A method for calculating the dynamic reliability of electromechanical systems based on inter-component interoperability

Abstract

This invention discloses a method for calculating the dynamic reliability of electromechanical systems based on inter-component interoperability, comprising: (1) constructing a hidden Markov model for system risk transmission and an inter-component risk state transmission matrix; (2) combining load effects to calculate inter-component interoperability and resistance coefficients, quantifying relevant parameters of the state transition matrix, and calculating the probability that the risk of a component will not escalate after risk transmission; (3) applying inter-component interoperability, determining the final state sequence of the system based on the idea of ​​stochastic computation, and calculating the dynamic reliability of the system. For complex electromechanical systems, the interoperability calculation method of this invention can make the system reliability calculation closer to the actual situation, and based on this, an improved maintenance strategy is proposed. Compared with the traditional maintenance strategy, the maintenance strategy considering inter-component interoperability proposed in this invention can maintain the system at a higher reliability and have a lower maintenance cost in the long term.

Description

Technical Field

[0001] This invention belongs to the field of dynamic reliability assessment of complex electromechanical systems, and specifically relates to a method for calculating the dynamic reliability of electromechanical systems based on inter-component interoperability. Background Technology

[0002] With the development of my country's economy and engineering technology, the design and manufacturing of electromechanical systems are steadily moving towards precision. Due to the complex internal structure of modern large-scale electromechanical equipment, critical subsystems, such as control systems and power systems, experience frequent, difficult-to-monitor, and highly unpredictable failures. However, the broad market prospects are driving further innovation in equipment towards higher speeds and precision, thus placing higher demands on the functionality, structure, and performance of equipment within the industry.

[0003] Complex electromechanical systems consist of components that are coupled and connected through electrical and informational means to achieve different functions in a "component-subsystem-system" manner. The degree of interaction and dependence between components varies. Therefore, it is necessary to quantify these interactions to more accurately calculate and predict the dynamic reliability of the system. This will guide the development of maintenance plans, reduce equipment maintenance costs, ensure the stable and safe operation of equipment, and prevent accidents.

[0004] However, existing reliability calculations for complex electromechanical systems do not consider the interaction relationships and risk transmission effects among the components within the system. Instead, they are mostly based on the independence between components, resulting in inaccurate dynamic calculations. Summary of the Invention

[0005] This invention aims to provide a method for calculating the dynamic reliability of electromechanical systems based on inter-component interoperability, to address the aforementioned problems. It includes the following steps:

[0006] Step 1: Based on the physical structure of the complex electromechanical system, construct a hidden Markov model for risk transmission and calculate the risk transmission state matrix between components.

[0007] Step 2: Apply the load effect to calculate the interoperability and resistance coefficients between system components, and calculate the probability that the risk level of a component will not escalate after risk transmission.

[0008] Step 3: Apply the interoperability of the system, use random computation to calculate the final state sequence of the system, calculate the reliability of the system, and propose an improved maintenance strategy and compare it with the traditional maintenance strategy.

[0009] Preferably, step one specifically includes:

[0010] 1.1 Based on the physical structure of the complex electromechanical system, a hidden Markov model composed of various nodes is established, and the node v aDefine the state matrix: A = [α1, a2, ..., a3] n ], where α i Represents node v a In the probability of state i, the magnitude of i represents the severity of the risk. The larger the value of i, the more severe the risk. When i = n, the risk causes a failure.

[0011] For node v a To node v b Transmitting risk status, defined as: B a→b =A·R a→b , where R a→b For node v a to node v b Risk transmission matrix, B a→b This indicates that at node v a Affecting the next node v b The state matrix is ​​abbreviated as B; for the risk state transfer matrix of a single path such as A→B→…→F, we have: A·R a→b ·...·R e→f =F, that is: F = A·ΠR;

[0012] Where A represents node v a The state matrix, R a→b For node v a to node v b Risk transmission matrix, R e→f Represents node v e to node v f The risk transmission matrix, F represents the risk transmission matrix of node v. f The state matrix;

[0013] For the scenario of risk propagation from multiple nodes to a single node, two operations are defined based on the risk state type and intensity:

[0014] The ⊙ operation: Given rows and k columns of matrices A, B, and C, satisfying A = B⊙C, that is...

