Fault root cause analysis method for discriminating edge group sparse principal component analysis
By distinguishing the sparse principal component analysis of edge group (DESPCA) method, the degree of change of each variable before and after the failure occurs, and the causal relationship is calculated by transferring entropy, the problem of difficulty in quickly and accurately identifying the root cause of the failure in the existing technology is solved, and the fault is improved Diagnostic accuracy and efficiency.
Patent Information
- Application Number
- CN202411376733.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-02-18
AI Technical Summary
The prior art is difficult to quickly and accurately identify the root cause of failure in complex multivariable systems, resulting in inefficient fault diagnosis.
A method of root cause analysis of faults for discriminating edge group sparse principal component analysis (DESPCA) is proposed. Through the concept of relevant weights of dynamic metadata network sparse principal component analysis (DM-ESPCA), the degree of change of each variable before and after the failure occurs is analyzed, and the screening is carried out. The group of variables most relevant to the root cause of the failure is derived, and the causal relationship between the extracted variables is calculated by transferring entropy.
Effectively filter out the variable groups that are most relevant to the root cause of the fault, improve the accuracy and efficiency of fault diagnosis, and can quickly identify the root cause of the fault.
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Figure CN119474840A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of data-driven chemical soft measurement, and in particular to a fault root cause analysis method for discriminating edge group sparse principal component analysis. Background Art
[0002] Fault diagnosis plays a vital role in industrial production because it can improve production capacity and reduce production losses. When a fault occurs, if the root cause of the fault can be identified quickly and accurately, so that on-site personnel can adjust the process in time, the losses caused by the fault can be effectively reduced. Fault diagnosis includes fault detection, fault isolation, and fault root cause diagnosis. Traditional fault detection and isolation methods can usually only identify variables related to the fault, but cannot trace the root cause of the fault. Therefore, fault root cause analysis has received more and more attention. In particular, data-based root cause analysis methods can track the propagation path of the fault in complex multivariable systems, thereby determining the root cause of the fault.
[0003] In today's big data era, data-driven methods are becoming increasingly important in scientific research and engineering applications. However, models that rely solely on data often lack physical reality, which may lead to poor prediction results or lack of physical interpretability. Therefore, this study aims to introduce physical information into data-driven methods, improve their shortcomings and improve the interpretability of the model, and apply it to the fields of fault diagnosis and program control.
[0004] The Tennessee Eastman process consists of five main equipment: reactor, condenser, separation tower, stripping tower and circulating compressor. The gaseous reactants are A, C, D, E, and the liquid products are G and H as shown in Formula 1. There are a total of 52 variables, including 11 manipulated variables and 41 process variables. According to the changes in the set points, a total of 20 different fault disturbances are simulated for various research on control tests. In fault diagnosis, we focus on the isolation method. According to relevant literature, isolation methods mainly include factor analysis and principal component analysis. Principal component analysis has a wide range of applications in many fields, such as image recognition, genetic data analysis, chemical processes, and thermal imaging analysis. In terms of time series causal analysis, transfer entropy has a good effect on nonlinear data.
[0005]
[0006] The present invention proposes a fault root cause analysis method of discriminative edge group sparse principal component analysis, and the discriminative edge-group sparse PCA (DESPCA) proposed in this study applies the concept of correlation weights of dynamic metadata network sparse principal component analysis (Dynamic Meta-data Network Sparse PCA, DM-ESPCA) to analyze the degree of change of each variable before and after the fault occurs, which helps to group highly correlated variables and extract the variable group most relevant to the root cause of the fault into the first principal component analysis, use DESPCA to screen the fault variables, and then perform root cause analysis through transfer entropy, calculate the causal relationship between the extracted variables, and find out the variables most relevant to the root cause of the fault. Summary of the invention
[0007] In view of the problems existing in the prior art, the present invention provides a fault root cause analysis method for discriminating edge group sparse principal component analysis.
