Industrial production process abnormal root cause diagnosis method

Abstract

The invention discloses a root cause diagnosis method for complex industrial process abnormity, and provides a modeling process fusing priori knowledge and data driving aiming at the characteristics of high coupling among variables, complex causal structure and incomplete priori knowledge in an industrial process. The method comprises the following steps: firstly, preprocessing production data, embedding process knowledge into a constraint-based structure learning algorithm, and preliminarily constructing a causal network skeleton; on the basis, an intelligent search optimization mechanism with randomness is introduced to perfect a network structure, potential correlation is found and complemented, and finally a comprehensive network reflecting causal transfer and statistics correlation is obtained. The influence path is calculated by using the network, propagation of production abnormity in the system can be effectively tracked, and accurate positioning of the root cause is realized. The method is excellent in causal structure identification accuracy, the constructed propagation path is high in interpretability, and technical support can be provided for optimization control of various industrial enterprises and improvement of product quality and process stability.

Description

Technical Field

[0001] This invention relates to the source tracing of anomalies in industrial production processes, specifically a knowledge- and data-driven method for diagnosing the root causes of anomalies in process industrial production processes. Background Technology

[0002] Complex industrial processes are a core component of modern manufacturing, and their operational stability directly impacts production efficiency, energy consumption, and final product quality. In actual operation, industrial processes frequently encounter various abnormal conditions, such as material loss and imbalance, abnormal energy transfer, or deviations of key parameters from set ranges. These problems, once they occur, can easily trigger production fluctuations, leading to decreased product quality, resource waste, and even potential safety risks. Because modern industrial processes typically involve numerous interacting variables and complex dynamic coupling relationships, these anomalies are often not triggered by a single factor, but rather are the result of the combined effects and gradual evolution of multiple process stages or parameters. Relying solely on operational experience or simple threshold alarms is often insufficient to quickly and accurately trace the root cause of the anomaly, thus affecting the efficiency and effectiveness of problem-solving. Therefore, there is an urgent need for a universal method that can effectively combine historical operational data with domain process knowledge to deeply analyze anomaly propagation mechanisms and assist in locating key influencing factors, providing strong support for the stable operation and continuous optimization of various complex industrial processes.

[0003] Traditional methods for identifying and diagnosing industrial process anomalies can be broadly categorized into two types: mechanistic model-based and data-driven. However, for many large-scale, highly coupled modern industrial processes, the internal physicochemical reaction mechanisms are extremely complex and highly nonlinear. Coupled with variable operating conditions and limitations in measurement methods, establishing accurate and comprehensive mechanistic models often presents significant challenges. Therefore, with the rapid development of industrial big data acquisition, storage, and computing capabilities, data-driven methods that incorporate domain-specific process knowledge have become a crucial technical approach for analyzing the operational status of complex industrial processes and identifying and diagnosing various production anomalies.

[0004] However, data-driven methods still face many challenges in practical applications. Industrial processes typically involve a large number of dynamically changing process variables, which exhibit significant nonlinearity and coupling relationships. Furthermore, their measurement data inevitably contains random noise and unmodeled external disturbances. These complex factors make it easy for true anomalous signals to be masked by background fluctuations, or for their early manifestations to be unclear, thus significantly increasing the difficulty of identifying potential propagation paths and tracing their root causes. Most existing data analysis methods either rely excessively on statistical correlations between variables or focus on capturing the most drastically changing features on the surface of the data. When faced with complex operating conditions and changes in process conditions, they often struggle to deeply reveal the underlying mechanisms of anomalous evolution and the true causal transmission chains between variables.

[0005] Therefore, there is an urgent need to construct a general analytical framework that can effectively integrate prior domain knowledge with the deep features of historical data and accurately construct a network representing the causal relationships between variables. This framework aims to more accurately identify the propagation paths and key influencing factors of typical production anomalies in various industrial processes. Such methods will enhance the ability to understand the inherent operational laws of complex industrial processes and the interpretability of anomaly diagnosis, providing crucial technical support for ensuring the operational stability of various industrial systems, improving the consistency of final product quality, and optimizing overall production efficiency. Summary of the Invention

[0006] This invention addresses the challenges of highly coupled variables, complex causal structures, and incomplete prior knowledge in industrial processes. It proposes a method for diagnosing the root causes of anomalies in industrial production processes. By integrating prior knowledge with data-driven approaches to construct a causal relationship graph model between variables, this method effectively tracks the propagation of key abnormal parameters within the system and achieves precise location of the root cause.