[0015]

[0016] Among them, a i Let b represent the i-th element in matrix A. i b j Let c represent the i-th and j-th elements in matrix B. i c j This represents the i-th and j-th elements in matrix C;

[0017] Operations: Suppose there are k-row matrices A, B, and C that satisfy... Then a i =∑m+n＝i+1 b m ·c n (i < k), a k =∑ m+n＞k b m ·c n ;

[0018] Among them, a i Let b represent the i-th element in matrix A. m c represents the m-th element in matrix B. n Let m represent the nth element in matrix C, where m and n are any non-zero positive integers.

[0019] 1.2 Establish a state matrix for risk transmission from multiple nodes to a single node, such as node v a v b To node v c When transmitting risk, we have: C a→c =A·R a→c and C b→c =A·R b→c When the risk status types are the same, then C ab→c =C a→c ⊙C b→c When the risk status types are different, then Among them, C a→c For v a to v c Risk state transmission matrix, where A represents node v a The state matrix, C ab→c Represents node v a With node v b to node v c The risk transmission matrix;

[0020] When there are multiple nodes such as v a v b ..., v e v f ... v i v j Directly to node v g When transmitting risk, if there is a v a v b ..., v e The risk status type is the same, v e v f ..., v i v j Different types of risk states have Where G represents the distance from each node to v g The risk state transmission matrix, G a→g G b→g Ge→g G f→g G i→g G j→g They represent nodes v respectively a v b v e v f v i v j to node v g The risk transmission matrix.

[0021] Preferably, step two specifically includes:

[0022] 2.1 Based on load balancing, when quantifying the degree of mutual influence between components, the amount of information flow is used as an important criterion. For component j (node ​​v) j It receives information streams from multiple functions, using one of its components i (node ​​v) i The proportion of information flow i to total information flow j can represent the degree of correlation between i and j; when all information j comes from i, it means that the interoperability coefficient between i and j is 1, that is, when i fails, the probability of j failing is higher.

[0023] With D ij To represent the interoperability of component i to component j (information flow is i→j), use Γ. e H represents the set of all adjacent components of j in the system. i→j Let represent the number of paths through which information flows from adjacent component i to component j. Then, for component i, j:

[0024] Where H l→j H represents the number of transmission paths from any adjacent component l to component j in the system. i→j This represents the number of paths from adjacent component i to component j; the formula shows that the interoperability of component i to j depends on the degree to which j receives the load from i, and the higher the degree of reception, the stronger the interoperability.

[0025] For interoperable components i and j, the transmission of risk depends not only on i as the source of failure, but also on j's ability to resist the risk transmitted by i. That is, in the case of information flow error, j has the ability to maintain the risk level without escalation. This ability is called the resistance of j. The resistance coefficient r is the probability that the component can maintain its own risk level when an error or failure occurs in the previous stage, which represents the degree of resistance of j to risk transmission.

[0026] 2.2 The resistance coefficient r is negatively correlated with component interoperability, positively correlated with component reliability, and positively correlated with unavailability. The formula for the resistance coefficient r is:

[0027] Where R(t) represents the reliability of the component at time t, and D ij This indicates the interoperability between component i and component j;

[0028] We can obtain r(t, D) ij The range of ) is To ensure that the range of r for all transmission components is ultimately between (0, 1), a correction factor is multiplied by the original formula, resulting in: Let C be the minimum interoperability among the system components, i.e., D. min The transition matrix R is determined using the resistance coefficient r. i→j For specific values, take an n-order matrix as an example;

[0029]

[0030] Where P ij The probability that the state i of the previous component triggers the state j of the next component;

[0031] Analysis shows that the first row of the matrix represents the state of the previous component when it is working normally. Therefore, P(i>j) is only related to the state of the component itself. Since the risk cannot be eliminated or downgraded, P... ij =0 (i>j), P nn =1; the first row of the matrix is ​​the state when the previous component is working normally, so P ij (i>j) only depends on the state of the component itself and is a known quantity; for the rest of P ij (i≤j, 1<i<n), can be calculated based on the resistance coefficient r:

