Mining electromechanical equipment health assessment method based on Bayesian network model
The equipment health status matrix and map are constructed through Bayesian network model, which solves the problem of artificial experience dependence and accuracy of health assessment in coal mine machinery and equipment maintenance, realizes accurate assessment of equipment health status and fault warning, and improves maintenance efficiency and Security.
Patent Information
- Application Number
- CN202411301280.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-18
- Publication Date
- 2024-12-17
AI Technical Summary
The maintenance of existing coal mine machinery and equipment relies on manual experience, is low in efficiency and strong subjectivity, which may lead to safety hazards in equipment operation, and there are difficulties in accuracy in equipment health assessment of fault prediction and health management technologies.
Using the Bayesian network model, the health assessment method of mining electromechanical equipment is constructed through natural language processing and machine learning, and the equipment health status matrix and state map are collected and processed in real time. The Bayesian formula calculates the health status of the equipment is provided. Accurate fault warning and maintenance support.
It realizes accurate assessment of equipment health status, reduces maintenance costs, improves maintenance efficiency and safety, and provides more accurate fault warning and preventive maintenance support.
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Figure CN119151515A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of mining equipment health management, and in particular to a mining electromechanical equipment health assessment method based on a Bayesian network model. Background Art
[0002] In the current field of coal mine machinery and equipment maintenance, the commonly used mode is regular inspection and post-failure maintenance. This method often relies on manual experience and judgment to formulate maintenance plans when equipment fails. This is not only inefficient and labor-intensive, but also highly subjective and requires high professional skills. More importantly, this traditional method may bring safety hazards to equipment operation, such as over-maintenance or under-maintenance. In view of the above challenges, the demand for more efficient and accurate equipment maintenance technology is becoming increasingly prominent.
[0003] In this context, fault prediction and health management (PHM) technology came into being. PHM technology is mainly used in the field of aerospace equipment, but with the continuous advancement and innovation of technology, it has been widely used in the maintenance of various advanced and complex equipment including spacecraft, fighter jets, and ships. PHM technology is essentially a method to reduce safety risks by evaluating system reliability, predicting failure probability, and taking corresponding management and maintenance measures. It mainly relies on sensors to monitor and evaluate the health status of equipment in real time, diagnose any abnormal behavior, and predict the remaining service life of the equipment throughout its life cycle. However, since the evaluation of the health status of the equipment and the remaining service life is often based on mathematical and physical models, or statistical laws, it is often very difficult to obtain accurate models or statistical data. Even if it is obtained, it is based on static or laboratory conditions and cannot accurately reflect the health status of the equipment. Summary of the invention
[0004] The purpose of the present invention is to provide a health assessment method for mining electromechanical equipment based on a Bayesian network model to address the deficiencies of the above-mentioned prior art.
[0005] To achieve the above object, the present invention adopts the following technical solutions:
[0006] A method for health assessment of mining electromechanical equipment based on a Bayesian network model comprises the following steps:
[0007] S1. Collect relevant data on mining electromechanical equipment and use natural language processing technology to convert the information in the data into nodes and edges;
[0008] S2. Determine the dependency relationship and conditional probability distribution between nodes according to the nodes and edges, and construct a Bayesian network model;
[0009] S3. Collect historical operation data of mining electromechanical equipment and classify the health of mining electromechanical equipment into three levels: normal, warning, and shutdown;
[0010] S4. Preprocess the historical operation data of mining electromechanical equipment, learn the characteristic parameters that can characterize the operation status of mining electromechanical equipment through machine learning algorithms, and construct a state matrix of the health status of mining electromechanical equipment;
[0011] S5. According to the three operating states of normal, warning and shutdown, the state matrix is normalized based on the threshold range of characteristic parameters of each mining electromechanical equipment under different operating states to generate a state reference map;
[0012] S6, collecting characteristic parameters that can characterize the operating status of mining electromechanical equipment in real time and performing preprocessing, and generating a real-time state map characterizing the current operating parameters in real time according to step S5;
[0013] S7, performing similarity identification between the state map generated in real time and the state reference map, and calculating the failure probability according to the similarity value;
[0014] S8. The failure probability is designated as the conditional probability or marginal probability of each node, and the real-time operation data of the mining electromechanical equipment is input into the Bayesian network model. The posterior probability of each node is calculated according to the Bayesian formula and the conditional independence hypothesis to obtain the health status assessment result of the equipment.
