A reliability calculation method for a multi-state system equipped with protection devices

Abstract

The present invention proposes a reliability calculation method for a multi-state system equipped with a protection device. The method includes determining the arrival rate of impacts from different sources during the operation of the multi-state system based on historical information of the multi-state system. Degradation rules are derived based on the internal degradation rates of components and protection devices in each subsystem of the multi-state system and the degradation conditions after being subjected to effective external environmental impacts. A state transition rate matrix is ​​obtained for each subsystem when the protection device is operating in different states, thereby obtaining the reliability function of each subsystem in the multi-state system and the probability of each subsystem being in each state. Based on the probability of each subsystem being in each state, a probability function for the satisfaction of each subsystem's requirements is obtained using a universal generating function method. The universal generating function method is then used to determine the number of subsystems in the multi-state system whose requirements are satisfied. The reliability of the multi-state system is then calculated based on the number of subsystems whose requirements are satisfied. This method enables more accurate calculation of the reliability of a multi-state system equipped with a protection device.

Description

Technical Field

[0001] The invention belongs to the field of system reliability calculation, and particularly discloses a reliability calculation method for a polymorphic system equipped with a protection device.

[0002] Background

[0003] Systems operating in complex environments are inevitably affected by the external environment and may degrade. System failures can lead to serious consequences, such as mission interruption and economic loss. To improve system reliability and extend their lifespan, protective devices are often installed to mitigate degradation. These devices are currently used in a variety of systems, such as pumping and discharge line protection devices, accumulator buffers in hydraulic systems, and protective relays in power systems. Depending on the specific situation, protective devices have different protection mechanisms. For example, under the influence of shocks, auxiliary components can partially protect primary components from external impacts; in multi-state systems, protective devices can reduce external damage to the system through defense factors; multi-state protective devices can improve system reliability by protecting the system from external shocks, and their protection capabilities are related to their state; in multi-component protective device systems, protective devices can reduce the probability of effective shocks, which has benefits for system recovery, and the protection level of the protective device is related to the number of active protective components.

[0004] In addition to the effects of shocks, systems may experience state degradation due to internal degradation. For example, in a system with two subsystems, the auxiliary subsystem protects the critical subsystem by mitigating its degradation. Systems protected by protection devices may also be affected by both internal degradation and external shocks. Furthermore, internal degradation may be affected by external shocks. For example, a shock can cause a sudden increase in the degradation level; from a performance perspective, a shock can have direct and indirect performance impairments, reflected in shortened state transition times. In addition to protection mechanisms based on the effects of external shocks and the internal degradation of components, there is another type of protection device that protects the system by isolating faulty components, such as overload protection relays in motors and protection relays in substations.

[0005] Existing technologies provide reliability analysis methods for systems equipped with protective devices that isolate faulty components. These methods also model the degradation process of the system under independent shocks and degradation conditions, and account for the potential for protective device activation failure, represented by a certain probability of activation failure. The system fails when the number of faulty and isolated components in the system reaches a threshold or when the faulty components are not successfully isolated. However, in actual engineering systems, the protective devices used to isolate faulty components can still trigger inadvertently, and existing technologies ignore this failure mode. Furthermore, internal degradation and external shocks in systems equipped with protective devices can interact, a relationship that is overlooked by existing technologies. Furthermore, there is no reliability modeling for systems protected by protective devices that aim to meet requirements. Therefore, a reliability analysis method for systems composed of multiple polymorphic demand-based subsystems is needed, where the protective devices account for two types of activation errors. To address these issues, it is necessary to develop a novel reliability calculation method for polymorphic systems equipped with protective devices to overcome the limitations of existing reliability analysis methods for systems equipped with protective devices. Summary of the Invention

[0006] The present invention proposes a reliability calculation method for a polymorphic system equipped with protection devices to solve the problems existing in existing reliability analysis methods for systems equipped with protection devices, such as incomplete research on protection mechanisms in systems equipped with protection devices, inability to solve the reliability of a system composed of multiple demand-based polymorphic subsystems equipped with protection devices, and failure to consider the relationship between internal degradation and external impact in existing models.

[0007] The present invention provides a method for calculating the reliability of a multi-state system equipped with a protection device, comprising the following steps:

[0008] S1. Determine the arrival rate of shocks from different sources during the operation of the multi-state system based on historical information of the multi-state system, derive degradation rules based on the internal degradation rates of components and protection devices in each subsystem of the multi-state system and their degradation after being subjected to effective external environmental shocks, and, using the degradation rules and a Markov process embedding method, derive a state transition rate matrix for each subsystem when the protection device operates in different states;

[0009] S2. The reliability function of each subsystem in the multi-state system is obtained according to the state transition rate matrix of each subsystem when the protection device is running in different states obtained in step S1;

[0010] S3. According to the reliability function of each subsystem obtained in step S2 and the state division criteria of the subsystem, the probability of each subsystem being in each state is obtained;

[0011] S4. Based on the probabilities of each subsystem being in each state obtained in step S3, the supply level of each subsystem in each state and the demand of each subsystem in each state are obtained, and a probability function of the demand satisfaction of each subsystem is obtained using a general generating function method;

[0012] S5. Based on the probability function of the satisfaction of the requirements of each subsystem obtained in step S4, the number of subsystems whose requirements are satisfied in the polymorphic system is obtained by a universal generating function method, and the reliability of the polymorphic system is obtained by the number of subsystems.

