A Reliability Assessment Method for Railway Overhead Contact Systems Based on Markov Chains and Dynamic Bayesian Networks

Abstract

This invention discloses a railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks. By constructing a catenary monitoring data acquisition system, and utilizing multi-source data integration, multi-node multivariate modeling, and hierarchical time-scale monitoring, a systematic monitoring and fault early warning system for the operating status of catenary equipment is achieved. The solution integrates multiple factors such as weather, load, and equipment status to ensure comprehensive collection and analysis of key parameters of the catenary system. Through the combined application of dynamic Bayesian networks and Markov chains, multi-node, multivariate modeling accurately captures the dynamic impact of factors such as equipment aging, load fluctuations, and external environmental changes on system reliability. Furthermore, by refining the time scale, high-frequency sampling is performed on short-term variables such as weather and load fluctuations, while low-frequency monitoring is performed on long-term factors such as equipment aging and corrosion, thereby enabling a detailed assessment of the catenary status at different time scales.

Description

Technical Field

[0001] This invention relates to the field of power supply system reliability assessment, and in particular to a method for assessing the reliability of railway catenary based on Markov chains and dynamic Bayesian networks. Background Technology

[0002] In recent years, my country's high-speed rail, subway, and other rail transit systems have developed rapidly. The overhead contact system is crucial for the safe operation of trains and is a vital guarantee for their safe operation. Therefore, reliability assessment of railway overhead contact systems is essential. However, existing methods for assessing the reliability of railway overhead contact systems have several problems: the reliability of the railway overhead contact system is affected by various dynamic factors, such as weather and temperature changes; the overhead contact system changes in real time, making real-time feedback and dynamic adjustment of the system's status impossible; and the reliability assessment of railway overhead contact systems does not fully consider the impact of individual components on the system's reliability. Summary of the Invention

[0003] To overcome the aforementioned problems in the existing technology, this invention proposes a reliability assessment method for railway catenary based on Markov chains and dynamic Bayesian networks.

[0004] The technical solution adopted by this invention to solve its technical problem is: a railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, comprising the following steps:

[0005] Step 1: Construct a dynamic Bayesian network model of the overhead contact system. Utilize the state transition characteristics of Markov chains and the probabilistic reasoning capabilities of Bayesian networks to describe the state transitions and fault evolution processes of each subsystem at different times. Real-time monitoring and collection of the operating data of the railway overhead contact system will be carried out to construct a real-time data acquisition system.

[0006] Step 2: Introduce the real-time monitoring data and reliability assessment indicators obtained in Step 1 into the overhead contact line reliability assessment indicator system, while also considering the impact of maintenance on system reliability.

[0007] Step 3: Classify the reliability of the overhead contact system by using historical operating data and system operating status.

[0008] Step 4: Calculate the membership degree of the catenary system indicators using the Gaussian membership function. By analyzing the historical monitoring and operation data of the catenary system as sample data for different levels, the Gaussian membership function for different levels is calculated.

[0009] Step 5: Determine the evaluation time interval in days, construct a judgment matrix based on the importance of the indicators, and calculate the consistency ratio (CR) of the constructed matrix. If the calculated CR < 0.1, the consistency of the judgment matrix is ​​considered to be within a reasonable range. If the calculated CR ≥ 0.1, the importance of the indicators is revised.

[0010] Based on the judgment matrix, the weight vector is calculated, and the weights of all time intervals are combined to obtain the dynamic weight of each indicator criterion.

[0011] Step 6: Set the system state credibility and merge multiple belief functions into a unified belief degree using Dempster's rules; establish a credibility allocation matrix based on the belief functions of multiple indicators, and obtain the probability distribution function of the system state through the integration of evidence theory.

[0012] Step 7: Divide the system into different states based on the historical operating data of the railway catenary system, and obtain the system state level by mapping the probability distribution function of the system to the system state level, and finally obtain the reliability assessment result.

