A method for detecting minor faults in industrial processes based on canonical variable analysis and JS divergence fusion

Abstract

The present invention provides a method for detecting minor faults in industrial processes based on the fusion of canonical variable analysis and JS divergence. Firstly, the training data is preprocessed by normalization to reduce the influence of data dynamic characteristics. Secondly, the JS divergence, which is sensitive to changes in data distribution, is introduced to calculate the difference JS divergence between the canonical variables corresponding to normal and faulty data with the help of a sliding window with a width of w. Then, the detection control limits obtained based on the sliding window of the canonical variables of normal data are compared to determine whether a minor fault occurs in the industrial process. Finally, the proposed method is used to monitor three different types of minor faults in the Tennessee Eastman Chemical process. The simulation results show that the proposed method is more effective than the traditional PCA and CVA T 2 , and Q statistics, the fault detection rate of the divergence index of the proposed CVA‑JS method is significantly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of data-driven industrial process minor fault detection, and in particular to a minor fault detection method based on canonical variable analysis and JS divergence. Background Art

[0002] With the continuous improvement of science and technology, industrial processes or equipment are becoming more complex and large-scale. Once a minor fault occurs in a production process or equipment, if it is not discovered in time and effectively handled, it will gradually develop into a serious fault over time, and may even cause major safety accidents, causing casualties and huge economic losses, and will also have irreversible effects on the ecological environment. Faults are undesirable characteristics or any abnormal phenomena that occur in the process. In modern industrial processes, fault detection is a necessary technology to improve system reliability and prevent system performance from deteriorating. Fault detection and diagnosis are of great significance to ensuring the safe and reliable operation of modern industrial processes.

[0003] Most existing fault detection methods have good effects on sudden faults with large amplitudes. However, with the long-term operation of the production process, it is inevitable that there will be hidden minor faults such as sensor drift, pipeline material leakage, and equipment component wear, which pose a huge hidden danger to the safe operation of the industrial process. Usually, the amplitude of the fault is smaller than the standard deviation of the corresponding variable under normal working conditions, which is a minor fault. In recent years, minor fault detection has become one of the research hotspots of common concern in the scientific research field and the engineering community. Its main purpose is to timely detect and identify minor faults in the early stage, eliminate potential safety hazards, and avoid serious faults or accidents.

[0004] The effect of traditional fault detection based on expert knowledge and analytical models is limited by the accuracy of the mathematical model of the established industrial process. It is difficult to achieve accurate modeling for large and complex processes, and it is difficult to obtain a large amount of effective expert knowledge from the industrial process. For complex industrial processes with different data characteristics, traditional fault detection methods based on models and knowledge often have poor effects; highly automated and complex industrial processes have accumulated a huge amount of data, so fault detection methods based on data-driven methods have emerged. This method does not require the accurate mathematical model or knowledge of the known industrial process. It uses the collected sensor data and establishes a detection model based on multivariate statistical theory to detect minor faults in the industrial process. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to solve the problem that the traditional data-driven fault detection method is not sensitive to minor fault detection and is easily submerged by noise, resulting in a low detection rate. The present invention proposes a method for detecting minor faults in industrial processes based on the fusion of canonical variable analysis and JS divergence. This method has a higher fault detection rate when used for minor fault detection.

[0006] Divergence is highly sensitive to small changes in data distribution. It can be used to determine the similarity of the probability distribution of two sets of data. Therefore, the divergence index can be used to detect small faults in industrial processes.

[0007] Technical solution, the present invention proposes a method for detecting minor faults in industrial processes based on canonical variable analysis and JS divergence fusion, comprising the following steps:

[0008] Step 1: Offline modeling:

[0009] (I) Dynamic data preprocessing and obtaining standard variables:

[0010] (1) Using the historical data matrix Y∈R collected from the industrial process m×l , where m is the number of variables in the data, and l is the number of samples of m variables;

[0011] (2) Combine the Hankel matrices Y of past observations according to the formula p =[y p,p+1 y p,p+2 … y p,p+N ]∈R mp×N and the Hankel matrix Y of future observations f =[y f,p+1 y f,p+2 … y f,p+N ]∈R mp×N ; Where p is the number of sampling moments in the past based on the current sampling moment; N = l-2p-1 is the Hankel matrix Y p and Y f The number of columns;

[0012] Where r = p-1, p-2, ... pN;

[0013] The above past observation vector y p,r and the future observation vector y f,r , respectively composed of the measurement vectors of the past and future p sampling moments in the data matrix Y;

[0014] (3) Calculate the covariance of past and future observation vectors and the cross-variance matrix The superscript T indicates the transpose of the matrix;

[0015] (4) Perform singular value decomposition on the H matrix Where V is the unitary matrix after singular value decomposition;

[0016] (5) Determine k main normative variables by cumulative contribution rate method Where k = 1, 2, 3 ... mp;

[0017] (II) JS divergence calculation between canonical variables generated by normal data:

[0018] The k main canonical variables are divided into two parts, front and back, and the JS divergence values ​​of the k main canonical variables are obtained respectively using a sliding window with a width of w and the JS divergence calculation formula;

[0019] (III) Determine the control limits:

[0020] According to the kernel density estimation method, the control limits of the JS divergence index of k main canonical variables with confidence level α are determined respectively.

