Fault operation and maintenance knowledge graph combined with fault tree complex production line reliability analysis method

Abstract

The application discloses a complex production line reliability analysis method combining a fault operation and maintenance knowledge graph with a fault tree, constructs a multilevel production line fault operation and maintenance knowledge graph based on a production line-equipment-fault-method, inputs fault information to perform production line layer fault matching query, constructs an available equipment subgraph, analyzes the logical relationship between each factor causing the fault of the production line and the fault, constructs a production line fault tree, finally performs qualitative analysis on the production line fault tree and quantitatively calculates the production line fault rate, and realizes reliability analysis of the production line. The method is simple and easy to implement, can improve the reliability analysis of the current production system from the equipment level to the whole production line level considering the coupling between the equipment, and is helpful for production managers to understand the rules of equipment or system fault and formulate reasonable maintenance strategies by utilizing the production line characteristics and the reverse fault knowledge to standardize and verify the mode layer.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of reliability analysis, and particularly relates to a complex production line reliability analysis method combining a fault operation and maintenance knowledge graph and a fault tree. BACKGROUND

[0002] There are many types of aviation logistics equipment products, and the parts are complex, and the manufacturing process involves a large number of processing equipment. For a complete production line, a plurality of processing personnel groups and various production equipment are usually included, and a large amount of information in the form of text such as device maintenance operation procedures, accident disposal plans, troubleshooting manuals, and troubleshooting logs is stored in the daily maintenance system. Most of these information are semi-structured and unstructured data with low processing efficiency. These unstructured data are difficult to be utilized by subsequent fault diagnosis. As a structured knowledge representation tool, the knowledge graph can effectively integrate the multi-level, multi-source, and multi-cause information of the production line fault, construct a comprehensive and visual fault operation and maintenance knowledge graph, further study the production line fault and reliability reasoning analysis method, and realize accurate positioning of the fault and health assessment of the production line. The traditional knowledge graph construction is non-automatic, time-consuming and requires a large amount of manual work, which is insufficient to meet the requirements of the modern manufacturing mode. Therefore, the research on automatically constructing a high-quality fault operation and maintenance knowledge graph is particularly important.

[0003] With the continuous improvement of the automation level of the production line, its production capacity has been significantly improved. However, the highly integrated and serial production mode makes the reliability of the production line face greater challenges: once a device in the production line fails or fails, it may cause the production activities of the entire production line to be interrupted. Therefore, the production line layout in the mixed production of multiple products usually adopts a mixed mode of series and parallel to organize flexible production. At the same time, for the running state of multiple devices in the production line, a scientific and reasonable maintenance decision is made, which is crucial for the continuous and efficient operation of the enterprise. Production line reliability analysis is an important research direction to ensure the efficient operation of the production system. Unlike the existing reliability analysis which takes a single device or independent system as the object, the production line reliability analysis focuses on the synergistic effect and overall performance of the entire production line, aiming to identify potential weak links through in-depth analysis of each link in the production process, and optimize system design and operation and maintenance strategies.

[0004] Current reliability analysis methods mainly include fault tree analysis (FTA), Markov chain analysis, Monte Carlo simulation, and data-driven machine learning models. Among them, fault tree analysis is widely used due to its clear logic and easy understanding. The production line is a complex system composed of multiple devices and process links, and fault tree analysis can effectively identify the fault correlation and key nodes between devices. Existing reliability analysis methods are often targeted at a specific system or a specific device, however, in reality, there is a certain correlation and coupling effect between device failures. When a device component fails, it may affect other components, and even trigger a chain reaction in extreme cases. Therefore, it is innovative, theoretically significant and practically valuable to study the reliability analysis method of complex production line systems with device coupling and mixed series-parallel mode. SUMMARY

[0005] To solve the above technical problems, the present application provides a complex production line reliability analysis method combining fault operation and maintenance knowledge graph and fault tree, which constructs a production line fault operation and maintenance knowledge graph and performs reliability analysis on complex production lines with mixed series-parallel mode based on fault tree.

[0006] The technical scheme adopted by the present application is as follows: A complex production line reliability analysis method combining fault operation and maintenance knowledge graph and fault tree, the specific steps are as follows:

[0007] S1, construct a multi-level production line fault operation and maintenance knowledge graph based on production line-device-fault-method;

[0008] S11, construct a production line fault operation and maintenance knowledge graph mode layer;

[0009] First, sort out the related concepts of production line fault operation and maintenance knowledge, obtain fault text through data source, summarize and refine, determine fault operation and maintenance knowledge entities and attributes, then use Protégé ontology modeling to define the data of each entity and attribute, obtain production line fault knowledge ontology, finally use the constructed ontology to export "RDF / XML" in Protégé, further import into a graph database, and realize the construction of the production line fault operation and maintenance knowledge graph mode layer.

[0010] Among them, the data source includes: manufacturing information system, fault log and equipment manual; the fault operation and maintenance knowledge entities in the production line fault operation and maintenance knowledge graph mode layer include: equipment, component, process, fault phenomenon, fault reason, solution; the fault operation and maintenance knowledge attributes in the production line fault operation and maintenance knowledge graph mode layer include: product, team, name, specification, manufacturer, equipment code, purchase date, start time, end time, alarm number, alarm text.

[0011] S12, based on the mode layer constructed in step S1, knowledge extraction is performed on the fault text, and a data layer of the production line fault operation and maintenance knowledge graph is constructed;

[0012] First, the pre-processed fault operation and maintenance original data is labeled, after the data is labeled, the data is divided into training set, validation set and test set, and input into the BERT-BILSTM-CRF entity extraction model built, the production line fault operation and maintenance knowledge is automatically recognized and entity extraction, and then the relationship extraction is performed based on the template, and the data layer of the production line fault operation and maintenance knowledge graph is obtained.

[0013] S13, based on step S12, the fault knowledge triplets obtained through entity extraction and relationship extraction are fused, stored and visualized by Neo4j, and the production line fault operation and maintenance knowledge graph based on production line-equipment-fault-method multi-level is constructed.

[0014] Among them, the graph database in the data layer of the production line fault operation and maintenance knowledge graph stores data in a graph structure, and Neo4j graph database is selected to store and visualize the extracted triplets. In the knowledge graph, entities are represented by nodes, relationships between entities are represented by edges, and attributes are used to describe the characteristics of nodes or edges.

