Quality correlation monitoring method based on difference-orthogonal correlation analysis and difference-principal component analysis

Abstract

The invention discloses a quality correlation monitoring method based on difference-orthogonal correlation analysis and difference-principal component analysis, and is suitable for the field of quality analysis of complex data sets. According to the method, a data set is divided into a plurality of subspaces, and monitoring accuracy and efficiency are improved by adopting different analysis technologies. Specifically, the method comprises the following steps of: firstly, dividing a process data set into a quality-related dynamic subspace, a quality-related non-dynamic subspace, a quality-independent dynamic subspace and a quality-independent non-dynamic subspace according to the correlation degree of a process variable and a quality variable and whether process data has autocorrelation or not; secondly, after difference calculation is carried out in the quality-related dynamic subspace and the quality-related non-dynamic subspace, an operation state monitoring model is constructed by adopting orthogonal correlation analysis; and after difference calculation is carried out in the quality-independent dynamic subspace and the quality-independent non-dynamic subspace, an operation state monitoring model is constructed by applying a principal component analysis technology. And finally, integrating the results of the subspaces through a Bayesian method. The method provided by the invention can effectively process and analyze the complex data set and improve the accuracy of running state monitoring.

Description

[0001] The present invention relates to a data-driven operation status monitoring method, and in particular to a quality correlation monitoring method based on differential-orthogonal correlation analysis and differential-principal component analysis, which is applicable to fields requiring quality analysis of complex industrial data sets. Background Art

[0002] In today's rapidly developing industrial and technological fields, there is an increasing demand for quality analysis of complex industrial data sets. This demand has given rise to the need for efficient and accurate monitoring methods to ensure product quality and process efficiency. The present invention aims to provide a quality-related monitoring method based on differential-orthogonal correlation analysis and differential-principal component analysis. This method is particularly suitable for fields where quality analysis of complex industrial data sets is required. By dividing the data set into multiple subspaces and using specific analysis techniques for each subspace, the accuracy of operating status monitoring is improved.

[0003] Specifically, the present invention first divides the process data set into a quality-related dynamic subspace, a quality-independent dynamic subspace, a quality-related non-dynamic subspace, and a quality-independent non-dynamic subspace according to the degree of correlation between the process variables and the quality variables and the strength of the temporal correlation of the variables, and performs differential calculations in each subspace to extract the change characteristics of the data. Secondly, in the two quality-related subspaces, an operation status monitoring model is constructed using orthogonal correlation analysis to capture and analyze information directly related to quality. In the two quality-independent subspaces, principal component analysis technology is applied to construct an operation status monitoring model to comprehensively cover various information in the data set. Finally, the results of the subspaces are integrated through the Bayesian method to achieve comprehensive analysis and quality monitoring of complex data sets. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a quality correlation monitoring method based on difference-orthogonal correlation analysis and difference-principal component analysis.

[0005] Compared with the prior art, the present invention has the following advantages and technical effects:

[0006] Based on the subspace partitioning model, different analysis techniques are applied to different subspaces to extract features of process data in a more targeted manner, which can discover the main information that affects product quality, thereby improving the accuracy of fault detection. The main steps include:

[0007] Step (1): Collect sample data of industrial production objects under normal operation to form a training data set, where the process variable set is The quality variable set is Then the data set is normalized to a distribution with a mean of 0 and a variance of 1.

[0008] Step (2): Divide the data into dynamic variables and non-dynamic variables according to their time series correlation. Specifically, different variables x i With different degrees of time series correlation, the size of the autocorrelation function is calculated to measure x i (t) and x i (t+k), k is the lag parameter, for x i , the autocorrelation function formula is: ACF(k)=S k / S 0 ,

[0009]

[0010] When k is positive and ACF is within the control limit, the variable is considered to have no time series correlation; if ACF exceeds the limit, the variable is considered to have time series correlation. Based on statistical significance, the control limit of the autocorrelation function is set to 0.05, and then the training data set is Divided into dynamic variables and non-dynamic variables. Among dynamic variables and non-dynamic variables, according to the mutual information value between process variables and quality variables, they are further subdivided into quality-related dynamic subspace, quality-independent dynamic subspace, quality-related non-dynamic subspace and quality-independent non-dynamic subspace. The division process is as follows:

