (3.2) According to the defined moment condition, the sample moment condition is constructed using sample data. The sample moment condition is expressed as: Where n represents the number of samples in the data set X; (3.3) Constructing the objective function, NS-GMM adds L1 and L2 regularization terms to the objective function Jj(θ), and the specific expression is: Where W represents the weight matrix, λ and β are regularization parameters, ||||1 represents the L1 norm, ||||2 represents the L2 norm, and θ is the model parameter in NS-GMM; (3.4) Similar to the traditional generalized moment estimation method, the objective function with regularization constraints is minimized through optimization algorithm Get parameter estimates It represents the relationship between different variables in X and y. The absolute value of is used as an indicator to evaluate the importance of the variable. The larger the value, the greater the influence of the variable on the model. Thus, a group of key variables X_new that have a significant impact on the target variable are selected.

4. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression as claimed in claim 3, characterized in that: The kernel function is a polynomial kernel, a radial basis kernel, or a Gaussian kernel.

5. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 1, characterized in that: The specific implementation of step S4 is as follows: (4.1) The RVR model is expressed as: y=f(X_new,w)+∈ Among them, y is the target variable, X_new is the set of input variables, w is the model parameter in RVR, f(X_new,w) represents the regression function determined by the kernel function, and ∈ is the noise term; (4.2) By combining the prior distribution and observed data, the posterior distribution of the model parameters is estimated through the Bayesian inference method: p(w|y,X_new)∝p(y|X_new,w)p(w) Here, p(y|X_new,w) is the likelihood function of the target variable y under X_new and model parameters w; p(w) is the prior distribution of model parameters w, and p(w|y,X_new) is the posterior distribution of model parameters w. ∝ means proportional or proportional to; (4.3) By maximizing the posterior distribution and optimizing the model parameters, we can obtain a regression model RVR_model with strong sparsity: in are the optimal model parameters.

6. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 1, characterized in that: In step S5, the trained model RVR_model is used to predict X_new_test to obtain the corresponding target variable. The specific implementation method is as follows: Among them, f represents the trained model RVR_model, ∈ is the noise term.

7. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 1, characterized in that: The method further includes step S6 of evaluating the generalization ability of the trained RVR model, specifically evaluating the performance of the RVR model using mean square error (MSE) and determination coefficient.

8. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 7, characterized in that: The formula for mean square error MSE is: Where y i is the actual value, y ipre is the predicted value, n represents the number of samples, Represents the mean value of the target variable.

9. The industrial soft sensing method based on nonlinear sparse moment estimation and correlation vector regression according to claim 7, characterized in that: Coefficient of determination R 2 The formula is: Where y i is the actual value, y ipre is the predicted value, n represents the number of samples, Represents the mean value of the target variable.

10. An industrial soft sensor system based on nonlinear sparse moment estimation and correlation vector regression, characterized in that: Includes the following modules: The data acquisition module is used to obtain relevant data in the industrial process, including multiple features and target variables measured by sensors in the industrial process that may affect the target variable and the target variable, as well as several sample data collected corresponding to each feature. The set of features that affect the target variable is recorded as Where N represents the number of samples and M represents the number of variable features; The data preprocessing module is used to standardize the sample data corresponding to each variable in X_o to obtain the data set X, and divide the sample data corresponding to the features in the data set X into a training set and a test set; The variable selection module is used to select variables for the data set X using the nonlinear sparse moment estimation model NS-GMM. By defining nonlinear moment conditions and introducing regularization constraints, variable selection indicators are constructed to screen out a set of key variables X_key that have a significant impact on the target variable. The training set in X corresponding to the variables in X_key is X_new, and the corresponding test set is X_new_test. The model training module is used to train the relevant vector regression RVR model using X_new to obtain the trained RVR model RVR_model; The prediction execution module is used to use the trained RVR_model model to predict X_new_test and obtain the corresponding target variable value.

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