[0007] To achieve the above objectives, this invention provides a method for diagnosing the root causes of anomalies in industrial production processes. This method, targeting the production process, establishes a process anomaly tracing model and performs root cause analysis on the anomalies, including the following steps:

[0008] (1) Select n variables v1, v2, ..., v that are related to production anomalies. n ;

[0009] (2) Initialize a completely undirected graph G to represent the connection relationships between variables;

[0010] (3) Perform conditional independence checks on all variable pairs. If the variable pair (v i ,v j There exists a d-separated point set O. d Then remove v i ,v j By identifying the edges between them, a preliminary optimized graph structure can be obtained;

[0011] (4) Apply preset process knowledge constraints to the preliminarily optimized graph structure, adjust the direction or relationship of the edges, and generate an initial graph model group {G}. k};

[0012] (5) For the initial graph model group {G k Each candidate graph model G in} k Iterative optimization is performed, and the iterative optimization process includes:

[0013] 5.1 Perturbation of the newly generated graphical model G' k Generate new candidate graph models;

[0014] 5.2. Compare the highest historical scores of individuals with the highest graph model. And the historical graph model G with the highest global score best Randomly modify the new candidate graph model G k ;

[0015] 5.3 Calculate the graph model score (G) of the new candidate graph model. k );

[0016] 5.4 Update the individual historical best graph model and the global historical optimal graph model G best ;

[0017] (6) Output the current global historical best graph model G that satisfies the preset iteration termination condition. best , as the final causal relationship graph model;

[0018] (7) Calculate the final causal relationship graph model G based on the above. best The probability P of abnormal propagation is used to determine the abnormal propagation path and root cause.

[0019] More specifically, this invention establishes an industrial production anomaly propagation graph model and uses this model to analyze the propagation path and locate the root cause of anomalies in the industrial production process.

[0020] The process of establishing the industrial production anomaly propagation diagram model is as follows:

[0021] (1) Select n variables v1, v2, ..., v that may be related to industrial production anomalies. n ;

[0022] (2) Sample variables within a preset time period to obtain production data; preprocess the production data to serve as training set samples;

[0023] (3) Initialize a complete undirected graph G to represent the connections between variables. This graph has the following assumptions:

[0024] ① Assume that the parent node is treated as the row index and the child node is treated as the column index.

[0025] ②g ij =1 indicates that the variable v i ,v j There exists a path from parent node v i Pointing to child node v j The directed edge, g ij =0 indicates that such a directed edge does not exist.

[0026] The completely undirected graph G can be represented as:

[0027]

[0028] (4) Perform conditional independence checks on variable pairs and initially optimize the graph structure. If the variable pair (v i ,v j There exists a d-separated point set O. d Remove the v i ,v j The edges between them. d separates the set of points O. d The solution steps are as follows:

[0029] ① For the current variable pair (v i ,v j ), retrieve the set of adjacent nodes under its current graph structure, denoted as Adj(v i )\{v j} and Adj(v j )\{v i}, the former represents v i Remove v from adjacent nodes j The remaining nodes, the latter representing v j Remove v from adjacent nodes i The remaining nodes; and take the union of them as the candidate condition variable set C.

[0030] ② Enumerate all subsets of size q (increasing from 0) from the candidate set C, denoted as For each S in turn q Fisher-Z test is used to determine v i and v j Is it in S? q Independent under certain conditions (denoted as v) i ⊥v j |S q ).

[0031] ③If v is satisfied i ⊥v j |S q Then S q That is, the set of points O separated by d. d Delete v i and v j The edges between them.

[0032] Repeat the above process for all unprocessed variable pairs, gradually eliminating conditionally independent edges until all variable pairs have been tested at the current order q; gradually increase the order until the upper limit of the order of the maximum condition set is reached or all edges have been processed.