[0013] According to a reliability calculation method for a multi-state system equipped with a protection device in some embodiments of the present application, in step S1, the source impact includes source I and source II, the impact of source I affects the state of the component, and the effective impact of source II affects the state of the protection device;

[0014] The degradation rules include degradation rules of components and degradation rules of protection devices;

[0015] The degradation rule of the component includes failure of the component due to internal degradation or external impact from source I. The impact from source I includes type A impact, type B impact and type C impact according to the intensity. The type A impact has no effect on the component state, the type B impact causes the component state to deteriorate, and the type C impact causes the component to fail.

[0016] The degradation rules of the protection device include that the protection device ensures the normal operation of the subsystem by isolating the failed components from the subsystem. The protection device will undergo state transition due to internal degradation or external effective impact from source II. When the cumulative number of effective impacts received by the protection device reaches a threshold, the internal degradation rate of the protection device will accelerate. The startup errors of the protection device include startup failure and erroneous startup.

[0017] According to a reliability calculation method for a multi-state system equipped with a protection device in some embodiments of the present application, in step S1, the impact arrival rate of the source I is The impact arrival rate of source II is The probability of the type A shock from source I is The probability of the type B shock from source I is The B-type impact causes the component condition to deteriorate The probability of the C-type impact is The probability that the source II shock is a valid shock is The components in the polymorphic system are polymorphic components. The components in different subsystems are different. There are n components in subsystem i. i components, the normal internal degradation rate of the components is When the cumulative B-type shock reaches the threshold Internal degradation rate increases to in It represents the multiple of the internal degradation rate of the component in subsystem i based on the initial normal internal degradation rate;

[0018] The state of the subsystem i is divided according to the number of components in different states. The state space of the components in the subsystem i is Ω i ={0,1,...,u i}, where 0 is the failure state, u i Is the perfect working state, vector Contains the subsystem i in 0,1,...,u i The number of parts in each state, where Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components incorrectly isolated by the protection device in the subsystem i. When the number of components in state 0 in subsystem i reaches k i When Subsystem failure k i represents the failure threshold of subsystem i, The status of the components in the subsystem i is When , the state of the subsystem i, the working state of the subsystem i is divided into the following:

[0019] (1) When subsystem i is in u i The number of parts is not less than hour, Equal to u i ;

[0020] (2) When the number of components in subsystem i that is greater than or equal to state l is less than k i,l , where (j+1≤l≤u i ), and there are at least k i,j When the state of the components is not less than j, the state of the subsystem is j;

[0021] (3) When the number of components in subsystem i that are greater than or equal to state l is less than k i,l When (l=1,2,...,u i ), subsystem i fails;

[0022] In order to ensure that all possible component state combinations in subsystem i have corresponding subsystem states and avoid repeated state divisions in subsystem i, k i,1 =n i -k i +1,

[0023] The state space of the protection device in the multi-state system is Where 0 is the failure state, g i is the optimal working state of the i-th protection device. The protection device ensures the normal operation of the subsystem by isolating the failed components from the subsystem. The internal degradation rate of the protection device is The protective device degrades after receiving an effective impact When the cumulative number of effective impacts received by the protection device reaches When the internal degradation rate of the protection device becomes in It represents the multiple of the internal degradation rate of the protection device in subsystem i increased on the basis of the initial normal internal degradation rate, and the protection device is in state o during operation. i The probability Successful start, with probability Failed to start, o i Indicates the status of the i-th protection device, o i ∈{0,1,...,g i}, the protection device is in state o i The maximum number of startup attempts under The protection device is in state o i The probability of being started incorrectly is When the shock to the subsystem is type A, the probability that the protection device mistakenly isolates a normally functioning component in the subsystem is When the subsystem is subjected to a Type B shock, the state of the component will be degraded but will not fail, and the component with the degraded state will be mistakenly isolated by the protection device.

[0024] According to a method for calculating reliability of a multi-state system equipped with a protection device in some embodiments of the present application, in step S1, a random point process {X i (t),t≥0}, y i =1,2,...,Y i , X i (t) represents the state of subsystem i at time t, represents the yth subsystem i i possible states, Yi represents the total number of possible states of subsystem i, where Contains(u i +4) random variables, among which Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components incorrectly isolated by the protection device. The cumulative number of B-type shocks suffered by the subsystem i is given by Indicates that i represents the state of the i-th protection device, is the total number of effective impacts received by the protection device. The multi-state system consists of m subsystems. When the number of subsystems whose requirements are not met reaches k, the multi-state system fails. The transition rules between the states of the subsystem i are as follows:

[0025] Scenario 1: Degradation of the i-th protection device:

[0026] (1) For i = 1, 2, ..., m, if 0<o1≤o i ≤g i ,

[0027] The state transition is:

[0028]

[0029] The state transition rate is:

[0030] (2) For i = 1, 2, ..., m, if 0<o1≤o i ≤g i ,

[0031] The state transition is:

[0032]

[0033] The state transition rate is:

[0034] (3) For i = 1, 2, ..., m, if

[0035] The state transition is;

[0036]

[0037] The state transition rate is

[0038] (4) For i = 1, 2, ..., m, if

[0039] The state transition is:

[0040]

[0041] The state transition rate is: represents the impact arrival rate of source II;

[0042] Scenario 2: Component degradation without component failure:

[0043] (5) For i = 1, 2, ..., m, if 0<α<β≤u i , α represents the state of the component after degradation, and β represents the state of the component before degradation. represents the cumulative B-type shock threshold that causes an increase in the internal degradation rate of components in subsystem i;