[0032]

[0033] Preferably, step three specifically includes:

[0034] 3.1 Based on the component's own reliability variation function R over time (t) The state transition matrix R between components i→j The final state distribution of the component [R′] is obtained. (t) ]:

[0035] [R′ (t) ] = R (t) *R i→j

[0036] Random computation represents a signal using a fixed-length bit sequence, so that operations between the probability values ​​expressed by the signal can be achieved through operations on their corresponding bit sequences;

[0037] The final state distribution of each component [R′] (t)The sequence is transformed into S = [s1, s2, ..., s3], where s3 represents the unreliable component, and the proportion is the final state distribution [R′]. (t) In the diagram, R′3;s2 represents defective components, and the percentage is the final state distribution R′. (t) In the diagram, R′2; s1 represents the reliability of a component, and the percentage is the final state distribution [R′ (t) R′1 in ];

[0038] By randomly selecting the final state of each component, several final state distribution matrices of the system are obtained. Based on the physical structure of the system, the reliability sequence S' = [x1, x2, ..., x3] of the system is calculated, where the proportion of x1 is the probability of the system working normally, the proportion of x2 is the probability of the system working malfunctioning, and the proportion of x3 is the probability of the system failing. The reliability of the system is the sum of the proportion of normal operation and the proportion of malfunctioning.

[0039] 3.2 Cost of Preventive Maintenance Strategy: Under the premise of ensuring the system does not affect the safety of train crew and the economic benefits of the railway, all costs related to preventive maintenance, including inspections, component replacements, and manual operations, are calculated within a set time period Δt. The following assumptions are made: each inspection will definitely find a problem, and the inspection time is t; after maintenance, the risk level of a component will not decrease to 0, but will return to a previous working state; its service life will be reduced by αt, and its failure rate will return to the time before maintenance (1-α)t, where (1-α) is the residual factor, (1-α)t is called the residual service life, and the component's state also has no aftereffect; component failures in the system (inability to transmit information, transmission of incorrect information, etc.) will inevitably lead to system failure.

[0040] Scheduled maintenance involves inspecting all components. When the system's reliability curve approaches the most sensitive component, i.e., when the most sensitive component reaches the safety threshold, a comprehensive overhaul of the system is required. The maintenance cost includes the cost of inspecting each component and the cost of replacing faulty or obviously faulty components.

[0041] The beneficial effects of this invention are as follows:

[0042] According to the hidden Markov model provided by the present invention, the interoperability between system components can be quantified and applied to reliability calculation and maintenance strategy optimization. When the overall system reliability is lower than the threshold, a decision is made to repair the component with the lowest ratio of usage time to maintenance cost and update its reliability curve. When the curve reaches the threshold, the system reliability assessment continues, thereby saving maintenance costs and achieving the purpose of accurate maintenance, and verifying the effectiveness of interoperability between components. Attached Figure Description

[0043] Figure 1A flowchart illustrating a method for calculating the dynamic reliability of an electromechanical system based on inter-component interoperability, provided in an embodiment of the present invention;

[0044] Figure 2 A connection diagram of an electrical system component is provided for an embodiment of the present invention to illustrate a method for calculating the dynamic reliability of an electromechanical system based on inter-component interoperability.

[0045] Figure 3 This invention provides a comparison of system reliability variation diagrams for a method of calculating the dynamic reliability of an electromechanical system based on inter-component interoperability, as provided in an embodiment of the invention.

[0046] Figure 4 This is a comparison chart of cumulative system maintenance costs for a method for calculating the dynamic reliability of an electromechanical system based on inter-component interoperability, provided in an embodiment of the present invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. The embodiments of the present invention are not limited thereto.

[0048] Example 1

[0049] like Figure 1 As shown, a method for calculating the dynamic reliability of an electromechanical system based on inter-component interoperability includes the following steps:

[0050] Step 1: Based on the physical structure of the complex electromechanical system, construct a hidden Markov model for risk transmission and calculate the risk transmission state matrix between components.

