Multi-modal industrial process sensor fault detection method based on neighbor graph feature analysis

Abstract

The invention relates to a method for detecting a fault of a multi-modal industrial process sensor by using a neighbor graph feature analysis method, which comprises the following steps of: firstly, preprocessing a historical operation data set of the multi-modal industrial process sensor, solving a variable clustering result by using a k-means clustering method, and constructing a variable neighbor graph relation matrix according to the variable clustering result; further calculating a neighbor degree vector, and extracting sensor variable multi-dimensional features as a training data set according to the neighbor degree vector; standardizing the training data set, and establishing a fault detection model for the standardized data by using a principal component analysis method; extracting sensor variable multi-dimensional features in a new multi-modal industrial data set as a test data set according to the neighbor vector; and standardizing the test data set, and finally performing fault detection by calculating the statistical magnitude of the test data set. The multi-modal industrial process sensor fault detection method can obviously improve the accuracy of multi-modal industrial process sensor fault detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial process sensor fault detection, and relates to a method for detecting multimodal industrial process sensor faults by using a neighbor graph feature analysis method (abbreviated as NGFA). Background Art

[0002] With the continuous development of computer technology, the scale of industrial process production is increasing, and the number of sensors in industrial production processes is also increasing. These sensors play an important role in responding to variable changes and participating in system control. Data-driven fault detection technology helps to detect sensor failures in a timely manner, thereby improving equipment stability and production efficiency, and is conducive to ensuring the safety of equipment and production personnel. Therefore, the study of sensor fault detection technology is of great significance to industrial production.

[0003] Principal Component Analysis (PCA) is a classic multivariate statistical analysis method that has been widely used in the field of sensor fault identification. The algorithm maps high-dimensional related information to low-dimensional unrelated space by linearly transforming the original data, and retains the main data information for analysis. Due to the reduction of the dimension of the data, PCA is conducive to simplifying data analysis, improving computational efficiency, and is suitable for processing high-dimensional complex data. It has been widely used in many fields such as image processing, pattern recognition, and fault diagnosis. However, the PCA method has obvious limitations in sensor fault detection. First, PCA does not take into account the impact of industrial process modal changes on fault detection and cannot effectively process multimodal data. Secondly, PCA only performs fault detection on the original data, ignoring the features related to the sensor variables, so that some feature information that is helpful for fault detection is ignored, thereby reducing the detection accuracy. Therefore, how to improve the existing PCA method to make it better suitable for multimodal sensor fault detection has become a topic worthy of study. Summary of the invention

[0004] Aiming at the problem that PCA is difficult to effectively detect multimodal industrial process sensor faults, the present invention provides a multimodal industrial process sensor fault detection method based on neighbor graph feature analysis. The method can extract sensor variable features that are unchanged under multimodal normal working conditions based on the neighbor relationship between variables, eliminate the impact of modal changes on fault detection, and improve the accuracy of fault detection.

[0005] In order to achieve the above object, the present invention provides a multimodal industrial process sensor fault detection method based on neighbor graph feature analysis, comprising the following steps:

[0006] (i) Collect a historical operating data set X0 of multimodal industrial process sensors, where each column vector in X0 corresponds to the value of a sensor variable at different times. After preprocessing X0, use the k-means clustering method to cluster the sensor variables in the data set, and construct a variable neighbor graph relationship matrix A based on the clustering results;

[0007] (ii) Calculate the neighbor degree vector s according to the variable neighbor graph relationship matrix A, extract the multi-dimensional features of the sensor variables in the historical data set according to the neighbor degree vector s, and save the extracted features into the neighbor graph feature matrix X1 as the training data set;

[0008] (iii) using the mean mX1 and standard deviation sX1 of the neighbor graph feature matrix X1 to standardize the training data set, and using the principal component analysis method to establish a fault detection model for the standardized data;

[0009] (IV) Collecting new industrial process sensor datasets X t , extract the new data set X according to the neighbor degree vector s t The multi-dimensional features of sensor variables are extracted and saved into the neighbor graph feature matrix X2 as the test data set;

[0010] (V) Use the mean mX1 and standard deviation sX1 of the training data set to standardize the test data set X2 to obtain the standardized data set Computational Dataset The corresponding fault detection statistics are analyzed to obtain the fault detection results.

