Quality-related fault comprehensive monitoring method based on causal cooperative enhancement and root diagnosis method based on causal uniqueness

Abstract

The invention discloses a quality-related fault comprehensive monitoring method based on causal collaborative enhancement and a root diagnosis method based on causal uniqueness. Firstly, a Granger test is used for identifying a process variable carrying quality-related information in quality-related monitoring, and extraction of quality-related features is enhanced through a synergistic effect of a causal relationship so as to cope with a complex causal relationship between the process variable and the quality-related information. And secondly, due to cooperative causality among variable groups, dynamic characteristics of the variable groups are captured and further modeled, so that the monitoring precision is ensured, quality variable fault monitoring is expanded to process variables, and comprehensive monitoring is realized. Finally, in the fault diagnosis process, causal uniqueness analysis needs to be carried out on the complex and undefined relation between the root variables so as to eliminate negative effects of irrelevant factors. According to the method, the problems that information extraction is incomplete when quality-related variables are explored, the causal relationship in root variable mining is not clear and the like due to the fact that existing causal mining has certain limitation in the aspect of fully explaining the causal relationship between the variables are solved, so that the fault monitoring effect is improved, and the root diagnosis process is simplified; and the algorithm complexity is reduced.

Description

Technical Field

[0001] This invention belongs to the field of industrial process fault monitoring and diagnosis, specifically a method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness. Background Technology

[0002] In industrial production, fault monitoring and diagnosis are crucial. Fault monitoring enables operators to issue timely warnings and proactively detect potential problems; simultaneously, fault diagnosis helps accurately identify the root cause of faults, preventing accidents. In actual industrial production, greater attention is paid to the condition of industrial products, especially quality variables. Therefore, the monitoring of quality-related faults has received increasing attention. Despite significant progress in the industrial application of statistical learning methods, considerable challenges continue to hinder their widespread implementation. These include incomplete extraction of quality-related features and insufficient consideration of data and variable relationships during model construction. These limitations lead to overly simplistic monitoring models or an overemphasis on process variables, ultimately resulting in poor monitoring performance.

[0003] Existing methods, such as Partial Least Squares (PLS), Kernel PLS (KPLS), Input-Output KPLS, Deep Learning-Based Deep KPLS (DeKPLS), and Enhanced DeKPLS (ReKPLS), have achieved satisfactory results for the aforementioned problems. To address the issue of variable relationships, an improved LiNGAM causal method has been used to calculate the causal strength between variables, leading to a proposed method for quality-related monitoring using causal weighted PLS. This method effectively limits the influence of variables unrelated to quality variables. To resolve complex causal relationships between variables, a Quality-PLS (Q-PLS) method has been developed, which incorporates transfer entropy to extract quality-related information from process variables. The proposed framework, through an optimized variable selection mechanism, successfully establishes two PLS models for fault monitoring.

[0004] For root cause diagnosis of faults, some existing contribution-based methods, while possessing high interpretability, have limitations in diagnosing faults in complex processes. Therefore, some have proposed using kernel principal component analysis (KPCA) for variable isolation, followed by fault diagnosis using a causal iterative discovery method. To address the complexity of causal relationships, a proposed approach employs the minimum redundancy maximum correlation (mRMR) algorithm for variable dimensionality reduction and feature space partitioning, followed by nonlinear dynamic Granger causality analysis to identify the root cause.

[0005] Traditional quality-related fault monitoring methods address inherent nonlinearity by mapping to a nonlinear space using kernel mapping, while multi-layer feature extraction mitigates information loss during dimensionality reduction. Causal relationship-based monitoring methods enhance the impact of quality variables and improve monitoring performance, but further improvements require consideration of deep quality features and the complex relationships between variables. Therefore, a complete description of causal relationships between variables has become a core issue requiring immediate attention. In causal mining, bivariate modeling often fails to fully explore causal relationships between variables, especially in complex industrial environments where variable coupling effects are prominent. In the context of fault diagnosis, previous research has primarily focused on the accuracy of variable partitioning or causal relationships, while the uniqueness of causal dependencies between variables is indeed the most pressing issue. Summary of the Invention