[0021] Step 2: Online monitoring

[0022] 1) After obtaining the m observation values ​​at the 2pth sampling time online, assemble the past observation vector y pp ;

[0023] 2) Using the formula Obtain k main canonical variables corresponding to the fault measurement data;

[0024] 3) Perform sliding windows with a width of w on the k main canonical variables obtained from normal data and the k main canonical variables obtained from faulty data, and obtain the JS divergence value between each pair of sliding windows;

[0025] 4) If the JS divergence values ​​of the k main canonical variables corresponding to the fault data do not exceed their corresponding control limits Indicates that the process is running normally; if Indicates that a minor fault has been detected.

[0026] Furthermore, the calculation of the JS divergence between the canonical variables generated by the normal data specifically includes: dividing the k main canonical variables into two parts, front and back, and using the JS divergence formula to obtain the JS divergence values ​​of the k main canonical variables respectively; the JS divergence is the symmetric operation of the Kullback-Leibler (KL) divergence function, which is recorded as:

[0027] in and are the first and second halves of the kth main canonical variable, respectively; yes and Mixed distribution of Indicates the calculation of the KL divergence value of the kth main canonical variable; the superscript KL represents the KL divergence; yes and Mixed distribution of

[0028] in, is the first half of the kth canonical variable corresponding to the normal data The variance of in, is the second half of the kth canonical variable corresponding to the normal data The variance of m is the canonical variable and The mean of the variance.

[0029] Compared with the prior art, the above technical solution of the present invention has the following advantages: a method for detecting minor faults in industrial processes based on the fusion of canonical variable analysis and JS divergence, which reduces the influence of data dynamic characteristics by normalizing the training data for preprocessing; by introducing JS divergence that is sensitive to changes in data distribution, the JS divergence calculation of the difference between the canonical variables corresponding to normal and faulty data is realized with the help of a sliding window with a width of w; by comparing with the detection control limit, it is determined whether a minor fault occurs in the industrial process; the proposed method is used for monitoring three different types of minor faults in the Tennessee Eastman Chemical Process; the simulation results show that the T of the traditional PCA and CVA is better than that of the traditional PCA and CVA. 2 , and Q statistics, the fault detection rate of the divergence index of the proposed CVA-JS method is significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic diagram of the principle of the detection method of the present invention;

[0031] Figure 2 A schematic diagram of determining monitoring limits in offline modeling of the present invention;

[0032] Figure 3 This is a schematic diagram of divergence calculation during online detection of the present invention;

[0033] Figure 4 It is a simulation comparison diagram of TE process fault 3 of the present invention;

[0034] Figure 5 It is a simulation comparison diagram of TE process fault 9 of the present invention;

[0035] Figure 6 It is a simulation comparison diagram of TE process fault 15 of the present invention. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0037] Figure 1 The schematic diagram of the detection method of the present invention is shown in FIG. 1 . It can be seen that the proposed detection method includes two parts: offline modeling and online detection. Offline modeling mainly uses normal data to obtain control limits. Figure 2 The online detection part is to calculate the divergence values ​​between different canonical variables generated by normal data and fault data respectively, and compare them with the control limits obtained in the offline stage to determine whether the process is running normally or a minor fault has occurred. Figure 3 The divergence calculation method for online detection is presented in detail.

[0038] A method for detecting minor faults in industrial processes based on canonical variable analysis and JS divergence fusion includes the following steps: Step 1: Offline modeling:

[0039] (I) Dynamic data preprocessing and obtaining standard variables

[0040] Using the historical data matrix Y∈R collected from the Tennessee Eastman Chemical process m×l , combining past observation vector y p,r and the future observation vector y f,r They are composed of the measured values ​​of the past and future p sampling moments in the data matrix Y:

[0041]

[0042] Among them, y r are the measurements from the training dataset; r = p+1, p+2, …, p+N;

[0043] Hankel matrix Y of past observation vectors p and the Hankel matrix Y of the future observation vector f They are defined as follows:

[0044] Y p =[y p,p+1 y p,p+2 … y p,p+N ]∈R mp×N

[0045] Y f =[y f,p+1 y f,p+2 … yf,p+N ]∈R mp×N

[0046] Where N = l-2p+1, that is, the Hankel matrix contains N columns. The covariance and mutual variance matrices of past and future observation vectors are calculated using the following formulas:

[0047]

[0048]

[0049]

[0050] The solution to the optimal linear combination can be obtained by performing a singular value decomposition on the Hankel matrix H:

[0051]

[0052]

[0053] The k main canonical variables are determined by the criterion that the cumulative contribution rate of singular values ​​reaches 90%. Where k = 1, 2, 3...mp.

