Multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis

Abstract

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

Description

Technical Field

[0001] This invention belongs to the field of industrial process sensor fault detection technology, and relates to a method for detecting faults in multimodal industrial process sensors using nearest neighbor graph feature analysis (NGFA). Background Technology

[0002] With the continuous development of computer technology, the scale of industrial production is increasing daily, and the number of sensors in industrial production processes is also constantly growing. These sensors play a significant role in responding to changes in variables and participating in system control. Data-driven fault detection technology helps to detect sensor faults in a timely manner, thereby improving equipment stability and production efficiency, and contributing to the safety of equipment and production personnel. Therefore, research on sensor fault detection technology is of great significance to industrial production.

[0003] Principal Component Analysis (PCA) is a classic multivariate statistical analysis method widely used in sensor fault detection. This algorithm maps high-dimensional relevant information to a low-dimensional uncorrelated space by linearly transforming and combining the original data, retaining the main data information for analysis. Due to the reduction of data dimensionality, PCA simplifies data analysis, improves computational efficiency, and is suitable for processing high-dimensional complex data. It has been widely applied in image processing, pattern recognition, fault diagnosis, and other fields. However, PCA has significant limitations in sensor fault detection. First, it does not consider the impact of modal variations in industrial processes on fault detection, and cannot effectively handle multimodal data. Second, PCA only performs fault detection on the raw data, ignoring features related to sensor variables, causing some helpful feature information to be overlooked, thus reducing detection accuracy. Therefore, how to improve existing PCA methods to better suit multimodal sensor fault detection has become a worthy research topic. Summary of the Invention

[0004] This invention addresses the problem that PCA (Positive Calibration Analysis) is ineffective in detecting faults in multimodal industrial process sensors by providing a fault detection method based on nearest-neighbor graph feature analysis. This method can extract sensor variable features that remain unchanged under normal multimodal operating conditions based on the nearest-neighbor relationships between variables, eliminating the influence of modal changes on fault detection and improving fault detection accuracy.

[0005] To achieve the above objectives, this invention provides a multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis, comprising the following steps:

[0006] (i) Collect the historical operation dataset 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 k-means clustering to cluster the sensor variables in the dataset. Construct a variable nearest neighbor graph relation matrix A based on the clustering results.

[0007] (ii) Calculate the nearest neighbor degree vector s based on the nearest neighbor graph relation matrix A, extract multi-dimensional features of sensor variables in the historical dataset based on the nearest neighbor vector s, and save the extracted features into the nearest neighbor graph feature matrix X1 as the training dataset.

[0008] (iii) The training dataset is standardized using the mean mX1 and standard deviation sX1 of the feature matrix X1 of the nearest neighbor graph, and a fault detection model is built on the standardized data using the principal component analysis method.

[0009] (iv) Acquiring new industrial process sensor datasets X t Extract a new dataset X based on the nearest neighbor vector s. t Multidimensional features of sensor variables are extracted and saved into the nearest neighbor graph feature matrix X2 as a test dataset.

[0010] (v) Standardize the test dataset X2 using the mean mX1 and standard deviation sX1 of the training dataset to obtain the standardized dataset. Compute dataset The corresponding fault detection statistics are analyzed to obtain the fault detection results.

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

[0012]

[0013] In the formula, mX0 and sX0 are the mean and variance of the historical dataset of the industrial process, respectively;

[0014] k-means clustering achieves sensor variable clustering by optimizing the objective function Q in formula (2), which is expressed as follows:

[0015]

[0016] In the formula, m is the number of sensor variables in dataset X0′; k is the number of classes; x (i)Let X be all sample values ​​of the i-th sensor variable in dataset X0′; C be the class to which each variable belongs; μ be the center of all classes; μ j The center of the j-th class; d(x) (i) ,μ j Let x be the i-th variable. (i) To class center μ j The distance;

[0017] The clustering results of variables are obtained by optimizing the objective function Q in formula (2). Based on the clustering results, a nearest neighbor graph relation matrix A is constructed. The nearest neighbor graph relation matrix A is expressed as:

[0018]

[0019] In the formula, a ij Let represent the nearest neighbor relationship between the i-th variable and the j-th variable. Its value is calculated using formula (4), and the expression of formula (4) is:

[0020]

[0021] Furthermore, in step (ii), based on the nearest neighbor graph relation matrix A, the nearest neighbor degree vector s is calculated using formula (5). The number of multi-dimensional features to be extracted from the sensor variables is determined according to the value of the nearest 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 nearest neighbor graph relation matrix, respectively, and s i It is the i-th element in the nearest neighbor vector s; if s i =0, then extract the rate of change and relative trend variance features of the i-th variable; if s i If the value is not equal to 0, then extract the rate of change, relative trend variance, bias, and correlation coefficient of the i-th variable.

[0024] The rate of change characteristic is calculated using formula (6), and the expression for 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 using formula (7), which is expressed as follows:

[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. It is the trend value of the variable at time ti;

[0030] The deviation characteristic is calculated using formula (8), and the expression for 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 variable x at all times, and x... nn (t) represents the value of the variable most strongly correlated with variable x in the class to which variable x belongs at all times;

[0033] The correlation coefficient characteristic is calculated using 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 calculation;

[0036] The features of all extracted sensor variables are saved into the nearest neighbor graph feature matrix X1 as the training dataset.

[0037] Furthermore, in step (iii), the mean mX1 and standard deviation sX1 of the nearest neighbor graph feature matrix dataset X1 are used to standardize the training dataset using formula (10). Principal component analysis is then used to establish a fault detection model for the standardized data. The expression of formula (10) is as follows:

[0038]

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

[0040] (1) Training computation covariance matrix Where n is The sample size is used to perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​λ and their corresponding eigenvectors. The eigenvalues ​​λ and their corresponding eigenvectors are then reordered in descending order. All eigenvectors are arranged as column vectors to obtain the loading matrix P.

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

[0042] (3) Calculate T 2 Statistic Where P k The first k columns of the load matrix P are given, and Λ is a diagonal matrix composed of the first k eigenvalues. Let T be the first k columns of the load matrix P. 2 (X1) The cumulative 90% probability density value is used as the control limit.

[0043] Furthermore, in step (iv), a new dataset X is extracted based on the nearest neighbor vector s. t The multi-dimensional features of sensor variables in the dataset are extracted and saved into the nearest neighbor graph feature matrix X2 as the test dataset. The extraction method is the same as that in step (II) to extract the multi-dimensional features of sensor variables in the historical dataset based on the nearest neighbor degree vector s.

[0044] Furthermore, in step (v), the mean mX1 and standard deviation sX1 of the training dataset X1 are used to standardize the test dataset X2 using formula (11) to obtain the standardized test dataset. The expression for formula (11) is:

[0045]

[0046] The test dataset is calculated using formula (12). The corresponding fault detection statistics T 2 The expression for formula (12) is:

[0047]

[0048] T 2 (X2) and the control limit in the fault detection model By comparison, the fault detection result Y is obtained:

[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 exceeds its corresponding control limit, it indicates a sensor system malfunction.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] This invention provides a multimodal industrial process sensor fault detection method based on nearest-neighbor graph feature analysis. The method preprocesses historical industrial process sensor data, uses k-means clustering to obtain sensor variable clustering results, constructs a nearest-neighbor graph relationship matrix and a nearest-neighbor degree vector based on the clustering results, extracts multi-dimensional features of sensor variables from the nearest-neighbor degree vector as a training dataset, standardizes the training dataset, and uses PCA to build a fault detection model on the standardized data. For newly acquired industrial process sensor datasets, multi-dimensional features of sensor variables are extracted from the nearest-neighbor degree vector as a test dataset. The test dataset is standardized using the mean and variance of the training dataset, and then the fault detection statistics of the standardized test dataset are calculated to obtain the fault detection results. This invention finds nearest-neighbor relationships between sensor variables through clustering, extracts sensor variable features that remain unchanged under normal multimodal operating conditions based on these relationships, eliminates the influence of modal changes on fault detection, and improves fault detection accuracy. Attached Figure Description

[0053] Figure 1 This is a flowchart of the multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis as described in this invention; Detailed Implementation

[0054] The present invention will now be described in detail through exemplary embodiments. However, it should be understood that, without further description, elements, structures, and features in one embodiment may be advantageously incorporated into other embodiments.

