Quality-related fault detection method based on dynamic and non-dynamic multi-subspace division

Abstract

The invention discloses a quality-related fault detection method based on dynamic and non-dynamic multi-subspace division, and aims to introduce dynamic characteristics of data and research a construction mode of a quality-related fault detection model for quality-related and quality-independent fault data. The main core of the method is that the time correlation of process data variables is used as a criterion to divide a dynamic space, then correlation and irrelevant variables are divided by using the correlation between the process variables and quality variables, data expansion is performed on the variables in the dynamic space, dynamic characteristics are enhanced, and the dynamic performance is improved. And related fault detection is performed on quality related variables by using an elastic network, 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 fault detection method, and in particular to a quality-related fault detection method based on dynamic and non-dynamic multi-subspace division. Background Art

[0002] Modern process industry is developing rapidly, and the requirements for its safety and reliability are gradually increasing. It is particularly important to detect and warn the faults of complex industrial systems. In recent years, with the development of sensor technology, a large amount of process data has been collected and recorded. Based on this, data-driven multivariate statistical process monitoring has won the favor of researchers. Among them, common multivariate statistical analysis methods include principal component analysis (PCA), partial least squares (PLS), and neighborhood preserving embedding (NPE). However, according to whether the fault affects the product quality, it can be divided into quality-related faults that have an impact and quality-irrelevant faults that have no impact. However, traditional monitoring methods are difficult to effectively distinguish quality-related faults from quality-irrelevant faults, resulting in a large number of process data fluctuations that are not related to product quality. Early warning.

[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 detection and diagnosis technologies have been developed, such as canonical correlation analysis (CCA) and elastic network (EN). The distinction between quality-related and quality-irrelevant faults has been solved to a certain extent. Quality-related detection 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 detection and diagnosis. However, conventional quality-related technology ignores the dynamic characteristics of process data. The process variables corresponding to key quality indicators have obvious time series relationships, which leads to an increase in the missed reporting rate of dynamic-related faults; in addition, the confusion between dynamic variables and non-dynamic variables will interfere with the detection effect of the detection model, resulting in an increase in the false alarm rate. Based on the above discussion, considering the limitations of the current related technologies, in order to effectively extract quality-related information of process variables, the present invention proposes a quality-related fault detection method based on dynamic and non-dynamic multi-subspace partitioning on the basis of traditional quality-related fault detection technology. Summary of the invention

[0004] The present invention first uses the time correlation of the process data variables themselves as a criterion, and divides the dynamic and non-dynamic subspaces according to the dynamic characteristics, wherein the dynamic subspace introduces time delay, constructs a delay matrix, and captures the changing trend of the variables over time. Then, the elastic network modeling is used to construct the regression relationship between the quality variables and the process variables, and the dynamic quality-related and irrelevant subspaces and the non-dynamic quality-related and irrelevant subspaces are projected on the basis of the dynamic subspace and the non-dynamic subspace, and finally the corresponding statistics are established in each subspace and monitored. Finally, the statistics with the same characteristics are integrated using the Bayesian method to calculate the joint statistics.

[0005] The technical solution adopted by the present invention to solve the above problems is: a quality-related fault detection method based on dynamic and non-dynamic multi-subspace division, comprising the following steps:

[0006] Step (1): Data collection and data preprocessing. The specific implementation process is as follows:

[0007] Step (1.1): Collect sample data under normal operating conditions of the industrial process to form a training sample data set, where the process variable data set is The quality variable data set is

[0008] Step (1.2): The collected sensor data is preprocessed using the z-score standardization method to obtain a 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. The specific calculation formula is as follows:

[0009]

[0010] in is the variable before standardization, x is the variable after standardization, μ is the mean of the variable, and σ is its standard deviation;

[0011] Step (2): The division of dynamic and non-dynamic subspaces is based on the temporal correlation of the variables themselves, that is, if the variables have temporal correlation, they are classified as dynamic variables, otherwise they are non-dynamic variables. i ∈R n×1 (i=1,2,…,m) have different degrees of time series correlation, and the autocorrelation function (ACF) is used to measure x i (t) and x i (t+k), where k is the lag. i ∈Rn×1 (i=1,…,m), the autocorrelation formula with lag k is

[0012] ACF(k)=S k / S0 (2)

[0013]

[0014]