[0013] The aforementioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks involves real-time monitoring and data acquisition in step 1. This monitoring and data acquisition system comprises a data acquisition layer, a diagnostic analysis layer, a data storage layer, and an application execution layer. The data acquisition layer captures and feeds back the equipment's operational status data in real time. The diagnostic analysis layer analyzes and diagnoses the data from the data acquisition layer to identify potential system faults. The data storage layer stores historical operational status data, operational analysis and monitoring of the catenary equipment, and various intelligent algorithms related to training and equipment operation control. The application execution layer transforms the data processing and management results into actual operation and maintenance measures.

[0014] The above-mentioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, the specific process of real-time monitoring using Markov chains in step 1 is as follows: a first-order Markov chain is used to simulate the rapid response to short-term meteorological factors and load changes, a second-order Markov chain is used to integrate long-term historical information to reflect the long-term dependence of equipment aging and failure probability, a unified spatial state is defined, and the two Markov chains are merged.

[0015] Among them, meteorological state W t and power load status L t As a short-term state variable, it is only affected by the previous time step; Equipment aging state A t and failure probability F t As a long-term state variable, its current state depends on the states of the previous two time steps.

[0016] The aforementioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, in step 2, includes a catenary reliability assessment index system comprising a target layer, an index layer, and a sub-index layer. The target layer assesses the operational status of the railway catenary, and the index layer is derived from real-time monitoring data from the system. System performance indicators Equipment status monitoring indicators and related reliability indicators The sub-index layer consists of steady-state availability, average failure frequency, average repair time, equipment maintenance rate, and contact wire relative condition index.

[0017] The above-mentioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, in step 4, the membership degree... The calculation method is as follows:

[0018] ;

[0019] ;

[0020] ;

[0021] Where j = 1, 2, 3, 4, 5 represent the system grades as very good, good, average, poor, and very poor, respectively, and n is the number of sample points. For the i-th sample point, With the center point, The standard deviation is denoted as .

[0022] The above-mentioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, specifically includes step 5: determining the assessment time interval in days. Assign initial weights to each indicator , ,…, The initial weights reflect the relative importance of each indicator without considering the time factor. Indicator data are collected at different time intervals, and the indicator weights are adjusted according to the time intervals.

[0023] ;

[0024] ;

[0025] in, The attenuation coefficient is... Let be the time decay function. To determine the importance of indicator i relative to indicator j at time t;

[0026] For each time interval Construct the judgment matrix R(t):

[0027] ;

[0028] Calculate the maximum eigenvalue λmax(t) of the judgment matrix for each time interval, and calculate the consistency index CI(t) and consistency ratio CR(t):

[0029] ;

[0030] ;

[0031] Where RI is the random consistency index, which depends on the order of the matrix; m is the order of the judgment matrix;

[0032] A consistency check is performed on the judgment matrix for each time interval to ensure the consistency of the evaluation. If CR(t) < 0.1, the judgment matrix has satisfactory consistency; if CR(t) ≥ 0.1, the judgment matrix needs to be readjusted. Solve for the eigenvector q. Given a unit vector q, after normalizing the eigenvector q, the weight vector Q(t) is:

[0033] ;

[0034] ;

[0035] in, It is the weight of criterion k at time t. Let be the e-th vector in the feature vector q, and r be the number of evaluation metrics;

[0036] By combining the weights of all time intervals, we obtain the dynamic weight of each indicator criterion at different time points:

[0037] ;

[0038] Where T is the total number of time intervals.

[0039] The above-mentioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, specifically step 6, is as follows:

[0040] The identification framework for railway overhead contact lines is H={ , , , , }, set the belief level for each state of the system. The system is in a state Credibility:

[0041] ;

[0042] in, For the system under conditions The system is in the following state. The probability of ; r is the number of evaluation indicators, and k is the kth indicator;

[0043] The Dempster rules are used to fuse belief functions. When multiple belief functions come from different sources, they are merged into a unified belief degree.

[0044] ;

[0045] Where i represents the i-th state of the system;

[0046] A confidence allocation matrix Y is formed by fusing belief functions based on multiple indicators:

[0047] ;

[0048] By integrating evidence theories, the probability distributions of each system state are obtained, and the probability allocation function of the system state is defined. for:

[0049] ;

[0050] in, for Degree of belief in a given state;

[0051] The railway overhead contact system operates in a dynamic environment, and the state probability of the system changes over time. A state transition matrix is ​​then introduced. The probability distribution of the state of the overhead contact system at each time step is obtained. :

[0052] .