[0015] Furthermore, the relevant information of the mining electromechanical equipment in step S1 is obtained by means of web crawler technology, data API interface or data set, including but not limited to the equipment manufacturer's technical documents, operation manuals, historical fault reports, maintenance records and information obtained through expert interviews and training materials.
[0016] Furthermore, in step S1, the information in the data is converted into nodes and edges using natural language processing technology, which is specifically achieved by the following method: the collected relevant data of mining electromechanical equipment is subjected to text cleaning processing including but not limited to format standardization, removal of special characters and irrelevant content, and unified word forms; the cleaned text is then subdivided into more manageable units, such as sentences or paragraphs; and NLP tools are used to automatically identify the boundaries of sentences or paragraphs and the identification of key entities, such as equipment components, fault types, operating parameters, and specific actions. The identified entities are defined as nodes, and the relationships between entities are connected as edges. The edges include the relationships between components, the association between faults and maintenance methods, and specific attribute information is added to the nodes.
[0017] Furthermore, in the step S2, the dependency relationship and conditional probability distribution between nodes are determined based on the nodes and edges by using domain expert knowledge.
[0018] Furthermore, in step S4, the historical operation data of the mining electromechanical equipment is obtained from the equipment monitoring system, and the historical operation data of the mining electromechanical equipment includes reliability data, maintenance records, fault types and frequencies, or other data that can characterize the historical operation status of the mining electromechanical equipment.
[0019] Furthermore, in step S4, the historical operation data of the mining electromechanical equipment is preprocessed, including but not limited to removing outliers, processing missing values, standardizing, and normalizing. This is specifically achieved by the following methods: the outlier processing uses a box plot, Z-score, or other statistical methods to identify and decide to delete or correct data; the missing value processing uses a mean method, a median method, or an interpolation method to process the data; the data standardization processing is represented by the following formula (1); the data normalization processing is represented by the following formula (2):
[0020]
[0021] In formulas (1) and (2), x represents the collected historical operating data of mining electromechanical equipment; z represents the data after normalization; μ is the mean; σ is the standard deviation; x′ represents the data after normalization; min(x) represents the minimum value in the original data; max(x) represents the maximum value in the original data.
[0022] Furthermore, in step S5, the generation of the state reference map is specifically achieved by the following steps:
[0023] S51. Define the state matrix: Let M be the state matrix, where the element M t,s It represents the probability that the equipment is in state s at time point t, where state s includes normal, warning, and shutdown;
[0024] S52, Calculation of matrix elements: Through the machine learning algorithm Model, the feature vector X of the input device t , including the features obtained from the historical operation data of the device, outputs the probability distribution of the device in each state at time point t; this step is expressed by the following formula (3):
[0025] M t,s =P(s|X t )=Model(X t )[s] (3)
[0026] In formula (3): P(s|X t ) means that given the feature vector X y The probability that the device is in state s under the condition of t )[s] represents the input X of the model at time point tt , the probability of output state s;
[0027] S53, defining the thresholds of normal, warning and shutdown states of each operating parameter;
[0028] S54, set the RGB color mapping specification, assign a color to each state, and clearly express the state in the map;
[0029] S56. Display each parameter through a bar graph, wherein the length of the bar graph represents the size of the parameter value, and the color represents its status. According to the normal operation, abnormality, and shutdown status, the corresponding RGB color value is assigned to each parameter to generate a series of reference graphs of the equipment in normal, abnormal, shutdown, etc. states.
[0030] Furthermore, in the step S6, the characteristic parameters capable of characterizing the operating status of the mining electromechanical equipment are collected in real time through equipment sensors and a monitoring system, the collected characteristic parameters of the real-time operating status of the mining electromechanical equipment are preprocessed according to the data processing method in the step S4, and a state map characterizing the real-time operating parameters of the mining electromechanical equipment is generated through the state map generation method in the step S5.