[0006] This invention provides a method for comprehensive monitoring of quality-related faults based on causal synergy enhancement and root cause diagnosis based on causal uniqueness. The technical solution of this invention mainly focuses on the integrity of causal relationships among multiple variables. Causal synergy decomposition provides profound insights into resolving complex relationships between variables. Specifically, a variable can exert a synergistic effect on other variables through coexistence, establishing causal relationships that go beyond simple pairwise connections. However, merely ensuring the integrity of causal information for quality variables is insufficient. The synergistic effects between variables create complex dynamic characteristics within the variable group, and the potential interference from these influences must be explicitly considered during fault monitoring modeling. In the field of fault diagnosis, the technical solution of this invention mainly focuses on determining the uniqueness of causal relationships between variables. By explicitly identifying the absence of certain causal relationships, irrelevant variables are directly eliminated. This reduces redundancy in causal discovery caused by irrelevant variables, achieving clear causal mining and more reasonable diagnostic results.

[0007] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0008] A method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness includes the following steps:

[0009] Step 1: Collect industrial process variable data and perform grouping preprocessing;

[0010] Step 2: Decompose the data into synergistic and unique components, and establish a causal relationship decomposition model;

[0011] Step 3: Calculate the causal relationship between quality variables and process variables, and identify process variables and quality variables that contain quality-related information;

[0012] Step 4: Use the quality variable group and process variable group selected by causal mining to perform two dynamic internal partial least squares (DiPLS) models to achieve comprehensive monitoring of quality-related faults.

[0013] Step 5: Calculate the causal relationship between variables using the unique causal analysis results to find the root cause of the failure.

[0014] The grouping preprocessing involves grouping the data into quality data groups and process data groups.

[0015] The causal relationship decomposition model is as follows:

[0016] (1)

[0017] in, It is a group of variables variables in With target variable Causal relationships between the future It is entropy, representing the sum of causal relationships between variables. Mutual information represents variables For variables Unique causal relationship It is the number of variables. Mutual information represents a set of variables. For variables Cooperative causality It is a group of variables.

[0018] Whether a variable is a quality-related variable is determined by assessing the strength of the causal relationship between the quality variable and the process variable.

[0019] Step 3 includes:

[0020] Follow steps 3.1-3.3 to obtain the process variable group, deep process variable group, and quality variable group;

[0021] Step 3.1: Select one of the quality variables as the target quality variable, calculate the Granger causality and synergy of the causal relationship between the target quality variable and the process variables, identify the process variables containing quality-related information, and calculate using formulas (2) and (3) to obtain the process variable group, such as... , in It is the number of variables selected;

[0022] (2)

[0023] (3)

[0024] Wherein, formula (2) is a set of degrees of freedom. and degrees of freedom The F-distribution, where and It is the sum of squared residuals for univariate and bivariate models. It is a process variable in the variable group. It is the target variable. It is a process variable For target variable Cooperative causality It is an increase in information. It's a probability.

[0025] Step 3.2: Select one variable from the process variable group as the target process variable. Use formulas (2) and (3) to calculate the Granger causality and synergy of causal relationships between all process variables and the target process variable to obtain the deep process variable group, such as... , in It is the number of deep process variables selected;

[0026] Step 3.3: Using the same method, obtain the set of mass variables using Granger causality formula (2), such as... ,in It is the number of variables selected.

[0027] It utilizes causal synergy to select variables containing quality-related information and performs two DiPLS models, extending the statistics to the process variable part to achieve comprehensive monitoring.