[0015] S2, based on the production line fault operation and maintenance knowledge graph constructed in step S1, input fault information to perform production line layer fault matching query, and construct a device subgraph, that is, query the current product process data to obtain a process device subgraph;

[0016] S3, based on step S2, the logical relationship between the factors causing the fault of the production line is analyzed, and a production line fault tree is constructed.

[0017] S4, based on step S3, qualitative analysis is performed on the production line fault tree, and the production line fault rate is calculated quantitatively to realize the reliability analysis of the production line.

[0018] Further, the step S12 is specifically as follows:

[0019] S121, the pre-processed fault operation and maintenance original data is labeled;

[0020] The fault operation and maintenance original data is the fault text in step S11; the characteristics of the fault operation and maintenance original data include: structured, semi-structured, unstructured; and the sources of the fault operation and maintenance original data include: manufacturing information system, PDF document; the fault operation and maintenance original data is pre-processed, specifically as follows:

[0021] (1) Preprocessing of fault operation and maintenance original data obtained from the manufacturing information system;

[0022] The raw fault operation and maintenance data obtained by the manufacturing information system includes: equipment fault logs and equipment ledgers; it is structured data, stored in a relational database, with clear data meaning, standardized naming, and preprocessing including: missing value handling, outlier handling, and date and time formatting;

[0023] Specifically, missing and outlier values ​​in equipment fault logs and equipment ledgers are handled by deleting missing values. Dates and times are formatted to conform to the ISO 8601 standard format.

[0024] (2) Preprocessing of raw fault operation and maintenance data obtained from PDF documents;

[0025] The raw fault operation and maintenance data obtained from the PDF document is semi-structured and unstructured data from the equipment manual. The data is displayed in two formats: tables and plain text. The specific preprocessing is as follows:

[0026] For data in tabular form, important data is integrated row by row and transformed into a one-dimensional text sequence for subsequent named entity recognition knowledge extraction. For data in plain text form, the acquired fault-related text undergoes data cleaning and text annotation, removing line breaks, spaces, useless characters, and unclear records.

[0027] After performing the corresponding data preprocessing operations, the production line fault operation and maintenance knowledge graph pattern layer constructed in step S11 is used. The BIO method is employed to annotate important fault-related information. The category and position expressions of named entities for character sequences using the BIO method are as follows:

[0028]

[0029] The key information related to the fault includes: fault symptoms, fault causes, and solutions; item i This represents the sequence of named entity pairs for the i-th production line fault text, and fully records the position and type of each named entity character in the production line fault text. This indicates the position of the j-th character in the n-th named entity within the i-th production line fault text sequence; This represents the named entity category of the j-th character in the n-th named entity within the i-th production line fault text sequence. The collected text is annotated using a labeling tool to obtain a dataset containing record numbers, entity categories, start character numbers, end character numbers, and entity content.

[0030] S122, based on step S121, and divide the labeled data into training set, validation set, test set, input into the built BERT-BILSTM-CRF entity extraction model, the training set and the validation set are used to train the model, and the experimental parameters are adjusted, and the best model during training is used to automatically identify and extract entities of the production line fault operation and maintenance knowledge of the test set data

[0031] Among them, the data division ratio is set according to the actual situation; when training the model with the training set and the validation set, the precision P, the recall rate R and the harmonic average F1 of the two are selected as the three indexes to evaluate the performance of the model, and the calculation formulas of the three indexes are as follows:

[0032]

[0033] Among them, TP represents the number of production line fault operation and maintenance knowledge entities correctly identified by the entity extraction model; FP represents the number of production line fault operation and maintenance knowledge entities incorrectly identified by the knowledge extraction model; and FN represents the number of production line fault operation and maintenance knowledge entities not identified.

[0034] The entity extraction is realized by the BERT-BILSTM-CRF algorithm model, that is, the BERT distributed input representation method is used on the basis of the BILSTM-CRF model. First, the input text sequence is converted into a corresponding word vector representation through the pre-trained BERT model. On the basis of the BERT output, a bidirectional LSTM layer is introduced.

[0035] Then the hidden state from the bidirectional LSTM is used as the feature of the subsequent CRF layer. Finally, the CRF layer is used to infer the category of each word.

[0036] Among them, the input vector E of the BERT model is composed of the sum of the word vector, the position vector and the segment vector embedding , the expression is as follows:

[0037] E embedding = E wordpiece + E segment + E position

[0038] Among them, E wordpiece represents the word vector, E segment represents the segment vector, and E position represents the position vector; in the BERT structure, the self-attention mechanism is introduced, and the calculation expression is as follows:

[0039]

[0040] Among them, Q, K and V represent word vector matrices, T represents the transpose operation, d kThe dimension of the input vector is represented. And the single-layer bidirectional long short-term memory network BILSTM is composed of two long short-term memory networks, one of which is responsible for processing the forward information of the input sequence, and the other is responsible for processing the reverse information of the input sequence. After the forward and reverse sequences are processed, the output results of the two LSTMs are spliced together to obtain the final BILSTM output result.

[0041] S123, based on step S122, using a template-based method to extract relationships, and constructing a production line fault knowledge graph data layer;

[0042] After the fault text named entity recognition is performed, the knowledge graph node part is constructed. By using a template-based method to extract relationships from the entities obtained in step S122, that is, sequentially querying whether the matching contains a given entity pair, outputting the corresponding triple after the matching is successful, and finally obtaining the knowledge triple, that is, the edge of the knowledge graph.

[0043] Among them, the relationship of the entity pair "Parts-Device" is "Belong_to", the relationship of the entity pair "Fault_phenomenon-Parts" is "Located", the relationship of the entity pair "Fault_cause-Fault_phenomenon" is "Cause", and the relationship of the entity pair "Solution-Fault_cause" is "Solve"; The knowledge triple records the subject and object and their relationship, and the form is <entity1, relationship, entity2>.

[0044] Further, the step S2 is specifically as follows:

[0045] Based on the knowledge graph constructed in step S1, first connect the graph database, input the known information, that is, the product information and the fault equipment information, then query out the processes possessed by the product and the teams to which the fault equipment belongs, and then query the processing areas required by the product processes and the processing areas to which the teams belong, and finally query the available equipment of the processing area to obtain the available equipment subgraph of each process.