[0031] Furthermore, in step S7, similarity recognition is performed between the state graph generated in real time and the state reference graph, and the failure probability is calculated according to the similarity value, which is specifically achieved by the following steps:
[0032] S71, extracting features from each real-time state graph and state reference graph using a shape descriptor method, and converting a bar graph or a color block representation into a feature vector, wherein the feature vector includes but is not limited to the length and color of the bar graph;
[0033] S72, using the cosine similarity distance measurement method to simultaneously calculate the similarity between the two feature vectors; this step is represented by the following formulas (4) and (5):
[0034]
[0035] f=λ×cos(θ) (5)
[0036] In formulas (4) and (5), cos(θ) represents the familiarity value; x·y represents the dot product of two vectors, ||x|| and ||y|| represent the modulus of the vectors; f represents the failure probability; and λ represents the state value of the reference map.
[0037] Furthermore, in step S8, the Bayesian formula is expressed by the following formula (6):
[0038]
[0039] In formula (6), p(Y|X) is the posterior probability, which indicates the probability of event Y occurring when condition X is met; p(X|Y) is the conditional probability, which indicates the probability of condition X being met when event Y occurs; p(Y) is the marginal probability of event Y; and p(X) is the marginal probability of condition X.
[0040] It can be seen from the above technical scheme that the present invention collects and processes various operating parameters of mining electromechanical equipment and generates a status map of the equipment, which intuitively reflects the health status of mining electromechanical equipment; at the same time, through the similarity recognition between the status map and the reference map, the failure rate (health level) of the equipment is dynamically calculated, which provides accurate data support for the preventive maintenance and fault warning of the equipment, and effectively reduces the maintenance cost of the equipment. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 Schematic diagram of the steps of the diagnostic method of the present invention. DETAILED DESCRIPTION
[0042] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.
[0043] like Figure 1 A method for health assessment of mining electromechanical equipment based on a Bayesian network model is shown, comprising the following steps:
[0044] S1. Collect relevant data on mining electromechanical equipment, and use natural language processing technology to convert the information in the data into nodes and edges.
[0045] The relevant information of the mining electromechanical equipment described in this preferred embodiment is obtained by using web crawler technology, data API interface or data set, including but not limited to the equipment manufacturer's technical documents, operation manuals, historical fault reports, maintenance records and information obtained through expert interviews and training materials.
[0046] Specifically, the natural language processing technology is used to convert the information in the data into nodes and edges through the following methods: the collected relevant data of mining electromechanical equipment are subjected to text cleaning processing including but not limited to format standardization, removal of special characters and irrelevant content, and unified word forms; the cleaned text is then subdivided into more manageable units, such as sentences or paragraphs; and NLP tools are used to automatically identify the boundaries of sentences or paragraphs and the identification of key entities, such as equipment components, fault types, operating parameters and specific actions. The identified entities are defined as nodes, and the relationships between entities are connected as edges. The edges include the relationships between components and the associations between faults and maintenance methods, such as "motor-connected to-drive belt", and specific attribute information is added to the nodes, such as the name, type, specific value and other attribute information of the nodes.
[0047] S2. Determine the dependency relationship and conditional probability distribution between nodes according to the nodes and edges, and construct a Bayesian network model.
[0048] In a specific operation, the dependency relationship and conditional probability distribution between nodes are determined based on the nodes and edges through domain expert knowledge, such as expert meetings and expert questionnaires.
[0049] S3. Collect historical operation data of mining electromechanical equipment, and divide the health level of mining electromechanical equipment into three levels: normal, warning, and shutdown.
[0050] S4. Preprocess the historical operation data of mining electromechanical equipment, learn the characteristic parameters that can characterize the operating status of mining electromechanical equipment through machine learning algorithms, and construct a state matrix of the health status of mining electromechanical equipment.
[0051] The historical operation data of the mining electromechanical equipment described in this preferred embodiment is obtained from the equipment monitoring system, and the historical operation data of the mining electromechanical equipment includes reliability data, maintenance records, fault types and frequencies, or other data that can characterize the historical operation status of the mining electromechanical equipment. Specifically, the preprocessing of the historical operation data of the mining electromechanical equipment includes but is not limited to the removal of outliers, missing value processing, standardization processing, and normalization processing; it is specifically implemented by the following methods: the processing of outliers uses box plots, Z-scores or other statistical methods to identify and decide to delete or correct data; the missing value processing uses the mean method, median method or interpolation method to process the data; the standardization processing of the data is represented by the following formula (1); the normalization processing of the data is represented by the following formula (2):
[0052]
[0053] In formulas (1) and (2), x represents the collected historical operating data of mining electromechanical equipment; z represents the data after normalization; μ is the mean; σ is the standard deviation; x′ represents the data after normalization; min(x) represents the minimum value in the original data; max(x) represents the maximum value in the original data.