[0011] Furthermore, the industrial process historical data set X0 is preprocessed using formula (1) to obtain the preprocessed industrial process data set X0′. For the preprocessed industrial process data set X0′, the sensor variables in X0′ are classified using the k-means clustering method. The variable neighbor graph relationship matrix A is constructed based on the classification results. The expression of formula (1) is:

[0012]

[0013] Where mX0 and sX0 are the mean and variance of the industrial process historical data set, respectively;

[0014] The k-means clustering method realizes sensor variable clustering by optimizing the objective function Q in formula (2). The expression of formula (2) is:

[0015]

[0016] Where m is the number of sensor variables in the data set X0′; k is the number of classes; x (i)are all sample values ​​of the i-th sensor variable in the data set X0′; C is the class to which each variable belongs; μ is the center of all classes; μ j is the center of the jth class; d(x (i) ,μ j ) is the i-th variable x (i) To the cluster center μ j distance;

[0017] The variable clustering result is obtained by optimizing the objective function Q in formula (2). The variable neighbor graph relationship matrix A is constructed according to the variable clustering result. The variable neighbor graph relationship matrix A is expressed as:

[0018]

[0019] In the formula, a ij It represents the neighbor relationship between the i-th variable and the j-th variable. Its value is calculated by formula (4). The expression of formula (4) is:

[0020]

[0021] Furthermore, in step (ii), the neighbor degree vector s is calculated using formula (5) based on the variable neighbor graph relationship matrix A, and the number of multi-dimensional features to be extracted from the sensor variable is determined according to the value of the neighbor degree vector s. Formula (5) is expressed as:

[0022]

[0023] In the formula, i and j represent the number of rows and columns of the neighbor graph relationship matrix, respectively, and s i is the i-th element in the neighbor degree vector s; if s i = 0, then extract the change rate and relative trend variance characteristics of the i-th variable; if s i ≠0, then the change rate, relative trend variance, deviation, and correlation coefficient characteristics of the i-th variable are extracted;

[0024] The change rate characteristic is calculated by formula (6), and the expression of formula (6) is:

[0025] dx=x(t)-x(t-1) (6)

[0026] In the formula, dx is the rate of change of the variable, x(t) is the value of the variable at time t, and x(t-1) is the value of the variable at time t-1;

[0027] The relative trend variance characteristic is calculated by formula (7), and the expression of formula (7) is:

[0028]

[0029] In the formula, vn(x) is the relative trend variance of the variable, n is the number of samples in the data window used to calculate the variance, and x(ti) is the value of the variable at time ti. is the trend value of the variable at time ti;

[0030] The deviation characteristic is calculated by formula (8), and the expression of formula (8) is:

[0031] xbias(x)=x(t)-x nn (t) (8)

[0032] In the formula, xbias(x) is the deviation of the variable, x(t) is the value of the variable x at all times, and x nn (t) is the value of the variable at all times that is most correlated with the variable in the class to which the variable x belongs;

[0033] The correlation coefficient feature is calculated by formula (9), and the expression of formula (9) is:

[0034] xsim=corr(x(t),x nn (t)) (9)

[0035] In the formula, xsim is the correlation coefficient of variable x, and corr represents the correlation coefficient operation;

[0036] The features of all extracted sensor variables are saved in the neighbor graph feature matrix X1 as a training data set.

