Non-stationary industrial process anomaly monitoring method based on stationary subspace analysis

Abstract

The invention discloses a non-stationary industrial process anomaly monitoring method based on stationary subspace analysis, and belongs to the technical field of industrial process monitoring and fault diagnosis. The method comprises the following steps: acquiring sensor measurement data under a normal working condition in a non-stationary industrial process as a training data set, constructing an analytic stationary subspace analysis model based on the training data set, and solving stationary and non-stationary subspaces in offline process data; collecting sensor measurement data under a real-time working condition in a non-stationary industrial process as test data; appropriate sliding window parameters are given, and online stationary and non-stationary subspaces based on the stationary subspace analysis model are solved; and constructing monitoring statistics based on a principal angle, collecting operation data of the non-stationary industrial process under a normal working condition, constructing a threshold value, determining a data set, and realizing monitoring of the abnormity of the non-stationary industrial process. The method does not need a mathematical model of a non-stationary industrial process, and can be applied to various data-driven monitoring scenes.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process monitoring and fault diagnosis, and in particular relates to a non-stationary industrial process anomaly monitoring method based on analytical stationary subspace analysis. Background Art

[0002] With the continuous expansion of production scale and the increasing sophistication of process technology, various links in the industrial process are interconnected and mutually influential. Once an anomaly occurs in the process, it may cause huge economic losses and even endanger personal safety. As a key support for ensuring the safe, stable and efficient operation of industrial production, the importance of industrial process anomaly monitoring technology is becoming increasingly prominent in today's industrial production process. Due to the influence of various factors such as equipment aging, operational errors, environmental changes, and fluctuations in raw material quality, modern industrial processes are often in a non-stationary operating state. Abnormal information in industrial processes can easily be obscured by the non-stationary change trend of data. Therefore, timely and accurate monitoring of non-stationary industrial process anomalies is of vital importance to preventing accidents and ensuring the smooth progress of industrial production.

[0003] Non-stationary anomaly monitoring methods, such as stationary subspace analysis and cointegration analysis, have made significant progress over the past few years. As one of the most effective monitoring methods, non-stationary industrial process anomaly monitoring methods based on stationary subspace analysis have seen rapid development in recent years and are being applied to industrial processes such as petrochemicals and semiconductor manufacturing. However, most existing monitoring methods based on stationary subspace analysis only monitor the stationary components isolated from non-stationary process data, failing to fully utilize these isolated non-stationary components, which can easily lead to false positives and false negatives. Summary of the Invention

[0004] In response to the above-mentioned technical problems existing in the prior art, the present invention proposes a method for monitoring abnormalities in non-stationary industrial processes based on analytical stationary subspace analysis. The purpose is to address the problem that the existing traditional stationary subspace analysis method is unable to monitor the separated non-stationary components. The design is reasonable, overcomes the shortcomings of the prior art, and has good results.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The method for monitoring abnormalities in non-stationary industrial processes based on analytical stationary subspace analysis includes the following steps:

[0007] Step 1: Collect measurement data from m sensors under normal operating conditions of a non-stationary industrial process, divide it into N equal-length data segments as a training dataset, and establish an offline analytical stationary subspace analysis model based on the training dataset;

[0008] Step 2: Solve the stationary and non-stationary subspaces of offline process data;

[0009] Step 3: Collect sensor measurement data under real-time conditions of non-stationary industrial processes as test data, give appropriate sliding window parameters, and solve the online stationary and non-stationary subspaces based on the analytical stationary subspace analysis model;

[0010] Step 4: Based on the online and offline stationary / non-stationary online subspaces, construct a monitoring statistic based on the protagonist to monitor the changes in the online and offline subspaces;

[0011] Step 5: Collect measurement data under normal operating conditions of non-stationary industrial processes, construct a threshold determination data set, calculate the monitoring threshold based on kernel density estimation, and realize the monitoring of abnormalities in non-stationary industrial processes.