[0054] S5. According to the three operating states of normal, warning and shutdown, the state matrix is normalized based on the threshold range of the characteristic parameters of each mining electromechanical equipment under different operating states to generate a state reference map.
[0055] Specifically, the generation of the state reference map is achieved by the following steps:
[0056] S51. Define the state matrix: Let M be the state matrix, where the element M t,sIt represents the probability that the equipment is in state s at time point t, where state s includes normal, warning, and shutdown;
[0057] S52, Calculation of matrix elements: Through the machine learning algorithm Model, the feature vector X of the input device t , including the characteristics obtained from the historical operation data of the device (such as temperature, vibration, voltage, etc.), and outputting the probability distribution of the device in each state at time point t; this step is expressed by the following formula (3):
[0058] M t,s =P(s|X t )=Model(X t )[s] (3)
[0059] In formula (3): P(s|X t ) means that given the feature vector X t The probability that the device is in state s under the condition of t )[s] represents the input X of the model at time point t t , the probability of output state s;
[0060] S53, defining the thresholds of normal, warning and shutdown states of each operating parameter;
[0061] For example, for temperature: normal: <50℃; warning: 50℃-70℃; shutdown: >70℃;
[0062] For vibration: normal: <2.5mm / s; warning: 2.5mm / s-5mm / s; shutdown: >5mm / s;
[0063] S54, set the RGB color mapping specification, assign a color to each state, and clearly express the state in the map;
[0064] For example, normal state: green (RGB: 0, 255, 0); warning state: yellow (RGB: 255, 255, 0); shutdown state: red (RGB: 255, 0, 0).
[0065] S56. Display each characteristic parameter through a bar graph, wherein the length of the bar graph represents the size of the parameter value, and the color represents its status. According to the normal operation, abnormality, and shutdown status, the corresponding RGB color value is assigned to each characteristic parameter, and a series of reference graphs of the equipment in normal, abnormal, shutdown, etc. states are generated.
[0066] Specifically, for k characteristic parameters, each characteristic parameter has three states: normal, warning, and downtime. The time series data covers the period from t=1 to t=n. The size of the state matrix M is n×3, each row represents a time point, and each element represents the probability of the parameter state. The state matrix M is represented by the following formula:
[0067]
[0068] For example, when t=5, the model predicts that the state probability of the device is [0.8, 0.15, 0.05], then the state matrix M is filled in the row t=5 as follows: 5,Normal =0.8; M 5,Warning =0.15; M 5,Downtime =0.05;
[0069] S6. Collect characteristic parameters that can characterize the operating status of mining electromechanical equipment in real time and perform preprocessing, and generate a real-time status map that characterizes the current operating parameters in real time according to step S5.
[0070] The characteristic parameters capable of characterizing the operating state of the mining electromechanical equipment described in this preferred embodiment are collected in real time through the equipment sensors and the monitoring system, and then the collected characteristic parameters of the real-time operating state of the mining electromechanical equipment are preprocessed according to the data processing method in step S4, and a state spectrum generating method in step S5 is used to generate a state spectrum characterizing the real-time operating parameters of the mining electromechanical equipment. The equipment sensors and the monitoring system are equipped with an analog-to-digital converter. The analog-to-digital converter (ADC) is a device that converts a continuous signal in analog form into a discrete signal in digital form. Because most modern digital systems and algorithms cannot directly process the analog signals generated by the sensors, these analog signals can be converted into digital signals through the analog-to-digital converter, so that the sensor data can be read, processed and analyzed by a computer, a microprocessor or other digital device.
[0071] S7. Perform similarity identification between the real-time generated state map and the state reference map, and calculate the failure probability based on the similarity value.