[0046] Further, the step S3 is specifically as follows:

[0047] Z independent events constitute a fault tree, and the faults between events are independent, let φ(X) represent the structure function of the fault tree, and the variable x i represents the state variable of the bottom event of the fault tree, the value of φ(X) is 0 or 1, indicating that the top event fails or is normal, and the value of x i is 0 or 1, indicating that the subcomponent fails or is normal. The structure function expression of the fault tree is as follows:

[0048]

[0049] The logical symbols of the fault tree include: "and gate", "or gate", and "not gate". The fault tree "and gate" structure function expression is as follows:

[0050]

[0051] When x i Only take 0 or 1, then there is the following expression:

[0052]

[0053] When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, when all the available devices in the production line fail in parallel, the production line fails.

[0054] The fault tree "or gate" structure function expression is as follows:

[0055]

[0056] When x i Only take 0 or 1, then there is the following expression:

[0057]

[0058] When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, when all the available devices in the production line fail in parallel, the production line fails.

[0059] The logical relationships in the fault tree are sorted out, and the "or gate" and "and gate" are connected respectively, and finally the complete production line fault tree is obtained.

[0060] Further, the step S4 is specifically as follows:

[0061] To analyze the reliability of the production line, first, the internal mechanical equipment is analyzed, and the mean time between failures MTBF and failure rate are used to evaluate the reliability of the production equipment.

[0062] The mean time between failures MTBF refers to the average time experienced by the mechanical equipment during continuous normal operation, that is, the average time interval between the occurrence of a failure and the occurrence of the next failure. The MTBF calculation expression is as follows:

[0063]

[0064] Where, r i represents the failure frequency of the i-th device in the evaluation period, t i represents the actual working time of the i-th device in the evaluation period, and N represents the number of device samples.

[0065] First, the minimum cut set is qualitatively analyzed, and the expression is as follows:

[0066]

[0067] Wherein, c j The jth minimum cut set is x i The jth minimum cut set is x Z The expression of the fault tree structure function is as follows, which means that the top event occurs when there is a minimum cut set in the fault tree.

[0068]

[0069] The production line is composed of multiple devices in parallel, and each device can complete the corresponding processing procedure. At the same time, each station is connected to form an entire production line, forming a complex series-parallel system for production and manufacturing. The system has Z minimum cut sets, which are E1, E2, …, and E Z The probability P(T1) of the top event T1 of the system failure is expressed as follows:

[0070]

[0071] Wherein, The "not intersection" operation means that the input variables are not intersected and then the Boolean algebra "and" operation is performed, that is, The superscript'indicates that the event does not occur.

[0072] After evaluating the production line failure rate, the importance of each device unit is calculated, and the critical importance is the key indicator of importance, which is used to measure the importance of the bottom event to the top event, identify the weak link of the system, and the calculation expression is as follows:

[0073]

[0074] Wherein, I cr (j) represents the critical importance of the jth device unit, Q1 represents the system failure probability, and q j (j) represents the failure probability of the device unit j.

[0075] In summary, all possible failure modes that cause the production line to fail can be qualitatively found, that is, the minimum cut set MCS of the fault tree is found; at the same time, according to the minimum cut set found, the weak link of the system is determined, and the production line failure probability and the critical importance of each device unit are quantitatively calculated.

[0076] The method of the present application realizes the reliability analysis of the production line by constructing a multi-level production line fault operation and maintenance knowledge graph based on the production line-equipment-fault-method, inputting fault information for production line layer fault matching query, constructing an available equipment subgraph, analyzing the logical relationship between the factors causing the fault of the production line and the factors leading to the fault, constructing a production line fault tree, and finally performing qualitative analysis on the production line fault tree and quantitatively calculating the production line failure rate. BRIEF DESCRIPTION OF DRAWINGS

[0077] Figure 1 The flowchart of a complex production line reliability analysis method combining a fault operation and maintenance knowledge graph and a fault tree according to the present application.

[0078] Figure 2 The production line fault operation and maintenance knowledge graph construction framework diagram in the embodiment of the present application.

[0079] Figure 3 The production line fault operation and maintenance knowledge graph mode layer schematic diagram in the embodiment of the present application.

[0080] Figure 4 The BERT-BILSTM-CRF entity extraction model schematic diagram in the embodiment of the present application.

[0081] Figure 5 The production line fault operation and maintenance knowledge graph based on the production line-equipment-fault-method multi-level in the embodiment of the present application.

[0082] Figure 6 The production line layer fault matching flowchart in the embodiment of the present application.

[0083] Figure 7 The available equipment query result subgraph of the "milling profile" process in the embodiment of the present application.

[0084] Figure 8 The schematic diagram of the production line structure in the embodiment of the present application.

[0085] Figure 9 A schematic diagram of a production line fault tree in an embodiment of the present application. DETAILED DESCRIPTION

[0086] The method of the present application is further described below in conjunction with the accompanying drawings and embodiments.

[0087] As Figure 1 shown, a complex production line reliability analysis method flowchart of a fault operation and maintenance knowledge graph of the present application in combination with a fault tree, the specific steps are as follows:

[0088] S1, as Figure 2 shown, a multi-level production line fault operation and maintenance knowledge graph based on production line-equipment-fault-method is constructed;

[0089] In the production line reliability analysis process based on the production line fault operation and maintenance knowledge graph and the fault tree, the construction of the knowledge graph and the construction of the production line fault tree based on the knowledge graph are crucial, which provides an effective solution for reliability analysis not only staying at the equipment level but also at the more complex production line level.

[0090] S11, a production line fault operation and maintenance knowledge graph mode layer is constructed;

[0091] The constructed production line fault operation and maintenance knowledge graph mode layer is as Figure 3 shown, first, the related concepts of production line fault operation and maintenance knowledge are sorted out, the fault text is obtained through data sources for summarization and refinement, the fault operation and maintenance knowledge entities and attributes are determined (the scope of production line fault knowledge field and the purpose of knowledge graph construction are determined, the related concepts in the manufacturing field and the relationship between the concepts are refined, and the manufacturing field knowledge system is formed), then the data definition of each entity and attribute is carried out with the help of Protégé ontology modeling, the production line fault knowledge ontology is obtained, finally, the constructed ontology is used to export "RDF / XML" in Protégé, and further imported into a graph database, realizing the construction of the production line fault operation and maintenance knowledge graph mode layer.