[0012] Preferably, in step 1, for m-dimensional non-stationary industrial process data, M data samples are collected offline and divided into N data segments. The sample mean and covariance matrix in each segment are first calculated, and then the average value of the overall sample mean and covariance matrix is ​​calculated as follows:

[0013]

[0014] Among them, μ i and Σ i are the sample mean and sample covariance matrix of the i-th data segment respectively;

[0015] Calculate the analytical stationary subspace analysis objective function to obtain the data unmixing matrix B:

[0016]

[0017] Where I is the identity matrix and S is in the form of:

[0018]

[0019] Preferably, in step 2, the stationary and non-stationary subspaces of the offline process data are calculated according to the singular value decomposition of equations (1) and (2);

[0020] First, the projection matrices of the stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem:

[0021]

[0022] Where γ=[γ1,γ2,…,γ m ] are the eigenvalues ​​arranged from small to large; is the m eigenvectors corresponding to the eigenvalues; define the stationary subspace dimension d, the stationary component projection matrix B sWith the non-stationary component projection matrix B n The eigenvectors The different columns are:

[0023]

[0024] According to the above derivation, for B s With B n Perform the following singular value decomposition to obtain offline stationary and non-stationary subspaces:

[0025] U n S n V n =B n (1);

[0026] U s S s V s =B s (2);

[0027] Among them, U n with U s are the calculated non-stationary and stationary subspaces, S n With S s Respectively represent B n With B s The singular value obtained by singular value decomposition, V n With V s is a right singular vector.

[0028] Preferably, in step 3, first, given the sliding window size s, construct the online data x s (t)=[x(t-s+1),x(t-s+2),...,x(t)], and calculate the sample mean and covariance matrix as follows:

[0029]

[0030] Solve the following optimization problem;

[0031] Calculate the online data unmixing matrix B on :

[0032]

[0033] Where I is the identity matrix, S on and The form is as follows:

[0034]

[0035] and are the mean and covariance matrices after online data update;

[0036] For the above optimization problem, the projection matrices of the online stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem;

[0037]

[0038] Among them, γ on =[γ on,1 ,γ on,2 ,…,γ on,m ] are the eigenvalues ​​arranged from small to large; Represents the eigenvector corresponding to the eigenvalue, and the projection matrix of the online stationary and non-stationary components is composed of the eigenvector The different columns are:

[0039]

[0040] According to the above derivation, the following singular value decomposition is solved to obtain the online stationary and non-stationary subspaces:

[0041] U on,n S on,n V on,n =B on,n (3);

[0042] U on,s S on,s V on,s =B on,s (4);

[0043] Among them, U on,n with U on,s is the non-stationary and stationary subspace calculated online at time t, S on,n With S on,s Respectively represent B on,n With B on,s The singular value obtained by singular value decomposition, V on,n With V on,s are right singular vectors.

[0044] Preferably, in step 4, the constructed abnormal monitoring statistic is in the form of

[0045]

[0046]

[0047] Among them, J p1 With J p2 They are used to monitor non-stationary and stationary components respectively, d is the stationary subspace dimension, S p1 =[s p1,1,s p1,2 ,...,s p1,d ] represents the cosine value of the angle between the online and offline stationary subspaces in the 1st,…,dth dimensions, S p2 =[s p2,1 ,s p2,2 ,...,s p2,m-d ] represents the cosine value of the angle between the online and offline non-stationary subspaces in the 1,…,md dimensions respectively; S p1 With S p2 The following singular value decomposition is obtained

[0048]

[0049] U p1 with U p2 They represent the left singular vectors of the singular value decomposition, V p1 With V p2 They represent the right singular vectors of the singular value decomposition.

[0050] Preferably, the normal operation data of the non-stationary industrial process is collected and divided into N1 data segments of length s as the threshold determination data set, and the monitoring results of the threshold determination data set are calculated using formula (5) and formula (6) respectively. Finally, the monitoring threshold J is determined based on the kernel density estimation method. th1 With J th2 , and based on the following logic and Determine whether an exception occurs:

[0051]

[0052] The beneficial technical effects brought about by the present invention are:

[0053] The present invention provides a method for monitoring abnormalities in non-stationary industrial processes based on analytical stationary subspace analysis. This method does not require precise mathematical models of the industrial process and operating data under abnormal conditions of the industrial process, and is therefore convenient for practical application. It can fully mine abnormal information in non-stationary data, solve the problem of abnormal information being masked by normal data fluctuations, and improve monitoring performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0055] Figure 2 This is a schematic diagram of anomaly monitoring based on the traditional analytical stationary subspace analysis method;

[0056] Figure 3 This is a schematic diagram of the stable component monitoring results based on the proposed method;

[0057] Figure 4 Schematic diagram of the non-stationary component monitoring results based on the proposed method. DETAILED DESCRIPTION

[0058] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0059] like Figure 1 As shown in FIG, a method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis includes the following steps:

[0060] Step S110: collecting measurement data from m sensors under normal operating conditions of a non-stationary industrial process, dividing the data into N equal-length data segments as a training data set, and establishing an analytical stationary subspace analysis model based on the training data set;

[0061] Specifically, for m-dimensional non-stationary industrial process data, M data samples are collected offline and divided into N data segments. First, the sample mean and covariance matrix in each segment are calculated separately, and then the average value of the overall sample mean and covariance matrix is ​​calculated separately as follows:

[0062]

[0063] Among them, μ i and Σ i are the sample mean and sample covariance matrix of the i-th data segment respectively;

[0064] Calculate the analytical stationary subspace analysis objective function to obtain the data unmixing matrix B:

[0065]

[0066] Where I is the identity matrix and S is in the form of:

[0067]

[0068] Step S120: solving the stationary and non-stationary subspaces of the offline process data;

[0069] The stationary and non-stationary subspaces of the offline process data are calculated based on the singular value decomposition of equations (1) and (2);

[0070] First, the projection matrices of the stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem:

[0071]

[0072] Where γ=[γ1,γ2,…,γ m ] are the eigenvalues ​​arranged from small to large; is the m eigenvectors corresponding to the eigenvalues; define the stationary subspace dimension d, the stationary component projection matrix B s With the non-stationary component projection matrix B n The eigenvectors The different columns are:

[0073]

[0074] According to the above derivation, for B s With B n Perform the following singular value decomposition to obtain offline stationary and non-stationary subspaces:

[0075] U n S n V n =B n (1);

[0076] U s S s V s =B s (2);

[0077] Among them, U n with U s are the calculated non-stationary and stationary subspaces, S n With S s Respectively represent B n With B s The singular value obtained by singular value decomposition, V n With V s is a right singular vector.

[0078] Step S130: collecting sensor measurement data under real-time working conditions of a non-stationary industrial process as test data, giving appropriate sliding window parameters, and solving the stationary and non-stationary online subspaces based on the analytical stationary subspace analysis model;

[0079] Specifically, first, given the sliding window size s, take the online time t as an example, construct the online data x s (t)=[x(t-s+1),x(t-s+2),…,x(t)], and calculate the sample mean and covariance matrix as follows:

[0080]

[0081] Solve the following optimization problem;

[0082] Calculate the online data unmixing matrix B on :

[0083]

[0084] Where I is the identity matrix, S on and The form is as follows:

[0085]

[0086] and are the mean and covariance matrices after online data update;

[0087] For the above optimization problem, the projection matrices of the online stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem;

[0088]

[0089] Among them, γ on =[γ on,1 ,γ on,2 ,…,γ on,m ] are the eigenvalues ​​arranged from small to large; Represents the eigenvector corresponding to the eigenvalue, and the projection matrix of the online stationary and non-stationary components is composed of the eigenvector The different columns are:

[0090]

[0091] According to the above derivation, the following singular value decomposition is solved to obtain the online stationary and non-stationary subspaces:

[0092] U on,n S on,n V on,n =B on,n (3);

[0093] U on,s S on,s V on,s =B on,s (4);

[0094] Among them, U on,n with U on,s is the non-stationary and stationary subspace calculated online at time t, S on,n With S on,s Respectively represent B on,n With B on,s The singular value obtained by singular value decomposition, V on,n With V on,s is a right singular vector.

[0095] Step S140: constructing monitoring statistics based on the protagonist to monitor changes in online and offline subspaces;

[0096] Specifically, the constructed anomaly monitoring statistic is in the form of

[0097]

[0098] Among them, J p1 With J p2 They are used to monitor non-stationary and stationary components respectively, d is the stationary subspace dimension, S p1 =[s p1,1 ,s p1,2 ,...,s p1,d ] represents the cosine value of the angle between the online and offline stationary subspaces in the 1st,…,dth dimensions, S p2 =[s p2,1 ,s p2,2 ,…,s p2,m-d ] represents the cosine value of the angle between the online and offline non-stationary subspaces in the 1,…,md dimensions respectively; S p1 With S p2 The following singular value decomposition is obtained

[0099]

[0100] U p1 with U p2 They represent the left singular vectors of the singular value decomposition, V p1 With V p2 They represent the right singular vectors of the singular value decomposition.

[0101] Step S150: Collect measurement data of a non-stationary industrial process under normal operating conditions, construct a threshold determination data set, calculate a monitoring threshold based on kernel density estimation, and realize monitoring of abnormalities in the non-stationary industrial process.