[0033] (5) Add the following process knowledge constraints to the preliminarily optimized graph structure:

[0034] ① Assume v i and v j In the same part of the model structure, vi and v j They can influence each other, i.e., v i and v j For correlations, the edges of the correlations are processed according to the following formula:

[0035] g ij =g ji =0.5;

[0036] ② Assume process variable v i and output variable v j If a dependency exists, then the process variable v i Set as the parent node, output variable v j Set as a child node:

[0037] g ij =1,g ji =0;

[0038] Randomly orient the unoriented edges in the initial graph model. This concludes the graph model initialization section.

[0039] (6) Repeat step (5) to initialize the graph model N times, generating a total of N different graphs {G1, G2, ... G...} N}, where the k-th graph G k It can be represented as:

[0040]

[0041] Where v i →v j Represents v i Point to v j A one-way edge exists. Represents v i Point to v j The edge does not exist. Represents v i and v j The edges between them represent a bidirectional relationship.

[0042] (7) For each G k The graph model score (G) is obtained. k As the highest score in history, the corresponding graph is: The graph model with the highest score among all graph models is the highest historical score, and the corresponding graph model is denoted as G. best .

[0043] score(G k The calculation method for ) is as follows:

[0044]

[0045] Where n represents the total number of variables related to the production anomalies; m is the total number of samples in the training dataset used for modeling; r i For the variable v i The number of discrete states; m ijk In the training dataset, when variable v i Take its k-th state (k ranges from 1 to r) i And its parent node set Pa(v) i The sample count when the j-th state combination (j from 1 to qi); m ij That is, the total number of samples when the parent node combination is the j-th state; qi is Pa(v i The number of all possible state combinations of ) (if there is no parent node, qi = 1).

[0046] (8) Repeat the graph model initialization N times to generate N different graphs {G'1, G'2, ... G'}. N}

[0047] (9) For each G' k Add or remove an edge randomly. That is, for a random v i and v j If g' ij =1, then after transformation g' ij =0; if g' ij =0, then after transformation g' ij =1.

[0048] (10) Solve for Mov for k = 1, 2, ..., N. k as follows:

[0049] Mov k =G′ k -G k

[0050] (11) For all G k Randomly select whether to accept Mov k :

[0051] G k =c2(Mov k +G k c2 = randomint(0,1)

[0052] The randomint(0,1) method represents randomly selecting an integer from 0 and 1 (i.e., 0 or 1).

[0053] (12) For all G k Randomly choose to accept or reject. and G best China is different from G k The edges are as follows:

[0054]

[0055] Where c0 and c1 are random numbers of 0 or 1; Is for the graph And Figure G k For each distinct edge in graph G, randomly select graph G. k The decision to modify (c1=1) or not modify (c1=0) the edges in the array is made; the same applies to the c0 part.

[0056] (13) For all G k Recalculate the graph model score (G). k ),renew and G best .

[0057] (14) Repeat steps (6) to (13) until all scores (G) are achieved. k The continuous iterations no longer change or reach the set number of iterations.

[0058] (15) Take G at this time best As the output of the graph model structure.

[0059] (16) Collect variable data for the test phase, perform data preprocessing, and use it as a test set sample.

[0060] (17) For structure G best Based on the dependencies in the dataset, calculate the propagation probability of anomalies in the test set data. Assume the anomaly node is v. i One of its parent nodes is par(v i ), and so on, the root node is par m (v i If the probability of abnormal propagation along this path is given by the formula:

[0061]

[0062] In the formula, P(alarm) represents the probability of that specific "alarm" or "abnormal state" occurring; P(par) m (v i )) represents the starting node of the path, par m (v i The prior or marginal probability of itself occurring abnormally; P(par) j-1 (v i )|par j (v i )) represents the upstream node par on the path. j (v i Under abnormal conditions, its direct downstream node parj-1 (v i The probability of abnormalities also occurs.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] This invention discloses a method for identifying the propagation path and locating the root cause of anomalies in complex industrial processes. Addressing the characteristics of highly coupled process variables and complex, concealed anomaly evolution paths in industrial processes, this method effectively combines domain-specific process knowledge with historical process data. By constructing a causal relationship graph model between variables, it can accurately identify key anomaly parameters and their propagation chains within the system, deeply analyzing the diffusion patterns and underlying mechanisms of anomaly impacts among various variables. Compared to traditional diagnostic methods relying on statistical correlation analysis or simple rule thresholds, this invention significantly improves the explanatory power and root cause tracing accuracy of process anomalies. It has significant engineering application value and promising prospects for ensuring the stable operation of various complex industrial processes, improving final product quality and production efficiency, and reducing energy consumption and potential operational risks. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method for locating the root cause of anomalies in industrial production processes according to the present invention;