[0092] Among them, the data sources include: manufacturing informatization system, fault log and equipment manual; the fault operation and maintenance knowledge entities (core ontology elements) in the production line fault operation and maintenance knowledge graph mode layer include: equipment, component, process, fault phenomenon, fault reason, solution; the fault operation and maintenance knowledge attributes in the production line fault operation and maintenance knowledge graph mode layer include: product, team, name, specification and model, manufacturer, equipment code, purchase date, start time, end time, alarm number, alarm text.

[0093] S12, based on the guidance of the mode layer constructed in step S1, the knowledge extraction of the fault text is carried out, and the data layer of the production line fault operation and maintenance knowledge graph is constructed;

[0094] The BERT-BILSTM-CRF entity extraction model, as shown in Figure 4 As shown in the figure, first, the preprocessed fault operation and maintenance original data is labeled, after the data is labeled, the data is divided into training set, validation set and test set, and input into the built BERT-BILSTM-CRF entity extraction model, the production line fault operation and maintenance knowledge is automatically identified and entity extraction, and then the relationship extraction is carried out based on the template, and the data layer of the production line fault operation and maintenance knowledge graph is obtained.

[0095] S13, based on step S12, the fault knowledge triplets obtained by entity extraction and relationship extraction are fused, and stored and visualized by Neo4j, and the production line fault operation and maintenance knowledge graph based on production line-equipment-fault-method multi-level is constructed.

[0096] Among them, considering that the knowledge graph and the graph database adopt similar data models, this similarity makes the graph database more naturally store and represent the data of the knowledge graph. At the same time, the production line fault operation and maintenance knowledge graph involves complex relationships between entities, such as the relationships between equipment, processes, teams, and fault phenomena. The graph database in the data layer of the production line fault operation and maintenance knowledge graph stores data in a graph structure, which can effectively process and query these complex relationships, making the data of the knowledge graph more intuitive and effective to manage and analyze. Therefore, the Neo4j graph database is selected to store and visualize the extracted triplets, thereby constructing the production line fault operation and maintenance knowledge graph based on production line-equipment-fault-method multi-level as shown in Figure 5 The production line layer describes the overall structure of the production process, which is composed of multiple processes, and there is a process dependency relationship between each process. Each process corresponds to different tasks, which require specific equipment. Each equipment contains multiple attribute information, and the equipment can be further divided into components. The fault layer and the method layer are mainly the faults that may occur in the equipment and the corresponding solutions. These hierarchical relationships are inseparable. The method layer is to solve the faults in the fault layer, and these faults often occur in specific equipment or their components in the equipment layer. When the equipment fails, it will also affect the completion of the corresponding process in the production line layer. In the knowledge graph, entities are represented by nodes, relationships between entities are represented by edges, and attributes are used to describe the characteristics of nodes or edges.

[0097] S2, based on the production line fault operation and maintenance knowledge graph constructed in step S1, input fault information to query the production line layer fault, and construct a device subgraph, that is, query the current product process data to obtain a process device subgraph;

[0098] S3, based on step S2, constructing a production line fault tree by analyzing the logical relationship between the production line failure and various factors causing the failure, including the coupling effect between devices and devices;

[0099] S4, based on step S3, qualitative analysis of the production line fault tree and quantitative calculation of the production line failure rate to realize reliability analysis of the production line.

[0100] In this embodiment, the step S12 is specifically as follows:

[0101] S121, labeling the preprocessed fault operation and maintenance original data;

[0102] The fault operation and maintenance original data is the fault text of step S11; the characteristics of the fault operation and maintenance original data include: structured, semi-structured, unstructured; and the sources of the fault operation and maintenance original data include: manufacturing information system, PDF document; the preprocessing of the fault operation and maintenance original data is as follows:

[0103] (1) Preprocessing of fault operation and maintenance original data obtained by manufacturing information system;

[0104] The fault operation and maintenance original data obtained by the manufacturing information system includes: device fault log, device account; it is structured data, stored in a relational database, the data meaning is clear, the naming is more normative, the preprocessing includes: missing value processing, outlier processing, date and time formatting;

[0105] Among them, the number of missing values and outliers in the device fault log and the device account is not large, which may be caused by human data entry errors, so the missing values are deleted for processing, which will not affect the overall data characteristics. For date and time, the format is unified to ISO8601 standard format, which is convenient for sorting and comparison.

[0106] (2) Preprocessing of fault operation and maintenance original data obtained by PDF document;

[0107] The fault operation and maintenance original data obtained by the PDF document is the semi-structured data and unstructured data in the device manual, and the data display form is two forms of table and pure text. These two forms of data are also the main objects of knowledge extraction, and the preprocessing is as follows:

[0108] The data in table form considers the diversity of table format in the equipment manual, and the table data has important structure information, which cannot be directly extracted by mapping. Therefore, the important data is integrated according to the row to be converted into a one-dimensional text sequence, and the subsequent named entity recognition is carried out for knowledge extraction. The data in pure text form, the obtained fault related text is data cleaning and text labeling, because the corpus contains many useless characters, in order to improve the training quality of the algorithm, the line feed, space, useless character and fuzzy data are deleted.

[0109] After the corresponding data preprocessing operation is performed, the mode layer of the production line fault operation and maintenance knowledge graph is constructed in combination with step S11. The important information related to the fault is labeled by using the BIO method (BIO is a commonly used sequence labeling method, which can avoid the loss of part of the labeled information in the IOB method, and increase the prediction label type in the IBOES method). The class and position expression of the named entity of the character sequence by using the BIO method are as follows:

[0110]

[0111] The important information related to the fault includes: fault phenomenon, fault reason, solution. i The named entity pair sequence of the i-th production line fault text is represented, and the position and type of each named entity character in the production line fault text are recorded. The position of the j-th character in the n-th named entity in the i-th production line fault text sequence in the production line fault text is represented. The named entity class of the j-th character in the n-th named entity in the i-th production line fault text sequence is represented. The collected text is labeled by using a labeling tool to obtain a data set recording the number, entity class, starting character number, ending character number and entity content. In this embodiment, the BIO labeling method is used to represent the production line fault domain entity. According to the constructed mode layer of the production line fault operation and maintenance knowledge graph, 5 entities are set, including equipment, components, phenomena, reason and solution, and 10 labels are set.