[0102] Specifically, the normal operation data of the non-stationary industrial process is collected and divided into N1 data segments of length s as the threshold determination data set. The monitoring results of the threshold determination data set are calculated using formula (5) and formula (6) respectively. Finally, the monitoring threshold J is determined using the kernel density estimation method. th1 With J th2 , based on the following logic and Determine whether an exception occurs:

[0103]

[0104] To help understand the present invention and visually demonstrate its effectiveness for non-stationary anomaly monitoring, an example is described below. This example, based on Matlab tools, uses the Tennessee-Eastman Chemical process anomaly case to illustrate the present invention, and the effects of the present invention are demonstrated in conjunction with the accompanying figures.

[0105] (1) Generate non-stationary industrial process operation data as training data and establish an offline analytical stationary subspace analysis model based on the training data.

[0106] Specifically, this example uses the Tennessee-Eastman Chemical Process to verify the proposed method. The Tennessee-Eastman Chemical Process contains a total of 53 process variables, of which 12 are manipulated variables and 41 are monitored variables. The training data set size is 950, and N is set to 50, thus obtaining 19 groups of offline data samples with a length of 50. The mean and covariance matrix of each group of samples are calculated, as well as the average mean and covariance matrix of the 19 groups of samples. Based on this, the offline non-stationary and stationary subspaces U are calculated. n with U s .

[0107] (2) The 19th anomaly is imposed on the normally operating Tennessee-Eastman Chemical process to generate a test data set, and an online analytical stationary subspace analysis model is established based on the test data.

[0108] Specifically, it is still based on the Tennessee-Eastman chemical process. In order to test the effectiveness of the non-stationary anomaly monitoring method proposed in this invention, 960 test samples independent of the training data set are used as the test data set, and an anomaly is introduced at the 160th sample. Given an online sliding window length of 50, the online non-stationary and stationary subspace U can be obtained. on,n with U on,s .

[0109] (3) Calculate the monitoring statistic J based on the main character distance p1 With J p2 .

[0110] Specifically, the offline and online non-stationary / stationary subspaces obtained in (1) and (2) are used to calculate J p1 With J p2 Used to monitor the stationary and non-stationary components in process data.

[0111] (4) Calculate J separately p1 With J p2 The monitoring threshold J th1 With J th2 .

[0112] Specifically, 500 normal operation samples generated based on the Tennessee-Eastman chemical process model and independent of the training data set are used as the threshold determination data set. Given an online sliding window length of 50, the online non-stationary and stationary subspaces in the threshold determination data set are obtained, and the J in the threshold determination data set is calculated. p1 With J p2Based on the kernel density estimation method, given a confidence level of 95%, we solve J th1 With J th2 , for the J calculated by online samples p1 With J p2 , based on the following logic and Determine whether an exception occurs:

[0113]

[0114] In order to illustrate the effectiveness of the proposed method for monitoring abnormalities in non-stationary industrial processes, a comparative experiment was conducted with the traditional stationary subspace analysis method. Figure 2 The results of monitoring the stationary components by the traditional analytical stationary subspace analysis monitoring method are shown. It can be seen that after an anomaly occurs, the traditional method is insensitive to the anomaly and it is difficult to complete the anomaly monitoring. Figure 3 The proposed monitoring statistic J is given p1 From the monitoring results of the stationary components, we can see that by monitoring the changes in the stationary subspace, the proposed method can more effectively monitor anomalies. Figure 4 The proposed monitoring statistic J is given p2 Monitoring results of the separated non-stationary components. Since the mean and means of non-stationary components change over time, abnormal information in industrial processes can be easily masked by the changing trend of non-stationary data, so traditional methods are difficult to monitor this part. However, through Figure 4 It can be seen that the proposed method can monitor anomalies in a timely and accurate manner from the perspective of the subspace changes of non-stationary components.