[0011] Each variable x in the dynamic subspace and the non-dynamic subspace i The quality variable y in the quality variable set i The mutual information value between Where P represents the probability density function. By setting a threshold, if the mutual information value exceeds the threshold, the variable is considered to be related to quality; otherwise, it is considered to be a variable unrelated to quality. Using this strategy, the dynamic and non-dynamic subspaces can be divided, and the final subspace division result is:

[0012] Among them, X 1 is the mass-dependent dynamic subspace, X 2 is the mass-dependent non-dynamic subspace, X 3 is the mass-independent non-dynamic subspace, X 4 is the quality-independent dynamic subspace. Differential operations are performed in each subspace. Taking the quality-dependent dynamic subspace as an example, the specific process is as follows:

[0013] For the data matrix Each column is a measurement point, each row is a sample data, assuming that the variable The data sample is represented as Then the difference calculation is expressed as So we can get the difference after calculation.

[0014] Step (3): In the quality-dependent dynamic subspace, Orthogonal correlation analysis was performed to obtain the statistic T 1 2 and And the corresponding alarm threshold lim 1 ,lim 2 The steps of orthogonal correlation analysis are as follows:

[0015] First calculate the process variable Pearson correlation coefficient between in Σ represents the correlation matrix, I represents the identity matrix, and 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 Where κ = rank(Σ), we can know Right now Get the correlation matrix H = AΞ(B) -1 , and perform singular value decomposition to obtain in and Represent two mutually orthogonal projection spaces. Thus, the statistic is calculated Among them, inv() is the inverse function, and cov() is the covariance function. The control limit is determined by kernel density estimation. Finally, the statistic T is obtained. 1 2 , And the corresponding alarm threshold lim 1 ,lim 2 .

[0016] Step (4): For the quality-dependent non-dynamic spatial data matrix X 2 Perform the same operation as in step (3) to obtain the corresponding statistics And the corresponding alarm threshold lim 3 ,lim 4 .

[0017] Step (5): For the data matrix in the mass-independent non-dynamic space Through principal component analysis, the corresponding principal component matrix P is calculated 3 : Cv i =λ i v i, sort the eigenvectors in descending order according to the size of the eigenvalue, select the first k eigenvectors as the principal components, and form the principal component matrix P 3 . Calculate the corresponding statistics And use the kernel density estimation method to calculate the corresponding control limit lim 5 .

[0018] Step (6): For the data matrix X in the mass-independent dynamic subspace 4 Repeat the operation in step (5) to calculate the corresponding statistics And the corresponding control limit lim 6 .

[0019] Step (7): Use the following Bayesian fusion strategy to fuse the statistics to obtain the quality-related statistic BIC1(Q), the quality-independent statistic BIC2(NQ) and the corresponding control limits lim BIC1 and lim BIC2 .

[0020]

[0021] sum1=p(T 1 2 |F)+p(T 3 2 |F)

[0022] p(T 1 2 )=p(T 1 2 |N)p(N)+p(T 1 2 |F)p(F)

[0023] p(T 3 2 )=p(T 3 2 |N)p(N)+p(T 3 2 |F)p(F)

[0024] p(F|T 1 2 )=p(T 1 2 |F)p(F) / p(T 1 2 )

[0025] p(F|T 3 2 )=p(T 3 2 |F)p(F) / p(T 32 )

[0026] BIC1(Q)=(p(T 1 2 |F)p(F|T 1 2 )+p(T 3 2 |F)p(F|T 3 2 )) / sum1

[0027]

[0028] p(T 5 2 )=p(T 5 2 |N)p(N)+p(T 5 2 |F)p(F)

[0029]

[0030] p(F|T 5 2 )=p(T 5 2 |F)p(F) / p(T 5 2 )

[0031]

[0032] Where N represents the normal situation, F represents the fault situation, p(N) = α, p(F) = 1-α, α is the confidence level, and the control limit lim BIC1 =lim BIC2 =1-α.