[0051] Step 2: Apply the load effect to calculate the interoperability and resistance coefficients between system components, and calculate the probability that the risk level of a component will not escalate after risk transmission.

[0052] Step 3: Apply the interoperability of the system, use random computation to calculate the final state sequence of the system, calculate the reliability of the system, and propose an improved maintenance strategy and compare it with the traditional maintenance strategy.

[0053] Step one specifically includes:

[0054] 1.1 Based on the physical structure of the complex electromechanical system, a hidden Markov model composed of various nodes is established, and the node v a Define the state matrix: A = [a1, a2, ..., a3] n ], where a i Represents node v a In the probability of state i, the magnitude of i represents the severity of the risk. The larger the value of i, the more severe the risk. When i = n, the risk causes a failure.

[0055] For node v a To node v b Transmitting risk status, defined as: B a→b =A·R a→b , where R a→b For node v a to node v b Risk transmission matrix, B a→b This indicates that at node v a Affecting the next node v b The state matrix is ​​abbreviated as B; for the risk state transfer matrix of a single path such as A→B→…→F, we have: A·R a→b ·...·R e→f =F, that is: F = R·ΠR;

[0056] Where A represents node v a The state matrix, R a→b For node v a to node v b Risk transmission matrix, R e→f Represents node v e to node v f The risk transmission matrix, F represents the risk transmission matrix of node v. f The state matrix;

[0057] For the scenario of risk propagation from multiple nodes to a single node, two operations are defined based on the risk state type and intensity:

[0058] The ⊙ operation: Given rows and k columns of matrices A, B, and C, satisfying A = B⊙C, that is...

[0059]

[0060] Among them, a i Let b represent the i-th element in matrix A. i b j Let c represent the i-th and j-th elements in matrix B. i c j This represents the i-th and j-th elements in matrix C;

[0061] Operations: Suppose there are k-row matrices A, B, and C that satisfy... Then a i =∑ m+n＝i+1 b m ·c n (i < k), a k =∑ m+n＞k b m ·c n ;

[0062] Among them, a i Let b represent the i-th element in matrix A. m c represents the m-th element in matrix B. n Let m represent the nth element in matrix C, where m and n are any non-zero positive integers.

[0063] 1.2 Establish a state matrix for risk transmission from multiple nodes to a single node, such as node v a v b To node v c When transmitting risk, we have: C a→c =A·R a→c and C b→c =A·R b→c When the risk status types are the same, then C ab→c =C a→c ⊙C b→c When the risk status types are different, then Among them, C a→c For v a to v c Risk state transmission matrix, where A represents node v a The state matrix, C ab→c Represents node v a With node v b to node v c The risk transmission matrix;

[0064] When there are multiple nodes such as v a v b ... v e v f ..., v i v j Directly to node v g When transmitting risk, if there is a v a v b ... v e The risk status type is the same, v e v f ... v i v j Different types of risk states have Where G represents the distance from each node to v g The risk state transmission matrix, G a→g G b→g G e→g G f→g G i→g G j→g They represent nodes v respectively a v b v e v fv i v j to node v g The risk transmission matrix.

[0065] Step two specifically includes:

[0066] 2.1 Based on load balancing, when quantifying the degree of mutual influence between components, the amount of information flow is used as an important criterion. For component j (node ​​v) j It receives information streams from multiple functions, using one of its components i (node ​​v) i The proportion of information flow i to total information flow j can represent the degree of correlation between i and j; when all information j comes from i, it means that the interoperability coefficient between i and j is 1, that is, when i fails, the probability of j failing is higher.

[0067] With D ij To represent the interoperability of component i to component j (information flow is i→j), use Γ. e H represents the set of all adjacent components of j in the system. i→j Let represent the number of paths through which information flows from adjacent component i to component j. Then, for component i, j:

[0068] Where H l→j H represents the number of transmission paths from any adjacent component l to component j in the system. i→j This represents the number of paths from adjacent component i to component j; the formula shows that the interoperability of component i to j depends on the degree to which j receives the load from i, and the higher the degree of reception, the stronger the interoperability.

