Dynamic quality correlation monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis

Abstract

The invention discloses a dynamic quality correlation monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis, and aims to introduce dynamic features of data for quality-related and quality-independent fault data and research a construction mode of a quality-related fault detection model. The main core of the method is that time correlation of process data variables is used as a criterion to divide a dynamic space, correlation and irrelevant variables are divided by using correlation of the process variables and quality variables, and data expansion is performed on the variables in the dynamic space. And related fault detection is performed on quality related variables by using an orthogonal canonical correlation analysis method, and finally, comprehensive statistics are constructed by using Bayesian reasoning fusion. In addition, the method also considers the robustness of model training while considering the model effect. Compared with other methods, the method provided by the invention can better and faster distinguish and detect quality-related and quality-independent faults, and obtains a better effect. Therefore, the method provided by the invention is a more excellent quality-related fault detection method.

Description

Technical Field

[0001] The present invention relates to a data-driven operation status monitoring method, and in particular to a dynamic quality correlation monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis. Background Art

[0002] With the rapid development of modern process industries, fault detection and early warning for complex industrial systems have become particularly important. In recent years, due to the advancement of sensor technology, a large amount of process data has been obtained, and data-driven multivariate statistical process monitoring methods have gradually attracted attention. Currently, common multivariate statistical methods include principal component analysis (PCA), partial least squares (PLS), independent component analysis (ICA), etc. However, faults can be divided into quality-related faults and quality-irrelevant faults according to their impact on product quality. Traditional monitoring methods are difficult to effectively distinguish between these two types of faults, resulting in many quality-irrelevant process fluctuations being falsely reported as early warnings.

[0003] With the continuous growth of industrial scale, more and more key quality indicators need to be monitored. Based on this demand, quality-related fault monitoring technology has been developed, such as canonical correlation analysis (CCA). Quality-related monitoring technology generally starts from the correlation between process variables and final product quality, divides process variables into quality-related space and quality-irrelevant space, and then performs subsequent fault monitoring. However, the general CCA is not efficient in detecting quality-related faults. Based on this, orthogonal canonical correlation analysis (OCCA) is proposed. The quality-related projection direction is decomposed by SVD, and the quality-related and irrelevant information are represented separately. The orthogonal quality-related information and irrelevant information are extracted through the canonical correlation vector. This orthogonalization operation ensures that the quality-related information will not be interfered by irrelevant information, and improves the recognition accuracy of quality-related faults.

[0004] In addition, in order to improve the accuracy of fault detection, some researchers have introduced the dynamic characteristics of data based on the analysis of the static amplitude of single variable data, and extracted more relevant information that is helpful for fault monitoring by considering the time series relationship of the process variables themselves. For the dynamic characteristics of data, the dynamic characteristics of variables can be extracted through slow feature analysis (SFA), so as to realize the detection of dynamic characteristics. Based on the above discussion, a dynamic quality-related monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis is proposed, which takes into account the static and dynamic characteristics of data, and the correlation and irrelevance of variables, to achieve high-precision quality-related fault monitoring. Summary of the invention

[0005] The present invention first divides the process variable set into a related space and an unrelated space according to the correlation between the product quality variables, and on this basis, uses the time correlation of the process data variables themselves as a criterion to divide the two subspaces into a dynamic subspace and a non-dynamic subspace, a total of four subspaces. In view of the dynamic characteristics of the dynamic subspace data, SFA is used in combination with the augmented matrix of the process data in the subspace to extract the difference matrix of the data, and OCCA is further used in the related space for quality-related fault monitoring. The non-dynamic space is directly used without augmenting and expanding the variables, and SFA is directly used for differential feature extraction. Finally, corresponding statistics are established in each subspace and subspace monitoring is performed. Finally, the Bayesian method is used to integrate the statistics with the same characteristics to obtain a comprehensive statistic.