[0044] The state transition is:

[0045]

[0046] The state transition rate is: represents the number of components in subsystem i in state β before state transition;

[0047] (6) For i = 1, 2, ..., m, if 0<α<β≤u i ,

[0048] The state transition is:

[0049]

[0050] The state transition rate is:

[0051] (7) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0052] The state transition is:

[0053]

[0054] The state transition rate is: represents the impact arrival rate of source I;

[0055] Scenario 3: The number of components in state 0 increases due to internal degradation, external shocks, and false activation of protection devices:

[0056] (8) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0057] The state transition is:

[0058]

[0059] The state transition rate is:

[0060] (9) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0061] The state transition is:

[0062]

[0063] The state transition rate is:

[0064] (10) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0065] The state transition is:

[0066]

[0067] The state transition rate is: represents the internal degradation rate of the component in subsystem i from state β to state 0;

[0068] (11) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0069] The state transition is:

[0070]

[0071] The state transition rate is:

[0072] Scenario 4: Since the number of components in state 0 reaches the failure threshold k i The subsystem i fails as a result of:

[0073] (12) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0074] The state transition is:

[0075] F i represents the failure state of subsystem i;

[0076] The state transition rate is: represents the value of the component state degradation in subsystem i caused by the B-type shock;

[0077] (13) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0078] The state transition is:

[0079]

[0080] The state transition rate is:

[0081] Scenario 5: Failure of the i-th subsystem due to failure of the protection device to activate and isolate the failed component:

[0082] (14) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0083] The state transition is:

[0084]

[0085] The state transition rate is:

[0086] (15) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0087] The state transition is:

[0088]

[0089] The state transition rate is:

[0090] Scenario 6: In the case of failure of both the component and the protection device, the subsystem i fails:

[0091] (16) For i = 1, 2, ..., m, if 0<β≤u i ,0<β≤u i , o i =0;

[0092] The state transition is:

[0093]

[0094] The state transition rate is:

[0095] (17) For i = 1, 2, ..., m, if 0<β≤u i , o i =0;

[0096] The state transition is:

[0097]

[0098] The state transition rate is:

[0099] According to a method for calculating the reliability of a multi-state system equipped with a protection device in some embodiments of the present application, in step S2, the reliability function of the subsystem is as shown in formula (1):

[0100]

[0101] Among them, R i (t) represents the reliability function of subsystem i at time t, represents the initial state probability distribution, W i represents the set of all working states of subsystem i, The transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |'s one-step transfer rate matrix, I i It represents the identity matrix corresponding to the number of working states of subsystem i, and T represents the transpose.

[0102] According to a method for calculating reliability of a multi-state system equipped with a protection device in some embodiments of the present application, in step S3, the i-th subsystem has |Wi | possible transition states, the yth i Among the possible states, the number of parts in state b is The function getnum(W,l) is used to get the lth element in the vector W, (l=1,2,...,u i ), matrix B i,b Indicates the transition from state b to state u in subsystem i i The number of all components with a given threshold k i,b The relationship between B i,b Size is |W i |×1, is the matrix B i,b yth i elements, where (y i =1,2,…,|W i |), The value of is shown in formula (2):

[0103]

[0104] The probability of the subsystem i being in each transition state is shown in formula (3):

[0105]

[0106] in, represents the probability that subsystem i is in each transition state,

[0107] The probability of the subsystem i being in each state is shown in formula (4):

[0108]

[0109] in, represents the probability of subsystem i being in each state, r1 represents the state of subsystem i, r1∈(1,2,…,u i ), Indicates the transition from state b to state u in subsystem i i -1 the number of all components with a given threshold k i,b The relationship between B i,1 Represents the number of all components in subsystem i from state b to state 1 and the given threshold k i,b The relationship between them.

[0110] According to a reliability calculation method for a multi-state system equipped with a protection device in some embodiments of the present application, in step S4, the demand satisfaction status of the subsystem i in each state is as shown in formula (5):

[0111]

[0112] Among them, it means Indicates the demand satisfaction of subsystem i in state r1, represents the supply of subsystem i in state r1, The supply quantity of subsystem i in state r1 is β i represents the total number of all possible requirements for subsystem i, represents the probability corresponding to the r2th possible demand in subsystem i, represents the r2th possible demand in subsystem i, The difference between the supply and the possible demand of subsystem i in state r1 is represents the r0th difference between the supply and demand of subsystem i, represents the probability corresponding to the r0th difference between the supply and demand of subsystem i,

[0113] The probability of undersupply of subsystem i is shown in formula (6):

[0114]

[0115] in, represents the probability of insufficient supply of subsystem i, when When true, is 1, When it is false, is equal to 0,

[0116] The probability that the requirements of subsystem i are met is shown in formula (7):

[0117]

[0118] in, represents the probability that the requirements of subsystem i are met,

[0119] The probability function of the subsystem i's requirement satisfaction is shown in formula (8):

[0120]

[0121] in, The probability function of subsystem i's requirement satisfaction, z r Indicates the satisfaction of demand, z 0 It means that supply is less than demand, and demand is not met. 1 It means that supply is greater than or equal to demand, and demand is met;

[0122] According to a reliability calculation method for a multi-state system equipped with a protection device in some embodiments of the present application, in step S5, the probability function of the demand satisfaction of the multi-state system is shown in formula (9):

[0123]

[0124] in, The probability function of the polymorphic system's demand satisfaction is represented by H, which represents the maximum number of subsystems whose demand is satisfied, H = m, h represents the number of subsystems whose demand is satisfied, h∈(0,1,...,H), π h represents the probability of the number of subsystems whose requirements are met, z h The number of subsystems whose requirements are met is h,

[0125] The reliability of the multi-state system is shown in formula (10):

[0126]

[0127] Among them, R s (t) represents the reliability of the polymorphic system, and k represents the failure of the system when the number of subsystems whose requirements are not met reaches k.