[0008] The technical solution adopted by the present invention to solve the technical problem is as follows:
[0009] A fault root cause analysis method for discriminating edge group sparse principal component analysis comprises the following steps:
[0010] Step 1) Data acquisition and variable connection:
[0011] Divide, collect and integrate the data sets of TE simulation; construct a physical model based on the Tennessee Eastman process and establish variable connections;
[0012] Step 2) Discriminative node connection sparse principal component analysis DESPCA modeling training:
[0013] The relevant weights of the dynamic metadata network sparse principal component analysis DM-ESPCA are applied to analyze the degree of change of each variable before and after the fault occurs, and the variable group most related to the root cause of the fault is extracted into the first principal component analysis, thereby achieving the goal of feature extraction and simplifying the subsequent root cause analysis;
[0014] Step 3) Failure cause analysis:
[0015] Based on the DESPCA analysis method, the root cause analysis is performed through transfer entropy, the causal relationship between the extracted variables is calculated, and the variables most related to the root cause of the fault are found.
[0016] Further, the process of step 2) is:
[0017] Step 2.1: Project the high-dimensional L data onto the principal component PC of the low-dimensional K data, L>K; make the principal components orthogonal to each other and retain the maximum variability at the same time;
[0018] Define X as a data matrix with m variables and n samples, and extract the optimization problem of its first load as formula (1).
[0019]
[0020] p is the first load vector, v is the first principal component PC, and is denoted as Xp;
[0021] To solve the maximization problem, we need to target XX T The matrix is subjected to singular value decomposition SVD calculation, and the eigenvector corresponding to the maximum eigenvalue is the load of the first principal component. The eigenvalue represents the degree of variation in a certain direction. The eigenvalues are arranged from large to small, which is the load of each principal component direction.
[0022] Step 2.2: Apply the discriminant node connection sparse principal component analysis DESPCA to the fault root cause analysis, and use the linear discriminant analysis LDA to calculate the relevant weights to evaluate the degree of change of each variable before and after the fault occurs, as shown in formula (2),
[0023]
[0024] t i is the relevant weight, x i1 and i1 represents the mean and standard deviation of variable i before the failure occurs, x i2 and i2 represents the mean and standard deviation of variable i after the fault occurs;
[0025] Step 2.3: Calculate edge e h =(z i , z j )∈G h , as shown in formula (3):
[0026]
[0027] where z i and z j for e h The load vector elements corresponding to the variables on the left and right sides, Represents a vector with m rows and 1 column, so we get the weighted edge set G w ={e1',...,e' M}, Step 2.4: For G w Perform sparsification penalty, as shown in formula (4);
[0028]
[0029] Where G' w Represents G w The subset of V(G' w ) is from G' w The derived vertex set, |G' w |It's G' w The number of elements in support(p) is the index set of non-zero elements in the first principal component loading (p);
[0030] Step 2.5: Sparse projection operator [P(G w )(z,k)] i (i=1,...,m) satisfies formula (5):
[0031]
[0032] G w (i) is the index set of weighted edges containing variable i. If variable i is selected, then z i is retained, that is, [P(G w )(z,k)] i =z i , otherwise it is sparsely distributed to zero, that is, [P(G w )(z,k)] i =0;
[0033] Step 2.6: Update p and v by formula (6) and formula (7) until convergence;
[0034]
[0035]
[0036] Step 2.7: Finally, the DESPCA algorithm is expressed as formula (8),
[0037]
[0038] is the first principal component load, X is the process variable matrix, which is used to store process variable data, is the first principal component, and k is the sparsification parameter that determines the number of edges to be retained.