[0006] The technical solution adopted by the present invention to solve the above problems is: a dynamic quality correlation monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis, comprising the following steps:

[0007] Step (1): The implementation process of data collection and preprocessing is as follows:

[0008] Step (1.1): Collect process data in the normal operation state of the industrial process to form the original training data set, where the process variable data set is The quality variable data set is

[0009] Step (1.2): Use the z-score standardization method to preprocess the original training set data so that the mean of each variable in the two data sets is 0 and the variance is 1, thus obtaining the standardized data set X = [x1, x2, ..., x m ]∈R n×m and Y=[y1,y2,…,y l ]∈R n×l , where n is the number of data set samples, m is the number of process variables, l is the number of quality variables, and R is a real number set;

[0010] Step (2): The division of the dynamic subspace is based on the temporal correlation of the variables themselves. The dynamic and non-dynamic variables x i ∈R n×1 The time series correlation of (i=1,2,…,m) is significantly different. The autocorrelation function (ACF) is used to calculate the correlation between samples in each process variable. i ∈R n×1 (i=1,…,m), the autocorrelation formula for lag k>0 is

[0011] ACF(k)=S k / S0 (2)

[0012]

[0013] If ACF>0.05, the variable is considered to be time series-related and a dynamic variable; otherwise, the variable is a non-dynamic variable. Based on the above principle, the training data set X∈R n×m Dynamic subspace and non-dynamic subspace

[0014] Step (3): Based on the division of the dynamic subspace, the subspace is further divided into quality-related and quality-independent subspaces according to the mutual information (MI) value between each process variable and the quality variable. The implementation process is as follows:

[0015] Dynamic Subspace X D With the non-dynamic subspace X U The variable x in i and the quality variable y in the quality variable set Y j The mutual information value of is:

[0016]

[0017] Where P(x i ,y j ) represents the joint distribution probability between two variables. Set the threshold η. If MI>η, the process variable is a quality-related variable, otherwise it is a quality-irrelevant variable. The above strategy can further divide the dynamic and non-dynamic subspaces to obtain the dynamic-quality-related subspace X DQ , dynamic-mass-independent subspace X DU , non-dynamic-mass-dependent subspace X UQ , non-dynamic-mass-independent subspace X UU ;

[0018] Step (4): Introduce time delay in the dynamic subspace and construct a dynamic expansion matrix. The specific implementation process is as follows:

[0019] By selecting a suitable time delay h, the original matrix is ​​dynamically expanded as follows:

[0020]

[0021] Where A is the original data matrix, and the above formula is expressed in the new matrix In , each sample point contains the data of the current time and the data of h time delays in the past;

[0022] Step (5): For all subspaces, use slow feature analysis (SFA) to extract preliminary features and calculate the difference value matrix. The specific implementation process is as follows:

[0023] Step (5.1): SFA can extract slowly changing features from time series, which is particularly important for dynamic process monitoring. It can effectively identify key information hidden in noise or rapid changes, and help enhance the dynamic changes in the process. SFA optimizes the features of object data to minimize its rate of change, which can be achieved through the following objective function:

[0024]

[0025] W=PX (9)

[0026] Where P is the transformation matrix, W(i) represents the feature vector at the i-th time point, and the goal of formula (8) is to obtain the smallest transformation matrix P, thereby obtaining a suitable low-dimensional feature matrix W;

[0027] Step (5.2): Based on the obtained SFA feature matrix W, calculate the difference value matrix to further highlight the dynamic changes of process data:

[0028] diff(W)(i)=W(i+1)-W(i) (10)

[0029] Step (6): In the dynamic-mass related subspace X DQ In the process, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, orthogonal canonical correlation analysis (OCCA) is used to perform quality-related fault detection. The specific implementation process is as follows:

[0030] Step (6.1): Calculate the process variable diff (W DQ ) and the quality variable Y:

[0031]

[0032] A T ∑diff(W DQ )diff(W DQ )A=B T ∑YYB=I (12)

[0033] Among them, Σ represents the correlation matrix, I represents the identity matrix;

[0034] Step (6.2): ​​By changing the coefficient matrix

[0035]