[0054] (II) Calculation of JS divergence between canonical variables generated by normal data

[0055] The k main canonical variables are divided into two parts, the front and back parts, and the JS divergence values ​​of the k main canonical variables are obtained respectively using the JS divergence formula; the JS divergence is the symmetric operation of the Kullback-Leibler divergence function, which is recorded as:

[0056] in and are the first and second halves of the kth main canonical variable, respectively; yes and Mixed distribution of

[0057] in, is the first half of the kth canonical variable corresponding to the normal data The variance of in, is the second half of the kth canonical variable corresponding to the normal data The variance of m is the canonical variable and The mean of the variance;

[0058] (III) Determine the control limits

[0059] Determine the control limits of the JS divergence index of k main canonical variables with confidence level α according to the kernel density estimation method

[0060] Step 2: Online monitoring

[0061] 1) After obtaining the m observation values ​​of the first 2p sampling moments of the TE process fault test data online, assemble the past observation vector y pp ;

[0062] 2) Using the formula Get k main canonical variables corresponding to the fault data;

[0063] 3) Perform sliding windows of width w on the k main canonical variables obtained from normal data and the k main canonical variables obtained from faulty data, and obtain the JS divergence value between each pair of sliding windows. For details, see the schematic diagram. Figure 3 , the specific calculation formula is as follows;

[0064]

[0065] where z k is the kth main canonical variable of the normal data and The kth main canonical variable of the fault data Yes k and Mixed distribution of

[0066] Among them, λ k is the kth canonical variable z corresponding to the normal data k The variance of

[0067] in, is the kth canonical variable corresponding to the fault data The variance of m is the canonical variable z k and The mean of the variance;

[0068] 4) If the JS divergence values ​​of the k main canonical variables corresponding to the fault data do not exceed their corresponding control limits It indicates that the TE chemical process is operating normally; if there is a JS divergence value of the main canonical variable Indicates that a minor fault was detected in the TE chemical process.

[0069] Simulation Verification

[0070] The effectiveness and detection performance of the algorithm are verified by using three types of micro-fault data generated by the Tennessee Eastman (TE) chemical process simulation platform. The TE process simulation platform can simulate the nonlinear, non-Gaussian, time-varying and multimodal characteristics of industrial processes, and provides a standard simulation model for process modeling and control, fault monitoring and diagnosis methods. The TE process includes five main operating units: reactor, condenser, compressor, separator and stripper; and also includes 4 gas feeds, 2 main products generated by 2 gas-liquid exothermic reactions, and 2 by-products generated by two derivative exothermic reactions; the process includes multiple fault types such as step, random change, slow drift, viscosity and constant position. The process contains 41 measured variables and 12 controlled variables. Each measured variable contains additive noise to simulate the noise in the actual industrial process. Each data set has 52 variables, and the sampling time of most variables is 3 minutes; among them, the sampling time of 14 variables is 6 minutes, and the sampling time of 5 variables is 15 minutes. The training and testing data sets of the TE process can be downloaded from the Internet. The data sets include 1 (Fault 0) normal operation data and 20 (Fault 1-Fault 20) fault operation data. Three types of micro-fault data, namely step Fault 3, random change Fault 9 and sticking Fault 15, are used in the simulation example.

[0071] In order to compare the detection performance of PCA, CVA and CVA-JS for minor faults under the same conditions, the length p of the past and future observation windows of CVA and CVA-JS are set to 3; the number of principal components of PCA, CVA and CVA-JS is set to 3, and the sliding window width w is set to 120.

[0072] Figure 4 (a) Figure 5 (a) and Figure 6 (a) Plot the T values ​​of faults 3, 9, and 15 generated by PCA. 2 , Q statistic monitoring chart. Figure 4 (b) Figure 5 (b) and Figure 6 (b) The T values ​​of faults 3, 9, and 15 generated by CVA are plotted respectively. 2 , Q statistic monitoring chart. Figure 4 (c) Figure 5 (c) and Figure 6 (c) The JS divergence index detection effect diagrams corresponding to the first two main canonical variables of CVA-JS faults 3, 9, and 15 are respectively plotted. The TE process fault occurs at 161 sampling moments. Because the sliding window of w = 120 is introduced, the fault starts to appear at 41 sampling moments, which is slightly different from the case of PCA and CVA without sliding windows.