[0112] S122, based on step S121, and the labeled data is divided into training set, validation set and test set, and is input into the BERT-BILSTM-CRF entity extraction model built, the training set and the validation set are used for training the model, and the experimental parameters are adjusted, and the best model during training is used for automatic recognition and entity extraction of the production line fault operation and maintenance knowledge of the test set data

[0113] The data division ratio is set according to the actual situation, and the division ratio in the embodiment is 7:2:1; when the training set and the verification set train the model, the precision P, the recall rate R and the harmonic mean F1 of the two are selected as three indexes to evaluate the performance of the model, and the calculation formulas of the three indexes are as follows:

[0114]

[0115]

[0116] Wherein, TP represents the number of line fault operation and maintenance knowledge entities correctly identified by the entity extraction model; FP represents the number of line fault operation and maintenance knowledge entities incorrectly identified by the knowledge extraction model; FN represents the number of line fault operation and maintenance knowledge entities not identified.

[0117] The entity extraction is realized by the BERT-BILSTM-CRF algorithm model, that is, on the basis of the BILSTM-CRF model, the BERT distributed input representation method is adopted (the existing distributed input representation methods such as Skip-gram and Word2Vec perform well in calculation efficiency, and can quickly and effectively map words to unique dense word vectors, but there are certain challenges in dealing with polysemy. In contrast, the BERT model uses dynamic word embedding technology, which can extract semantic features at different levels and effectively solve the polysemy problem).

[0118] Firstly, the input text sequence is converted into corresponding word vector representation through the pre-trained BERT model. On the basis of BERT output, a bidirectional LSTM layer is introduced (this layer captures the context information in the sequence, helps to accurately locate the entity boundary and distinguish different entity categories).

[0119] Then the hidden state from the bidirectional LSTM is used as the feature of the subsequent CRF layer. Finally, the CRF layer is used to infer the category of each word.

[0120] Wherein, the input vector E of the BERT model is composed of the sum of the word vector, the position vector and the segment vector embedding , and the expression is as follows:

[0121] E embedding =E wordpiece +E segment +E position

[0122] Wherein, E wordpiece represents the word vector, E segment represents the segment vector, and E positionPosition vector represents the position vector; segment vector is used to distinguish different sentences; position vector is used to introduce the relative position information of the word in the sequence in the subsequent self-attention model, and the position embedding is used to provide the model with the position information of the word in the sequence; the word vector improves the processing ability of the model for multilingual and complex context language structure by dividing the word into subwords; in the BERT structure, the self-attention mechanism is introduced, and the expression is calculated as follows:

[0123]

[0124] Wherein, Q, K, V represent word vector matrix, T represents transposition operation, d k represents the dimension of the input vector, the attention mechanism can improve the weight parameter, highlight the important knowledge in the text, and focus on the extraction of important knowledge.

[0125] The single-layer bidirectional long short-term memory network (BILSTM) is composed of two long short-term memory networks, one of which is responsible for processing the forward information of the input sequence, and the other is responsible for processing the reverse information of the input sequence. After the forward and reverse sequences are processed, the output results of the two LSTMs are spliced together to obtain the final BILSTM output result. In this embodiment, for the text "main shaft vibration", the forward LSTM inputs "main", "shaft", "vibration", "dynamic" in turn to obtain four vectors {h L0 ,h L1 ,h L2 ,h L3}, the backward LSTM inputs "dynamic", "vibration", "shaft", "main" in turn to obtain four vectors {h R0 ,h R1 ,h R2 ,h R3}, and finally the forward and backward hidden vectors are spliced to obtain {[h L0 ,h R3 ], [h L1 ,h R2 ], [h L2 ,h R1 ], [h L3 ,h R0 ]}.

[0126] S123, based on step S122, the relationship extraction is performed by using the template-based method, and the production line fault knowledge graph data layer is constructed;

[0127] Considering that the constructed knowledge graph is a production line fault operation and maintenance knowledge graph, it has strong professionalism and requires high accuracy. Meanwhile, the fault operation and maintenance related engineering document record format is relatively unified, so the template based method is used for relation extraction. After the fault text named entity recognition, the knowledge graph node part is constructed. The entity obtained in step S122 is used for relation extraction based on the template method, that is, whether the given entity pair is matched is queried in turn, the corresponding triple is output after the matching is successful, and finally the knowledge triple is obtained, that is, the edge of the knowledge graph.

[0128] Among them, the relationship of the entity pair "Parts-Device" is "Belong_to", the relationship of the entity pair "Fault_phenomenon-Parts" is "Located", the relationship of the entity pair "Fault_cause-Fault_phenomenon" is "Cause", and the relationship of the entity pair "Solution-Fault_cause" is "Solve"; the knowledge triple records the subject and object and the relationship between them, and the form is <entity1, relationship, entity2>.

[0129] In this embodiment, the step S2 is specifically as follows:

[0130] Fault matching refers to that during the operation of the production line, if an abnormality of a related device or component is found, the fault cause, solution, related processing area and product that may cause the device to produce the fault phenomenon are matched by analyzing the fault phenomenon and abnormality source.

[0131] Through a production line layer matching method based on graph data, the knowledge graph constructed in step S1 is used for fault query to further obtain a query subgraph. First, the graph database is connected, the known information, that is, the product information and the fault device information are input, the processes possessed by the product and the team to which the fault device belongs are queried respectively, then the processing area required by the product process and the processing area to which the team belongs are queried, and finally the available devices of the processing area are queried to obtain a device subgraph available for each process. The fault matching query process for production line reliability analysis in this embodiment is shown in Table 1.

[0132] Table 1

[0133]

[0134] The production line in this embodiment is a small batch mixed line for producing product 1 and product 2. First, the process flow of the two products of the production line is determined. The process of the two products is divided into four parts, including forging process, heat treatment process, machining process and surface treatment process, wherein the machining process involves a large number of machining equipment. The machining process of product 1 and product 2 is shown in Tables 2 and 3.