[0037] Furthermore, in step (iii), the training data set is standardized by using the mean mX1 and standard deviation sX1 of the neighbor graph feature matrix data set X1 through formula (10), and the fault detection model is established for the standardized data using the principal component analysis method. The expression of formula (10) is:

[0038]

[0039] The steps to establish a fault diagnosis model using principal component analysis are as follows:

[0040] (1) Training calculation The covariance matrix of Where n is The number of samples, eigenvalue decomposition of the covariance matrix to obtain the eigenvalue λ and its corresponding eigenvector, re-arrange the eigenvalue λ and its corresponding eigenvector in descending order, and arrange all eigenvectors as column vectors to obtain the loading matrix P;

[0041] (2) Determine the number of principal components k according to the cumulative variance contribution rate method;

[0042] (3) Calculate T 2 Statistics Where P k is the first k columns of the load matrix P, Λ is the diagonal matrix consisting of the first k eigenvalues, and T 2 (X1) Cumulative 90% probability density value as control limit

[0043] Furthermore, in step (iv), a new data set X is extracted based on the neighbor degree vector s. t The multi-dimensional features of sensor variables in the data set are extracted and saved in the neighbor graph feature matrix X2 as a test data set. The extraction method is consistent with the multi-dimensional features of sensor variables in the historical data set extracted according to the neighbor degree vector s in step (ii).

[0044] Furthermore, in step (V), the test data set X2 is standardized using the mean mX1 and standard deviation sX1 of the training data set X1 through formula (11) to obtain the standardized test data set: The expression of formula (11) is:

[0045]

[0046] The test data set is calculated by formula (12) The corresponding fault detection statistic T 2 , the expression of formula (12) is:

[0047]

[0048] T 2 (X2) and the control limits in the fault detection model By comparison, we get the fault detection result Y:

[0049]

[0050] In the formula, if T 2 (X2) is less than its corresponding control limit, indicating that the sensor system is normal; T 2 If the statistic is greater than its corresponding control limit, it indicates a sensor system failure.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis provided by the present invention preprocesses the collected historical industrial process sensor data, obtains the sensor variable clustering result by using the k-means clustering method, constructs the variable neighbor graph relationship matrix and the neighbor degree vector according to the clustering result, extracts the multidimensional features of the sensor variables according to the neighbor degree vector as a training data set, standardizes the training data set, and uses PCA to establish a fault detection model for the standardized data. For the newly collected industrial process sensor data set, the multidimensional features of the sensor variables are extracted according to the neighbor degree vector as a test data set, and the test data set is standardized by using the mean and variance of the training data set, and the fault detection statistics of the standardized test data set are further calculated to obtain the fault detection result. The present invention searches for the neighbor relationship between sensor variables through clustering, extracts the sensor variable features that are unchanged under the normal working conditions of the multimodal according to the neighbor relationship between the variables, eliminates the influence of the modal change on the fault detection, and improves the fault detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to the present invention; DETAILED DESCRIPTION

[0054] The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that elements, structures, and features in one embodiment may also be beneficially combined in other embodiments without further description.

[0055] See also Figure 1 The present invention discloses a multimodal industrial process sensor fault detection method based on neighbor graph feature analysis, which comprises the following steps:

[0056] (I) Collect the historical operation data set X0 of the multimodal industrial process sensor and preprocess X0 using formula (1). The expression of formula (1) is:

[0057]

[0058] Where mX0 and sX0 are the mean and variance of the industrial process historical data set, respectively;

[0059] The k-means clustering method is used to cluster the sensor variables in the data set by optimizing the objective function Q in formula (2). The expression of formula (2) is:

[0060]

[0061] Where m is the number of sensor variables in the data set X0′; k is the number of classes; x (i)are all sample values ​​of the i-th sensor variable in the data set X0′; C is the class to which each variable belongs; μ is the center of all classes; μ j is the center of the jth class; d(x (i) ,μ j ) is the i-th variable x (i) To the cluster center μ j distance;

[0062] The variable neighbor graph relationship matrix A is constructed based on the variable clustering results. The variable neighbor graph relationship matrix A is expressed as:

[0063]

[0064] In the formula, a ij It represents the neighbor relationship between the i-th variable and the j-th variable. Its value is calculated by formula (4). The expression of formula (4) is:

[0065]

[0066] (II) Based on the variable neighbor graph relationship matrix A, the neighbor degree vector s is calculated using formula (5), which is expressed as:

[0067]