[0069] For interoperable components i and j, the transmission of risk depends not only on i as the source of failure, but also on j's ability to resist the risk transmitted by i. That is, in the case of information flow error, j has the ability to maintain the risk level without escalation. This ability is called the resistance of j. The resistance coefficient r is the probability that the component can maintain its own risk level when an error or failure occurs in the previous stage, which represents the degree of resistance of j to risk transmission.

[0070] 2.2 The resistance coefficient r is negatively correlated with component interoperability, positively correlated with component reliability, and positively correlated with unavailability. The formula for the resistance coefficient r is:

[0071] Where R(t) represents the reliability of the component at time t, and D ij This indicates the interoperability between component i and component j;

[0072] We can obtain r(t, D) ij The range of ) is To ensure that the range of r for all transmission components is ultimately between (0, 1), a correction factor is multiplied by the original formula, resulting in: Let C be the minimum interoperability among the system components, i.e., D. min The transition matrix R is determined using the resistance coefficient r. i→j For specific values, take an n-order matrix as an example;

[0073]

[0074] Where P ij The probability that the state i of the previous component triggers the state j of the next component;

[0075] Analysis shows that the first row of the matrix represents the state of the previous component when it is working normally. Therefore, P(i>j) is only related to the state of the component itself. Since the risk cannot be eliminated or downgraded, P... ij =0 (i>j), P nn =1; the first row of the matrix is ​​the state when the previous component is working normally, so P ij (i>j) only depends on the state of the component itself and is a known quantity; for the rest of P ij (i≤j, 1<i<n), can be calculated based on the resistance coefficient r:

[0076]

[0077] Step three specifically includes:

[0078] 3.1 Based on the component's own reliability variation function R over time (t) The state transition matrix R between components i→j The final state distribution of the component [R′] is obtained. (t) ]:

[0079] [R′ (t) ] = R (t) *R i→j

[0080] Random computation represents a signal using a fixed-length bit sequence, so that operations between the probability values ​​expressed by the signal can be achieved through operations on their corresponding bit sequences;

[0081] The final state distribution of each component [R′] (t) The sequence is transformed into S = [s1, s2, ..., s3], where s3 represents the unreliable component, and the proportion is the final state distribution [R′]. (t) In the diagram, R′3;s2 represents defective components, and the percentage is the final state distribution R′. (t) In the diagram, R′2; s1 represents the reliability of a component, and the percentage is the final state distribution [R′ (t)R′1 in ];

[0082] By randomly selecting the final state of each component, several final state distribution matrices of the system are obtained. Based on the physical structure of the system, the reliability sequence S' = [x1, x2, ..., x3] of the system is calculated, where the proportion of x1 is the probability of the system working normally, the proportion of x2 is the probability of the system working malfunctioning, and the proportion of x3 is the probability of the system failing. The reliability of the system is the sum of the proportion of normal operation and the proportion of malfunctioning.

[0083] 3.2 Cost of Preventive Maintenance Strategy: Under the premise of ensuring the system does not affect the safety of train crew and the economic benefits of the railway, all costs related to preventive maintenance, including inspections, component replacements, and manual operations, are calculated within a set time period Δt. The following assumptions are made: each inspection will definitely find a problem, and the inspection time is t; after maintenance, the risk level of a component will not decrease to 0, but will return to a previous working state; its service life will be reduced by αt, and its failure rate will return to the time before maintenance (1-α)t, where (1-α) is the residual factor, (1-α)t is called the residual service life, and the component's state also has no aftereffect; component failures in the system (inability to transmit information, transmission of incorrect information, etc.) will inevitably lead to system failure.

[0084] Scheduled maintenance involves inspecting all components. When the system's reliability curve approaches the most sensitive component, i.e., when the most sensitive component reaches the safety threshold, a comprehensive overhaul of the system is required. The maintenance cost includes the cost of inspecting each component and the cost of replacing faulty or obviously faulty components.

[0085] Example 2

[0086] Given an electrical system such as Figure 2 As shown, it consists of 6 components with known lifespans and complete repair costs (as shown in the table below). Assume that the failure rates of all components follow an exponential distribution, and that the cost of inspecting each component is 50 yuan.