[0135] Table 2

[0136]

[0137] Table 3

[0138]

[0139] After determining the available equipment of each process flow, the relevant information is obtained through the designed production line layer matching method based on a graph database, and the production line layer matching process is as shown in Figure 6 . This embodiment first performs fault matching on the "milling profile" process, and the team responsible for the "milling profile" process is Team 1. In the production line fault operation and maintenance knowledge graph, the adjacent entities having a "Has" relationship with the process "milling profile" are queried, or the adjacent entities having a "Belong_to" relationship with Team 1 are queried, to obtain all available equipment of the process, including the numerical control milling machine XK718, the vertical machining center VMC1000, and the vertical machining center VMC1000B, as shown in Figure 7 . Similarly, the available equipment of the remaining processes is sequentially queried to obtain the production line available equipment query subgraph. Subsequently, the entire system structure is determined, as shown in Figure 8 .

[0140] In this embodiment, the step S3 is specifically as follows:

[0141] The fault tree analysis method (FTA) is an important method for analyzing the reliability and safety of complex electronic equipment. An event that is not expected to occur in the system is taken as the analysis target, and all possible causes are traced layer by layer downward, and the direct causes of each layer are traced, so that the possible faults of the system can be found. It is usually represented by an inverted tree graph.

[0142] Z independent events are set to constitute a fault tree, and the faults between the events are independent. Let φ(X) represent the structure function of the fault tree, and x i represent the state variable of the bottom event of the fault tree. The value of φ(X) is 0 or 1, indicating that the top event fails or is normal, and the value of x i is 0 or 1, indicating that the subcomponent fails or is normal. The expression of the structure function of the fault tree is as follows:

[0143]

[0144] The logic symbols of the fault tree include "AND gate", "OR gate", and "NOT gate". The structure function expression of the fault tree "AND gate" is as follows:

[0145]

[0146] When x i only takes 0 or 1, the following expression is obtained:

[0147]

[0148] When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, all the available equipment in the production line fails in parallel.

[0149] The fault tree "or gate" structure function expression is as follows:

[0150]

[0151] When x i Only 0 or 1 is taken, then the following expression is as follows:

[0152]

[0153] When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, all the available equipment in the production line fails in parallel.

[0154] The logical relationships in the fault tree are sorted out, and "or gate" and "and gate" connections are respectively corresponded, and finally a complete production line fault tree is obtained.

[0155] Based on the determination of the entire production line structure in step S2, the logical relationship between the failure of the production line and each factor causing the failure is analyzed to construct a production line fault tree. The failure state of the processing operation area is defined as all available equipment being in a failure state, that is, each processing area failure is connected to the top event through an "or gate"; the failure state of the production line is defined as any processing operation area being in a failure state, that is, each process available equipment failure is connected to the processing operation area failure through an "and gate". Finally, a complete production line fault tree is obtained, as shown in Figure 9 A, B, and C in the figure respectively represent one-shift area failure, two-shift area failure, and three-shift area failure; 1-11 represent each process available equipment obtained by querying the production line fault operation and maintenance knowledge graph.

[0156] In this embodiment, the step S4 is specifically as follows:

[0157] The production line refers to a complex system composed of a series of mechanical equipment, tools and workstations, which are combined together in a specific order and manner for the manufacturing or processing of specific products or workpieces.

[0158] To analyze the reliability of a production line, it is first necessary to analyze its internal mechanical equipment, using two indicators: Mean Time Between Failures (MTBF) and Failure Rate. MTBF refers to the average time a piece of machinery experiences during continuous normal operation; that is, the average time interval between the occurrence of one failure and the next. MTBF is one of the important indicators for measuring system reliability; a higher MTBF value indicates a lower frequency of production line failures and higher reliability. The MTBF calculation formula is as follows:

[0159]

[0160] Where, r i t represents the failure frequency of the i-th device during the evaluation period. i This represents the actual working time of the i-th device during the evaluation period, and N represents the number of devices sampled.

[0161] First, a qualitative analysis of the minimal cut set is performed, and the expression is as follows:

[0162]

[0163] Among them, c j Let x represent the j-th minimal cut set. i Let represent the i-th bottom event in the j-th minimum cut set. The fault tree structure function expression is as follows, which means that when a minimum cut set occurs in the fault tree, the top-level event occurs.

[0164]

[0165] The solution for the minimum cut set of the fault tree in this embodiment is shown in Table 4.

[0166] Table 4

[0167]

[0168] Then, this embodiment estimates the failure rate of each piece of equipment based on the equipment failure record table and equipment operation history obtained from the enterprise's MDC system (Manufacturing Information System) for the past 10 months. Some equipment failure record tables and historical operation data are shown in Tables 5 and 6.

[0169] Table 5

[0170]

[0171] Table 6

[0172]

[0173] The average failure interval time of the 11 devices is obtained by calculating the device failure frequency and the total running time, and the device failure rate is finally calculated. The device failure frequency and the running time are shown in Table 7.

[0174] Table 7

[0175]

[0176]

[0177] Each station of the production line is composed of multiple devices in parallel, each device can complete the corresponding processing procedure, and each station is connected in series to form an entire production line, forming a complex series-parallel system facing production and manufacturing. The system has Z minimal cut sets, which are E1, E2, …, E Z The probability P(T1) of the top event T1 of system failure is expressed as follows:

[0178]

[0179] wherein, represents the "not intersection" ("logical not intersection and") operation, which means that the input variables are not intersection processed first and then the Boolean algebra "and" operation is performed, that is, The superscript'indicates that the event does not occur.

[0180] Let a-k represent the failure of the above devices 1-11, respectively, and the failure probability P(P1) of the production line is expressed as follows:

[0181]

[0182] After evaluating the failure rate of the production line, the importance of each device unit needs to be calculated, wherein the critical importance is a key indicator of importance, which is used to measure the importance of the bottom event to the top event, identify the weak link of the system, and the calculation expression is as follows:

[0183]

[0184] wherein, I cr (j) represents the critical importance of the jth device unit, Q1 represents the system failure probability, and q j (j) represents the failure probability of the device unit j. In this embodiment, the critical importance of each device unit is shown in Table 8.

[0185] Table 8

[0186]

[0187] It can be seen that the critical importance of devices 5, 6, and 7 is the largest, that is, they are most likely to cause the failure of the production line, and fault diagnosis and risk control can be focused on the above devices.

[0188] Based on the above process, all possible failure modes that cause the line failure can be qualitatively found out, that is, the minimal cut sets (MCS) of the fault tree are obtained; meanwhile, the weak link of the system can be determined according to the obtained minimal cut sets, and the line failure probability and the critical importance of each equipment unit are quantitatively obtained.