[0015] When lag k>0, if ACF is within the given control range, the variable is considered to have no time series correlation; otherwise, the variable is considered to have time series correlation. For variables that are strictly time-series-free, ACF=0. Considering statistical significance, the control limit of ACF is set to 0.05, so that the training data set X∈R n×m Dynamic subspace and non-dynamic subspace

[0016] Step (3): In the dynamic subspace and the non-dynamic subspace, the mutual information (MI) value between the process variable and the quality variable is further divided into the quality-related-dynamic subspace, the quality-independent-dynamic subspace, the quality-related-non-dynamic subspace, and the quality-independent-non-dynamic subspace. The specific implementation process is as follows:

[0017] For the dynamic subspace X D With the non-dynamic subspace X U Each variable x in i , which is related to the quality variable y in the quality variable set Y j The mutual information value of is:

[0018]

[0019] In the formula, P(x i ,y j ) represents the joint distribution probability between process variables and quality variables. Set the threshold η. If MI>η, the variable is considered to be quality-related, otherwise it is considered to be quality-independent. The above strategy can be used to divide the dynamic and non-dynamic subspaces, and the resulting subspace division is:

[0020] X=X DQ +X DU +X UQ +X UU (6)

[0021] Among them, the dynamic-quality related subspace is X DQ , the dynamic-mass-independent subspace is X DU , the non-dynamic-mass-related subspace is XUQ , the non-dynamic-mass-independent subspace is X UU ;

[0022] Step (4): In the dynamic-quality related subspace, time delay is introduced, a delay matrix is ​​constructed, and then an elastic network is used for quality related fault detection. The specific implementation process is as follows:

[0023] Step (4.1): According to the industrial process requirements, select the appropriate time delay h. The process of matrix expansion can be described as:

[0024]

[0025] Where A is the original data matrix, and in this step it is the dynamic-quality related subspace X DQ , Formula (7) means that in the new matrix In , each time point contains the data of the current time t and the data of the past h time delays, which can effectively capture the dynamic characteristics of the data;

[0026] Step (4.2): Use the elastic network to build a quality-related fault detection model. The regression coefficient vector matrix β is obtained by minimizing the elastic network loss function L(β). The elastic network formula is as follows:

[0027]

[0028] Among them, Y quality variable data set, To dynamically expand the matrix data set, ||β||1 is the Lasso regularization term (L1 norm), that is, the sum of the absolute values ​​of the regression coefficients, is the ridge regression regularization term (L2 norm), i.e., the sum of squares of regression coefficients, and λ1 and λ2 are the regularization strength parameters for Lasso and ridge regression.

[0029] Step (4.3): Use the constructed elastic network model to implement quality-related fault detection and obtain corresponding statistics and control limits;

[0030] Step (5): In the dynamic-quality-independent subspace, firstly, the time delay is introduced to construct the delay matrix, and then the principal component analysis (PCA) is used to perform quality-independent fault detection. The specific implementation process is as follows:

[0031] Step (5.1): Same as step (4.1), for the dynamic-mass-independent subspace X DU Perform matrix expansion of the time delay h as a basis for capturing the dynamic characteristics in the data;

[0032] Step (5.2): For the expanded Use PCA for feature extraction, the formula is as follows;

[0033]

[0034] C vi =λ i v i (10)

[0035] Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR:

[0036]

[0037] Select the first k eigenvectors whose CCR accounts for more than 85% as the principal components to form the principal component matrix P, project the original data into the low-dimensional space, and obtain the reduced-dimensional data L:

[0038]

[0039] Step (5.3): Construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics:

[0040]

[0041] Among them, i is the i-th sample of L;

[0042] Step (5.4): 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:

[0043]

[0044]

[0045] F -1 (α)=inf{F J (j)≥α} (16)

[0046] 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;

[0047] Step (6): In the non-dynamic-mass-related subspace X UQ In the above method, the elastic network is directly used for quality-related fault detection. The specific operation process is the same as step (4.2) to step (4.3), and the statistics and control limits of the non-dynamic-quality related subspace are determined;

[0048] Step (7): In the non-dynamic-mass-independent subspace X UU In the process, principal component analysis is directly used to detect quality-independent faults. The specific operation process is the same as step (5.2) to step (5.4), and the statistics and control limits of the non-dynamic-quality-independent subspace are determined;

[0049] Step (8): Use Bayesian inference to statistically merge the statistics of quality-related classes and quality-irrelevant classes in all subspaces to obtain the monitoring results. The specific implementation process is as follows:

[0050] Step (8.1): Use Bayesian inference to statistically merge the statistics of the subspaces, where the statistics related to the quality are integrated into related joint statistics, and the statistics unrelated to the quality are integrated into unrelated joint statistics. Single subspace X b The failure probability calculation formula is:

[0051]

[0052] P(X b )=P(X b |N)P(N)+P(X b |F)P(F) (18)

[0053] Among them, the conditional probability P(X b |B) and P(X b |F) are respectively

[0054]

[0055]

[0056] 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 statistic of the b-th sub-block in the online detection dataset, J b,lim is the corresponding control limit;

[0057] Step (8.2): Combine the detection results of all different sub-blocks through Bayesian reasoning and calculate the sum of the joint statistics:

[0058]

[0059] Set the confidence level to 0.99 and construct the related joint statistical control limit BIC in the offline stage QL = 0.01 and BIC NL =0.01;

[0060] The above steps (1) to (8) are the offline modeling stage of the method of the present invention, and the following steps (9) to (16) are the implementation process of the online analysis of the method of the present invention.

[0061] Step (9): Collect noisy sample data at the new sampling time Where n is the number of data set samples, m is the number of process variables, and R is a real number set;

[0062] Step (10): Apply the mean U = [μ1, μ2, …, μ m ] and standard deviation Φ=[σ1,σ2,…,σ m ] to obtain the standardized test sample data XT = [xt1, xt2, …, xt m ]∈R n×m ;

[0063] 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 DQ , dynamic-mass-independent subspace XT DU , non-dynamic-mass-dependent subspace XT UQ , non-dynamic-mass-independent subspace XT UU ;

[0064] Step (12): In the dynamic-quality related subspace, introduce time delay to construct a delay matrix as in step (4), use elastic network to perform quality related fault detection, and obtain quality related monitoring statistics

[0065] Step (13): In the dynamic-quality-independent subspace, introduce time delay to construct a delay matrix as in step (5), and then use principal component analysis (PCA) to perform quality-independent fault detection to obtain the quality-independent T 2 Statistics;

[0066] Step (14): Perform quality-independent fault detection using an elastic network in the dynamic-quality-independent subspace as in step (6) to obtain the quality-independent T 2 Statistics;

[0067] Step (15): In the non-dynamic-quality-independent subspace, directly use principal component analysis to perform quality-independent fault detection in the same manner as in step (7) to obtain the quality-independent T 2 Statistics;

[0068] Step (16): Obtain the relevant results BIC of the Bayesian inference fusion of the test data set in the same way as in step (8) QAnd 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.

[0069] Compared with the traditional method, the advantages of the method of the present invention are:

[0070] First, the method of the present invention achieves accurate classification of variables by dividing the dynamic and dynamic characteristics between variables, and the quality-related and irrelevant relationships, accurately extracts the characteristics of process data, and improves the accuracy of fault detection; secondly, the method of the present invention also introduces data extension sequences to enhance the changing trend of dynamic data, and can more effectively extract dynamic characteristics. Finally, compared with other traditional multivariate statistical methods, the method of the present invention can better distinguish between quality-related and irrelevant faults, and can more efficiently and stably perform high-performance fault detection on quality-related faults. 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

[0071] Figure 1 is a flow chart of the method of the present invention;

[0072] Figure 2 It is the TEP industrial flow chart;

[0073] Figure 3 It is a simulation experiment diagram of the method of the present invention; DETAILED DESCRIPTION

[0074] The method of the present invention is described in detail below with reference to the accompanying drawings and specific implementation cases.

[0075] The present invention discloses a quality-related fault detection method based on dynamic and non-dynamic multi-subspace partitioning. 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.

[0076] 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 2As 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.

[0077] Table 1: 22 continuous variables in the TE process

[0078]

[0079] Table 2: 11 manipulated variables in the TE process

[0080]

[0081] Table 3: Two typical failures in TE process

[0082]

[0083] 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:

[0084] 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 ;

[0085] Step (2): Divide the process variable X according to its own temporal correlation and use the autocorrelation function (ACF) to measure x i (t) and x i The correlation between (t+k) i ∈R n×1 (i=1,2,…,m)), where k is the lag. i ∈R n×1 (i=1,…,m), the autocorrelation formula with lag k is

[0086] ACF(k)=S k / S0 (2)

[0087]

[0088]