[0068] In the formula, i and j represent the number of rows and columns of the neighbor graph relationship matrix, respectively, and s i is the i-th element in the neighbor degree vector s; if s i = 0, then extract the change rate and relative trend variance characteristics of the i-th variable; if s i ≠0, then the change rate, relative trend variance, deviation, and correlation coefficient characteristics of the i-th variable are extracted;

[0069] The change rate characteristic is calculated by formula (6), and the expression of formula (6) is:

[0070] dx=x(t)-x(t-1) (6)

[0071] In the formula, dx is the rate of change of the variable, x(t) is the value of the variable at time t, and x(t-1) is the value of the variable at time t-1;

[0072] The relative trend variance characteristic is calculated by formula (7), and the expression of formula (7) is:

[0073]

[0074] In the formula, vn(x) is the relative trend variance of the variable, n is the number of samples in the data window used to calculate the variance, and x(ti) is the value of the variable at time ti. is the trend value of the variable at time ti;

[0075] The deviation characteristic is calculated by formula (8), and the expression of formula (8) is:

[0076] xbias(x)=x(t)-x nn (t) (8)

[0077] In the formula, xbias(x) is the deviation of the variable, x(t) is the value of the variable x at all times, and x nn (t) is the value of the variable at all times that is most correlated with the variable in the class to which the variable x belongs;

[0078] The correlation coefficient feature is calculated by formula (9), and the expression of formula (9) is:

[0079] xsim=corr(x(t),x nn (t)) (9)

[0080] In the formula, xsim is the correlation coefficient of variable x, and corr represents the correlation coefficient operation;

[0081] The features of all extracted sensor variables are saved in the neighbor graph feature matrix X1 as a training data set.

[0082] (III) The training data set is standardized using the mean mX1 and standard deviation sX1 of the neighbor graph feature matrix X1 through formula (10). The expression of formula (10) is:

[0083]

[0084] The principal component analysis method is used to establish a fault detection model for the standardized data. The steps to establish the fault diagnosis model are:

[0085] (1) Calculation The covariance matrix of Where n is The number of samples, eigenvalue decomposition of the covariance matrix to obtain the eigenvalue λ and its corresponding eigenvector, re-arrange the eigenvalue λ and its corresponding eigenvector in descending order, and arrange all eigenvectors as column vectors to obtain the loading matrix P;

[0086] (2) Determine the number of principal components k according to the cumulative variance contribution rate method;

[0087] (3) Calculate T 2 Statistics Where P k is the first k columns of the load matrix P, Λ is the diagonal matrix consisting of the first k eigenvalues, and T 2 (X1) Cumulative 90% probability density value as control limit

[0088] (IV) Collecting new industrial process sensor datasets X t , extract the new data set X according to the neighbor degree vector s t The multi-dimensional features of sensor variables in the data set are extracted and saved in the neighbor graph feature matrix X2 as the test data set. The extraction method is the same as that in step (ii) in which the multi-dimensional features of sensor variables in the historical data set are extracted according to the neighbor degree vector s. ;

[0089] (V) Using the mean mX1 and standard deviation sX1 of the training data set X1, the test data set X2 is standardized by formula (11) to obtain the standardized test data set The expression of formula (11) is:

[0090]

[0091] The test data set is calculated by formula (12) The corresponding fault detection statistic T 2 , the expression of formula (12) is:

[0092]

[0093] T 2 (X2) and the control limits in the fault detection model By comparison, we get the fault detection result Y:

[0094]

[0095] In the formula, if T 2 (X2) is less than its corresponding control limit, indicating that the sensor system is normal; T 2 If the statistic is greater than its corresponding control limit, it indicates a sensor system failure.

[0096] In the above method, steps (1) to (3) are the offline modeling stage, and steps (4) to (5) are the online testing stage.

[0097] The above fault detection method in the present invention pre-processes the historical operation data set of the industrial process sensor, obtains the sensor variable clustering result by using the k-means clustering method, constructs the variable neighbor graph relationship matrix and the neighbor degree vector, and then extracts the variable features to obtain the training data set; extracts features from the new industrial process sensor data set to obtain the test data set; on this basis, the training and test data sets are standardized; a PCA fault detection model is established through the training data, and fault detection is performed on the test data set. The present invention searches for the neighbor relationship between sensor variables through clustering, extracts the sensor variable features that are unchanged under normal multi-modal working conditions according to the neighbor relationship between variables, eliminates the influence of modal changes on fault detection, and improves the accuracy of fault detection.