[0053] The aforementioned railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks, specifically step 7, involves: calculating the boundary points of each state based on the state distribution of historical operating data of the railway catenary system, and obtaining the dynamic boundary value b. 1， b 2， b 3， b4, mapping different state levels to corresponding evaluation results based on the system's probability distribution:

[0054] Excellent: The probability distribution value is higher than b1, indicating that the system has very high reliability and a very low probability of failure.

[0055] Good: The probability distribution values ​​are between [b2, b1), indicating a relatively healthy system state, but some minor faults exist;

[0056] Generally: If the probability distribution value is between [b3, b2), the system has certain faults and may require attention and maintenance;

[0057] Poor: The probability distribution values ​​are between [b4, b3), indicating that the system has a high risk or multiple failures and poor reliability;

[0058] Very poor: The probability distribution value is below b4, the system has a very high risk of failure, and the reliability is severely reduced.

[0059] The beneficial effects of this invention are that it constructs a catenary monitoring data acquisition system, utilizing multi-source data integration, multi-node multivariate modeling, and hierarchical time-scale monitoring to achieve systematic monitoring and fault early warning of the catenary equipment's operating status. By integrating multiple factors such as meteorology, load, and equipment status, it ensures comprehensive collection and analysis of key parameters of the catenary system. Through the combined application of dynamic Bayesian networks and Markov chains, multi-node, multivariate modeling can accurately capture the dynamic impact of factors such as equipment aging, load fluctuations, and changes in the external environment on system reliability. Furthermore, by refining the time scale, high-frequency sampling is performed on short-term variables such as meteorology and load fluctuations, while low-frequency monitoring is performed on long-term factors such as equipment aging and corrosion, thereby enabling a detailed assessment of the catenary status at different time scales.

[0060] The monitoring and data acquisition system integrates multiple data sources, including meteorological, load, and equipment status data, enabling a comprehensive understanding of the overhead contact system's operational status and effectively improving the accuracy of fault identification and early warning. Secondly, based on dynamic Bayesian networks and Markov chains, a multi-node, multi-variable modeling method is used to analyze the interaction between equipment and environmental factors, enhancing the accuracy of the overhead contact system's reliability assessment. Furthermore, this invention employs hierarchical time-scale monitoring, combining high-frequency sampling of short-term variables with low-frequency sampling of long-term variables to achieve short-term fluctuation response and long-term trend analysis. The impact of maintenance rates on the overhead contact system is considered within the reliability assessment system. Finally, a dynamic analytic hierarchy process (AHP) is used to dynamically adjust the weights of each indicator in the model based on the system status reflected by real-time monitoring data, more accurately reflecting the reliability of the overhead contact system. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the process of this invention;

[0062] Figure 2 This is a structural framework diagram of the monitoring data acquisition system of the present invention;

[0063] Figure 3 This is a schematic diagram of the dynamic network structure of the overhead contact line of the present invention;

[0064] Figure 4 This is a schematic diagram of the contact network reliability evaluation index system of the present invention. Detailed Implementation

[0065] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] This invention discloses a method for evaluating the reliability of railway catenary based on Markov chains and dynamic Bayesian networks, such as... Figure 1 As shown, the specific steps include the following:

[0067] Step 1: Construct a dynamic Bayesian network model of the overhead contact system. Utilize the state transition characteristics of Markov chains and the probabilistic reasoning capabilities of Bayesian networks to describe the state transitions and fault evolution processes of each subsystem at different times. Real-time monitoring and collection of the operating data of the railway overhead contact system will be carried out to construct a real-time data acquisition system.

[0068] Step 2: Introduce the real-time monitoring data and reliability assessment indicators obtained in Step 1 into the overhead contact line reliability assessment indicator system, while also considering the impact of maintenance on system reliability.

[0069] Step 3: Classify the reliability of the overhead contact system by using historical operating data and system operating status.

[0070] Step 4: Calculate the membership degree of the catenary system indicators using the Gaussian membership function. By analyzing the historical monitoring and operation data of the catenary system as sample data for different levels, the Gaussian membership function for different levels is calculated.