[0128] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program; the processor is configured to execute the computer program in the memory to implement the above method.

[0129] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above method when executed by a processor.

[0130] The present invention proposes a method for calculating the reliability of a polymorphic system equipped with protective devices. The polymorphic system of the present invention is composed of polymorphic subsystems under multiple protective devices. The method fully considers the situation where the protective device fails to start, as well as the relationship between internal degradation and external impacts of the polymorphic system. It is used to solve the problems in existing reliability calculation methods, such as incomplete research on protection mechanisms in systems equipped with protective devices, inability to solve the system reliability composed of multiple demand-based polymorphic subsystems equipped with protective devices, and the failure of existing models to consider the relationship between internal degradation and external impacts. The present method can more accurately calculate the reliability of a polymorphic system equipped with protective devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0131] Figure 1 A schematic flow chart of a reliability calculation method for a multi-state system equipped with a protection device according to the present invention;

[0132] Figure 2 Graph showing the reliability functions of the three subsystems under different relay false-touch probabilities in Example 3 of the present invention;

[0133] Figure 3 Graph showing the reliability function of a multi-state system with three subsystems under different relay startup failure probabilities in Example 3 of the present invention;

[0134] Figure 4 Graph showing the reliability function of the system under different failure thresholds of subsystem 1 in Example 3 of the present invention;

[0135] Figure 5 Graph showing the reliability function of a multi-state system under different fault thresholds in Example 3 of the present invention;

[0136] Figure 6 Graph showing the reliability function of a multi-state system under different demand probability distributions in Example 3 of the present invention. DETAILED DESCRIPTION

[0137] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0138] It should be noted that the terms "including," "having," and any variations thereof in the embodiments and drawings of this application are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to the process, method, product, or apparatus.

[0139] Example 1: This example provides a method for calculating the reliability of a multi-state system equipped with a protection device. Figure 1 As shown, the following steps are included:

[0140] S1. Determine the arrival rate of shocks from different sources during the operation of the multi-state system based on the historical information of the multi-state system. Determine the degradation rules based on the internal degradation rates of the components and protection devices in each subsystem of the multi-state system and their degradation after being subjected to effective external environmental shocks. Determine the state transition rate matrix of each subsystem when the protection device operates in different states using the degradation rules and the Markov process embedding method.

[0141] S2. The reliability function of each subsystem in the multi-state system is obtained according to the state transition rate matrix of each subsystem when the protection device is running in different states obtained in step S1;

[0142] S3. According to the reliability function of each subsystem obtained in step S2 and the state division criteria of the subsystem, the probability of each subsystem being in each state is obtained;

[0143] S4. Based on the probabilities of each subsystem in each state obtained in step S3, the supply level of each subsystem in each state and the demand of each subsystem in each state are obtained, and the probability function of the demand satisfaction of each subsystem is obtained using the general generating function method;

[0144] S5. Based on the probability function of the satisfaction of the requirements of each subsystem obtained in step S4, the number of subsystems whose requirements are satisfied in the polymorphic system is obtained by the general generating function method, and the reliability of the polymorphic system is obtained from the number of subsystems.

[0145] Example 2: This embodiment provides a method for calculating the reliability of a multi-state system equipped with a protection device, comprising the following steps:

[0146] S1. Determine the arrival rate of shocks from different sources during the operation of the multi-state system based on the historical information of the multi-state system. Determine the degradation rules based on the internal degradation rates of the components and protection devices in each subsystem of the multi-state system and their degradation after being subjected to effective external environmental shocks. Determine the state transition rate matrix of each subsystem when the protection device operates in different states using the degradation rules and the Markov process embedding method.

[0147] Specifically, the source impact includes source I and source II. The impact of source I affects the status of the component, and the effective impact of source II affects the status of the protective device.

[0148] Degradation rules include degradation rules for components and degradation rules for protection devices;

[0149] The degradation rules of components include failure due to internal degradation or external impact from source I. Source I impacts include type A impact, type B impact, and type C impact according to their intensity. Type A impact has no effect on the component state, type B impact causes the component state to deteriorate, and type C impact causes component failure.

[0150] The degradation rules of the protection device include: the protection device ensures the normal operation of the subsystem by isolating the failed component from the subsystem; the protection device will undergo state transition due to internal degradation or external effective impact from source II; when the cumulative number of effective impacts received by the protection device reaches the threshold, the internal degradation rate of the protection device will accelerate; the startup errors of the protection device include startup failure and false startup; when the protection device has a startup error, even if the corresponding protection device of the subsystem is running, the subsystem may still fail. The occurrence of both types of errors is related to the state of the protection device.