[0073] As can be seen from the figure, in the case of faults 3, 9, and 15, due to the small fault amplitude and noise interference, PCA and CVA cannot effectively detect minor faults. However, in the three cases of faults 3, 9, and 15, the divergence indicators of the two main canonical variables of CVA-JS can effectively detect the change trend of minor faults, which is different from the traditional T 2 , Q statistics have significantly improved the fault detection rate.

[0074] The above description is only an exemplary embodiment of the present invention, and does not limit the scope of patent protection of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the scope of patent protection of the present invention.

Claims

1. A method for detecting minor faults in industrial processes based on the fusion of canonical variable analysis and JS divergence, characterized by: The following steps are involved: Step 1: Offline modeling: (I) Dynamic data preprocessing and obtaining standard variables: (1) Using the historical data matrix Y∈R collected from the industrial process m×l , where m is the number of variables in the data, and l is the number of samples of m variables; (2) Combine the Hankel matrices Y of past observations according to the formula p =|y p，p+1 y p，p+2 …y p，p+N |∈R mp×N and the Hankel matrix Y of future observations f =|y f，p+1 y f，p+2 …y f，p+N ]∈R mp×N ; Where p is the number of sampling moments in the past based on the current sampling moment, where m is the number of variables in the industrial process data collection, p is a specific integer, p>2; N = l-2p-1 is the Hankel matrix Y p and Y f The number of columns, where l is the total number of samples of the industrial process variable, and l is an integer much larger than 2p; Where r = p-1, p-2, ... pN; The above past observation vector y p，r and the future observation vector y f，r , respectively composed of the measurement vectors of the past and future p sampling moments in the data matrix Y; (3) Calculate the covariance of past and future observation vectors and the cross-variance matrix The superscript T indicates the transpose of the matrix; (4) Perform singular value decomposition on the H matrix Where V is the unitary matrix after singular value decomposition, and the H matrix is ​​equal to The product of , where U is the unitary matrix after singular value decomposition, and its column vector is the left singular vector; (5) Determine k main normative variables by cumulative contribution rate method Where k = 1, 2, 3 ... mp; (II) JS divergence calculation between canonical variables generated by normal data: The k main canonical variables are divided into two parts, front and back, and the JS divergence values ​​of the k main canonical variables are obtained respectively using a sliding window with a width of w and the JS divergence calculation formula; The JS divergence value is the symmetric operation of the Kullback-Leibler divergence function, which is recorded as: in and are the first and second halves of the kth main canonical variable, respectively; yes and Mixed distribution of (III) Determine the control limits: According to the kernel density estimation method, the control limits of the JS divergence index of k main canonical variables with confidence level α are determined respectively. Among them, UCL is the abbreviation of Upper Control Limit, which means the upper control limit during fault detection; Step 2: Online monitoring 1) After obtaining the m observation values ​​at the 2pth sampling time online, assemble the past observation vector ypp; 2) Using the formula Get the k main canonical variables corresponding to the fault data, where y pp After obtaining m observation values ​​at the 2pth sampling time online; 3) Perform sliding windows with a width of w on the k main canonical variables obtained from normal data and the k main canonical variables obtained from faulty data, and obtain the JS divergence value between each pair of sliding windows; 4) If the JS divergence values ​​of the k main canonical variables corresponding to the fault data do not exceed their corresponding control limits Indicates that the process is running normally; if there is a JS divergence value of a main standard variable Indicates that a minor fault has been detected.

2. According to claim 1, a method for detecting minor faults in industrial processes based on the fusion of canonical variable analysis and JS divergence is characterized in that: The calculation of JS divergence between the canonical variables generated by the normal data (ii) specifically includes: dividing the k main canonical variables into two parts, front and back, respectively, and using the JS divergence formula to obtain the JS divergence values ​​of the k main canonical variables respectively; the JS divergence is the symmetric operation of the Kullback-Leibler (KL) divergence function, which is expressed as: in and are the first and second halves of the kth main canonical variable, respectively; Indicates the calculation of the KL divergence value of the kth main canonical variable; the superscript KL represents the KL divergence; yes and Mixed distribution of in, is the first half of the kth canonical variable corresponding to the normal data The variance of in, is the second half of the kth canonical variable corresponding to the normal data The variance of m is the canonical variable and The mean of the variance.

Images