[0036] Perform singular value decomposition to obtain ΓΞΛ T, respectively represent the left singular matrix, eigenvalue matrix and right singular matrix, and use the left and right singular matrices to get the typical variables:

[0037] A=∑diff(W DQ )diff(W DQ ) -1 / 2 Γ(:,1:κ) (14)

[0038] B=∑YY -1 / 2 Λ(:,1:κ) (15)

[0039] where κ = rank(Σ);

[0040] Step (6.3): Calculate the correlation matrix:

[0041] H=(B T ) -1 ΞA T (16)

[0042] Performing singular value decomposition on it yields:

[0043]

[0044] in and Respectively represent two mutually orthogonal subspaces;

[0045] Step (6.4): Calculate the quality-related and quality-independent statistics, the formula is as follows:

[0046]

[0047] Among them, inv() is the inverse function, cov() is the covariance function, and the control limit is determined by kernel density estimation to obtain the alarm thresholds lim1 and lim2 corresponding to the statistics of the two subspaces.

[0048] Step (7): In the dynamic-mass-independent subspace X DU In the process, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, principal component analysis (PCA) is directly used for fault detection. The specific implementation process is as follows:

[0049] Step (7.1): For the difference matrix diff(W DU ), PCA is used for feature extraction, the formula is as follows;

[0050]

[0051] Cv i =λ i v i(twenty one)

[0052] Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR:

[0053]

[0054] Select the first k eigenvectors that account for 85% of the CCR as the principal components to form the principal component matrix Q. Project the original data into the low-dimensional space to obtain the reduced-dimensional data L:

[0055] L = diff(W DU )Q (23)

[0056] Step (7.2): Construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics:

[0057]

[0058] Among them, l i is the i-th sample of L, is the mean of all samples;

[0059] Step (7.3): For T 2 The statistics use the kernel density estimation (KDE) method to determine the control limit. Given the confidence level α, the specific formula is as follows:

[0060]

[0061] F -1 (α)=inf{F J (j)≥α} (27)

[0062] Among them J i represents different observations in the training sample, h is the kernel width, and the kernel function uses the Gaussian kernel function. The control limit of the dynamic-quality-independent subspace is determined by the given confidence level α;

[0063] Step (8): In the non-dynamic-mass-related subspace X UQ In step (5), based on the difference value matrix of SFA feature extraction obtained in step (5), orthogonal canonical correlation analysis (OCCA) is used to perform quality-related fault detection, and statistics are constructed and control limits are estimated by calculating the quality-related and irrelevant related information to achieve quality-related fault detection;

[0064] Step (9): In the non-dynamic-mass-independent subspace X UUIn the above, based on the difference value matrix of SFA feature extraction obtained in step (5), PCA is directly used for fault detection in accordance with steps (7.1)-(7.3) to determine the control limits of the non-dynamic-quality-independent subspace;

[0065] Step (10): Use Bayesian inference to statistically merge the statistical data of all subspaces to obtain the monitoring results. The specific implementation process is as follows:

[0066] Step (10.1): Use Bayesian inference to statistically combine the statistics of all subspaces, and a single subspace x b The failure probability calculation formula is:

[0067]

[0068] P(X b )=P(X b |N)P(N)+P(X b |F)P(F) (29)

[0069] Among them, the conditional probability P(X b |N) and P(X b |F) are respectively

[0070]

[0071] In the above formula, N and F represent the normal state and fault state respectively; P(N) and P(F) represent the prior probability under normal and fault conditions respectively; J b,new is the statistical data of the b-th sub-block in the online detection dataset, J b,lim is the control threshold corresponding to the training set;

[0072] Step (10.2): Combine the detection results of all different sub-blocks through Bayesian reasoning and calculate the sum of the joint statistics:

[0073]

[0074] Set the confidence level to 0.99 and construct the relevant statistical confidence limit BIC in the offline phase QL = 0.01 and BIC NL =0.01, and finally the construction of multi-subspace quality-related fault detection model is completed;

[0075] The above steps (1) to (10) are the offline modeling stage of the method of the present invention, and the following steps (11) to (19) are the implementation process of the online analysis of the method of the present invention.