[0087]

[0088] Taking the working status on the twentieth day as an example, calculate the working status of each component, and the failure rate and reliability of each component when working independently (as shown in the table below).

[0089]

[0090] The state distribution of each component in the system at this time is shown in the table below.

[0091]

[0092] The interoperability of components i to j is calculated based on the component topology (as shown in the table below).

[0093]

[0094] Calculate the resistance coefficients of components i to j based on their state and topology (as shown in the table below).

[0095]

[0096] Calculate the state transition matrix of the internal components of the system (as shown in the table below).

[0097]

[0098] Based on the independent working state, resistance coefficient, and state transition matrix, the final working state of each component is obtained (as shown in the table below).

[0099]

[0100] According to random calculations, the reliability of the entire system in this operation is 0.8436999565916573, indicating that maintenance is required.

[0101] Maintenance was performed with a residual factor of (1-α) = 0.05, and the results are as follows: Figure 3 As shown: Strategy 1 is the strategy proposed in this invention, and Strategy 2 is the classic maintenance strategy. Both maintenance strategies can maintain the system reliability at a high level. This is because Strategy 1 considers the coordination between components to arrive at the system reliability, while Strategy 2 simply approximates the reliability of the most sensitive component in the system. Therefore, Strategy 2 can maintain the system reliability at a slightly lower level than Strategy 1.

[0102] The cumulative maintenance cost of the system is shown in the figure below. Figure 4 As shown, the maintenance of Strategy 1 is unpredictable and depends on the overall reliability of the system. It does not require maintenance of all components at once, as the maintenance of components is determined by the program algorithm. It does not require additional inspection of other components, thus avoiding increased labor costs. Therefore, it is superior to the classic strategy in the long run.

[0103] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the processes depicted in the drawings are not necessarily essential for implementing the present invention.

Claims

1. A method for calculating the dynamic reliability of an electromechanical system based on inter-component interoperability, characterized in that, It comprises the following steps: Step one, according to the physical structure of complex electromechanical system, construct the hidden Markov model of risk transmission, and calculate the risk transmission state matrix between components; Step two, apply load effect, calculate the interoperability and resistance coefficient between system components, and calculate the probability that the risk level of components does not upgrade after risk transmission; Step three, apply the interoperability of the system, calculate the final state sequence of the system using random calculation, calculate the reliability of the system, and compare the improved maintenance strategy with the traditional maintenance strategy; Wherein, Step two specifically comprises: Step S21 According to load balancing, when quantifying the degree of mutual influence between components, the number of information flow is an important basis, for component j, it receives information flow from multiple functions, and the proportion of the information flow of a certain component i in the total information flow received by j can represent the correlation degree between i and j; When all the information of j comes from i, it means that the interoperability coefficient of i and j is 1, that is, the higher the possibility of j failure when i fails; D ij represents the interoperability of component i with component j, with represents the set of all neighboring components of j in the system, represents the number of paths that neighboring component i transmits information flows to component j, then for component i, j, then: ； wherein represents the number of transmission paths in the system from any adjacent component i to component j, represents the number of paths from adjacent component i to component j; the formula indicates that the interoperability of component i with j depends on the degree of load reception by j from i, the higher the reception degree the stronger the interoperability; For components i and j with interoperability, the transmission of risk depends not only on i as the source of failure, but also on the resistance of j to the risk transmitted by i, that is, in the case of information flow transmission error, j has the ability to maintain the risk level, which is called the resistance of j, and the resistance coefficient r is the probability that the component can maintain its own risk state level unchanged when the previous stage occurs error or failure, which represents the resistance degree of j to risk transmission; Step S22 The resistance coefficient r is negatively correlated with the component interoperability, positively correlated with the reliability of the component, and positively correlated with the unavailability, and the resistance coefficient r is calculated according to the formula: ; where R(t) represents the reliability of the component at time t, D ij represents the interoperability of component i with component j; r(t, ) is in the range of (0, ), to ensure that all the transfer components of r in the end in the range of (0, 1), the original formula multiplied by a correction factor, finally get: , take C as the smallest interoperability in the system components, that is ; through the resistance coefficient , determine the specific value of the transfer matrix , for example, n order matrix; wherein is the state of the previous component initiates the state of the next component the probability of By analysis, the first row of the matrix is the state of the previous component when it is working normally, so only related to the state of the component itself, and the risk cannot be eliminated or degraded, so , ; the first row of the matrix is the state of the previous component when it is working normally, so only related to the state of the component itself, and is a known quantity; for the remaining , according to the resistance coefficient can be calculated: 。 2. A method for dynamic reliability computation of an electromechanical system based on inter-component interoperability as claimed in claim 1, wherein, Step one specifically comprises: Step S11: Establishing a hidden Markov model composed of nodes according to the physical structure of the complex electromechanical system, and determining the probability of each node Define the state matrix: Wherein represents the node In the state The probability of The size of the risk severity, The greater the value, the more serious the risk, when The risk triggers a failure; For a node To a node Passing the risk state, define: where For a node To a node The risk passing matrix, denotes the state matrix of the node under the influence of the node , which is simply written as ; for a single path risk state passing matrix as , there is: that is: ; wherein, a state matrix of a node , a risk transfer matrix from a node to a node , 𝑒→𝑓 . a risk transfer matrix from a node v e to a node v f , F a state matrix of a node v f ; For the risk transmission from multiple nodes to a single node, according to the different risk state types and intensities, two operations are defined: ⊙ operation, there is a row k column matrix , , satisfy = , that is , 1≤i≤k; where a i represents the i-th element in matrix A, b i , b j represents the i, j-th element in matrix B, c i , c j represents the i, j-th element in matrix C; ⊕ operation, there is a row k column matrix , , satisfies = then , ; wherein a i represents the ith element in matrix A, b m represents the mth element in matrix B, c n represents the nth element in matrix C, m, n are any non-zero positive integers; Step S12 establishes a state matrix of multi-node to single-node risk transfer, such as 、 When transferring risks to the node , there are: and When the risk state types are the same, then ; when the risk state types are different, then , wherein, is a risk state transfer matrix from to , When there are multiple nodes like directly passing risk to the node , if there are risk status types same, risk status types different, then there are , where, is the risk status passing matrix of each node to .