[0039] Further, the process of step 3) is:
[0040] Transfer entropy combines entropy and KL divergence as shown in formula (9); it is used to measure the information flow between two time series, where x and y represent l- and k-order Markov processes, and l and k represent the length of the time series delay;
[0041]
[0042] The multivariate transfer entropy is shown in formula (10), where X and Y represent N and P order Markov processes;
[0043]
[0044] When the transfer entropy value is less than the set threshold, the causal relationship of the information is displayed by normalizing the directional transfer entropy NDTE, as shown in formula (11). The value range of NDTE is between positive and negative 1. A positive value indicates that X is the cause, and a negative value indicates that Y is the cause.
[0045]
[0046] The beneficial effects of the present invention are mainly manifested in: the present invention proposes a fault root cause analysis method of discriminant edge group sparse principal component analysis, builds the physical connection of the model by connecting data variables, then uses DESPCA to screen fault variables to extract features for subsequent further analysis of the root cause, and finally performs root cause analysis through transfer entropy, calculates the causal relationship between the extracted variables, and finds out the variables most relevant to the root cause of the fault. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] Figure 1 It is a topological structure diagram of TE process variables of the present invention;
[0048] Figure 2 This is a graph showing the results of the relevant weight (IDV1) of the present invention;
[0049] Figure 3 This is a graph showing the results of the relevant weight (IDV4) of the present invention;
[0050] Figure 4 is the DESPCA load diagram PC1 / PC2 (IDV1) of the present invention;
[0051] Figure 5 is the DESPCA load diagram PC1 / PC2 (IDV4) of the present invention;
[0052] Figure 6 It is a fault diagnosis flow chart of the present invention;
[0053] Figure 7 Schematic diagram of the DESPCA algorithm of the present invention. DETAILED DESCRIPTION
[0054] The present invention will be further described below in conjunction with the accompanying drawings.
[0055] A fault root cause analysis method for discriminating edge group sparse principal component analysis, the method comprising the following steps:
[0056] Step (1) Data acquisition and variable linking
[0057] Divide, collect and integrate the data sets of TE simulation. Build a physical model based on the Tennessee Eastman process and establish variable connections.
[0058] The process of step (1) is:
[0059] Step 1.1: The sampling frequency in the TE process is 3 minutes, with a total of 960 sampling points. In this study, 22 process variables related to the reactor unit were selected as the analysis objects. The process variables are shown in Table 1.
[0060] Table 1. Tennessee Eastman process variables
[0061]
[0062] Step 1.2: Then, according to the physical model of the Tennessee Eastman process, establish variable connections, such as Figure 1 Among them, V1~V3 and V42~V44 are three main feed pipelines, and together with the reflux pipeline of V5, they converge into V6 and enter the reactor. V6~V9 are variables in the reactor. The reactor is connected to the component analyzers of V23~V28, and V8 is connected to the total feed pipeline of V4 and V51. V9 is connected to the cooling water pipeline of V21 and V51.
[0063] Step (2) DESPCA modeling training
[0064] The concept of correlation weight of DM-ESPCA is applied to the analysis of the degree of change of each variable before and after the fault occurs, which helps to group highly correlated variables and extract the variable group most related to the root cause of the fault into the first principal component analysis, thereby achieving the goal of feature extraction and simplifying the subsequent root cause analysis.
[0065] The process of step (2) is:
[0066] Step 2.1: Principal component analysis (PCA) is a multivariate statistical analysis method and is often used for data dimensionality reduction. By projecting high-dimensional (L-dimensional) data onto low-dimensional (K-dimensional) principal components (PC) (L>K), the principal components are made orthogonal to each other and the maximum variability can be retained at the same time.
[0067] Define X as a data matrix with m variables and n samples, and extract the optimization problem of its first loading as shown in Formula 2.
[0068]
[0069] p is the first load vector, v is the first principal component (PC), and can be expressed as Xp. To solve the maximization problem, we first need to calculate XX T The matrix is subjected to singular value decomposition (SVD) calculation, and the eigenvector corresponding to the maximum eigenvalue obtained is the load of the first principal component. The eigenvalue represents the degree of variation in a certain direction. The eigenvalues are arranged from large to small, which is the load of each principal component direction.