[0055] See Figure 1 This invention discloses a multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis, comprising the following steps:

[0056] (a) Collect the historical operation dataset X0 of the multimodal industrial process sensors, and preprocess X0 using formula (1). The expression of formula (1) is:

[0057]

[0058] In the formula, mX0 and sX0 are the mean and variance of the historical dataset of the industrial process, respectively;

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

[0060]

[0061] In the formula, m is the number of sensor variables in dataset X0′; k is the number of classes; x (i)Let X be all sample values ​​of the i-th sensor variable in dataset X0′; C be the class to which each variable belongs; μ be the center of all classes; μ j The center of the j-th class; d(x) (i) ,μ j Let x be the i-th variable. (i) To class center μ j The distance;

[0062] Based on the clustering results of the variables, construct the nearest neighbor graph relation matrix A, which is represented as follows:

[0063]

[0064] In the formula, a ij Let represent the nearest neighbor relationship between the i-th variable and the j-th variable. Its value is calculated using formula (4), and the expression of formula (4) is:

[0065]

[0066] (ii) Based on the nearest neighbor graph relation matrix A, the nearest 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 nearest neighbor graph relation matrix, respectively, and s i It is the i-th element in the nearest neighbor vector s; if s i =0, then extract the rate of change and relative trend variance features of the i-th variable; if s i If the value is not equal to 0, then extract the rate of change, relative trend variance, bias, and correlation coefficient of the i-th variable.

[0069] The rate of change characteristic is calculated using formula (6), and the expression for 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 using formula (7), which is expressed as follows:

[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. It is the trend value of the variable at time ti;

[0075] The deviation characteristic is calculated using formula (8), and the expression for 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 variable x at all times, and x... nn (t) represents the value of the variable most strongly correlated with variable x in the class to which variable x belongs at all times;

[0078] The correlation coefficient characteristic is calculated using 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 calculation;

[0081] The features of all extracted sensor variables are saved into the nearest neighbor graph feature matrix X1 as the training dataset.

[0082] (iii) The training dataset is standardized using the mean mX1 and standard deviation sX1 of the nearest neighbor graph feature matrix X1 using formula (10). The expression of formula (10) is as follows:

[0083]

[0084] The steps for establishing a fault detection model and a fault diagnosis model are as follows: Principal component analysis is used to build a fault detection model from the standardized data.

[0085] (1) Calculation covariance matrix Where n is The sample size is used to perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues ​​λ and their corresponding eigenvectors. The eigenvalues ​​λ and their corresponding eigenvectors are then reordered in descending order. All eigenvectors are arranged as column vectors to obtain the loading matrix P.

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

[0087] (3) Calculate T 2 Statistic Where P k The first k columns of the load matrix P are given, and Λ is a diagonal matrix composed of the first k eigenvalues. Let T be the first k columns of the load matrix P. 2 (X1) The cumulative 90% probability density value is used as the control limit.

[0088] (iv) Acquiring new industrial process sensor datasets X t Extract a new dataset X based on the nearest neighbor vector s. t The multi-dimensional features of sensor variables in the dataset are extracted and stored in the nearest neighbor graph feature matrix X2 as the test dataset. The extraction method is consistent with step (II) for extracting multi-dimensional features of sensor variables from the historical dataset based on the nearest neighbor degree vector s.

[0089] (v) Using the mean mX1 and standard deviation sX1 of the training dataset X1, the test dataset X2 is standardized using formula (11) to obtain the standardized test dataset. The expression for formula (11) is:

[0090]

[0091] The test dataset is calculated using formula (12). The corresponding fault detection statistics T 2 The expression for formula (12) is:

[0092]

[0093] T 2 (X2) and the control limit in the fault detection model By comparison, the fault detection result Y is obtained:

[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 exceeds its corresponding control limit, it indicates a sensor system malfunction.