[0071] Step 5: Determine the evaluation time interval in days, construct a judgment matrix based on the importance of the indicators, and calculate the consistency ratio (CR) of the constructed matrix. If the calculated CR < 0.1, the consistency of the judgment matrix is ​​considered to be within a reasonable range. If the calculated CR ≥ 0.1, the importance of the indicators is revised.

[0072] Based on the judgment matrix, the weight vector is calculated, and the weights of all time intervals are combined to obtain the dynamic weight of each indicator criterion.

[0073] Step 6: Set the system state credibility and merge multiple belief functions into a unified belief degree using Dempster's rules; establish a credibility allocation matrix based on the belief functions of multiple indicators, and obtain the probability distribution function of the system state through the integration of evidence theory.

[0074] Step 7: Divide the system into different states based on the historical operating data of the railway catenary system, and obtain the system state level by mapping the probability distribution function of the system to the system state level, and finally obtain the reliability assessment result.

[0075] In one specific embodiment, step 1 involves real-time monitoring and data acquisition using a monitoring data acquisition system, the structural framework of which is as follows: Figure 2 As shown, it specifically includes a data acquisition layer, a diagnostic analysis layer, a data storage layer, and an application execution layer. The data acquisition layer captures and feeds back the operating status data of the equipment in real time; the diagnostic analysis layer analyzes and diagnoses the data from the data acquisition layer to discover potential faults in the system; the data storage layer is used to store historical operating status data, operation analysis and monitoring of the overhead contact line equipment, and various intelligent algorithms related to training and equipment operation control; the application execution layer transforms the data processing and management results into actual operation and maintenance measures.

[0076] The overhead contact system consists of multiple subsystems connected in series, including contact suspension, positioning devices, supports and foundations, support devices, auxiliary devices, and compensation devices. These subsystems have complex dependencies and mutual influences. A failure in any subsystem can cause the entire system to malfunction. Therefore, when constructing a dynamic Bayesian network (DBN) model of the overhead contact system, the state transition characteristics of Markov chains and the probabilistic reasoning capabilities of Bayesian networks are utilized to describe the state transitions and fault evolution processes of each subsystem at different times. By analyzing the structural characteristics of the overhead contact system, short-term and long-term factors are modeled separately, and a unified dynamic network structure for the overhead contact system is constructed by combining the state transition matrices between time slices. Figure 3 As shown, where D represents a contact wire fault, M1 represents a contact suspension fault, M2 represents a positioning device fault, M3 represents a support post and foundation fault, M4 represents a support device fault, M5 represents an auxiliary device fault, M6 represents a compensation device fault, X1 represents a dropper wire fault, X2 represents a catenary wire fault, X3 represents a contact wire fault, X4 represents a wire clamp fault, X5 represents a positioning rod fault, X6 represents a combined positioning device fault, X7 represents a positioning hook fault, X8 represents a windproof guy wire fault, X9 represents a support post fault, X10 represents a foundation fault, X11 represents an insulator fault, X12 represents a cantilever arm fault, X13 represents a base fault, X14 represents a bushing double ear fault, X15 represents an auxiliary conductor fault, X16 represents an auxiliary conductor conduit suspension device fault, X17 represents a compensation rope fault, X18 represents a tension compensation fault, G1 represents a positioning wire clamp fault, G2 represents a positioning pin fault, and G3 represents an insulator fault.

[0077] To accurately assess the reliability of the overhead contact system, it is necessary to combine short-term and long-term monitoring information and select an appropriate Markov chain order to capture dependencies at different time scales. By monitoring and recording multivariate influencing factors at different scales, an effective reliability assessment of the overhead contact system can be conducted. First, short-term frequent monitoring of meteorological factors and overhead contact load changes is performed. Combined with long-term historical data, fault information, and equipment status information of the overhead contact system, and through multivariate processing at different time scales, the overhead contact system can respond in the short term, reduce the risk of emergencies, better adapt to the changing characteristics of different factors in the overhead contact system, and improve the accuracy of overhead contact system reliability assessment.