[0089] The control limit of ACF is set to 0.05, so that the training data set X∈R n×m Dynamic subspace and non-dynamic subspace

[0090] Step (3): Further divide the subspaces into subspaces according to the mutual information (MI) values ​​between process variables and quality variables in the dynamic subspace and the non-dynamic subspace. The specific implementation process is as follows:

[0091] For the dynamic subspace X D With the non-dynamic subspace X U Each variable x in i , which is related to each quality variable y in the quality variable set Y j The mutual information value of is:

[0092]

[0093] Set a reasonable threshold η to divide the quality-related variables and quality-irrelevant variables. If MI>η, the variable is considered to be quality-related, otherwise it is considered to be a quality-irrelevant variable. The above strategy can be used to divide the dynamic and non-dynamic subspaces, and the resulting subspace division is:

[0094] X=X DQ +X DU +X UQ +X UU (6)

[0095] Among them, 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 quality-related variables reflect the changes of quality variables to a certain extent and have mutual influence or dependence in time, the quality-related variables are all dynamic variables in the variable division results, and there are no quality-related but non-dynamic process variables. Therefore, X UQ is an empty set;

[0096] Step (4): In the dynamic-quality related subspace, firstly, the time delay is introduced, the delay matrix is ​​constructed, and then the elastic network is used for quality related fault detection. The specific implementation process is as follows:

[0097] Step (4.1): According to the industrial process requirements, select the appropriate time delay h = 2. The process of matrix expansion can be described as:

[0098]

[0099] Step (4.2): Use the elastic network to build a quality-related fault detection model. The regression coefficient vector matrix β is obtained by minimizing the elastic network loss function L(β). The elastic network formula is as follows:

[0100]

[0101] Set α=0.5 and use the elastic network to combine the properties of Lasso regression and ridge regression;

[0102] Step (4.3): Transpose the regression coefficient vector matrix β obtained by the elastic network and perform singular value decomposition:

[0103] β=USV (9)

[0104] Step (4.4): Construct the quality-related and quality-irrelevant monitoring statistics as follows:

[0105]

[0106]

[0107] Step (4.5): The confidence level is 0.99 and the control limits are determined using the kernel density estimation (KDE) method;

[0108] Step (5): In the dynamic-quality-independent subspace, firstly, the time delay is introduced to construct the delay matrix, and then the principal component analysis (PCA) is used to perform quality-independent fault detection. The specific implementation process is as follows:

[0109] Step (5.1): Same as step (4.1), for the dynamic-mass-independent subspace X DU Perform matrix expansion with time delay h=2;

[0110] Step (5.2): For the expanded Use PCA for feature extraction, the formula is as follows;

[0111]

[0112] Cv i =λ i v i (13)

[0113] Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR:

[0114]

[0115] Select the first k eigenvectors that account for 85% of the CCR as the principal components to form the principal component matrix P, project the original data into the low-dimensional space, and obtain the reduced-dimensional data L:

[0116]

[0117] Step (5.3): Same as step (4.4), construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics;

[0118]

[0119] Among them, i is the i-th sample of L;

[0120] Step (5.4): For T 2 The statistics use the kernel density estimation (KDE) method to determine the control limit, given the confidence level α = 0.99, the specific formula is as follows:

[0121]

[0122]

[0123] F -1 (α)=inf{F J (j)≥α} (19)

[0124] Step (6): In the non-dynamic-mass-independent subspace X UU In the process, principal component analysis is directly used for quality-independent fault detection. The specific operation process is the same as step (5) to determine the control limits of the non-dynamic-quality-independent subspace;

[0125] Step (7): Use Bayesian inference to statistically merge the statistics of the subspaces, where the statistics related to quality are integrated into related joint statistics, and the statistics unrelated to quality are integrated into unrelated joint statistics. Then the single subspace x b The failure probability calculation formula is:

[0126] Step (7.1): Use Bayesian inference to statistically combine the statistics of all subspaces, and a single subspace x b The failure probability calculation formula is:

[0127]

[0128] P(X b )=P(X b |N)P(N)+P(X b |F)P(F) (21)

[0129] Among them, the conditional probability P(X b |N) and P(X b |F) are respectively

[0130]

[0131]

[0132] Step (7.2): Combine the detection results of all different sub-blocks through Bayesian reasoning and calculate the sum of the joint statistics:

[0133]