[0070] Discriminative edge-group sparse PCA (DESPCA) is applied to fault root cause analysis. The concept of linear discriminant analysis (LDA) is used to calculate the correlation weight to evaluate the degree of change of each variable before and after the fault occurs, as shown in Formula 3.
[0071]
[0072] t i is the relevant weight, x i1 and i1 represents the mean and standard deviation of variable i before the failure occurs, x i2 and i2 Represents the mean and standard deviation of variable i after the fault occurs.
[0073] Then calculate the edge (edge, e h =(z i , z j )∈G) h ), as shown in Formula 4:
[0074]
[0075] where z i and z j for e h The load vector elements corresponding to the variables on the left and right sides can thus obtain the weighted edge set (G w ={e1',...,e' M}), then for G w Perform sparse penalty, such as
[0076] Formula 5.
[0077]
[0078] Where G' w Represents G w The subset of V(G' w ) is from G' w The derived vertex set, |G' w |It's G' w The number of elements in , support(p) is the index set of non-zero elements in the first principal component load (p). Finally, the DESPCA algorithm can be expressed as Formula 6.
[0079]
[0080] is the first principal component load, X is the process variable matrix, which is used to store process variable data, is the first principal component, and k is the sparsification parameter that determines the number of edges to be retained.
[0081] The key to solving Formula 6 is to solve a projection problem, so we use a greedy strategy to obtain an approximate solution of DESPCA (Algorithm 1). Algorithm 1 The DESPCA algorithm is as follows:
[0082]
[0083] Step 2.2: The sparse projection operator ([P(G w )(z,k)] i (i=1,...,m)) satisfies Formula 7:
[0084]
[0085] G w (i) is the set of indices of weighted edges containing variable i. If variable i is selected, then z i Retained ([P(G w )(z,k)] i =z i ), otherwise it is sparsely spaced to zero ([P(G w )(z,k)] i =0).
[0086] According to Algorithm 1, p and v can be updated by Formula 8 and Formula 9 until convergence.
[0087]
[0088]
[0089] In addition, the DESPCA method can also be used to calculate multiple principal components (PCs) and their corresponding principal component loadings, and to calculate subsequent principal components and their loadings given the current principal component.
[0090] Step (3) Fault Cause Analysis
[0091] Based on the DESPCA analysis method, the root cause analysis is performed through transfer entropy, the causal relationship between the extracted variables is calculated, and the variables most related to the root cause of the fault are found.
[0092] The process of step (3) is: The transfer entropy combines the concept of entropy KL divergence (Kullback-Leibler Divergence), as shown in formula 10. It is used to measure the information flow between two time series, where x and y represent l- and k-order Markov processes, and l and k represent the length of the time series delay.
[0093]
[0094] The concept of multivariate transfer entropy is the same, where X and Y represent N and P order Markov processes, as shown in Equation 11.
[0095]
[0096] When the transfer entropy value is small, the causal relationship of the information can be displayed by the Normalized Directional Transfer Entropy (NDTE), as shown in Formula 12. The value range of NDTE is between positive and negative 1. A positive value indicates that X is the cause, and a negative value indicates that Y is the cause.
[0097]
[0098] Example:
[0099] A fault root cause analysis method for discriminating edge group sparse principal component analysis comprises the following steps:
[0100] (1) Obtain the TE dataset. The process is as follows:
[0101] Step 1.1: IDV 1 and IDV 4 process disturbances are used as study cases. The specific description of the process disturbances is shown in Table 2.
[0102] Table 2 Tennessee Eastman process disturbances
[0103]
[0104] Step 1.2: IDV1 means that the proportion of component A in flow 4 changes from 48.5 mol% to 45.5 mol%, and the proportion of component C changes from 51 mol% to 54 mol%. It can be seen from the feed data of component A that the fault occurred at about point 161 and entered another new steady state at about point 500. The direction of fault propagation is that the proportion of component A in flow 4 decreases, resulting in the component instrument detecting a change in component A when passing through flow 6. The controller increases the opening of the component A feed valve to maintain the composition, increases the flow rate of flow 1, and reaches a new steady state at about point 500.