[0078] The specific process of using Markov chains for real-time monitoring in step 1 is as follows: a first-order Markov chain is used to simulate the rapid response to short-term meteorological factors and load changes, a second-order Markov chain is used to integrate long-term historical information to reflect the long-term dependence of equipment aging and failure probability, a unified spatial state is defined, and the two Markov chains are merged.

[0079] Among them, meteorological state W t and power load status L t As a short-term state variable, it is only affected by the previous time step; Equipment aging state A t and failure probability F t As a long-term state variable, its current state depends on the states of the previous two time steps. This effectively captures long-range dependencies across time steps. The equipment maintenance status 𝐵𝑡 is directly related to the equipment maintenance situation and has a significant impact on system reliability.

[0080] Assuming weather conditions Given m possible states, the transition matrix of the meteorological state is... for A matrix. Each element in the matrix. Indicates weather conditions from Transferred to The probability of:

[0081] .

[0082] Assuming power load conditions There are n possible states, and the transition of load states depends not only on the current load state but also on the weather conditions. Assuming weather conditions Load state transition matrix For one The matrix, Indicates weather conditions Below, the load condition changes from Transferred to The probability of:

[0083] ;

[0084] In this matrix, rows represent the load status at the current moment, columns represent the load status at the next moment, and the matrix is ​​designed for specific weather conditions. The sum of the elements in each row should be 1.

[0085] State transition matrix of a short-term Markov chain:

[0086] ;

[0087] Among them, short-term factors =( , ).

[0088] Assuming the equipment is in an aging state There are p possible states, and the transition of equipment aging states depends on the history of load states. The transition matrix for equipment aging states is shown below. For one The matrix, elements Indicates the state under load Under the influence of aging, the equipment... Transferred to The probability of:

[0089] .

[0090] Equipment Fault Status There are four possible states: normal operation, minor fault, major fault, and under maintenance. The transition between equipment fault states depends not only on the current fault state but also on the combined effects of equipment aging, load conditions, and weather conditions. The equipment fault state transition matrix is ​​shown below. Given a 4x4 matrix, elements Indicates the device's state Transferred to The probability of:

[0091] ;

[0092] Among them, long-term factors .

[0093] State transition matrix of a long-term Markov chain:

[0094] ;

[0095] Among them, long-term factors .

[0096] Define a unified spatial state By merging two Markov chains, the space includes all possible combinations of states for both short-term and long-term factors. The merged state transition matrix for:

[0097] ;

[0098] The merged Markov chain provides a comprehensive framework for monitoring the changes of multiple variables in the railway catenary system at different time scales and their impact on the system state.

[0099] In one specific embodiment, the contact network reliability assessment index system in step 2 is as follows: Figure 4 As shown, it specifically includes a target layer, an indicator layer, and a sub-indicator layer. The target layer is for assessing the operational status of the road contact network, and the indicator layer consists of real-time monitoring data from the system. System performance indicators Equipment status monitoring indicators and related reliability indicators The sub-index layer consists of steady-state availability, average failure frequency, average repair time, equipment maintenance rate, and contact wire relative condition index.

[0100] Taking maintenance into account, the identification framework for the condition of the railway overhead contact system is H={ , , , , The steady-state availability of the overhead contact system is the state in which the system operates normally over a long period of time. The probability, the steady-state probability distribution satisfies: If the steady-state distribution is =[ , , , ], The steady-state availability A of the overhead contact system is:

[0101] ;

[0102] in, This represents the probability of the system operating normally under steady-state conditions. This is the state transition matrix;

[0103] Average Failure Frequency of Overhead Contact System The frequency of transition from a normal state to a fault state:

[0104] ;

[0105] Where j represents different system state levels, t represents the current running time, T0 represents the system running time period, and H... t Let H be the system state at time t. j Let P be the state corresponding to system level j, and P be the conditional probability.

[0106] Mean Time To Repair (MTTR) of an overhead contact system is the average rate at which it transitions from a fault state to a normal state.

[0107] ;

[0108] Where j represents the different state levels of the system.

[0109] In one specific embodiment, in order to more intuitively reflect the actual operating status of the system, the reliability assessment of the overhead contact system is divided into 5 levels based on historical experience:

[0110] (1) Very good ( In this state, the monitoring data of the overhead contact system or equipment are all in optimal condition, and the possibility of overhead contact system failure is extremely low.