[0066] Figure 2 This is a correlation and causal relationship diagram of production variables of a steel blast furnace in the embodiment;

[0067] Figure 3 This is the root cause localization result of an anomaly in the production process of a steel blast furnace in the embodiment. Detailed Implementation

[0068] The following, with reference to the accompanying drawings and specific examples, illustrates the implementation effect of this method in the steel blast furnace production process through a concrete operational procedure. This embodiment is implemented based on the technical solution of this invention, but the scope of protection of this invention is not limited to the following embodiments.

[0069] This invention takes the ironmaking process of a small blast furnace in a steel enterprise as an example. This blast furnace plays a crucial role in reducing iron ore to qualified liquid pig iron, and its smelting process involves complex physicochemical reactions and dynamic coupling of multiple variables. However, in actual production, due to various factors such as operational adjustments or equipment status, the blast furnace frequently faces the problem of unstable pig iron quality, affecting the enterprise's economic benefits. To verify the effectiveness of the method proposed in this invention, the following will use an abnormal event of excessive sulfur content in pig iron occurring in this blast furnace during a specific period as an example to detail the application of this invention in diagnosing the root cause of the abnormality.

[0070] This study selected continuous production data from February 26, 2023 to March 25, 2023 (a total of 28 days) of the blast furnace as the training set to construct a root cause diagnosis model; and selected production data from March 26, 2023 to April 25, 2023 (a total of 31 days) as the test set to evaluate the diagnostic performance and practical application effect of the model.

[0071] The implementation process is as follows: Figure 1 As shown, the specific implementation steps are as follows:

[0072] (1) Based on the blast furnace structure, analyze the location of the sensors and select relevant control variables and measurement variables. A total of 13 relevant variables were selected: sulfur content in pig iron (output variable), furnace bottom temperature, furnace body temperature, furnace throat temperature, furnace top temperature, furnace top pressure, total pressure difference, hot blast temperature of hot blast stove, hot blast pressure of hot blast stove, oxygen enrichment, coal injection quantity, blower air pressure, and blower air volume. The abbreviations and names of the variables are shown in Table 1.

[0073] Table 1 Variable Names and Abbreviations

[0074] Variable name Variable abbreviation blower air pressure AP air volume of blower AVB Coal injection volume CI Oxygen-rich OG Hot air pressure of hot blast stove HFP Hot air temperature of hot air furnace HFT Furnace bottom temperature T(b) Furnace body temperature T Furnace throat temperature T(h) Furnace top temperature T(top) Furnace top pressure P(top) Total differential pressure DP Sulfur content in pig iron C(S)

[0075] (2) Select data from February 26 to March 25, a total of 28 days. Except for the sulfur content in pig iron (output variable), the sampling interval for variables is 1 hour. The sulfur content in pig iron is sampled by furnace, with a total of 18 furnaces per day.

[0076] (3) The least squares method was used to fit the variables other than the output variable to obtain the theoretical values ​​of the pig iron tapping time other than the output variable, and a training set of 504 samples was constructed.

[0077] (4) Perform smoothing filtering on each variable and determine the outlier limit according to relevant production requirements. Use 0 to indicate that the sample is within the normal range and 1 to indicate that the sample is an outlier.