[0115] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A non-stationary industrial process anomaly monitoring method based on analytical stationary subspace analysis, characterized in that: The steps include: Step 1: Collect measurement data from m sensors under normal operating conditions of a non-stationary industrial process, divide it into N equal-length data segments as a training dataset, and establish an offline analytical stationary subspace analysis model based on the training dataset; Step 2: Solve the stationary and non-stationary subspaces of offline process data; Step 3: Collect sensor measurement data under real-time conditions of non-stationary industrial processes as test data, give appropriate sliding window parameters, and solve the online stationary and non-stationary subspaces based on the analytical stationary subspace analysis model; Step 4: Based on the online and offline stationary / non-stationary online subspaces, construct a monitoring statistic based on the protagonist to monitor the changes in the online and offline subspaces; Step 5: Collect measurement data under normal operating conditions of non-stationary industrial processes, construct a threshold determination data set, calculate the monitoring threshold based on kernel density estimation, and realize the monitoring of abnormalities in non-stationary industrial processes.

2. The method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis according to claim 1, characterized in that: In step 1, for m-dimensional non-stationary industrial process data, M data samples are collected offline and divided into N data segments. First, the sample mean and covariance matrix of each segment are calculated separately, and then the average of the overall sample mean and covariance matrix is ​​calculated separately as follows: Among them, μ i and Σ i are the sample mean and sample covariance matrix of the i-th data segment respectively; Calculate the analytical stationary subspace analysis objective function to obtain the data unmixing matrix B: Where I is the identity matrix and S is in the form of:

3. The method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis according to claim 1, characterized in that: In step 2, the stationary and non-stationary subspaces of the offline process data are calculated according to the singular value decomposition of equations (1) and (2); First, the projection matrices of the stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem: Where γ=[γ1,γ2,…,γ m ] are the eigenvalues ​​arranged from small to large; is the m eigenvectors corresponding to the eigenvalues; define the stationary subspace dimension d, the stationary component projection matrix B s and the non-stationary component projection matrix B n The eigenvectors The different columns are: According to the above derivation, for B s With B n Perform the following singular value decomposition to obtain offline stationary and non-stationary subspaces: U n S n V n =B n (1); U s S s V s =B s (2); Among them, U n with U s are the calculated non-stationary and stationary subspaces, S n With S s Respectively represent B n With B s The singular value obtained by singular value decomposition, V n With V s are right singular vectors.

4. The method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis according to claim 1, characterized in that: In step 3, first, given the sliding window size s, construct the online data x s (t)=[x(t-s+1),x(t-s+2),...,x(t)], and calculate the sample mean and covariance matrix as follows: Solve the following optimization problem; Calculate the online data unmixing matrix B on : Where I is the identity matrix, S on and The form is as follows: and are the mean and covariance matrices after online data update; For the above optimization problem, the projection matrices of the online stationary and non-stationary components are obtained by solving the following generalized eigenvalue problem; Among them, γ on =[γ on,1 ,γ on,2 ,…,γ on,m ] are the eigenvalues ​​arranged from small to large; Represents the eigenvector corresponding to the eigenvalue, and the projection matrix of the online stationary and non-stationary components is composed of the eigenvector The different columns are: According to the above derivation, the following singular value decomposition is solved to obtain the online stationary and non-stationary subspaces: U on,n S on,n V on,n =B on,n (3); U on,s S on,s V on,s =B on,s (4); Among them, U on,n with U on,s is the non-stationary and stationary subspace calculated online at time t, S on,n With S on,s Respectively represent B on,n With B on,s The singular value obtained by singular value decomposition, V on,n With V on,s are right singular vectors.

5. The method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis according to claim 1, characterized in that: In step 4, the constructed abnormal monitoring statistic is in the form of Among them, J p1 With J p2 They are used to monitor non-stationary and stationary components respectively, d is the stationary subspace dimension, S p1 =[s p1,1 ,s p1,2 ,...,s p1,d ] represents the cosine value of the angle between the online and offline stationary subspaces in the 1st,…,dth dimensions, S p2 =[s p2,1 ,s p2,2 ,...,s p2,m-d ] represents the cosine value of the angle between the online and offline non-stationary subspaces in the 1,…,md dimensions respectively; S p1 With S p2 The following singular value decomposition is obtained U p1 with U p2 They represent the left singular vectors of the singular value decomposition, V p1 With V p2 They represent the right singular vectors of the singular value decomposition.

6. The method for monitoring abnormalities in a non-stationary industrial process based on analytical stationary subspace analysis according to claim 1, characterized in that: The normal operation data of the non-stationary industrial process is collected and divided into N1 data segments of length s as the threshold determination data set. The monitoring results of the threshold determination data set are calculated using formula (5) and formula (6) respectively. Finally, the monitoring threshold J is determined based on the kernel density estimation method. th1 With J th2 , and based on the following logic and Determine whether an exception occurs:

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