[0096] In the above method, steps (i) to (iii) are the offline modeling stage, and steps (iv) to (v) are the online testing stage.

[0097] The fault detection method described in this invention preprocesses the historical operating dataset of industrial process sensors, uses k-means clustering to obtain sensor variable clustering results, constructs a variable nearest neighbor graph relationship matrix and nearest neighbor degree vector, and then extracts variable features to obtain a training dataset. Features are extracted from new industrial process sensor datasets to obtain a test dataset. Based on this, the training and test datasets are standardized. A PCA fault detection model is established using the training data, and fault detection is performed on the test dataset. This invention finds nearest neighbor relationships between sensor variables through clustering, extracts sensor variable features that remain unchanged under multimodal normal operating conditions based on these relationships, eliminates the influence of modal changes on fault detection, and improves fault detection accuracy.

[0098] To more clearly illustrate the beneficial effects of the fault detection method of the present invention, the following detailed description of the fault detection method of the present invention is provided in conjunction with specific embodiments.

[0099] Example: A set of multimodal industrial process data was simulated, with three variable measurement points set up. Each measurement point was 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 were used in the experiment, as shown in Table 2, to verify the detection accuracy of each method. The detection accuracy was determined by the Tfault values ​​of the fault samples in the test set. 2 The percentage of statistically exceeding limits is used to derive the total number of fault samples.

[0104] Table 2

[0105]

[0106] In this implementation, the main focus is on detecting three types of faults in the simulation process: fault 1, fault 2, and fault 3. The training set contains 300 normal samples, and the test set contains 100 fault samples.

[0107] Principal Component Analysis (PCA) and the Next-Nearest Neighbor Graph Feature Analysis (NGFA) method of this invention were used to detect the above three types of faults. The fault detection accuracy results are shown in Table 3.

[0108] Table 3

[0109] PCA 0.05 0.04 0.02 0.0367 NGFA 1 0.70 0.84 0.8467

[0110] As shown in Table 3 above, the fault detection method based on nearest neighbor graph feature analysis proposed in this invention can significantly improve the accuracy of fault detection.

[0111] The embodiments described above are merely illustrative of the present invention and are not intended to limit the scope of protection of the present invention. Any simple modifications and variations made by those skilled in the art within the scope of the technical solutions described in the present invention should be included within the scope of the above-mentioned patent applications.