[0078] (5) Initialize a completely undirected graph G to represent the connection relationship between variables, and perform d-separation on all variable pairs;

[0079] (6) Add two types of process knowledge to the graph after discrimination. In this example, the process knowledge mainly includes: the inner wall of the blast furnace has a certain thermal conductivity, so the temperatures of different parts are related variables; the sulfur content in pig iron is an output variable, so any variable connected to the sulfur content in pig iron is a process variable → output variable. The result is as follows: Figure 2 As shown;

[0080] (7) Randomly orient the undirected edges in the graph generated in step (6) to complete one graph model initialization. In this example, the graph model is initialized 10 times, resulting in 10 initial graph models {G1, G2, ... G...}.10};

[0081] (8) Obtain the scores of the 10 initial graph models. In this example, the BIC scoring is used to obtain the score of each graph, as well as the global historical highest score and the corresponding graph G. best ;

[0082] (9) Perform 10 more graph model initializations to obtain {G'1,G'2,…G' 10}, and for each G' of k = 1…10 k Randomly add or delete an edge;

[0083] (10) For G, k = 1…10 k Calculate Mov k And randomly select whether to accept Mov k ;

[0084] (11) Mov for random acceptance or rejection k G k (k = 1…10), randomly select to accept or reject. and G best China is different from G k The edges, and recalculate the score, update and G best ;

[0085] (12) Repeat steps (8) to (11). In this example, the number of iterations is 200. After the iteration is complete, output G. best ,like Figure 3 As shown;

[0086] (13) Perform the data preprocessing steps (2) to (4) on the test set from March 26 to April 25 to obtain 546 samples, and calculate the results based on G. best The probability of anomalous propagation of sulfur content in pig iron based on variable dependencies is shown in Table 2.

[0087] Table 2 shows the propagation probability between nodes along the abnormal propagation path.

[0088] transmission path Conditional probability T(b)→C(S) 0.4091 CI→C(S) 0.3095 OG→CI 0.5011 T→T(b) (Related)

[0089] Regarding the abnormal sulfur content in pig iron that occurred during the company's testing period, the root cause diagnosis method proposed in this invention was used for analysis. The diagnosis results and key propagation paths are as follows: Figure 3As shown in Table 2, when an abnormal sulfur content in pig iron is detected, the causal network constructed by this method clearly reveals how the anomaly starts from certain key process parameters upstream (e.g., oxygen enrichment, pulverized coal ratio, furnace temperature, etc.), gradually propagates through a series of intermediate variables, and ultimately leads to an abnormal sulfur content in downstream pig iron. As shown in Table 2, changes in oxygen enrichment (OG) affect the pulverized coal ratio (CI) with a conditional probability of 0.5011, which in turn affects the sulfur content (C(S)) in pig iron with a probability of 0.3095. Simultaneously, the correlation between furnace temperature (T) and furnace bottom temperature (T(b)) and the direct impact of furnace bottom temperature (T(b)) on the sulfur content (C(S)) in pig iron with a probability of 0.4091 together constitute the key chain of problem evolution.

[0090] As can be seen, compared with traditional methods based on experience-based judgment or single-indicator analysis, this method, by integrating prior process knowledge with data-driven causal discovery, can provide a structured and visualized panoramic view of fault evolution. The fault propagation paths it provides are highly consistent with relevant process knowledge, demonstrating the accuracy and reliability of this method in root cause analysis of complex industrial processes. This provides clear guidance for enterprises to adjust process parameters and improve operating procedures in a timely manner, and has significant practical implications for controlling product quality and improving production stability from the source.

Claims

1. A method for diagnosing the root causes of abnormalities in an industrial production process, characterized in that, For the production process, an anomaly tracing model is established and root cause analysis is performed on the anomalies, including the following steps: (1) Select n variables v1, v2, ..., v that are related to production anomalies. n ; (2) Initialize a completely undirected graph G to represent the connection relationships between variables; (3) Perform conditional independence checks on all variable pairs. If the variable pair (v i ,v j There exists a set of d-separated points O. d Then remove v i ,v j By identifying the edges between them, a preliminary optimized graph structure can be obtained; (4) Apply preset process knowledge constraints to the preliminarily optimized graph structure, adjust the direction or relationship of the edges, and generate an initial graph model group {G}. k }; (5) For the initial graph model group {G k Each candidate graph model G in} k Iterative optimization is performed, and the iterative optimization process includes: 5.1 Perturbation of the newly generated graphical model G ' k Generate new candidate graph models; 5.