[0189] In summary, the method of the present application sequentially obtains the relevant information of production line-product-process-available equipment from the knowledge graph by the designed production line layer query matching method based on graph data search, and constructs a fault tree model from production line failure-work operation area failure-equipment according to the logical relationship, and then utilizes the model to qualitatively analyze and quantitatively calculate the critical importance of the equipment unit, so as to identify the weak link and the weakness of the production line system in real time. The method of the present application is simple and easy to implement, and can improve the reliability analysis of the current production system from the equipment level to the entire production line level considering the coupling between devices, and through the utilization of the characteristics of the production line and the reverse specification and verification of the mode layer by using the failure knowledge, it is helpful for the production management personnel to understand the rules of device or system failure and to develop a reasonable maintenance strategy; compared with the existing knowledge graph, there are more information and multi-level structure of the production line layer, and in addition, the fault tree model of the production line is obtained by using the knowledge graph to perform reliability analysis and calculation, compared with the existing device level and single system fault tree analysis, it can more accurately reveal the device coupling effect and key node bottleneck in the production process, so as to provide more targeted operation and maintenance strategy.

[0190] Those skilled in the art will realize that the embodiments described herein are for the purpose of helping the reader understand the principles of the present application and should be understood as not limiting the scope of protection of the present application to such specific statements and embodiments. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. A complex production line reliability analysis method combining a fault operation and maintenance knowledge graph with a fault tree, and the specific steps are as follows: S1, constructing a multi-level production line fault operation and maintenance knowledge graph based on production line-equipment-fault-method; S11, constructing a production line fault operation and maintenance knowledge graph mode layer; First, the related concepts of production line fault operation and maintenance knowledge are sorted out, the fault text is obtained through data sources for summary and refinement, the fault operation and maintenance knowledge entities and attributes are determined, then the data of each entity and attribute is defined in detail with the help of Protégé ontology modeling, the production line fault knowledge ontology is obtained, finally the ontology constructed is exported as "RDF / XML" in Protégé, and further imported into a graph database to realize the construction of the production line fault operation and maintenance knowledge graph mode layer; wherein The data sources include: manufacturing information system, fault log and equipment manual; the fault operation and maintenance knowledge entities in the production line fault operation and maintenance knowledge graph mode layer include: equipment, component, process, fault phenomenon, fault cause, solution; the fault operation and maintenance knowledge attributes in the production line fault operation and maintenance knowledge graph mode layer include: product, team, name, specification, manufacturer, equipment code, purchase date, start time, end time, alarm number, alarm text; S12, based on the guidance of the mode layer constructed in step S1, knowledge extraction is performed on the fault text to construct a data layer of the production line fault operation and maintenance knowledge graph; First, the preprocessed fault operation and maintenance original data is labeled, after the data is labeled, the data is divided into a training set, a validation set and a test set, and input into the BERT-BILSTM-CRF entity extraction model built, the production line fault operation and maintenance knowledge is automatically recognized and entity extracted, and then the relationship extraction is performed based on the template to obtain the data layer of the production line fault operation and maintenance knowledge graph; S13, based on step S12, the fault knowledge triplets obtained through entity extraction and relationship extraction are fused, stored and visually displayed through Neo4j, and the construction of the production line fault operation and maintenance knowledge graph based on the production line-equipment-fault-method multi-level is completed; Among them, the graph database in the data layer of the production line fault operation and maintenance knowledge graph stores data in a graph structure, and Neo4j graph database is selected to store and visually display the extracted triplets, in the knowledge graph, entities are represented by nodes, relationships between entities are represented by edges, and attributes are used to describe the characteristics of nodes or edges; S2, based on the production line fault operation and maintenance knowledge graph constructed in step S1, input fault information to perform production line layer fault matching query, and construct an available equipment subgraph, that is, query the current product process data to obtain each process available equipment subgraph; S3, based on step S2, the logical relationship between each factor causing the fault of the production line is analyzed to construct a production line fault tree; S4, based on step S3, the production line fault tree is qualitatively analyzed and the production line fault rate is quantitatively calculated to realize the reliability analysis of the production line.