[0134] Set the confidence level to 0.99 and construct the relevant statistical confidence limit BIC in the offline phase QL BIC is irrelevant to statistical confidence limits NL , and finally completed the construction of multi-subspace quality-related fault detection model;

[0135] Step (8): 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 ;

[0136] Step (9): Divide the data into process variables XT according to the process of steps (2)-(3) to obtain the dynamic-quality related subspace XT DQ , dynamic-mass-independent subspace XT DU , non-dynamic-mass-independent subspace XT UU ;

[0137] Step (10): In the dynamic-quality related subspace, introduce time delay to construct a delay matrix as in step (4), use elastic network to perform quality related fault detection, and obtain quality related and quality irrelevant monitoring statistics. and

[0138] Step (11): In the dynamic-quality-independent subspace, introduce time delay to construct a delay matrix as in step (5), and then use the elastic network to perform quality-independent fault detection to obtain the quality-independent T 2 Statistics;

[0139] Step (12): Perform quality-independent fault detection in the non-dynamic-quality-independent subspace using principal component analysis (PCA) as in step (6) to obtain the quality-independent T 2 Statistics;

[0140] Step (13): Obtain the quality-related and quality-independent Bayesian inference fusion results BIC(Q) and BIC(NQ) of the test data set in the same manner as in step (7), 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.

[0141] 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 2 in TE are shown in Table 4;

[0142] Table 4: Detection results of quality-related faults in the quality-related subspace

[0143]

[0144] The detection results of the two methods for quality-independent fault 4 in TE are shown in Table 5:

[0145] Table 5: Detection results of quality-independent faults in the quality-dependent subspace.

[0146]

[0147] Finally, the simulation results of the method of the present invention for quality-related fault 2 and quality-independent fault 3 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.