[0151] The impact arrival rate of source I is The impact arrival rate of source II is The probability of a type A shock from source I is The probability of a type B shock is Type B impact causes degradation of component condition The probability of a type C shock is The probability that the source II shock is a valid shock is The components in a polymorphic system are polymorphic components. The components in different subsystems are different. There are n components in subsystem i. i components, the normal internal degradation rate of the components is When the cumulative B-type shock reaches the threshold Internal degradation rate increases to in It represents the multiple of the internal degradation rate of the component in subsystem i based on the initial normal internal degradation rate;

[0152] The state of subsystem i is divided according to the number of components in different states. The state space of components in subsystem i is Ω i ={0,1,...,u i}, where 0 is the failure state, u i Is the perfect working state, vector Contains subsystem i in 0,1,...,u i The number of parts in each state, where Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components incorrectly isolated by protection devices in subsystem i. When the number of components in state 0 in subsystem i reaches k i When Subsystem failure k i represents the failure threshold of subsystem i, The state of the component in subsystem i is When , the state of subsystem i, the working state of subsystem i is divided into the following:

[0153] (1) When subsystem i is in u i The number of parts is not less than hour, Equal to u i ;

[0154] (2) When the number of components in subsystem i that is greater than or equal to state l is less than k i,l , where (j+1≤l≤u i ), and there are at least k i,j When the state of the components is not less than j, the state of the subsystem is j;

[0155] (3) When the number of components in subsystem i that are greater than or equal to state l is less than k i,l When (l=1,2,...,u i ), subsystem i fails;

[0156] In order to ensure that all possible component state combinations in subsystem i have corresponding subsystem states and avoid repeated state divisions in subsystem i, k i,1 =n i -k i +1,

[0157] The state space of the protection device in the multi-state system is Where 0 is the failure state, g i is the optimal working state of the i-th protection device. The protection device ensures the normal operation of the subsystem by isolating the failed components from the subsystem. The internal degradation rate of the protection device is The protective device degrades after receiving an effective impact When the cumulative effective impact number of the protective device reaches When the internal degradation rate of the protection device becomes in It represents the multiple of the internal degradation rate of the protection device in subsystem i based on the initial normal internal degradation rate. i The probability Successful startup, with probability Failed to start, o i Indicates the status of the i-th protection device, o i ∈{0,1,...,g i}, the protection device is in state o i The maximum number of startup attempts under The protection device is in state o i The probability of being started incorrectly is When the shock to the subsystem is type A, the probability that the protection device mistakenly isolates a normally functioning component in the subsystem is When a subsystem is subjected to a Type B shock, the component's condition will degrade but will not fail, and the component with the degraded condition will be mistakenly isolated by the protective device;

[0158] Define the random point process {X i (t),t≥0}, y i =1,2,...,Y i , X i (t) represents the state of subsystem i at time t, represents the yth subsystem i i possible states, Y i represents the total number of possible states of subsystem i, where Contains(u i +4) random variables, among which Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components incorrectly isolated by the protection device. The cumulative number of B-type shocks suffered by subsystem i is given by Indicates that i represents the state of the i-th protection device, is the total number of effective shocks received by the protection device. The polymorphic system consists of m subsystems. When the number of subsystems whose requirements are not met reaches k, the system fails. The transition rules between the states of subsystem i are as follows:

[0159] Scenario 1: Degradation of the i-th protection device:

[0160] (1) For i = 1, 2, ..., m, if 0<o1≤o i ≤g i ,

[0161] The state transition is:

[0162]

[0163] The state transition rate is:

[0164] (2) For i = 1, 2, ..., m, if 0<o1≤o i ≤g i ,

[0165] The state transition is:

[0166]

[0167] The state transition rate is:

[0168] (3) For i = 1, 2, ..., m, if

[0169] The state transition is;

[0170]

[0171] The state transition rate is

[0172] (4) For i = 1, 2, ..., m, if

[0173] The state transition is:

[0174]

[0175] The state transition rate is: represents the impact arrival rate of source II;

[0176] Scenario 2: Component degradation without component failure:

[0177] (5) For i = 1, 2, ..., m, if 0<α<β≤u i , α represents the state of the component after degradation, and β represents the state of the component before degradation. represents the cumulative B-type shock threshold that causes an increase in the internal degradation rate of components in subsystem i;

[0178] The state transition is:

[0179]

[0180] The state transition rate is: represents the number of components in subsystem i in state β before state transition;

[0181] (6) For i = 1, 2, ..., m, if 0<α<β≤u i ,

[0182] The state transition is:

[0183]

[0184] The state transition rate is: It represents the multiple of the internal degradation rate of the component in subsystem i based on the initial normal internal degradation rate;

[0185] (7) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0186] The state transition is:

[0187]

[0188] The state transition rate is: represents the impact arrival rate of source I;

[0189] Scenario 3: The number of components in state 0 increases due to internal degradation, external shocks, and false activation of protection devices:

[0190] (8) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0191] The state transition is:

[0192]

[0193] The state transition rate is:

[0194] (9) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0195] The state transition is:

[0196]

[0197] The state transition rate is:

[0198] (10) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0199] The state transition is:

[0200]

[0201] The state transition rate is: represents the internal degradation rate of the component in subsystem i from state β to state 0;

[0202] (11) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0203] The state transition is:

[0204]

[0205] The state transition rate is:

[0206] Scenario 4: Since the number of components in state 0 reaches the failure threshold k i Subsystem i failure caused by:

[0207] (12) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0208] The state transition is:

[0209] F i represents the failure state of subsystem i;

[0210] The state transition rate is: represents the value of the component state degradation in subsystem i caused by the B-type shock;

[0211] (13) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0212] The state transition is:

[0213]

[0214] The state transition rate is: Scenario 5: Failure of the i-th subsystem due to failure of the protection device to activate and isolate the failed component:

[0215] (14) For i = 1, 2, ..., m, if 0<o i ≤g i ;

[0216] The state transition is:

[0217]