[0033] Step (8): In the online monitoring phase, the process variable set X to be monitored is obtained. test .

[0034] Step (9): Same as steps (2) to (7), divide the space into four subspaces and calculate the statistics to obtain The Bayesian strategy is used to integrate relevant statistics and irrelevant statistics to obtain the comprehensive index BIC1. test (Q) and BIC2 test (NQ). and with the threshold lim BIC1 and lim BIC2 Compare them respectively, if the threshold is exceeded, an alarm will be issued, otherwise it is considered that the system is operating normally. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0036] Figure 1 It is a schematic diagram of the detection results of an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of a monitoring method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The method of the present invention is described in detail below with reference to the accompanying drawings and specific implementation cases.

[0039] like Figure 2 As shown, a quality correlation monitoring method based on difference-orthogonal correlation analysis and difference-principal component analysis is provided. The specific implementation process of the present invention is described below in conjunction with a specific industrial process case.

[0040] The application object is from the Tennessee-Eastman Chemical Process. The process includes five main units: reactor, condenser, compressor, separator and stripper. 22 measured variables are selected as process variables, and components G and H are used as quality variables for modeling. The introduction of related variables is shown in Table 1. Next, the specific implementation steps of the present invention are described in detail in conjunction with the process.

[0041] Table 1: Case variables.

[0042] Serial number Variable Description Serial number Variable Description Serial number Variable Description 1 Material A flow 2 Material D flow 3 Material E flow 4 Total feed flow 5 Circulation flow 6 Reactor feed 7 Reactor pressure 8 Reactor level 9 Reactor temperature 10 Emptying rate 11 Separator temperature 12 Separator level 13 Separator pressure 14 Separator bottom flow 15 Stripper Grade 16 Stripper pressure 17 Stripper bottom flow 18 Stripper temperature 19 Steam from the top of the stripping tower 20 Compressor power 21 Reactor cooling water outlet temperature 22 Separator cooling water outlet temperature 23 Molar concentration of ingredient G 24 Molar concentration of component H

[0043] First, the monitoring model is trained on 960 samples collected under normal operation, including the following steps:

[0044] Step (1): Collect sample data of industrial production objects under normal operation to form a training data set, where the process variable set is The quality variable set is Here, R represents the spatial dimension, each column of the data set is a measurement point, and each row is a sample data. Then, the data set is normalized by the Z_score standard.

[0045] Step (2): Divide the process variables into dynamic-quality related dynamic subspaces by calculating the autocorrelation function and mutual information Contains variables 2,4,7,10,11,13,16,18,19,22; quality-dependent non-dynamic subspace X 2 , is empty; mass-independent non-dynamic subspace Contains variables 5, 6, 12, 14, 15, 17; mass-independent dynamic subspace Contains variables 1, 3, 8, 9, 20, 21. And calculate the difference results for each subspace separately

[0046] Step (3): In the quality-dependent dynamic subspace, Orthogonal correlation analysis was performed to obtain the statistic T 1 2 and And the corresponding alarm threshold lim 1 ,lim 2 The steps of orthogonal correlation analysis are as follows:

[0047] First calculate the process variable Pearson correlation coefficient between in Σ represents the correlation matrix, I represents the identity matrix, and 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 Where κ = rank(Σ), we can know Right now Get the correlation matrix H = AΞ(B) -1 , and perform singular value decomposition to obtain in and Represent two mutually orthogonal projection spaces. Thus, the statistic is calculated Among them, inv() is the inverse function, and cov() is the covariance function. The control limit is determined by kernel density estimation. Finally, the statistic T is obtained. 1 2 , And the corresponding alarm threshold lim 1 ,lim 2 .

[0048] Step (4): For the data matrix in the mass-independent non-dynamic space Through principal component analysis, the corresponding principal component matrix P is calculated 3 : Cv i =λ i v i , sort the eigenvectors in descending order according to the size of the eigenvalue, select the first k eigenvectors as the principal components, and form the principal component matrix P 3 . Calculate the corresponding statistics And use the kernel density estimation method to calculate the corresponding control limit lim 5 .