[0148] 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 quality-related fault detection method based on dynamic and non-dynamic multi-subspace partitioning, characterized in that: The following steps are involved: The implementation process of the offline modeling phase is as follows: Step (1): Data collection and data preprocessing. The specific implementation process is as follows: Step (1.1): Collect sample data under normal operating conditions of the industrial process to form a training sample data set, where the process variable data set is The quality variable data set is Step (1.2): The collected sensor data is preprocessed using the z-score standardization method to obtain a 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. The specific calculation formula is as follows: in is the variable before standardization, x is the variable after standardization, μ is the mean of the variable, and σ is its standard deviation; Step (2): The division of dynamic and non-dynamic subspaces is based on the temporal correlation of the variables themselves, that is, if the variables have temporal correlation, they are classified as dynamic variables, otherwise they are non-dynamic variables. i ∈R n×1 (i=1,2,…,m) have different degrees of time series correlation, and the autocorrelation function (ACF) is used to measure x i (t) and x i (t+k), where k is the lag. i ∈R n×1 (i=1,…,m), the autocorrelation formula with lag k is ACF(k)=S k / S0 (2) When lag k>0, if ACF is within the given control range, the variable is considered to have no time series correlation; otherwise, the variable is considered to have time series correlation. For variables that are strictly time-series-free, ACF=0. Considering statistical significance, the control limit of ACF is set to 0.05, so that the training data set X∈R n×m Dynamic subspace and non-dynamic subspace Step (3): In the dynamic subspace and the non-dynamic subspace, the mutual information (MI) value between the process variable and the quality variable is further divided into the quality-related-dynamic subspace, the quality-independent-dynamic subspace, the quality-related-non-dynamic subspace, and the quality-independent-non-dynamic subspace. The specific implementation process is as follows: For the dynamic subspace X D With the non-dynamic subspace X U Each variable x in i , which is related to the quality variable y in the quality variable set Y j The mutual information value of is: In the formula, P(x i ,y j ) represents the joint distribution probability between process variables and quality variables. Set the threshold η. If MI>η, the variable is considered to be quality-related, otherwise it is considered to be quality-independent. The above strategy can be used to divide the dynamic and non-dynamic subspaces, and the resulting subspace division is: X=X DQ +X DU +X UQ +X UU (6) Among them, the dynamic-quality related subspace is X DQ , the dynamic-mass-independent subspace is X DU , the non-dynamic-mass-related subspace is X UQ , the non-dynamic-mass-independent subspace is X UU ; Step (4): In the dynamic-quality related subspace, time delay is introduced, a delay matrix is ​​constructed, and then an elastic network is used for quality related fault detection. The specific implementation process is as follows: Step (4.1): According to the industrial process requirements, select the appropriate time delay h. The process of matrix expansion can be described as: Where A is the original data matrix, and in this step it is the dynamic-quality related subspace X DQ , Formula (7) means that in the new matrix In , each time point contains the data of the current time t and the data of the past h time delays, which can effectively capture the dynamic characteristics of the data; Step (4.2): Use the elastic network to build a quality-related fault detection model. The regression coefficient vector matrix β is obtained by minimizing the elastic network loss function L(β). The elastic network formula is as follows: Among them, Y quality variable data set, To dynamically expand the matrix data set, ||β||1 is the Lasso regularization term (L1 norm), that is, the sum of the absolute values ​​of the regression coefficients, is the ridge regression regularization term (L2 norm), i.e., the sum of squares of regression coefficients, and λ1 and λ2 are the regularization strength parameters for Lasso and ridge regression. Step (4.3): Use the constructed elastic network model to implement quality-related fault detection and obtain corresponding statistics and control limits; Step (5): In the dynamic-quality-independent subspace, firstly, the time delay is introduced to construct the delay matrix, and then the principal component analysis (PCA) is used to perform quality-independent fault detection. The specific implementation process is as follows: Step (5.1): Same as step (4.1), for the dynamic-mass-independent subspace X DU Perform matrix expansion of the time delay h as a basis for capturing the dynamic characteristics in the data; Step (5.2): For the expanded Use PCA for feature extraction, the formula is as follows; Cv i =λ i v i (10) Sort all p eigenvectors by eigenvalue and calculate the cumulative contribution percentage CCR: Select the first k eigenvectors whose CCR accounts for more than 85% as the principal components to form the principal component matrix P, project the original data into the low-dimensional space, and obtain the reduced-dimensional data L: Step (5.3): Construct the dynamic-mass-independent subspace T based on the dimension-reduced L 2 Statistics: Among them, i is the i-th sample of L; Step (5.4): 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} (16) 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; Step (6): In the non-dynamic-mass-related subspace X UQ In the above method, the elastic network is directly used for quality-related fault detection. The specific operation process is the same as step (4.2) to step (4.3), and the statistics and control limits of the non-dynamic-quality related subspace are determined; Step (7): In the non-dynamic-mass-independent subspace X UU In the process, principal component analysis is directly used to detect quality-independent faults. The specific operation process is the same as step (5.2) to step (5.4), and the statistics and control limits of the non-dynamic-quality-independent subspace are determined; Step (8): Use Bayesian inference to statistically merge the statistics of quality-related classes and quality-irrelevant classes in all subspaces to obtain the monitoring results. The specific implementation process is as follows: Step (8.1): Use Bayesian inference to statistically merge the statistics of the subspaces, where the statistics related to the quality are integrated into related joint statistics, and the statistics unrelated to the quality are integrated into unrelated joint statistics. 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) (18) Among them, the conditional probability P(X b |B) 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 statistic of the b-th sub-block in the online detection dataset, J b,lim is the corresponding control limit; Step (8.2): 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 related joint statistical control limit BIC in the offline stage QL = 0.01 and BIC NL =0.

01.

2. A quality-related fault detection method based on dynamic and non-dynamic multi-subspace partitioning according to claim 1, characterized in that: In step (4), the elastic network is used to implement quality-related fault detection, construct statistics and estimate control limits. The specific implementation process is as follows: ① Use elastic network to build a quality-related fault detection model. The regression coefficient vector matrix β is obtained by minimizing the elastic network loss function L(β). The elastic network formula is as follows: Among them, Y quality variable data set, To dynamically expand the matrix data set, ||β||1 is the Lasso regularization term (L1 norm), that is, the sum of the absolute values ​​of the regression coefficients, is the ridge regression regularization term (L2 norm), i.e., the sum of squares of regression coefficients, and λ1 and λ2 are the regularization strength parameters for Lasso and ridge regression. ② Transpose the regression coefficient vector matrix β obtained by the elastic network and perform singular value decomposition: β=USV (23) Among them, S is a diagonal matrix containing singular values, U is the singular vector corresponding to zero singular values, and V is the singular vector corresponding to non-zero singular values; ③ In order to determine whether the process is normal and whether the fault affects the quality at the same time, the quality-related and quality-irrelevant monitoring statistics are constructed as follows: ④ The confidence level is 0.99, and the control limits of the above statistics are determined using the kernel density estimation (KDE) method.

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