[0218] The state transition rate is:

[0219] (15) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ;

[0220] The state transition is:

[0221]

[0222] The state transition rate is: Scenario 6: Subsystem i fails when both components and protection devices fail:

[0223] (16) For i = 1, 2, ..., m, if 0<β≤u i ,0<β≤u i , o i =0;

[0224] The state transition is:

[0225]

[0226] The state transition rate is:

[0227] (17) For i = 1, 2, ..., m, if 0<β≤u i , o i =0;

[0228] The state transition is:

[0229]

[0230] The state transition rate is:

[0231] S2. The reliability function of each subsystem in the multi-state system is obtained according to the state transition rate matrix of each subsystem when the protection device is running in different states obtained in step S1;

[0232] Specifically, the reliability function of the subsystem is shown in formula (1):

[0233]

[0234] Among them, Ri (t) represents the reliability function of subsystem i at time t, represents the initial state probability distribution, W i represents the set of all working states of subsystem i, The transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |'s one-step transfer rate matrix, I i represents the identity matrix corresponding to the number of working states of subsystem i, and T represents the transpose;

[0235] S3. According to the reliability function of each subsystem obtained in step S2 and the state division criteria of the subsystem, the probability of each subsystem being in each state is obtained;

[0236] Specifically, the i-th subsystem has |W i | possible transition states, the yth i Among the possible states, the number of parts in state b is The function getnum(W,l) is used to get the lth element in the vector W, (l=1,2,...,u i ), matrix B i,b Indicates the transition from state b to state u in subsystem i i The number of all components with a given threshold k i,b The relationship between B i,b Size is |W i |×1, is the matrix B i,b yth i elements, where (y i =1,2,...,|W i |), The value of is shown in formula (2):

[0237]

[0238] The probability of subsystem i being in each transition state is shown in formula (3):

[0239]

[0240] in, represents the probability that subsystem i is in each transition state,

[0241] The probability of subsystem i being in each state is shown in formula (4):

[0242]

[0243] in, represents the probability of subsystem i being in each state, r1 represents the state of subsystem i, r1∈(1,2,...,u i ), Indicates the transition from state b to state u in subsystem i i -1 the number of all components with a given threshold k i,b The relationship between B i,1 Represents the number of all components in subsystem i from state b to state 1 and the given threshold k i,b the relationship between;

[0244] S4. Based on the probabilities of each subsystem in each state obtained in step S3, the supply level of each subsystem in each state and the demand of each subsystem in each state are obtained, and the probability function of the demand satisfaction of each subsystem is obtained using the general generating function method;

[0245] Specifically, the demand satisfaction of subsystem i in each state is shown in formula (5):

[0246]

[0247] Among them, it means Indicates the demand satisfaction of subsystem i in state r1, represents the supply of subsystem i in state r1, The supply quantity of subsystem i in state r1 is β i represents the total number of all possible requirements for subsystem i, represents the probability corresponding to the r2th possible demand in subsystem i, represents the r2th possible demand in subsystem i, The difference between the supply and the possible demand of subsystem i in state r1 is represents the r0th difference between the supply and demand of subsystem i, represents the probability corresponding to the r0th difference between the supply and demand of subsystem i,

[0248] The probability of undersupply of subsystem i is shown in formula (6):

[0249]

[0250] in, represents the probability of insufficient supply of subsystem i, when When true, is 1, When it is false, is equal to 0,

[0251] The probability that the requirements of subsystem i are met is shown in formula (7):

[0252]

[0253] in, represents the probability that the requirements of subsystem i are met,

[0254] The probability function of the requirement satisfaction of subsystem i is shown in formula (8):

[0255]

[0256] in, The probability function of subsystem i's requirement satisfaction, z r Indicates the satisfaction of demand, z 0 It means that supply is less than demand, and demand is not met. 1 It means that supply is greater than or equal to demand, and demand is met;

[0257] S5. Based on the probability function of each subsystem's requirement satisfaction obtained in step S4, the number of subsystems whose requirements are satisfied in the polymorphic system is obtained by the universal generating function method, and the reliability of the polymorphic system is obtained by the number of subsystems;

[0258] Specifically, The probability function of the demand satisfaction of a multi-state system can be obtained by the following recursive steps:

[0259] Step (1): Let in, represents the demand satisfaction of the set Ω composed of subsystems, z 0 Indicates that supply is less than demand. At this time, the number of subsystems whose demands are met at the initial moment is 0;

[0260] Step (2): For i=1,2,...,n, repeat: Formula (9) And let Ω=Ω∪i.

[0261]

[0262] in, Indicates the satisfaction of the requirements of subsystem i, H Ω represents the maximum number of subsystems whose requirements are met in the set of subsystems Ω, π Ω,h represents the probability that the number of subsystems whose requirements are met in the set Ω of subsystems is h, represents the probability corresponding to the value r when the demand satisfaction of subsystem i is satisfied, HΩ∪i represents the maximum number of subsystems whose requirements are satisfied after subsystem i is incorporated into the set Ω, π Ω∪i,h represents the probability that the demand is satisfied when the number of subsystems is h after subsystem i is incorporated into the set Ω, z h+r The number of subsystems whose requirements are met is h+r, z h The number of subsystems whose requirements are met is h,

[0263] It can be obtained that the probability function of the requirements satisfaction of the polymorphic system is shown in formula (10):

[0264]

[0265] in, The probability function of the polymorphic system's demand satisfaction is represented by H, which represents the maximum number of subsystems whose demand is satisfied, and h, which represents the number of subsystems whose demand is satisfied, h∈(0,1,...,H). h It represents the probability corresponding to the number of subsystems whose requirements are met, so H = m,

[0266] According to the failure criterion of the multi-state system, the reliability of the multi-state system is shown in formula (10):

[0267]

[0268] Among them, R s (t) represents the reliability of the polymorphic system, and k represents the failure of the system when the number of subsystems whose requirements are not met reaches k.