[0111] (2) Better In this state, it indicates that the monitoring data of the overhead contact system or equipment are all in normal working condition, and the overall operating condition of the overhead contact system is good.

[0112] (3) General ( The overhead contact system in this operating state is susceptible to failure, and its performance will decrease to some extent, but it can still meet the basic operating requirements of the overhead contact system.

[0113] (4) Poor The overhead contact system or equipment in this operating state is at risk of failure or has already experienced a minor fault, requiring maintenance personnel to perform maintenance.

[0114] (5) Very bad The overhead contact system is in a faulty state under these operating conditions and cannot operate normally. Immediate inspection and maintenance are required. The performance of the overhead contact system has significantly decreased. It is essential to ensure that the system is restored to normal operation as soon as possible.

[0115] When calculating membership degrees, it is necessary to select an appropriate membership degree calculation method. This embodiment uses the Gaussian membership function to calculate the membership degrees of the overhead contact system indicators. By analyzing historical monitoring and operation data of the overhead contact system as sample data of different levels, the mean and standard deviation of the sample data of different levels are calculated as the center point C and standard deviation of the Gaussian membership function. :

[0116] ;

[0117] ;

[0118] Where j = 1, 2, 3, 4, 5 represent the system grades as very good, good, average, poor, and very poor, respectively, and n is the number of sample points. Let i be the i-th sample point.

[0119] The calculated center point and standard deviation are applied to different state levels to calculate the Gaussian membership function for each level.

[0120] The membership degree of the system's operating status is:

[0121] ;

[0122] in, For the i-th sample point, With the center point, The standard deviation is denoted as .

[0123] The railway catenary system is complex, so the analytic hierarchy process (AHP) is usually used to construct a multi-level analytical structure model and determine the weights of each indicator. Considering the dynamic characteristics of the railway catenary, this patent constructs a catenary monitoring data acquisition system. Based on the system status reflected by real-time monitoring data, the weights of each indicator in the model are dynamically adjusted. Furthermore, a time dimension is added to the traditional AHP, so that the indicator weights can be adjusted with time and environmental changes, thus more accurately reflecting the reliability of the catenary system.

[0124] In one specific embodiment, step 5 specifically includes: determining the evaluation time interval in days. Assign initial weights to each indicator , ,…, The initial weights reflect the relative importance of each indicator without considering the time factor. Indicator data are collected at different time intervals, and the indicator weights are adjusted according to the time intervals.

[0125] ;

[0126] ;

[0127] in, The attenuation coefficient is... Let be the time decay function. The importance of indicator i relative to indicator j at time t.

[0128] For each time interval Construct the judgment matrix R(t):

[0129] ;

[0130] Calculate the maximum eigenvalue λmax(t) of the judgment matrix for each time interval, and calculate the consistency index CI(t) and consistency ratio CR(t):

[0131] ;

[0132] ;

[0133] Where RI is the random consistency index, which depends on the order of the matrix; m is the order of the judgment matrix;

[0134] A consistency check is performed on the judgment matrix for each time interval to ensure the consistency of the evaluation. If CR(t) < 0.1, the judgment matrix has satisfactory consistency; if CR(t) ≥ 0.1, the judgment matrix needs to be readjusted. Solve for the eigenvector q. Given a unit vector q, after normalizing the eigenvector q, the weight vector Q(t) is:

[0135] ;

[0136] ;

[0137] in, It is the weight of criterion k at time t. Let be the e-th vector in the eigenvector q.

[0138] By combining the weights of all time intervals, we obtain the dynamic weight of each indicator criterion at different time points:

[0139] ;

[0140] Where T is the total number of time intervals.

[0141] In one specific embodiment, step 6 is as follows:

[0142] The identification framework for railway overhead contact lines is H={ , , , , }, set the belief level for each state of the system. The system is in a state Credibility:

[0143] ;

[0144] in, For the system under conditions The system is in the following state. The probability of ; r is the number of evaluation indicators, and k is the kth indicator.

[0145] The Dempster rules are used to fuse belief functions. When multiple belief functions come from different sources, they are merged into a unified belief degree.

[0146] ;

[0147] Where i represents the i-th state of the system.