[0076] Step (11): Collect sample data for online detection Where n is the number of data set samples, m is the number of process variables, and R is a real number set. The data is preprocessed using the mean and standard deviation obtained in step (1.2) to obtain standardized online data XT = [xt1, xt2, …, xt m ]∈R n×m ;

[0077] Step (12): Divide the data into process variables XT according to the process of steps (2)-(3) to obtain four subspaces corresponding to the training set;

[0078] Step (13): Introduce time delay in the dynamic subspace to construct a delay matrix in the manner of step (4);

[0079] Step (14): Based on step (4), the slow feature analysis (SFA) is used to extract preliminary features for all subspaces in the manner of step (5), and a difference value matrix is ​​calculated;

[0080] Step (15): Use OCCA to perform quality-related fault detection in the dynamic-quality-related subspace in the same manner as in step (6) to obtain the quality-related T 2 Statistics;

[0081] Step (16): Use PCA to perform quality-independent fault detection in the dynamic-quality-independent subspace in the same manner as in step (7) to obtain the quality-independent T 2 Statistics;

[0082] Step (17): Use OCCA to perform quality-related fault detection in the non-dynamic-quality-related subspace in the same manner as in step (8) to obtain the quality-related T 2 Statistics;

[0083] Step (18): Use PCA to perform quality-independent fault detection in the non-dynamic-quality-independent subspace in the same manner as in step (9) to obtain the quality-independent T 2 Statistics;

[0084] Step (19): Obtain the relevant results BIC of the Bayesian inference fusion of the test data set in the same way as in step (10) Q And irrelevant results BIC N , and the statistical confidence limit BIC of the offline stage QL 、BIC NL A one-by-one comparison is performed. If the confidence limit is exceeded, an alarm is triggered and a fault is considered to have occurred. If the limit is not exceeded, the system is considered to be operating normally.

[0085] Compared with the traditional method, the advantages of the method of the present invention are:

[0086] First, the method of the present invention can realize the precise division of variables based on the quality-related and irrelevant relationships between variables and the dynamic characteristics of variables, shift the detection perspective from the global to the local, and increase the accuracy of fault detection; secondly, the method of the present invention also enhances the changing trend of data by introducing data extension sequences, and further uses SFA to capture slowly changing trend characteristics, combined with the difference matrix to enhance dynamic characteristics. Finally, compared with other traditional multivariate statistical methods, the method of the present invention can more efficiently distinguish and detect quality-related and irrelevant faults using the improved OCCA. It can be said that the method of the present invention is a more excellent quality-related fault detection method. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 is a flow chart of the method of the present invention;

[0088] Figure 2 It is the TEP industrial flow chart;

[0089] Figure 3 It is a simulation experiment diagram of the method of the present invention; DETAILED DESCRIPTION

[0090] The method of the present invention is described in detail below with reference to the accompanying drawings and specific implementation examples.

[0091] The present invention discloses a multi-subspace quality-related fault detection method based on correlation and dynamic characteristics. Figure 1 The specific flow chart of the method is shown in FIG. 1 . The specific implementation process of the present invention and the superiority of the quality-related fault detection method compared with the conventional multivariate statistics are explained below in combination with a simulation platform case.

[0092] The Tennessee Eastman (TE) process is a reliable chemical plant simulation program based on actual chemical reaction processes and is widely used as a benchmark. Figure 2 As shown in the figure, it includes five main units: reactor, condenser, compressor, separator and stripper. The TE process contains 41 process variables and 11 operating variables. In addition, the TE process has 21 faults of different fault types. Among them, component G and component H, as key quality indicators, have a low sampling rate and are often difficult to obtain in real time. Therefore, component G and component H are selected as the key quality variables of the TE process to be predicted.