[0105] IDV4 is the change in the reactor cooling water feed temperature. Although this variable is not measured in the TE process, changes in related variables such as variable 9 (reactor temperature) and variable 51 (cooling water flow) can be observed after the fault occurs. The reaction of the reactor temperature to the change in the cooling water feed temperature is shown. In order to stabilize the reactor temperature, the controller increases the flow rate by increasing the opening of the cooling water outlet valve to reach a new stable state.
[0106] (2) Perform prediction model training. The process is as follows:
[0107] Step 2.1: According to the relevant variable analysis of the fault description, such as the content of component A in IDV1, the reactor temperature and the change of reactor cold water flow rate in IDV4, we regard the first 160 data points of IDV1 as normal data, and the data points from 161 to 500 as fault data. The first 160 data points of IDV4 are regarded as normal data, and the data points from 161 to 500 are regarded as fault data. Then calculate the relevant weight (t), and show the results as follows Figure 2 and Figure 3 .
[0108] Step 2.2: Using the previously defined TE variable relationship ( Figure 1 ) as the variable link of DESPCA, and set the sparsity k value of DESPCA to 3 and 2 on IDV1 and IDV4 respectively. Variable screening can be performed based on the loading diagram.
[0109] From the load diagram of DESPCA, on IDV1, such as Figure 4 , we can get variables 1 (component A feed flow rate), 6 (reactor feed flow rate), 23 (component A), 44 (component A feed valve opening) on the first principal component, and variables 7, 23, 25, 28 on the second principal component. On IDV4, Figure 5 , we can get variables 9 (reactor temperature), 24 (component B), and 51 (reactor cooling water flow) on the first principal component, and variables 7, 24, and 25 on the second principal component. Then we can perform root cause analysis on the three variables on the first principal component.
[0110] (3) The calculation results of the transfer entropy and NDTE of the first principal component variable group are shown in Tables 3, 4, 5 and 6. The root cause variable of the fault was finally determined to be variable 23 on IDV1, which means that the composition of component A in flow 4 has changed. When passing through the component analyzer, it was detected that component A decreased (variable 23). In order to maintain the composition, the opening of the component A feed valve was increased, resulting in an increase in the flow rate of flow 1.
[0111] In IDV4, the root dependent variable of the fault is finally determined to be variable 9 (reactor temperature). The analysis results of fault propagation show that the change of the reactor's cooling water feed temperature first affects the reactor temperature. Then, in order to stabilize the system, the controller adjusts the opening of the cooling water outlet valve to increase the flow rate, thereby achieving a new stable state. Therefore, it can be inferred that variable 9 is the root dependent variable of the fault.
[0112] Table 3 Transfer entropy of the first principal component variable group (IDV1)
[0113]
[0114] Table 4 The first principal component variable group NDTE (IDV1)
[0115]
[0116] Table 5 Transfer entropy of the first principal component variable group (IDV4)
[0117]
[0118] Table 6 The first principal component variable group NDTE (IDV4)
[0119]
[0120] The method of the present invention uses discriminative node connection sparse principal component analysis (DESPCA), which not only considers the physical connectivity between variables and incorporates the information of process group structure into the algorithm, but also strengthens the calculation of weights and applies sparsity to the load vector according to the degree of change of each variable before and after the fault, thereby improving the defect of insufficient explanatory power of ordinary PCA. Feature extraction is performed on the fault data of process variables to effectively screen out the variable group most related to the root cause of the fault, and then the calculation of transfer entropy is used to find the root cause variable of the fault, thereby achieving the effect of improving fault diagnosis.
[0121] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.