[0028] Step 3 is detailed below:

[0029] Step a: Select the first group of process variables that contains quality variable information;

[0030] a1. Randomly select one of the quality variables from the group as the target quality variable;

[0031] a2. Calculate Granger causality between the target quality variable and all variables in the process variable group. If the value is below a threshold... A causal relationship exists, and process variable group I is obtained by filtering process variable groups;

[0032] a3. Calculate the synergistic causality between the target quality variable and the remaining process variable group after screening group I. If it is higher than the threshold... A synergistic causal relationship exists, and process variable group II is obtained by screening process variable groups;

[0033] a4. Combine the two process variable groups I and II into a single process variable group I', which is used to represent variables that have Granger causal relationships and synergistic causal relationships with the target quality variable;

[0034] Step b selects the second group of deep process variables that contains information on quality variables;

[0035] b1. Randomly select one process variable from process variable group I' as the target process variable;

[0036] b2. Calculate Granger causality between the target process variable and all variables in the process variable group. If the result is below a threshold... A causal relationship exists, and process variable group III is obtained by filtering process variable groups;

[0037] b3. Calculate the synergistic causality between the target quality variable and the remaining process variable group after screening group III. If it is higher than the threshold... There is a synergistic causal relationship, and process variable group IV is obtained by screening process variable group;

[0038] b4. Merge the two process variable groups III and IV into a single process variable group III', which represents variables that have Granger causal relationships and synergistic causal relationships with the target process variable, and filter out the deep process variable groups that contain quality variable information;

[0039] Step c filters out the quality variable groups;

[0040] c. Calculate Granger causality between the target quality variable and all variables in the quality variable group. If the result is below a threshold... If a causal relationship exists, the quality variable group I is obtained by screening the quality variable group, which is used to represent the variables that have a Granger causal relationship with the target quality variable.

[0041] Step 4 is detailed below:

[0042] The three selected groups of variables are divided into two parts: the quality variable group and the process variable group; the process variable group and the deep process variable group.

[0043] Using data from the quality variable group and the process variable group, DiPLS modeling was performed according to the following formula (4) to obtain the statistic. and ;

[0044] Using process variable set and deep process variable set data, DiPLS modeling was performed according to the following formula (5) to obtain the statistics. and ;

[0045] (4)

[0046] (5)

[0047] in, and It is the potential score vector. and It is the residual vector. and It is the characteristic matrix. and Squared prediction error, and It is the Hotelling statistic, subscript and Used to differentiate between quality monitoring models and process monitoring models.

[0048] The determination of the root cause refers to determining that other variables have no causal relationship with a certain variable, but this variable has a causal relationship with multiple other variables. This variable is the root variable.

[0049] Step 5 is detailed below:

[0050] All process-related variable data after pretreatment are divided into Group;

[0051] The causal uniqueness between variables in each group is calculated using formula (6). If it exceeds the threshold... If so, it is determined that a unique causal relationship exists;

[0052] (6)

[0053] in, Represents variables, Representing variables With variables The unique causal relationship between them This indicates an increase in information. It's probability;

[0054] Based on the causal relationships between the variables, trace the root cause of the fault and draw a cause-effect diagram.

[0055] The present invention has the following beneficial effects and advantages:

[0056] This invention presents a synergistic enhancement-based comprehensive monitoring method for quality-related faults based on causal decomposition and a uniqueness-based root cause diagnosis. Comparative experiments with other quality-related fault monitoring methods verify the effectiveness of the proposed method in fault monitoring. It not only reduces interference from non-quality information but also extends the monitoring method to process variables, enabling comprehensive monitoring of quality-related faults using only process variables. In the fault diagnosis section, compared with commonly used root cause diagnosis methods, the results show that it not only improves the accuracy of root cause diagnosis but also significantly reduces the complexity of the fault diagnosis algorithm, and can accurately identify the root cause of complex faults. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method of the present invention;

[0058] Figure 2 This is a quality-related fault monitoring diagram of the present invention;

[0059] Figure 3 This is the cause-and-effect diagnostic diagram of the present invention. Detailed Implementation

[0060] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0061] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0062] like Figure 1 The diagram shown is a flowchart of the method of this invention. This invention provides a comprehensive monitoring system for quality-related faults based on causal synergistic enhancement and a root cause diagnosis based on causal uniqueness. The application scenario is: real-world complex industrial processes. The programming language used in the program execution steps of this invention is not limited to MATLAB, Python, etc. It includes:

[0063] Step 1: Collect industrial process variable data and perform preprocessing;

[0064] Step 2: Decompose the data into causal relationships: Establish a synergistic and uniqueness decomposition model;

[0065] Step 3: Calculate the causal relationship between quality variables and process variables, and identify process variables and quality variables that contain quality-related information;

[0066] Step 4: Use the quality variable group and process variable group selected by causal mining to perform two dynamic internal partial least squares (DiPLS) models to achieve comprehensive monitoring of quality-related faults;

[0067] Step 5: Calculate the causal relationship between variables using the unique causal analysis results to find the root cause of the failure.

[0068] The specific steps of this invention are as follows:

[0069] Step 1: Collect variable data related to the industrial process (taking chemical production process as an example, variables such as water pressure, material input, valve pressure, reactor pressure, and reactor temperature can all be used as variable data), and preprocess the collected data.

[0070] Table 1: Variable data related to the process

[0071]

[0072]

[0073] Step 1.1: Divide the variables into quality variables and process variables. As shown in Table 1, quality variables include variables 37-41, and process variables include variables 1-36 and 38-52. Among them, 500 normal data samples are used to construct the training dataset, and 960 fault data samples are used as the test dataset.

[0074] Step 2: Establish a causal relationship model between quality variables and process variables, retain the synergy and uniqueness of the causal relationship, and achieve the decomposition of the synergy and uniqueness of the causal relationship, as shown in formula (1):

[0075] (1)

[0076] in, It is a group of variables variables in With target variable Causal relationships between the future It is entropy (the sum of causal relationships between variables). Mutual information (variables) For variables Unique causal relationship) It is the number of variables. It is mutual information (a set of variables) For variables Cooperative causality It is a group of variables.

[0077] Step 3: Obtain the process variable group, deep process variable group, and quality variable group according to steps 3.1-3.3;

[0078] Step 3.1: Select one of the quality variables as the target quality variable, calculate the Granger causality and synergy of the causal relationship between the target quality variable and the process variables, identify the process variables containing quality-related information, and calculate using formulas (2) and (3) to obtain the process variable group, such as... , in It is the number of variables selected.

[0079] (2)

[0080] (3)

[0081] Wherein, formula (2) is a set of degrees of freedom. and degrees of freedom The F-distribution, where and It is the sum of squared residuals for univariate and bivariate models. It is a process variable in the variable group. It is the target variable. It is a process variable For target variable Cooperative causality It is an increase in information. It's a probability.

[0082] Step 3.2: Select one variable from the process variable group as the target process variable. Use formulas (2) and (3) to calculate the Granger causality and synergy of causal relationships between all process variables and the target process variable to obtain the deep process variable group, such as... , in It is the number of deep process variables selected;

[0083] Step 3.3: Using the same method, obtain the set of mass variables using Granger causality formula (2), such as... ,in It is the number of variables selected;

[0084] Step 4.1: Divide the three sets of variables (process variable set, deep process variable set, and quality variable set) into two parts:

[0085] 1) Quality variable group and process variable group;

[0086] 2) Process variable groups and deep process variable groups;

[0087] Step 4.2: Perform DiPLS modeling twice on each of the two variable groups:

[0088] 1) The process variable set serves as the input to the model, and the quality variable set serves as the output of the model;

[0089] 2) The deep process variable set serves as the input to the model, and the process variable set serves as the output of the model;

[0090] Step 4.3, the second DiPLS modeling yields the following four statistics:

[0091] (4)

[0092] (5)

[0093] in, and It is the potential score vector. and It is the residual vector. and It is the characteristic matrix. and Squared prediction error, and It is the Hotelling statistic, subscript and Used to differentiate between quality monitoring models and process monitoring models.

[0094] Squared prediction error primarily detects systematic faults related to principal components and is suitable for detecting faults that affect the main characteristics of a process; Hotelling statistic primarily detects local or random faults that cannot be explained by principal components and is suitable for detecting novel changes that deviate from the normal pattern.