[0049] Step (5): For the data matrix in the mass-independent dynamic subspace Repeat the operation in step (4) to calculate the corresponding statistics And the corresponding control limit lim 6 .

[0050] Step (6): Use the following Bayesian fusion strategy to fuse the statistics to obtain the quality-related statistic BIC1(Q), the quality-independent statistic BIC2(NQ) and the corresponding control limits lim BIC1 and lim BIC2 .

[0051] Step (7): In the online monitoring phase, the process variable set X to be monitored is obtained. test , the same as steps (1) to (6), after standardizing the data, divide the corresponding four subspaces and perform differential calculations respectively, and then calculate the statistics to obtain The Bayesian strategy is used to integrate relevant statistics and irrelevant statistics to obtain the comprehensive index BIC1. test (Q) and BIC2 test (NQ). and with the threshold lim BIC1 and lim BIC2 Compare them respectively, if the threshold is exceeded, an alarm will be issued, otherwise it is considered that the system is operating normally.

[0052] The fault case is caused by the sticking of the reactor cooling water valve. This fault will cause the reactor temperature to fluctuate, but because there is a control loop, the fault will not affect the product quality. When the fault occurs, G and H hardly change. For quality-independent faults, the false alarm rate is the proportion of normal samples (i.e., sample points 0 to 160) in the quality-independent space whose statistics are greater than the control limit. The false alarm rate is the proportion of faulty samples (i.e., sample points 161 to 960) whose statistics are less than the control limit.

[0053] The fault detection results of this method in this process are as follows Figure 1 As shown, blue represents normal samples, red represents faulty samples, and the dotted line represents the control limit:

[0054] It can be seen from the second sub-figure that the first 160 normal sample points are always below the control limit, with a false alarm rate of 0, and the last 800 sample points are always above the control limit, with a false alarm rate of 0.