2. Compare the highest historical scores of individuals with the highest graph model. And the historical graph model G with the highest global score best Randomly modify the new candidate graph model G k ; 5.3 Calculate the graph model score (G) of the new candidate graph model. k ); 5.4 Update the individual historical best graph model and the global historical optimal graph model G best ; (6) Output the current global historical best graph model G that satisfies the preset iteration termination condition. best , as the final causal relationship graph model; (7) Calculate the final causal relationship graph model G based on the above. best The probability P of abnormal propagation is used to determine the abnormal propagation path and root cause.

2. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, The training set data used in the final causal graph model establishment process and the test set data used in the anomaly propagation probability P calculation process both undergo preprocessing including the following steps: a. Select production data within a preset time period; b. Fit the process variable value change curve using the least squares method; c. Perform smoothing filtering on each variable; d. Take the estimated value of the output variable at the time node and convert the variable value into a binary state value representing normal or abnormal according to the preset abnormality limit.

3. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, The completely undirected graph G initialized in step (2) is as follows: In the formula, g ij =1 indicates that the variable v i ,v j There exists a path from parent node v i Pointing to child node v j The directed edge, g ij =0 indicates that such a directed edge does not exist.

4. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 3, characterized in that, In step (3), the variable pair (v) i ,v j When performing conditional independence checks, a subset S of the candidate condition variable set C, consisting of its adjacent nodes, is enumerated. q As a condition set, statistical tests are used to determine whether a set of d-separation points O exists. d Remove conditionally independent edges.

5. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 4, characterized in that, The process knowledge constraints applied in step (4) include: 4.1 Define the relationships between some process variables as follows: g ij =g ji =0.5; 4.2 Define other process variables v connected to the output variable. i To point to the output variable v j Dependent variable: g ij =1,g ji =0。 6. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 5, characterized in that, Step (4) in generating the initial graph model group includes the following steps: 4.3 Randomly orient the pairs of variables with undirected edges in the graph structure after applying process knowledge constraints; 4.4 Repeat the random orientation operation N init Next, generate N init An initial graph model is obtained, that is, an initial graph model group is obtained.

7. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, In step 5.3, the graphical model score (G) is calculated. k When using the BIC scoring standard, the expression is as follows: Where n represents the total number of variables related to the production anomalies; m is the total number of samples in the training dataset used for modeling; r i For the variable v i The number of discrete states; m ijk In the training dataset, when variable v i Take its k-th state, and its parent node set Pa(v) i The sample count when the j-th state combination is in which k takes values ​​from 1 to r. i j takes values ​​from 1 to qi; m ij That is, the total number of samples when the parent node combination is the j-th state; qi is Pa(v i The number of all possible combinations of states; when the variable v i When there is no parent node, qi = 1.

8. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 6, characterized in that, In step 5 of the iterative optimization process, before each structural perturbation of the graphical model, N is performed again. pert The secondary graph model is initialized to obtain N. pert A graphical model to be disturbed The structural perturbation of the graphical model includes perturbing each graphical model G to be perturbed. ' k Add or delete an edge randomly.

9. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, In step 5.4, update the individual historical optimal graph model. and the global historical optimal graph model G best Previously, the current graph model G was also discussed. k Perform the following operations: 5.4.1 Calculate the differential shift Mov k The Mov k Represented as G ' k With G k The difference, i.e., Mov k =G ' k -G k ; 5.4.

2. A decision on whether to accept the differential shift amount Mov is made based on random selection. k To update G k .

10. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, Step (5) updates the individual historical best graph model. and the global historical optimal graph model G best Subsequently, further research was conducted on the graphical model G. k Perform the following operations: Based on random selection, decide whether to accept the historical best graph model from previous individuals. And the previous global historical optimal graph model G best China is different from the current G k Edges to update graph model G k .

11. The method for diagnosing the root causes of abnormalities in an industrial production process according to claim 1, characterized in that, Step (6) Calculate the probability of anomaly propagation along the path according to the following formula: In the formula, P(alarm) represents the probability of that specific "alarm" or "abnormal state" occurring; P(par) m (v i )) represents the starting node of the path, par m (v i The prior or marginal probability of itself occurring abnormally; P(par) j-1 (v i )|par j (v i )) represents the upstream node par on the path. j (v i Under abnormal conditions, its direct downstream node par j-1 (v i The probability of abnormalities also occurs.

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