[0072] This preferred embodiment performs similarity recognition between the real-time generated state graph and the state reference graph, and calculates the failure probability according to the similarity value, which is specifically achieved by the following steps:
[0073] S71, extracting features from each real-time state graph and state reference graph using a shape descriptor method, and converting a bar graph or a color block representation into a feature vector, wherein the feature vector includes but is not limited to the length and color of the bar graph;
[0074] S72, using the cosine similarity distance measurement method to simultaneously calculate the similarity between the two feature vectors; this step is represented by the following formulas (4) and (5):
[0075]
[0076] f=λ×cos(θ) (5)
[0077] In formulas (4) and (5), cos(θ) represents the familiarity value; x·y represents the dot product of two vectors, ||x|| and ||y|| represent the modulus of the vectors; f represents the failure probability; and λ represents the state value of the reference map.
[0078] S8. The failure probability is designated as the conditional probability or marginal probability of each node, and the real-time operation data of the mining electromechanical equipment is input into the Bayesian network model. The posterior probability of each node is calculated according to the Bayesian formula and the conditional independence hypothesis to obtain the health status assessment result of the equipment.
[0079] Specifically, the Bayesian formula is expressed by the following formula (6):
[0080]
[0081] In formula (6), p(Y|X) is the posterior probability, which indicates the probability of event Y occurring when condition X is met; p(X|Y) is the conditional probability, which indicates the probability of condition X being met when event Y occurs; p(Y) is the marginal probability of event Y; and p(X) is the marginal probability of condition X.
[0082] The above-described embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.
Claims
1. A health assessment method for mining electromechanical equipment based on a Bayesian network model, characterized in that: The following steps are involved: S1. Collect relevant data on mining electromechanical equipment and use natural language processing technology to convert the information in the data into nodes and edges; S2. Determine the dependency relationship and conditional probability distribution between nodes according to the nodes and edges, and construct a Bayesian network model; S3. Collect historical operation data of mining electromechanical equipment and classify the health of mining electromechanical equipment into three levels: normal, warning, and shutdown; S4. Preprocess the historical operation data of mining electromechanical equipment, learn the characteristic parameters that can characterize the operation status of mining electromechanical equipment through machine learning algorithms, and construct a state matrix of the health status of mining electromechanical equipment; S5. According to the three operating states of normal, warning and shutdown, the state matrix is normalized based on the threshold range of characteristic parameters of each mining electromechanical equipment under different operating states to generate a state reference map; S6, collecting characteristic parameters that can characterize the operating status of mining electromechanical equipment in real time and performing preprocessing, and generating a real-time state map characterizing the current operating parameters in real time according to step S5; S7, performing similarity identification between the state map generated in real time and the state reference map, and calculating the failure probability according to the similarity value; S8. Specify the failure probability as the conditional probability or marginal probability of each node, input the real-time operation data of mining electromechanical equipment into the Bayesian network model, calculate the posterior probability of each node according to the Bayesian formula and the conditional independence assumption, and obtain the health status assessment result of the equipment.
2. According to claim 1, a method for health assessment of mining electromechanical equipment based on a Bayesian network model is characterized in that: The relevant information of the mining electromechanical equipment in step S1 is obtained by using web crawler technology, data API interface or data set, including but not limited to the equipment manufacturer's technical documents, operation manuals, historical fault reports, maintenance records and information obtained through expert interviews and training materials.
3. According to claim 2, a method for health assessment of mining electromechanical equipment based on a Bayesian network model is characterized in that: In the step S1, the information in the data is converted into nodes and edges using natural language processing technology, which is specifically achieved by the following method: the collected relevant data of mining electromechanical equipment is subjected to text cleaning processing including but not limited to format standardization, removal of special characters and irrelevant content, and unified word forms; the cleaned text is then subdivided into more manageable units, such as sentences or paragraphs; and NLP tools are used to automatically identify the boundaries of sentences or paragraphs and the identification of key entities, such as equipment components, fault types, operating parameters, and specific actions. The identified entities are defined as nodes, and the relationships between entities are connected as edges. The edges include the relationships between components, the association between faults and maintenance methods, and specific attribute information is added to the nodes.
4. According to the Bayesian network model-based health assessment method for mining electromechanical equipment in claim 1, it is characterized in that: In the step S2, the dependency relationship and conditional probability distribution between nodes are determined based on the nodes and edges by using domain expert knowledge.