[0055] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A quality-related monitoring method based on difference-orthogonal correlation analysis and difference-principal component analysis, characterized in that: The method comprises the following steps: Step (1): Collect sample data of industrial production objects under normal operation to form a training data set, where the process variable set is The quality variable set is Then the data set is normalized to a distribution with a mean of 0 and a variance of 1. Step (2): Divide the data into dynamic variables and non-dynamic variables according to their time series correlation. Specifically, different variables x i With different degrees of time series correlation, the size of the autocorrelation function is calculated to measure x i (t) and x i (t+k), k is the lag parameter, for x i , the autocorrelation function formula is: ACF(k)=S k / S0, When k is positive and ACF is within the control limit, the variable is considered to have no time series correlation; if ACF exceeds the limit, the variable is considered to have time series correlation. Based on statistical significance, the control limit of the autocorrelation function is set to 0.05, and then the training data set is Divided into dynamic variables and non-dynamic variables. Among dynamic variables and non-dynamic variables, according to the mutual information value between process variables and quality variables, they are further subdivided into quality-related dynamic subspace, quality-independent dynamic subspace, quality-related non-dynamic subspace and quality-independent non-dynamic subspace. The division process is as follows: Each variable x in the dynamic subspace and the non-dynamic subspace i The quality variable y in the quality variable set i The mutual information value between Where P represents the probability density function. By setting a threshold, if the mutual information value exceeds the threshold, the variable is considered to be related to quality; otherwise, it is considered to be a variable unrelated to quality. Using this strategy, the dynamic and non-dynamic subspaces can be divided, and the final subspace division result is: Among them, X1 is the quality-related dynamic subspace, X2 is the quality-related non-dynamic subspace, X3 is the quality-independent non-dynamic subspace, and X4 is the quality-independent dynamic subspace. Differential operations are performed in each subspace, taking the quality-related dynamic subspace as an example, the specific process is as follows: For the data matrix Each column is a measurement point, each row is a sample data, assuming that the variable The data sample is represented as Then the difference calculation is expressed as So we can get the difference after calculation. Step (3): In the quality-dependent dynamic subspace, Orthogonal correlation analysis was performed to obtain the statistic T1 2 and T2 2 And the corresponding alarm thresholds lim1 and lim2. The steps of orthogonal correlation analysis are as follows: First calculate the process variable Pearson correlation coefficient between in Σ represents the correlation matrix, I represents the identity matrix, and 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 Where κ = rank(Σ), we can know Right now Get the correlation matrix H = AΞ(B) -1 , and perform singular value decomposition to obtain in and Represent two mutually orthogonal projection spaces. Thus, the statistic is calculated Among them, inv() is the inverse function, and cov() is the covariance function. The control limit is determined by kernel density estimation. Finally, the statistic T1 is obtained 2 、T2 2 And the corresponding alarm thresholds lim1 and lim2. Step (4): Perform the same operation as step (3) on the quality-related non-dynamic spatial data matrix X2 to obtain the corresponding statistic T3 2 、T4 2 And the corresponding alarm thresholds lim3 and lim4. Step (5): For the data matrix in the mass-independent non-dynamic space Through principal component analysis, the corresponding principal component matrix P3 is calculated: Cv i =λ i v i , sort the eigenvectors in descending order according to the size of the eigenvalue, select the first k eigenvectors as the principal components, and form the principal component matrix P3. Calculate the corresponding statistics And use the kernel density estimation method to calculate the corresponding control limit lim5. Step (6): Repeat the operation in step (5) for the data matrix X4 in the mass-independent dynamic subspace and calculate the corresponding statistics And the corresponding control limit lim6. Step (7): Use the following Bayesian fusion strategy to fuse the statistics to obtain the quality-related statistic BIC1(Q), the quality-independent statistic BIC2(NQ) and the corresponding control limits lim BIC1 and lim BIC2 . sum1=p(T1 2 |F)+p(T3 2 |F) p(T1 2 )=p(T1 2 |N)p(N)+p(T1 2 |F)p(F) p(T3 2 )=p(T3 2 |N)p(N)+p(T3 2 |F)p(F) p(F|T1 2 )=p(T1 2 |F)p(F) / p(T1 2 ) p(F|T3 2 )=p(T3 2 |F)p(F) / p(T3 2 ) BIC1(Q)=(p(T1 2 |F)p(F|T1 2 )+p(T3 2 |F)p(F|T3 2 )) / sum1 sum2=p(T2 2 |F)+p(T4 2 |F)+p(T5 2 |F)+p(T6 2 |F) p(T2 2 )=p(T2 2 |N)p(N)+p(T2 2 |F)p(F) p(T4 2 )=p(T4 2 |N)p(N)+p(T4 2 |F)p(F) p(T5 2 )=p(T5 2 |N)p(N)+p(T5 2 |F)p(F) p(T6 2 )=p(T6 2 |N)p(N)+p(T6 2 |F)p(F) p(F|T2 2 )=p(T2 2 |F)p(F) / p(T2 2 ) p(F|T4 2 )=p(T4 2 |F)p(F) / p(T4 2 ) p(F|T5 2 )=p(T5 2 |F)p(F) / p(T5 2 ) p(F|T6 2 )=p(T6 2 |F)p(F) / p(T6 2 ) BIC2(NQ)=(p(T2 2 |F)p(F|T2 2 )+p(T4 2 |F)p(F|T4 2 )+p(T5 2 |F)p(F|T5 2 )+p(T6 2 |F)p(F|T6 2 )) / sum2 Where N represents the normal situation, F represents the fault situation, p(N) = α, p(F) = 1-α, α is the confidence level, and the control limit lim BIC1 =lim BIC2 =1-α. Step (8): In the online monitoring phase, the process variable set X to be monitored is obtained. test . Step (9): Same as steps (2) to (7), divide the space into four subspaces and calculate the statistics to obtain The Bayesian strategy is used to integrate relevant statistics and irrelevant statistics to obtain the comprehensive index BIC1. test (Q) and BIC2 test (NQ). and with the threshold lim BIC1 and lim BIC2 Compare them respectively, if the threshold is exceeded, an alarm will be issued, otherwise it is considered that the system is operating normally.

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