[0093] Table 1: 22 continuous variables in the TE process

[0094]

[0095]

[0096] Table 2: 11 manipulated variables in the TE process

[0097]

[0098] Table 3: Two typical failures in TE process

[0099]

[0100] The test set samples with faults were obtained under 48h running simulation. The fault was introduced at 8h. A total of 960 observations were collected, of which the first 160 observations were normal data. First, the 960 samples collected were used for offline training to establish a fault detection model, which includes the following steps:

[0101] Step (1): Collect samples under normal working conditions to form a training data set and Standardize the data using the z-score method to obtain data X∈R 960×33 With Y∈R 960×2 ;

[0102] Step (2): The division of the dynamic subspace is based on the temporal correlation of the variables themselves. The dynamic and non-dynamic variables x i ∈R 33×1 The time series correlation of (i=1,2,…,m) is significantly different. The autocorrelation function (ACF) is used to calculate the correlation between samples in each process variable. i ∈R n×1 (i=1,…,m), the autocorrelation formula for lag k>0 is

[0103] ACF(k)=S k / S0 (2)

[0104]

[0105]

[0106] If ACF>0.05, the variable is considered to be time series-related and is a dynamic variable; otherwise, the variable is a non-dynamic variable. Based on the above principle, the training data set X∈R n×m Dynamic subspace and non-dynamic subspace

[0107] Step (3): Based on the division of the dynamic subspace, the subspace is further divided into quality-related and quality-independent subspaces according to the mutual information (MI) value between each process variable and the quality variable. The implementation process is as follows:

[0108] Dynamic Subspace XD With the non-dynamic subspace X U The variable x in i and the quality variable y in the quality variable set Y j The mutual information value of is:

[0109]

[0110] Where P(x i ,y j ) represents the joint distribution probability between two variables. Set the threshold η. If MI>η, the process variable is a quality-related variable, otherwise it is a quality-irrelevant variable. The above strategy can be used to divide the dynamic and non-dynamic subspaces to obtain the dynamic-quality-related subspace X DQ , dynamic-mass-independent subspace X DU , non-dynamic-mass-dependent subspace X UQ , non-dynamic-mass-independent subspace X UU ; Since the quality-related variables are all dynamic variables in the variable partitioning results, there are no quality-related but non-dynamic process variables, so X UQ is an empty set;

[0111] Step (4): In the dynamic subspace X DQ and X DU In , time delay is introduced and delay matrix is ​​constructed. The specific implementation process is as follows:

[0112] According to the industrial process requirements, a suitable time delay h = 2 is selected, and the process of matrix expansion can be described as:

[0113]

[0114] Step (5): For all subspaces, use SFA to extract preliminary features and calculate the difference value matrix. The specific implementation process is as follows:

[0115] Step (5.1): SFA optimizes the characteristics of the object data to minimize its rate of change, which can be achieved through the following objective function:

[0116]

[0117] W=PX (9)

[0118] Step (5.2): Based on the obtained SFA feature matrix W, calculate the difference value matrix to further highlight the dynamic changes of process data:

[0119] diff(W)(i)=W(i+1)-W(i) (10)

[0120] Step (6): In the dynamic-mass related subspace X DQ In the process, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, orthogonal canonical correlation analysis (OCCA) is used to perform quality-related fault detection;

[0121] Step (7): In the dynamic-mass-independent subspace X DU In the process, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, principal component analysis (PCA) is directly used for fault detection. The specific implementation process is as follows:

[0122] Step (7.1): For the difference matrix diff(W DU ), PCA is used for feature extraction, the formula is as follows;

[0123]

[0124] Cv i =λ i v i (12)

[0125] Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR:

[0126]

[0127] Select the first k eigenvectors that account for 85% of the CCR as the principal components to form the principal component matrix Q. Project the original data into the low-dimensional space to obtain the reduced-dimensional data L:

[0128] L = diff(W DU )Q (14)

[0129] Step (7.2): Construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics:

[0130]

[0131] Step (7.3): For T 2 The statistics use the kernel density estimation (KDE) method to determine the control limit. Given the confidence level α, the specific formula is as follows:

[0132]

[0133] F -1 (α)=inf{F J (j)≥α} (18)

[0134] Step (8): In the non-dynamic-mass-independent subspace X UU In the above, based on the difference value matrix of SFA feature extraction obtained in step (5), PCA is directly used for fault detection in accordance with steps (7.1)-(7.3) to determine the control limits of the non-dynamic-quality-independent subspace;

[0135] Step (9): Use Bayesian inference to statistically merge the statistical data of all subspaces to obtain the monitoring results. The specific implementation process is as follows:

[0136] Step (9.1): Use Bayesian inference to statistically combine the statistics of all subspaces, and a single subspace x b The failure probability calculation formula is:

[0137]

[0138] Among them, the conditional probability P(X b |N) and P(X b |F) are respectively

[0139]

[0140]

[0141] In the above formula, N and F represent the normal state and fault state respectively; P(N) and P(F) represent the prior probability under normal and fault conditions respectively; J b,new is the statistical data of the b-th sub-block in the online detection dataset, J b,lim is the control threshold corresponding to the training set;

[0142] Step (9.2): Combine the detection results of all different sub-blocks through Bayesian reasoning and calculate the sum of the joint statistics:

[0143]

[0144] Set the confidence level to 0.99 and construct the relevant statistical confidence limit BIC in the offline phase QL = 0.01 and BIC NL =0.01, and finally the construction of multi-subspace quality-related fault detection model is completed;

[0145] Step (10): Samples collected online The training data set is standardized by its mean and standard deviation to obtain the standardized test sample data XT = [xt1, xt2, …, xt 33 ]∈R 960×33 ;

[0146] Step (11): Divide the data into process variables XT according to the process of steps (2)-(3) to obtain the dynamic-quality related subspace XT corresponding to the training set DQ , dynamic-mass-independent subspace XT DU , non-dynamic-mass-dependent subspace XT UQ , non-dynamic-mass-independent subspace XT UU ;

[0147] Step (12): Introduce time delay in the dynamic subspace to construct a delay matrix in the manner of step (4);

[0148] Step (13): Based on step (4), extract preliminary features using SFA for all subspaces in the manner described in step (5) and calculate the difference value matrix;

[0149] Step (14): Use OCCA to perform quality-related fault detection in the dynamic-quality-related subspace in the same manner as in step (6) to obtain the quality-related T 2 Statistics;

[0150] Step (15): Use PCA to perform quality-independent fault detection in the dynamic-quality-independent subspace in the same manner as in step (7) to obtain the quality-independent T 2 Statistics;

[0151] Step (16): Use PCA to perform quality-independent fault detection in the non-dynamic-quality-independent subspace in the same manner as in step (8) to obtain the quality-independent T 2 Statistics;

[0152] Step (17): Obtain the Bayesian inference fusion results BIC(Q) and BIC(NQ) of the test data set as in step (9), and the statistical confidence limit BIC in the offline stage L (Q) and BIC L (NQ) are compared one by one. If the statistic BIC(Q) of the online sample is greater than BIC L (Q), then according to the judgment criteria, a quality-related failure has occurred in the system; if BIC(Q) <BIC L (Q) and BIC(NQ)>BIC L (NQ), then a quality-independent failure has occurred in the system; if BIC(Q) <BIC L (Q) and BIC (NQ) <BIC L (NQ), then no fault occurs in the system.

[0153] This method is compared with the method of quality-related fault detection based on canonical correlation analysis. The detection results of the two methods for quality-related fault 5 in TE are shown in Table 4;

[0154] Table 4: Detection results for fault 5

[0155]

[0156] Finally, the simulation results of the method of the present invention for quality-related fault 5 are shown in FIG. Figure 3 It can be found that the detection effect of the method of the present invention is excellent and can achieve effective early warning for quality-related faults.

[0157] The above-mentioned implementation cases are only used to explain the specific implementation of the present invention, rather than to limit the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the scope of the present invention.