[0098] In order to more clearly illustrate the beneficial effects of the above-mentioned fault detection method of the present invention, the above-mentioned fault detection method of the present invention is further described below in conjunction with specific embodiments.

[0099] Embodiment: A set of multimodal industrial process data is simulated, and three variable measurement points are set, each of which is detected by 1, 2, and 3 sensors respectively. The variables are shown in Table 1.

[0100] Table 1

[0101]

[0102]

[0103] Three common sensor faults are used in the experiment, as shown in Table 2, to verify the detection accuracy of each method. The detection accuracy is calculated by the number of fault samples in the test set. 2 The number of statistical violations is calculated as the proportion of the total fault samples.

[0104] Table 2

[0105]

[0106] In this implementation, three types of faults, namely fault 1, fault 2 and fault 3, are mainly detected in the simulation process, wherein there are 300 normal samples in the training set and 100 fault samples in the test set.

[0107] The principal component analysis (PCA) and the neighbor graph feature analysis (NGFA) of the present invention are used to detect the above three types of faults. The fault detection accuracy results are shown in Table 3.

[0108] Table 3

[0109] Fault 1 Fault 2 Fault 3 average value PCA 0.05 0.04 0.02 0.0367 NGFA 1 0.70 0.84 0.8467

[0110] It can be seen from Table 3 above that the fault detection method based on neighbor graph feature analysis proposed in the present invention can significantly improve the accuracy of fault detection.

[0111] The above embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. Within the scope of the technical solution described in the present invention, various simple deformations and modifications made by technicians in the relevant technical field should be included in the above patent application scope.

Claims

1. A multimodal industrial process sensor fault detection method based on neighbor graph feature analysis, comprising the following steps: (i) Collect a historical operating data set X0 of multimodal industrial process sensors, where each column vector in X0 corresponds to the value of a sensor variable at different times. After preprocessing X0, use the k-means clustering method to cluster the sensor variables in the data set, and construct a variable neighbor graph relationship matrix A based on the clustering results; (ii) Calculate the neighbor degree vector s according to the variable neighbor graph relationship matrix A, extract the multi-dimensional features of the sensor variables in the historical data set according to the neighbor degree vector s, and save the extracted features into the neighbor graph feature matrix X1 as the training data set; (iii) Use the mean mX1 and standard deviation sX1 of the neighbor graph feature matrix X1 to standardize the training data set, and use the principal component analysis method to establish a fault detection model for the standardized data; (IV) Collecting new industrial process sensor datasets X t , extract the new data set X according to the neighbor degree vector s t The multi-dimensional features of sensor variables are extracted and saved into the neighbor graph feature matrix X2 as the test data set; (V) Use the mean mX1 and standard deviation sX1 of the training data set to standardize the test data set X2 to obtain the standardized test data set calculate The corresponding fault detection statistics are analyzed to obtain the fault detection results.

2. The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to claim 1 is characterized in that: In step (1), the industrial process historical data set X0 is preprocessed using formula (1) to obtain the preprocessed industrial process data set X0′. For the preprocessed industrial process data set X0′, the sensor variables in X0′ are classified using the k-means clustering method. The variable neighbor graph relationship matrix A is constructed based on the classification results. The expression of formula (1) is: Where mX0 and sX0 are the mean and variance of the industrial process historical data set, respectively; The k-means clustering method realizes sensor variable clustering by optimizing the objective function Q in formula (2). The expression of formula (2) is: Where m is the number of sensor variables in the data set X0′; k is the number of classes; x (i) are all sample values ​​of the i-th sensor variable in the data set X0′; C is the class to which each variable belongs; μ is the center of all classes; μ j is the center of the jth class; d(x (i) ,μ j ) is the i variable x (i) To the cluster center μ j distance; The variable clustering result is obtained by optimizing the objective function Q in formula (2). The variable neighbor graph relationship matrix A is constructed according to the variable clustering result. The variable neighbor graph relationship matrix A is expressed as: In the formula, a ij It represents the neighbor relationship between the i-th variable and the j-th variable. Its value is calculated by formula (4). The expression of formula (4) is:

3. The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to claim 3 is characterized in that: In step (ii), the neighbor degree vector s is calculated based on the variable neighbor graph relationship matrix A using formula (5), and the number of multi-dimensional features to be extracted from the sensor variable is determined according to the value of the neighbor degree vector s. Formula (5) is expressed as: In the formula, i and j represent the number of rows and columns of the neighbor graph relationship matrix, respectively, and s i is the i-th element in the neighbor degree vector s; if s i =0, then the change rate and relative trend variance characteristics of the i-th variable are extracted; If i ≠0, then the change rate, relative trend variance, deviation, and correlation coefficient characteristics of the i-th variable are extracted; The change rate characteristic is calculated by formula (6), and the expression of formula (6) is: dx=x(t)-x(t-1) (6) In the formula, dx is the rate of change of the variable, x(t) is the value of the variable at time t, and x(t-1) is the value of the variable at time t-1; The relative trend variance characteristic is calculated by formula (7), and the expression of formula (7) is: In the formula, vn(x) is the relative trend variance of the variable, n is the number of samples in the data window used to calculate the variance, and x(ti) is the value of the variable at time ti. is the trend value of the variable at time ti; The deviation characteristic is calculated by formula (8), and the expression of formula (8) is: xbias(x)=x(t)-x nn (t) (8) In the formula, xbias (x) is the deviation of the variable, x(t) is the value of the variable x at all times, and x nn (t) is the value of the variable at all times that is most correlated with the variable in the class to which the variable x belongs; The correlation coefficient feature is calculated by formula (9), and the expression of formula (9) is: xsim=corr(x(t),x nn (t)) (9) In the formula, xsim is the correlation coefficient of variable x, and corr represents the correlation coefficient operation; The features of all extracted sensor variables are saved in the neighbor graph feature matrix X1 as a training data set.

4. The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to claim 4 is characterized in that: In step (iii), the training data set is standardized by using the mean mX1 and standard deviation sX1 of the neighbor graph feature matrix data set X1 through formula (10), and the fault detection model is established for the standardized data using the principal component analysis method. The expression of formula (10) is: The steps to establish a fault diagnosis model using principal component analysis are as follows: (1) Calculation The covariance matrix of Where n is The number of samples, eigenvalue decomposition of the covariance matrix to obtain the eigenvalue λ and its corresponding eigenvector, re-arrange the eigenvalue λ and its corresponding eigenvector in descending order, and arrange all eigenvectors as column vectors to obtain the loading matrix P; (2) Determine the number of principal components k according to the cumulative variance contribution rate method; (3) Calculate T 2 Statistics Where P k is the first k columns of the load matrix P, Λ is the diagonal matrix consisting of the first k eigenvalues, and T 2 (X1) Cumulative 90% probability density value as control limit 5. The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to claim 5, characterized in that: In step (iv), the new data set X is extracted based on the neighbor degree vector s t The multi-dimensional features of sensor variables in the data set are extracted and saved in the neighbor graph feature matrix X2 as a test data set. The extraction method is consistent with the multi-dimensional features of sensor variables in the historical data set extracted according to the neighbor degree vector s in step (ii).

6. The multimodal industrial process sensor fault detection method based on neighbor graph feature analysis according to claim 6 is characterized in that: In step (5), the test data set X2 is standardized using the mean mX1 and standard deviation sX1 of the training data set X1 through formula (11) to obtain the standardized test data set The expression of formula (11) is: The test data set is calculated by formula (12) The corresponding fault detection statistic T 2 , the expression of formula (12) is: T 2 (X2) and the control limits in the fault detection model By comparison, we get the fault detection result Y: In the formula, if T 2 (X2) is less than its corresponding control limit, indicating that the sensor system is normal; T 2 If the statistic is greater than its corresponding control limit, it indicates a sensor system failure.

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