[0095] Statistic and This is a statistic in the quality monitoring model, using a set of quality variables and a set of process variables. It is used to calculate the fault monitoring accuracy, which represents the proportion of times a system state (fault occurred or did not occur) was correctly identified out of the total number of monitoring times. Similarly, The statistics used in the process monitoring model are process variables and deep process variables.

[0096] The four statistics are obtained by DiPLS modeling two sets of monitoring statistics from the three sets of variables selected in 4.1, and are used for comprehensive fault monitoring.

[0097] Figure 2 The four monitoring statistics for fault 7, as shown in the TE process, are 93.54%, 100.00%, 57.91%, and 100.00%. The red lines in the four graphs represent control limits. The first 160 represent normal data, and the last 800 represent fault variables. The detection accuracy represents the percentage of the total number of variables where the first 160 normal variables are below the control limits and the last 800 fault variables are above the control limits.

[0098] Step 5.1: Divide the pre-processed data of all process-related variables (52 variables in Table 1) into... Group;

[0099] Step 5.2: Use formula (6) to calculate the causal uniqueness between each group of variables, calculate the final result and draw a causal diagram to determine the root cause.

[0100] (6)

[0101] in, Represents variables, Representing variables With variables The unique causal relationship between them This indicates an increase in information. It's a probability.

[0102] By obtaining the causal relationships between variables, we can trace the causes to find the root cause of the failure and draw a causal diagram. The red variables in the causal diagram are the root variables.

[0103] like Figure 3 As shown in the diagram, the diagnostic results for process fault 1 in TE are as follows: Changes in the opening of feed valve A (x44) affect the feed flow rate A (x1), which is only affected by the valve opening. As the industrial process progresses, this change further affects the reactor feed rate (x6). Simultaneously, feed rates E (x3) and D both affect the reactor feed rate. Then, as the reaction proceeds, the reaction products are sent to the condenser and then to the separator, causing changes in the separator level (x12). The separated liquid eventually enters the stripper, causing changes in the stripper level. After the chemical reaction, the unreacted oil residue in the stripper is eventually recycled back into the entire reactor via circulation (x5), thus recycling the entire reaction process.

[0104] The above description and implementation rules will help those skilled in the art to further understand the present invention, but do not limit the present invention in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

Claims

1. A method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness, characterized in that, Includes the following steps: Step 1: Collect industrial process variable data and perform grouping preprocessing; Step 2: Decompose the data into synergistic and unique components, and establish a causal relationship decomposition model; Step 3: Calculate the causal relationship between quality variables and process variables, and identify process variables and quality variables that contain quality-related information; Step 4: Use the quality variable group and process variable group selected by causal mining to perform two dynamic internal partial least squares (DiPLS) models to achieve comprehensive monitoring of quality-related faults. Step 5: Calculate the causal relationship between variables using the unique causal analysis results to find the root cause of the failure.

2. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness as described in claim 1, characterized in that, The grouping preprocessing involves grouping the data into quality data groups and process data groups.

3. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness, as described in claim 2, is characterized in that... The causal relationship decomposition model is as follows: (1) in, It is a group of variables variables in With target variable Causal relationships between the future It is entropy, representing the sum of causal relationships between variables. Mutual information represents variables For variables Unique causal relationship It is the number of variables. Mutual information represents a set of variables. For variables Cooperative causality It is a group of variables.

4. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness according to claim 3, characterized in that, Whether a variable is a quality-related variable is determined by assessing the strength of the causal relationship between the quality variable and the process variable.

5. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness according to claim 4, characterized in that, Step 3 includes: Follow steps 3.1-3.3 to obtain the process variable group, deep process variable group, and quality variable group; Step 3.1: Select one of the quality variables as the target quality variable, calculate the Granger causality and synergy of the causal relationship between the target quality variable and the process variables, identify the process variables containing quality-related information, and calculate using formulas (2) and (3) to obtain the process variable group, such as... , in It is the number of variables selected; (2) (3) Wherein, formula (2) is a set of degrees of freedom. and degrees of freedom The F-distribution, where and It is the sum of squared residuals for univariate and bivariate models. It is a process variable in the variable group. It is the target variable. It is a process variable For target variable Cooperative causality It is an increase in information. It's a probability. Step 3.2: Select one variable from the process variable group as the target process variable. Use formulas (2) and (3) to calculate the Granger causality and synergy of causal relationships between all process variables and the target process variable to obtain the deep process variable group, such as... , in It is the number of deep process variables selected; Step 3.3: Using the same method, obtain the set of mass variables using Granger causality formula (2), such as... ,in It is the number of variables selected.

6. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness, as described in claim 1, is characterized in that... By utilizing the causal synergy of selected variables containing quality-related information, two DiPLS models are performed to extend the statistics to the process variable part, thereby achieving comprehensive monitoring.

7. The method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness as described in claim 6, characterized in that, Step 3 is detailed below: Step a: Select the first group of process variables that contains quality variable information; a1. Randomly select one of the quality variables from the group as the target quality variable; a2. Calculate Granger causality between the target quality variable and all variables in the process variable group. If the value is below a threshold... A causal relationship exists, and process variable group I is obtained by filtering process variable groups; a3. Calculate the synergistic causality between the target quality variable and the remaining process variable group after screening group I. If it is higher than the threshold... A synergistic causal relationship exists, and process variable group II is obtained by screening process variable groups; a4. Combine the two process variable groups I and II into a single process variable group I', which is used to represent variables that have Granger causal relationships and synergistic causal relationships with the target quality variable; Step b selects the second group of deep process variables that contains information on quality variables; b1. Randomly select one process variable from process variable group I' as the target process variable; b2. Calculate Granger causality between the target process variable and all variables in the process variable group. If the result is below a threshold... A causal relationship exists, and process variable group III is obtained by filtering process variable groups; b3. Calculate the synergistic causality between the target quality variable and the remaining process variable group after screening group III. If it is higher than the threshold... There is a synergistic causal relationship, and process variable group IV is obtained by screening process variable group; b4. Merge the two process variable groups III and IV into a single process variable group III', which represents variables that have Granger causal relationships and synergistic causal relationships with the target process variable, and filter out the deep process variable groups that contain quality variable information; Step c filters out the quality variable groups; c. Calculate Granger causality between the target quality variable and all variables in the quality variable group. If the result is below a threshold... If a causal relationship exists, the quality variable group I is obtained by screening the quality variable group, which is used to represent the variables that have a Granger causal relationship with the target quality variable.

8. The method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness as described in claim 7, characterized in that, Step 4 is detailed below: The three selected groups of variables are divided into two parts: the quality variable group and the process variable group; the process variable group and the deep process variable group. Using data from the quality variable group and the process variable group, DiPLS modeling was performed according to the following formula (4) to obtain the statistic. and ; Using process variable set and deep process variable set data, DiPLS modeling was performed according to the following formula (5) to obtain the statistics. and ; (4) (5) in, and It is the potential score vector. and It is the residual vector. and It is the characteristic matrix. and Squared prediction error, and It is the Hotelling statistic, subscript and Used to differentiate between quality monitoring models and process monitoring models.

9. The method for comprehensive monitoring of quality-related faults based on causal decomposition and root cause diagnosis based on causal uniqueness according to claim 1, characterized in that, The determination of the root cause refers to determining that other variables have no causal relationship with a certain variable, but this variable has a causal relationship with multiple other variables. This variable is the root variable.

10. The method for comprehensive monitoring of quality-related faults based on causal synergistic enhancement and root cause diagnosis based on causal uniqueness as described in claim 9, characterized in that, Step 5 is detailed below: All process-related variable data after pretreatment are divided into Group; The causal uniqueness between variables in each group is calculated using formula (6). If it exceeds the threshold... If so, it is determined that a unique causal relationship exists; (6) in, Represents variables, Representing variables With variables The unique causal relationship between them This indicates an increase in information. It's probability; Based on the causal relationships between the variables, trace the root cause of the fault and draw a cause-effect diagram.

Images