Claims

1. A multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis, comprising the following steps: （ 1) Collect historical operation datasets of multimodal industrial process sensors ,in Each column vector in the vector corresponds to the value of a sensor variable at different times. After preprocessing, use Mean clustering is used to cluster sensor variables in a dataset, and a nearest neighbor graph relation matrix is ​​constructed based on the clustering results. ; Using formula (1) to analyze historical datasets of industrial processes Preprocessing is performed to obtain the preprocessed industrial process dataset. For preprocessed industrial process datasets ,pass Mean clustering method The sensor variables are classified, and a nearest neighbor graph relation matrix is ​​constructed based on the classification results. The expression for formula (1) is: （1）； In the formula, and These are the mean and variance of the historical dataset of industrial processes, respectively. k-means clustering achieves sensor variable clustering by optimizing the objective function Q in formula (2), which is expressed as follows: （2）； In the formula, For dataset Number of sensor variables in the middle; The number of classes; For dataset The Middle All sample values ​​of each sensor variable; The class to which each variable belongs; It is the center of all classes; For the first The center of each class; For the first Variables To the class center The distance; The clustering results of variables are obtained by optimizing the objective function Q in formula (2), and a nearest neighbor graph relation matrix is ​​constructed based on the clustering results. Nearest neighbor graph relation matrix Represented as: （3）； In the formula, Let represent the nearest neighbor relationship between the i-th variable and the j-th variable. Its value is calculated using formula (4), and the expression of formula (4) is: （4）; (ii) Based on the nearest neighbor graph relation matrix of the variables Calculate the nearest neighbor vector Based on the nearest neighbor vector Extract multi-dimensional features of sensor variables from historical datasets and save the extracted features into a nearest neighbor graph feature matrix. This is used as the training dataset; In the nearest neighbor graph relation matrix of variables Based on this, the nearest neighbor vector is calculated using formula (5). Based on the nearest neighbor vector The value of determines the number of multi-dimensional features that need to be extracted from the sensor variable, as expressed in formula (5): （5）； In the formula, i and j represent the number of rows and columns of the nearest neighbor graph relation matrix, respectively. It is the nearest neighbor degree vector The i-th element in; if Then, extract the rate of change and relative trend variance features of the i-th variable; like Then, extract the rate of change, relative trend variance, bias, and correlation coefficient of the i-th variable. The rate of change characteristic is calculated using formula (6), and the expression for formula (6) is: （6）； In the formula, It is the rate of change of the variable. It is the value of the variable at time t. It is a variable The value at time; The relative trend variance characteristic is calculated using formula (7), and the expression for formula (7) is: （7）； In the formula, This represents the relative trend variance of the variable, where n is the number of samples within the data window used to calculate the variance. It is a variable The value at time, It is a variable Trend value at any given time; The deviation characteristic is calculated using formula (8), and the expression for formula (8) is: （8）； In the formula, It is the deviation of the variable. It is a variable Values ​​at all times, It is a variable The values ​​of the variable most strongly correlated with this variable within its class at all times; The correlation coefficient characteristic is calculated using formula (9), and the expression of formula (9) is: （9）； In the formula, It is a variable The correlation coefficient, where corr represents the correlation coefficient calculation; The features of all extracted sensor variables are saved into the nearest neighbor graph feature matrix. This is used as the training dataset; (iii) Using the nearest neighbor graph feature matrix mean and standard deviation The training dataset is standardized, and a fault detection model is built from the standardized data using principal component analysis. (iv) Acquiring new industrial process sensor datasets Based on the nearest neighbor vector Extract new dataset Multidimensional features of sensor variables are extracted and stored in a nearest neighbor graph feature matrix. This is used as the test dataset; (v) Using the mean of the training dataset and standard deviation For the test dataset The standardized test dataset is obtained by standardization. ,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 nearest neighbor graph feature analysis as described in claim 1, characterized in that, In step (iii), the nearest neighbor graph feature matrix dataset is used. mean and standard deviation The training dataset is standardized using formula (10), and a fault detection model is built using principal component analysis. The expression of formula (10) is as follows: （10); The steps for establishing a fault diagnosis model using principal component analysis are as follows: (1) Calculation covariance matrix ,in for The number of samples is used to perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues. And its corresponding eigenvector, the eigenvalues The corresponding eigenvectors are reordered in descending order, and all eigenvectors are arranged as column vectors to obtain the loading matrix. ; (2) Determine the number of principal components based on the cumulative variance contribution rate method. ; (3) Calculation Statistic ,in It is the load matrix The former List, It is from the front A diagonal matrix composed of eigenvalues, taking The cumulative 90% probability density value is used as the control limit. .

3. The multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis as described in claim 1, characterized in that, In step (iv), based on the nearest neighbor vector Extract new dataset Multidimensional features of sensor variables are extracted and stored in a nearest neighbor graph feature matrix. Using the test dataset as an example, the extraction method and steps (II) are based on the nearest neighbor vector. The multi-dimensional features of sensor variables extracted from historical datasets are consistent.

4. The multimodal industrial process sensor fault detection method based on nearest neighbor graph feature analysis as described in claim 1, characterized in that, In step (five), the training dataset is used. mean and standard deviation The test dataset is processed using formula (11). The standardized test dataset is obtained by standardization. The expression for formula (11) is: (11); The test dataset is calculated using formula (12). Corresponding fault detection statistics The expression for formula (12) is: (12); Will Control limits in the fault detection model By making comparisons, the fault detection results were obtained. : (13); In the formula, if If the value is less than its corresponding control limit, it indicates that the sensor system is normal; If the statistic exceeds its corresponding control limit, it indicates a sensor system malfunction.

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