[0148] A confidence allocation matrix Y is formed by fusing belief functions based on multiple indicators:

[0149] .

[0150] By integrating evidence theories, the probability distributions of each system state are obtained, and the probability allocation function of the system state is defined. for:

[0151] ;

[0152] in, for The degree of belief in a given state.

[0153] The railway overhead contact system operates in a dynamic environment, and the state probability of the system changes over time. A state transition matrix is ​​then introduced. The probability distribution of the state of the overhead contact system at each time step is obtained. :

[0154] .

[0155] In one specific embodiment, step 7 involves: calculating the boundary points of each state based on the state distribution of historical operating data of the railway catenary system, and obtaining the dynamic boundary value b. 1， b 2， b 3， b4, mapping different state levels to corresponding evaluation results based on the system's probability distribution:

[0156] Excellent: The probability distribution value is higher than b1, indicating that the system has very high reliability and a very low probability of failure.

[0157] Good: The probability distribution values ​​are between [b2, b1), indicating a relatively healthy system state, but some minor faults exist;

[0158] Generally: If the probability distribution value is between [b3, b2), the system has certain faults and may require attention and maintenance;

[0159] Poor: The probability distribution values ​​are between [b4, b3), indicating that the system has a high risk or multiple failures and poor reliability;

[0160] Very poor: The probability distribution value is below b4, the system has a very high risk of failure, and the reliability is severely reduced.

[0161] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its scope and spirit, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A reliability assessment method for railway catenary based on Markov chains and dynamic Bayesian networks, characterized in that, Includes the following steps: Step 1: Construct a dynamic Bayesian network model of the overhead contact system. Utilize the state transition characteristics of Markov chains and the probabilistic reasoning capabilities of Bayesian networks to describe the state transitions and fault evolution processes of each subsystem at different times. Real-time monitoring and collection of the operating data of the railway overhead contact system will be carried out to construct a real-time data acquisition system. Step 2: Introduce the real-time monitoring data and reliability assessment indicators obtained in Step 1 into the overhead contact line reliability assessment indicator system, while also considering the impact of maintenance on system reliability. Step 3: Classify the reliability of the overhead contact system by using historical operating data and system operating status. Step 4: Calculate the membership degree of the catenary system indicators using the Gaussian membership function. By analyzing the historical monitoring and operation data of the catenary system as sample data for different levels, the Gaussian membership function for different levels is calculated. Step 5: Determine the evaluation time interval in days, construct a judgment matrix based on the importance of the indicators, and calculate the consistency ratio (CR) of the constructed matrix. If the calculated CR < 0.1, the consistency of the judgment matrix is ​​considered to be within a reasonable range. If the calculated CR ≥ 0.1, the importance of the indicators is revised. Based on the judgment matrix, the weight vector is calculated, and the weights of all time intervals are combined to obtain the dynamic weight of each indicator criterion. Step 6: Set the system state credibility and merge multiple belief functions into a unified belief degree using Dempster's rules; establish a credibility allocation matrix based on the belief functions of multiple indicators, and obtain the probability distribution function of the system state through the integration of evidence theory. Step 7: Divide the system into different states based on the historical operating data of the railway catenary system, and obtain the system state level by mapping the probability distribution function of the system to obtain the final reliability assessment result. In step 1, real-time monitoring and data acquisition are performed through a monitoring data acquisition system. This system includes a data acquisition layer, a diagnostic analysis layer, a data storage layer, and an application execution layer. The data acquisition layer captures and feeds back the equipment's operating status data in real time. The diagnostic analysis layer analyzes and diagnoses the data from the data acquisition layer to identify potential system faults. The data storage layer stores historical operating status data, operational analysis and monitoring of the overhead contact line equipment, and various intelligent algorithms related to training and equipment operation control. The application execution layer transforms the data processing and management results into actual operation and maintenance measures. The specific process of using Markov chains for real-time monitoring in step 1 is as follows: a first-order Markov chain is used to simulate the rapid response to short-term meteorological factors and load changes, a second-order Markov chain is used to integrate long-term historical information to reflect the long-term dependence of equipment aging and failure probability, a unified spatial state is defined, and the two Markov chains are merged. Among them, meteorological conditions and power load status As a short-term state variable, it is only affected by the previous time step; equipment aging state and failure probability As a long-term state variable, its current state depends on the states of the previous two time steps.