Claims

1. A dynamic quality-related monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis, characterized in that: The following steps are involved: The implementation process of the offline modeling phase is as follows: Step (1): The implementation process of data collection and preprocessing is as follows: Step (1.1): Collect process data in the normal operation state of the industrial process to form the original training data set, where the process variable data set is The quality variable data set is Step (1.2): Use the z-score standardization method to preprocess the original training set data so that the mean of each variable in the two data sets is 0 and the variance is 1, thus obtaining the standardized data set X = [x1, x2, ..., x m ]∈R n×m and Y=[y1,y2,…,y l ]∈R n×l , where n is the number of data set samples, m is the number of process variables, l is the number of quality variables, and R is a real number set; Step (2): The division of the dynamic subspace is based on the temporal correlation of the variables themselves. The dynamic and non-dynamic variables x i ∈R n×1 The time series correlation of (i=1,2,…,m) is significantly different. The autocorrelation function (ACF) is used to calculate the correlation between samples in each process variable. i ∈R n×1 (i=1,…,m), the autocorrelation formula for lag k>0 is ACF(k)=S k / S0 (2) If ACF>0.05, the variable is considered to be time series-related and a dynamic variable; otherwise, the variable is a non-dynamic variable. Based on the above principle, the training data set X∈R n×m Dynamic subspace and non-dynamic subspace Step (3): Based on the division of the dynamic subspace, the subspace is further divided into quality-related and quality-independent subspaces according to the mutual information (MI) value between each process variable and the quality variable. The implementation process is as follows: Dynamic Subspace X D With the non-dynamic subspace X U The variable x in i and the quality variable y in the quality variable set Y j The mutual information value of is: Where P(x i ,y j ) represents the joint distribution probability between two variables. Set the threshold η. If MI>η, the process variable is a quality-related variable, otherwise it is a quality-irrelevant variable. The above strategy can further divide the dynamic and non-dynamic subspaces to obtain the dynamic-quality-related subspace X DQ , dynamic-mass-independent subspace X DU , non-dynamic-mass-dependent subspace X UQ , non-dynamic-mass-independent subspace X UU ; Step (4): Introduce time delay in the dynamic subspace and construct a dynamic expansion matrix. The specific implementation process is as follows: By selecting a suitable time delay h, the original matrix is ​​dynamically expanded as follows: Where A is the original data matrix, and the above formula is expressed in the new matrix In , each sample point contains the data of the current time and the data of h time delays in the past; Step (5): For all subspaces, use slow feature analysis (SFA) to extract preliminary features and calculate the difference value matrix. The specific implementation process is as follows: Step (5.1): SFA can extract slowly changing features from time series, which is particularly important for dynamic process monitoring. It can effectively identify key information hidden in noise or rapid changes, and help enhance the dynamic changes in the process. SFA optimizes the features of object data to minimize its rate of change, which can be achieved through the following objective function: W=PX (9) Where P is the transformation matrix, W(i) represents the feature vector at the i-th time point, and the goal of formula (8) is to obtain the smallest transformation matrix P, thereby obtaining a suitable low-dimensional feature matrix W; Step (5.2): Based on the obtained SFA feature matrix W, calculate the difference value matrix to further highlight the dynamic changes of process data: diff(W)(i)=W(i+1)-W(i) (10) Step (6): In the dynamic-mass related subspace X DQ In the method, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, orthogonal canonical correlation analysis (OCCA) is used to perform quality-related fault detection. On the basis of CCA, OCCA further processes the correlation obtained from process variables and quality variables, separates quality-related and quality-irrelevant features, and constructs statistics and estimates control limits through the calculated quality-related and irrelevant related information, thereby achieving quality-related fault detection. Step (7): In the dynamic-mass-independent subspace X DU In the process, based on the difference value matrix obtained in steps (4)-(5) after delay expansion and SFA feature extraction, principal component analysis (PCA) is directly used for fault detection. The specific implementation process is as follows: Step (7.1): For the difference matrix diff(W DU ), PCA is used for feature extraction, the formula is as follows; Cv i =λ i v i (12) Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR: Select the first k eigenvectors that account for 85% of the CCR as the principal components to form the principal component matrix Q. Project the original data into the low-dimensional space to obtain the reduced-dimensional data L: L=diff(W DU )Q (14) Step (7.2): Construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics: Among them, l i is the i-th sample of L; Step (7.3): For T 2 The statistics use the kernel density estimation (KDE) method to determine the control limit. Given the confidence level α, the specific formula is as follows: F -1 (α)=inf{F J (j)≥α} (18) Among them J i represents different observations in the training sample, h is the kernel width, and the kernel function uses the Gaussian kernel function. The statistics and control limits of the dynamic-quality-independent subspace are determined by a given confidence level α; Step (8): In the non-dynamic-mass-related subspace X UQ In step (5), based on the difference value matrix of SFA feature extraction obtained in step (5), orthogonal canonical correlation analysis (OCCA) is used to perform quality-related fault detection, and statistics are constructed and control limits are estimated by calculating the quality-related and irrelevant related information to achieve quality-related fault detection; Step (9): In the non-dynamic-mass-independent subspace X UU In the above, based on the difference value matrix of SFA feature extraction obtained in step (5), PCA is directly used for fault detection in accordance with steps (7.1)-(7.3), the statistics of the non-dynamic-quality-independent subspace are determined and the control limits are estimated; Step (10): Use Bayesian inference to statistically merge the statistical data of all subspaces to obtain the monitoring results. The specific implementation process is as follows: Step (10.1): Use Bayesian inference to statistically combine the statistics of all subspaces, and a single subspace x b The failure probability calculation formula is: P(X b )=P(X b |N)P(N)+P(X b |F)P(F) (20) Among them, the conditional probability P(X b |N) and P(X b |F) are respectively In the above formula, N and F represent the normal state and fault state respectively; P(N) and P(F) represent the prior probability under normal and fault conditions respectively; when the confidence level is determined to be ε, P(N) = ε, P(F) = 1-ε. b,new is the statistical data of the b-th sub-block in the online detection dataset, J b,lim is the control threshold corresponding to the training set; Step (10.2): Combine the detection results of all different sub-blocks through Bayesian reasoning and calculate the sum of the joint statistics: Set the confidence level to 0.99 and construct the relevant statistical confidence limit BIC in the offline phase QL = 0.01 and BIC NL =0.01, and finally the construction of the multi-subspace quality-related fault detection model is completed.