[0269] This embodiment further provides an electronic device, including a memory and a processor, wherein the memory stores a computer program; the processor is configured to execute the computer program in the memory to implement the above method.

[0270] This embodiment further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above method is implemented.

[0271] Example 3. This embodiment provides a reliability calculation method for a multi-state system equipped with protection devices. The multi-state system is composed of multiple demand-based multi-state subsystems. This method addresses the problems in existing reliability calculation methods, such as incomplete research on protection mechanisms in systems equipped with protection devices, an inability to calculate the reliability of a multi-state system composed of multiple demand-based multi-state subsystems equipped with protection devices, and a failure of existing models to consider the relationship between internal degradation and external shocks. The reliability calculation method of this embodiment determines the state of a subsystem based on the number of components in each state in the subsystem, further determines the supply of the subsystem and the satisfaction of the subsystem's demands, and ultimately determines the reliability of the multi-state system. This method also considers the impact of external shocks on the internal degradation of components and protection devices, as well as two types of startup errors of protection devices.

[0272] This embodiment mainly uses the Markov process embedding method to describe the operation process of the subsystem, calculate the probability indicators related to the subsystem, and use the general generating function method to obtain the subsystem demand satisfaction and corresponding probability, as well as the reliability of the entire system. This embodiment method takes the wind turbine system as an example and specifically includes the following steps:

[0273] Step 1: Define the state of the components in the subsystem, the supply under different states, the demand set corresponding to the subsystem and its corresponding probability distribution, and the conditions for accelerated degradation. Taking the wind turbine system as an example, according to the relevant parameters of the wind turbine system, the wind turbine system is divided into three subsystems. The number of components in the three subsystems of the wind turbine system is 3, 2, and 3 respectively (n1=3, n2=2, n3=3). The optimal states of the components in the three subsystems are 2, 2, and 3 respectively. The threshold for the state division of the three subsystems is k 1,2 =2,k 1,1 =2,k 2,2 =2,k 2,1 =1,k 3,3 =2,k 3,2 =3,k 3,1 =2. For the three subsystems, the power supply of the wind turbine system in each state can be obtained from the following sets S1 = {0, 3, 7}, S2 = {0, 4, 6} and S3 = {0, 2, 5, 10}. The demand set of the wind turbine system and the corresponding probability of obtaining each demand are D1 = {2, 4, 5}, D2={3,6}, D3={2,7,9} and The arrival rate of the external shock from source I is Impact strength is For the three subsystems, the probabilities of the three types of shocks and the associated internal degradation rates are listed in Table 1. When the cumulative number of type B shocks reaches 2, 2, and 1, respectively, the internal degradation rates of the three subsystems accelerate. The corresponding acceleration factors are and in, Indicates that the shock to subsystem i is the threshold of type A shock. When the shock intensity is When , it is a type A shock, Indicates that the shock to subsystem i is the threshold of type B shock. When the shock intensity is When the impact strength is greater than or equal to When it is a C-type impact, represents the probability of a type A shock from source I, represents the probability of a type B shock from source I, represents the probability of a C-type shock, Indicates that the B-type impact causes the condition of the component to deteriorate. represents the degradation rate of the component from state 3 to state 2, represents the degradation rate of the component from state 3 to state 1, represents the degradation rate of the component from state 3 to state 0, represents the degradation rate of the component from state 2 to state 1, represents the degradation rate of the component from state 2 to state 0, Indicates the degradation rate of a component from state 1 to state 0.

[0274] Table 1. Parameters related to component degradation and shock effects in wind turbine systems

[0275]

[0276] Step 2: Define the state space of each protection device in the subsystem and the parameters related to the two types of startup errors. The state space of the relays in the three subsystems of the wind turbine system are and The arrival rate of the source II shock is Impact strength is For the three relays, the internal degradation rate is accelerated after receiving an effective shock. The parameters related to the internal degradation and impact of the relay are listed in detail in Table 2. Among them, Indicates that the impact on the protection device in subsystem i is the threshold of effective impact. When the impact intensity is When , the impact is invalid. represents the probability that the source II shock is an invalid shock, represents the probability that the source II shock is a valid shock, Indicates the parameter of the protection device's state degradation after being effectively impacted. represents the degradation rate of the protection device from state 3 to state 2, represents the degradation rate of the protection device from state 3 to state 1, represents the degradation rate of the protection device from state 3 to state 0, represents the degradation rate of the protection device from state 2 to state 1, represents the degradation rate of the protection device from state 2 to state 0, Indicates the degradation rate of the protection device from state 1 to state 0.

[0277] Table 2. Parameters related to relay internal degradation and shock effects

[0278]

[0279] In addition, the parameters of the two starting errors of the relay are listed in Table 3, where: It represents the probability of successful startup in state 3 during the operation of the protection device. It represents the probability of successful startup in state 2 during the operation of the protection device. It represents the probability of successful startup in state 1 during the operation of the protection device. Indicates the maximum number of attempts to start the protection device in state 3. Indicates the maximum number of attempts to start the protection device in state 2. Indicates the maximum number of attempts to start the protection device in state 1. represents the probability of the protection device being falsely activated in state 3, represents the probability that the protection device is falsely activated in state 2, represents the probability that the protection device is falsely activated in state 1, It represents the probability that a protective device will mistakenly isolate a normally functioning component in a subsystem.