3. The method of claim 1, wherein the method is based on inter-component interoperability of the electromechanical system. Step three specifically comprises: Step S31 derives the reliability change function of the component itself over time with the state transition matrix between components to obtain the final state distribution of the components : Random calculation is to express the signal with a string of fixed length bit sequence, so that the operation between the probability values expressed by the signal can be realized through the operation of the corresponding bit sequence; Final state distribution of each component is converted into a sequence S = [s 1， 2, …, s3], where s3 represents a component that is unreliable, with a proportion of the final state distribution s2 represents a component that is defective, with a proportion of the final state distribution s1 represents a component that is reliable, with a proportion of the final state distribution ​​​​ Randomly select the final state of each component to obtain a number of final state distribution matrices of the system, and calculate the reliability sequence S'=[x1, x2, …, x3] of the system according to the physical structure of the system, wherein the proportion of x1 is the probability of normal operation of the system, the proportion of x2 is the probability of poor operation of the system, and the proportion of x3 is the probability of failure of the system; The reliability of the system is the sum of the proportion of normal operation and the proportion of poor operation; Step S32: Cost of preventive maintenance strategy: all the costs of inspection, component replacement, and manual operation for preventive maintenance within a certain period of time, provided that the system does not affect the safety of train crew and the economic benefits of the railway , are set: each inspection must find existing problems, and the inspection time is t; after maintenance, the risk of the component does not decrease to 0, but returns to a certain working state before; the amount of service life regression is , and the failure rate returns to before maintenance, where is a residual factor, , is called residual service life, and the state of the component also has no aftereffect; the failure of a component in the system must lead to the failure of the system; Periodic maintenance is to overhaul all components, and the reliability curve of the system tends to the most sensitive component, that is, when the most sensitive component reaches the safety threshold, the system needs to be overhauled, and the maintenance cost is the cost of checking each component and replacing the components with obvious failure trend.

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