2. The dynamic quality correlation monitoring method based on differential-slow feature analysis and differential-orthogonal correlation analysis according to claim 1 is characterized in that: In step (6), OCCA is used to implement quality-related and quality-independent fault detection, and to construct monitoring control limits. The specific implementation process is as follows: Step (6.1): First calculate the process variable diff (W DQ ) and the correlation coefficient between the quality variable Y. The specific operation process is as follows: A T ∑diss(W DQ )diss(W DQ )A=B T ∑YYB=I (25) Among them, Σ represents the correlation matrix, I represents the identity matrix; Step (6.2): ​​By changing the coefficient matrix Perform singular value decomposition to obtain ΓΞΛ T , respectively represent the left singular matrix, eigenvalue matrix and right singular matrix, and use the left and right singular matrices to get the typical variables: A=∑diff(W DQ )diff(W DQ ) -1 / 2 C(:,1:k) (27) B=∑YY -1 / 2 L(:,1:k) (28) where κ = rank(Σ); Step (6.3): Calculate the correlation matrix: H=(B T ) -1 ΞA T (29) Performing singular value decomposition on it yields: in and Respectively represent two mutually orthogonal subspaces; Step (6.4): Calculate the quality-related and quality-independent statistics, the formula is as follows: Among them, inv() is the inverse function, cov() is the covariance function, and the control limit is determined by kernel density estimation to obtain the alarm thresholds lim1 and lim2 corresponding to the statistics of the two subspaces.

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