Claims
1. A fault root cause analysis method for discriminating edge groups by sparse principal component analysis, characterized in that: The following steps are involved: Step 1) Data acquisition and variable connection: Divide, collect and integrate the data sets of TE simulation; construct a physical model based on the Tennessee Eastman process and establish variable connections; Step 2) Discriminative node connection sparse principal component analysis DESPCA modeling training: The relevant weights of the dynamic metadata network sparse principal component analysis DM-ESPCA are applied to analyze the degree of change of each variable before and after the fault occurs, and the variable group most related to the root cause of the fault is extracted into the first principal component analysis, thereby achieving the goal of feature extraction and simplifying the subsequent root cause analysis; Step 3) Failure cause analysis: Based on the DESPCA analysis method, the root cause analysis is performed through transfer entropy, the causal relationship between the extracted variables is calculated, and the variables most related to the root cause of the fault are found.
2. A fault root cause analysis method for discriminating edge group sparse principal component analysis as claimed in claim 1, characterized in that: The process of step 2) is: Step 2.1: Project the high-dimensional L data onto the principal component PC of the low-dimensional K data, L>K; make the principal components orthogonal to each other and retain the maximum variability at the same time; Define X as a data matrix with m variables and n samples, and extract the optimization problem of its first load as formula (1). p is the first load vector, v is the first principal component PC, and is denoted as Xp; To solve the maximization problem, we need to target XX T The matrix is subjected to singular value decomposition SVD calculation, and the eigenvector corresponding to the maximum eigenvalue is the load of the first principal component. The eigenvalue represents the degree of variation in a certain direction. The eigenvalues are arranged from large to small, which is the load of each principal component direction. Step 2.2: Apply the discriminant node connection sparse principal component analysis DESPCA to the fault root cause analysis, and use the linear discriminant analysis LDA to calculate the relevant weights to evaluate the degree of change of each variable before and after the fault occurs, as shown in formula (2), t i is the relevant weight, x i1 and i1 represents the mean and standard deviation of variable i before the failure occurs, x i2 and i2 represents the mean and standard deviation of variable i after the fault occurs; Step 2.3: Calculate edge e h =(z i , z j )∈G h , as shown in formula (3): where z i and z j for e h The load vector elements corresponding to the variables on the left and right sides, z i , Represents a vector with m rows and 1 column, so we get the weighted edge set G w ={e1',...,e' M }, Step 2.4: Target G w Perform sparse penalty, as shown in formula (4); Among them G w ' represents G w The subset of V(G w ') is from G w 'Exported vertex set, |G w '| is G w ', support(p) is the index set of non-zero elements in the first principal component load (p); Step 2.5: Sparse projection operator [P(G w )(z,k)] i , i=1,...,m satisfies formula (5): G w (i) is the index set of weighted edges containing variable i. If variable i is selected, then z i is retained, that is, [P(G w )(z,k)] i =z i , otherwise it is sparsely distributed to zero, that is, [P(G w )(z,k)] i =0; Step 2.6: Update p and v by formula (6) and formula (7) until convergence; Step 2.7: Finally, the DESPCA algorithm is expressed as formula (8), is the first principal component load, X is the process variable matrix, which is used to store process variable data, is the first principal component, and k is the sparsification parameter that determines the number of edges to be retained.
3. A fault root cause analysis method for discriminating edge group sparse principal component analysis as claimed in claim 1, characterized in that: The process of step 3) is: Transfer entropy combines entropy and KL divergence as shown in formula (9); it is used to measure the information flow between two time series, where x and y represent l- and k-order Markov processes, and l and k represent the length of the time series delay; The multivariate transfer entropy is shown in formula (10), where X and Y represent N and P order Markov processes; When the transfer entropy value is less than the set threshold, the causal relationship of the information is displayed by normalizing the directional transfer entropy NDTE, as shown in formula (11). The value range of NDTE is between positive and negative 1. A positive value indicates that X is the cause, and a negative value indicates that Y is the cause.