5. According to the Bayesian network model-based health assessment method for mining electromechanical equipment in claim 1, it is characterized in that: In step S4, the historical operation data of the mining electromechanical equipment is obtained from the equipment monitoring system, and the historical operation data of the mining electromechanical equipment includes reliability data, maintenance records, fault types and frequencies, or other data that can characterize the historical operation status of the mining electromechanical equipment.
6. According to claim 5, a method for health assessment of mining electromechanical equipment based on a Bayesian network model is characterized in that: In the step S4, the historical operation data of the mining electromechanical equipment is preprocessed, including but not limited to removing outliers, processing missing values, standardizing and normalizing. This is specifically achieved by the following methods: the outlier processing uses a box plot, Z-score or other statistical methods to identify and decide to delete or correct the data; the missing value processing uses the mean method, median method or interpolation method to process the data; the data standardization processing is represented by the following formula (1); the data normalization processing is represented by the following formula (2): In formulas (1) and (2), x represents the historical operating data of mining electromechanical equipment collected; z represents the data after standardization; μ is the mean; σ is the standard deviation; x ′ represents the normalized data; min(x) represents the minimum value in the original data; max(x) represents the maximum value in the original data.
7. According to claim 1, a method for health assessment of mining electromechanical equipment based on a Bayesian network model is characterized in that: In step S5, the generation of the state reference map is specifically achieved by the following steps: S51. Define the state matrix: Let M be the state matrix, where the element M t , s It represents the probability that the equipment is in state s at time point t, where state s includes normal, warning, and shutdown; S52, Calculation of matrix elements: Through the machine learning algorithm Model, the feature vector X of the input device t , including the features obtained from the historical operation data of the device, outputs the probability distribution of the device in each state at time point t; this step is expressed by the following formula (3): M t,s =P(s|X t )=Model(X t )[s] (3) In formula (3): P(s|X t ) means that given the feature vector X t The probability that the device is in state s under the condition of t )[s] represents the input X of the model at time point t t , the probability of output state s; S53, defining the thresholds of normal, warning and shutdown states of each operating parameter; S54, set the RGB color mapping specification, assign a color to each state, and clearly express the state in the map; S56. Display each parameter through a bar graph, wherein the length of the bar graph represents the size of the parameter value, and the color represents its status. According to the normal operation, abnormality, and shutdown status, the corresponding RGB color value is assigned to each parameter to generate a series of reference graphs of the equipment in normal, abnormal, shutdown, etc. states.
8. According to the health assessment method of mining electromechanical equipment based on the Bayesian network model in claim 1, in the step S6, the characteristic parameters capable of characterizing the operating status of the mining electromechanical equipment are collected in real time through equipment sensors and monitoring systems, and the collected characteristic parameters of the real-time operating status of the mining electromechanical equipment are preprocessed according to the data processing method in the step S4, and a state map characterizing the real-time operating parameters of the mining electromechanical equipment is generated through the state map generation method in the step S5.
9. According to the method for health assessment of mining electromechanical equipment based on the Bayesian network model of claim 7, similarity recognition is performed on the state map generated in real time and the state reference map, and the failure probability is calculated according to the similarity value, which is specifically achieved by the following steps: S71, extracting features from each real-time state graph and state reference graph using a shape descriptor method, and converting a bar graph or a color block representation into a feature vector, wherein the feature vector includes but is not limited to the length and color of the bar graph; S72, using the cosine similarity distance measurement method to simultaneously calculate the similarity between the two feature vectors; this step is represented by the following formulas (4) and (5): f=λ×cos(θ) (5) In formulas (4) and (5), cos(θ) represents the familiarity value; x·y represents the dot product of two vectors, ||x|| and ||y|| represent the modulus of the vectors; f represents the failure probability; and λ represents the state value of the reference map.
10. The method for health assessment of mining electromechanical equipment based on a Bayesian network model according to claim 1, characterized in that: The Bayesian formula is expressed by the following formula (6): In formula (6), p(Y|X) is the posterior probability, which indicates the probability of event Y occurring when condition X is met; p(X|Y) is the conditional probability, which indicates the probability of condition X being met when event Y occurs; p(Y) is the marginal probability of event Y; and p(X) is the marginal probability of condition X.