2. The complex production line reliability analysis method of claim 1, wherein, The step S12 is specifically as follows: S121, labeling the preprocessed fault operation and maintenance original data; The fault operation and maintenance original data is the fault text in step S11; The characteristics of the fault operation and maintenance original data include: structured, semi-structured, and unstructured; and the sources of the fault operation and maintenance original data include: manufacturing informationization system and PDF document; the pre-processing of the fault operation and maintenance original data is as follows: (1) Pre-processing of fault operation and maintenance original data obtained by manufacturing informationization system; The fault operation and maintenance original data obtained by the manufacturing informationization system includes: equipment fault log and equipment account book; it is structured data stored in a relational database, the data meaning is clear, the naming is standard, and the pre-processing includes: missing value processing, abnormal value processing, date and time formatting; Among them, for the missing values and abnormal values in the equipment fault log and equipment account book, the missing values are deleted; for the date and time, the format is unified to ISO8601 standard format; (2) Pre-processing of fault operation and maintenance original data obtained by PDF document; The fault operation and maintenance original data obtained by the PDF document is semi-structured data and unstructured data in the equipment manual, the data display form is table and pure text, and the pre-processing is as follows: The data in table form is integrated into one-dimensional text sequence according to important data in rows, and then named entity recognition is performed for knowledge extraction; for the data in pure text form, the obtained fault related text is data cleaned and text labeled, and the line feed, space, useless characters and fuzzy data are deleted; After the corresponding data pre-processing operation, the mode layer of the production line fault operation and maintenance knowledge graph constructed in step S11 is combined; the important information related to the fault is labeled by the BIO method, and the class and position expression of the named entity of the character sequence by the BIO method is as follows: The fault-related important information includes: fault phenomenon, fault cause, solution method; item i represents the i-th production line fault text named entity pair sequence, which records the position and type of each named entity character in the production line fault text; represents the position of the j-th character in the n-th named entity in the i-th production line fault text sequence in the production line fault text; represents the named entity category of the j-th character in the n-th named entity in the i-th production line fault text sequence; the collected text is labeled by using a labeling tool to obtain a data set recording number, entity category, starting character number, ending character number and entity content; S122, based on step S121, and divide the labeled data into training set, validation set and test set, input into the BERT-BILSTM-CRF entity extraction model, the training set and the validation set are used to train the model, and then the experimental parameters are adjusted, and the best model during training is used to automatically identify and extract the production line fault operation and maintenance knowledge from the test set data Among them, the data division ratio is set according to the actual situation; when training the model with the training set and the validation set, the precision P, the recall rate R and the harmonic average F1 of the two are selected as the three indexes to evaluate the performance of the model, and the calculation formulas of the three indexes are as follows: Among them, TP represents the number of production line fault operation and maintenance knowledge entities correctly identified by the entity extraction model; FP represents the number of production line fault operation and maintenance knowledge entities incorrectly identified by the knowledge extraction model; FN represents the number of production line fault operation and maintenance knowledge entities not identified; The entity extraction is realized by the BERT-BILSTM-CRF algorithm model, that is, the BERT distributed input representation method is adopted on the basis of the BILSTM-CRF model; first, the input text sequence is converted into corresponding word vector representation by the pre-trained BERT model; on the basis of BERT output, a bidirectional LSTM layer is introduced; Then the hidden state from the bidirectional LSTM is used as the feature of the subsequent CRF layer; finally, the CRF layer is used to infer the category of each word; Wherein, the input vector E of the BERT model is composed of the sum of the word vector, the position vector and the section vector embedding The expression is as follows: E embedding = E wordpiece + E segment + E position wherein, E wordpiece represents a word vector, E segment represents a segment vector, E position represents a position vector; in the BERT structure, a self-attention mechanism is introduced, and the expression is calculated as follows: wherein Q, K, V represent word vector matrices, T represents a transpose operation, d k denotes the dimension of the input vector; and the single-layer bidirectional long short-term memory network BILSTM is composed of two long short-term memory networks, one of which is responsible for processing the forward information of the input sequence, and the other is responsible for processing the reverse information of the input sequence. After the forward and reverse sequences are processed, the output results of the two LSTMs are spliced together to obtain the final BILSTM output result; S123, based on step S122, using a template-based method for relation extraction, constructing a production line fault knowledge graph data layer; After the fault text named entity recognition, the knowledge graph node part has been constructed. Through the template-based method for relation extraction on the entity obtained in step S122, that is, sequentially querying whether the matching contains a given entity pair, outputting the corresponding triple after successful matching, and finally obtaining the knowledge triple, that is, the edge of the knowledge graph. Among them, the relationship between the entity pair "Parts-Device" is "Belong_to", the relationship between the entity pair "Fault_phenomenon-Parts" is "Located", the relationship between the entity pair "Fault_cause-Fault_phenomenon" is "Cause", and the relationship between the entity pair "Solution-Fault_cause" is "Solve"; The knowledge triple records the subject and object and their relationship, which is in the form of <entity1, relationship, entity2>.

3. The complex production line reliability analysis method of claim 1, wherein, The step S2 is specifically as follows: Based on the knowledge graph constructed in step S1, first connect the graph database, input the known information, that is, product information and fault equipment information, then query out the process possessed by the product and the team to which the fault equipment belongs, and then query out the processing area required by the product process and the processing area to which the team belongs, and finally query out the available equipment in the processing area to obtain the available equipment subgraph of each process.

4. The complex production line reliability analysis method of claim 1, wherein, The step S3 is specifically as follows: Set Z independent events constitute a fault tree, and the failure between events is independent, let φ(X) represent the structure function of the fault tree, variable x i represents the state variable of the bottom event of the fault tree, the value of φ(X) is 0 or 1, indicating that the top event fails or is normal, x i The value of 0 or 1 indicates that the subcomponent fails or is normal; the structure function expression of the fault tree is as follows: The logical symbols of the fault tree include "and gate", "or gate" and "not gate"; the "and gate" structure function expression of the fault tree is as follows: When x i When only 0 or 1 is taken, then the following expression holds: When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, when all the available equipment of the production line fails in parallel, the production line fails; The "or gate" structure function expression of the fault tree is as follows: When x i When only 0 or 1 is taken, then the following expression holds: When the parallel system corresponds to the "and gate" structure of the fault tree, that is, when all the sub-components fail, the system fails, that is, when all the available equipment of the production line fails in parallel, the production line fails; After clarifying the logical relationship in the fault tree, connect them according to "or gate" and "and gate" respectively, and finally get the complete production line fault tree.

5. The complex production line reliability analysis method of claim 1, wherein, The step S4 is specifically as follows: To analyze the reliability of the production line, first analyze the mechanical equipment inside, and use the two indexes of mean time between failures MTBF and failure rate to evaluate the reliability of the production equipment; The mean time between failures MTBF refers to the average time that the mechanical equipment experiences during continuous normal operation, that is, the average time interval between the occurrence of one failure and the occurrence of the next failure; the MTBF calculation expression is as follows: wherein r i represents the failure frequency of the ith device in the evaluation period, t i represents the actual working time of the ith device in the evaluation period, and N represents the number of devices sampled. First, qualitatively analyze the minimal cut sets, and the expression is as follows: where c j represents the jth minimum cut set, x i represents the ith base event in the jth minimum cut set, the fault tree structure function expression is as follows, which indicates that the top event occurs when there is a minimum cut set in the fault tree. The workstations of the production line are composed of multiple devices in parallel, each device can complete the corresponding processing procedure, and the workstations are connected in series to form the whole production line, which forms a complex series-parallel system facing production and manufacturing; the setting system has Z minimal cut sets, which are E1, E2, …, E Z The probability P(T1) of the top event T1 of system failure is expressed as follows: wherein, denotes "not intersection" operation, which means that the input variables are first processed by not intersection and then Boolean "and" operation is performed, i.e. the superscript'indicates that the event does not occur; After evaluating the failure rate of the production line, the importance of each device unit is calculated, and the key importance is a key indicator of importance, which is used to measure the importance of the influence of the bottom event on the top event, identify the weak link of the system, and the calculation expression is as follows: where I cr (j) denotes the criticality of the jth equipment unit, Q1denotes the system failure probability, q j denotes the failure probability of equipment unit j; In conclusion, all possible failure modes that cause the line failure can be found, i.e. the minimal cut sets (MCS) of the fault tree are found; meanwhile, the weak links of the system are determined according to the found MCS, and the line failure probability and the critical importance of each equipment unit are quantitatively found.

Images