2. The railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks according to claim 1, characterized in that, In step 2, the catenary reliability assessment index system includes a target layer, an index layer, and a sub-index layer. The target layer assesses the operational status of the catenary, and the index layer is based on real-time monitoring data from the system. System performance indicators Equipment status monitoring indicators and related reliability indicators The sub-index layer consists of steady-state availability, average failure frequency, average repair time, equipment maintenance rate, and contact wire relative condition index.

3. The railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks according to claim 1, characterized in that, Membership degree in step 4 The calculation method is as follows: ; ; ; Where j = 1, 2, 3, 4, 5 represent the system grades as very good, good, average, poor, and very poor, respectively, and n is the number of sample points. For the i-th sample point, With the center point, The standard deviation is denoted as .

4. The railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks according to claim 1, characterized in that, Step 5 specifically includes: determining the evaluation time interval in days. Assign initial weights to each indicator , ,…, The initial weights reflect the relative importance of each indicator without considering the time factor. Indicator data are collected at different time intervals, and the indicator weights are adjusted according to the time intervals. ; ; in, The attenuation coefficient is... It is a time decay function. To determine the importance of indicator i relative to indicator j at time t; For each time interval Construct the judgment matrix R(t): ； Calculate the maximum eigenvalue λmax(t) of the judgment matrix for each time interval, and calculate the consistency index CI(t) and consistency ratio CR(t): ; ; Where RI is the random consistency index, which depends on the order of the matrix; m is the order of the judgment matrix; A consistency check is performed on the judgment matrix for each time interval to ensure the consistency of the evaluation. If CR(t) < 0.1, the judgment matrix has satisfactory consistency; if CR(t) ≥ 0.1, the judgment matrix needs to be readjusted. Solve for the eigenvector q. Given a unit vector q, after normalizing the eigenvector q, the weight vector Q(t) is: ; ; in, The criterion k in time t The weight, Let be the e-th vector in the feature vector q, and r be the number of evaluation metrics; By combining the weights of all time intervals, we obtain the dynamic weight of each indicator criterion at different time points: ; Where T is the total number of time intervals.

5. The railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks according to claim 1, characterized in that, Step 6 specifically involves: The identification framework for railway overhead contact lines is H={ , , , , }, set the belief level for each state of the system. The system is in a state Credibility: ; in, For the system under conditions The system is in the following state. The probability of ; r is the number of evaluation indicators, and k is the kth indicator; The Dempster rules are used to fuse belief functions. When multiple belief functions come from different sources, they are merged into a unified belief degree. ; Where i represents the i-th state of the system; A confidence allocation matrix Y is formed by fusing belief functions based on multiple indicators: ; By integrating evidence theories, the probability distributions of each system state are obtained, and the probability allocation function of the system state is defined. for: ; in, for Degree of belief in a given state; The railway overhead contact system operates in a dynamic environment, and the state probability of the system changes over time. A state transition matrix is ​​then introduced. The probability distribution of the state of the overhead contact system at each time step is obtained. : 。 6. The railway catenary reliability assessment method based on Markov chains and dynamic Bayesian networks according to claim 1, characterized in that, Step 7 specifically involves: calculating the boundary points of each state based on the state distribution of historical operating data of the railway catenary system, and obtaining the dynamic boundary values. b 1， b 2， b 3， b 4. Map different state levels to corresponding evaluation results based on the system's probability distribution: Very good: the probability distribution value is higher than b 1. The system has excellent reliability and a very low probability of failure. Better: The probability distribution value is in [ b 2, b 1) Between these points, the system is in relatively healthy condition, but some minor faults exist; Generally: probability distribution values ​​are in [ b 3, b 2) Between these points, the system has certain faults that may require attention and maintenance; Poor: The probability distribution value is in [ b 4, b 3) Between these points, the system has significant risks or multiple failures, resulting in poor reliability; Very poor: probability distribution value is lower than b 4. The system has a very high risk of failure and its reliability is severely reduced.

Images