[0280] Table 3. Parameters related to the two starting errors of the relay

[0281]

[0282] Step 3: Analyze the reliability of the relay under different false touch probabilities and obtain the following results: Figure 2 As shown, through Figure 2From the analysis, we can draw the following conclusions: when the probability of false contact of the relay is different, the reliability of the three subsystems is compared. It is found that the time required for the reliability of subsystem 2 (subsystem2) to converge to zero is the longest, followed by subsystem 3 (subsystem3) and subsystem 1 (subsystem1). When the probability of false contact of the relay in each subsystem is low, the reliability of the subsystem is higher.

[0283] Step 4: When the probability of relay failure to start changes, the reliability of the wind turbine system is as follows: Figure 3 As shown. Figure 3 It can be observed that as the probability of relay startup failure decreases in each subsystem, the corresponding subsystem's survival time increases. Furthermore, an increase in the probability of relay startup failure has a stronger marginal impact on the degradation of wind turbine system reliability. This is because the probability of relay startup failure is the base of a power function, and the derivative of a power function is increasing.

[0284] Step 5: When the fault threshold of each subsystem changes, the impact on the reliability of the multi-state system is as follows: Figure 4 As shown in Figure 1, the reliability of the multi-state system is improved as the failure threshold of subsystem 1 increases. Because subsystem 1 has a stricter failure standard as k1 increases, it is more likely to be in working condition and provide more supply, and thus the probability of it meeting demand also increases. In addition, as Figure 4 As shown in Figure 2, the marginal effect of increasing k1 on improving the reliability of the multi-state system decreases, which may be because when it increases to a certain level, the reliability of other subsystems gradually becomes the main factor affecting the reliability of the entire multi-state system.

[0285] Step 6: When the threshold of wind turbine system failure changes, analyze the change of multi-state system reliability, such as Figure 5 shown. Figure 5 Explains when the need to meet Figure 3 As the threshold shown increases, the reliability of the entire multi-state system decreases. When k = 3, the system can only operate normally if the requirements of all generator systems are met. Therefore, the reliability curve of the multi-state system is identical to that of the generator system that failed first. Similarly, when k = 1, the reliability function of the multi-state system is identical to that of the generator system that failed last.

[0286] Step 7: When the probability distribution of each generator demand changes, the reliability of the multi-state system is as follows: Figure 6 shown. The jth possible probability distribution represents the demand for the i-th generator system, and the corresponding values ​​are shown in Table 4. When j = 1, the probability of the three generator systems having the maximum demand is 1. Clearly, the demand on the generator system can only be met when the generator system is in optimal condition, so in this case, the reliability of the entire system is the lowest. From j = 1 to j = 3, the probability of the three generator systems having the minimum demand value gradually increases. As a result, the demands of all three generator systems are more likely to be met, which leads to an improvement in the reliability of the entire power system.

[0287] Table 4. Probability distribution of generator system demand

[0288]

[0289]

[0290] Based on the above embodiments, an embodiment of the present application also provides an electronic device, which includes: one or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs include instructions, which, when executed by the electronic device, enable the electronic device to execute the method provided in the above embodiments.

[0291] Based on the above embodiments, an embodiment of the present application further provides a computer storage medium, in which a computer program is stored. When the computer program is executed by a computer, the computer executes the method provided in the above embodiments.

[0292] The storage medium may be any available medium that can be accessed by a computer. By way of example and not limitation, computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage media or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer.

[0293] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0294] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0295] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0296] The embodiments of the present invention are presented for purposes of illustration and description and are not intended to be exhaustive or to limit the invention to the disclosed forms. Many modifications and variations will be apparent to those skilled in the art. The embodiments are chosen and described in order to better illustrate the principles of the invention and its practical application and to enable those skilled in the art to understand the invention and design various embodiments with various modifications as suited for specific applications.

Claims

1. A reliability calculation method for a multi-state system equipped with a protection device, characterized in that: The steps include: S1. Determine the arrival rate of shocks from different sources during the operation of the multi-state system based on historical information of the multi-state system, derive degradation rules based on the internal degradation rates of components and protection devices in each subsystem of the multi-state system and their degradation after being subjected to effective external environmental shocks, and, using the degradation rules and a Markov process embedding method, derive a state transition rate matrix for each subsystem when the protection device operates in different states; S2. The reliability function of each subsystem in the multi-state system is obtained according to the state transition rate matrix of each subsystem when the protection device is running in different states obtained in step S1; S3. According to the reliability function of each subsystem obtained in step S2 and the state division criteria of the subsystem, the probability of each subsystem being in each state is obtained; S4. Based on the probabilities of each subsystem being in each state obtained in step S3, the supply level of each subsystem in each state and the demand of each subsystem in each state are obtained, and a probability function of the demand satisfaction of each subsystem is obtained using a general generating function method; S5. Based on the probability function of the satisfaction of the requirements of each subsystem obtained in step S4, the number of subsystems whose requirements are satisfied in the polymorphic system is obtained by a general generating function method, and the reliability of the polymorphic system is obtained by the number of subsystems; In step S2, the reliability function of the subsystem is shown in formula (1): Among them, R i (t) represents the reliability function of subsystem i at time t, represents the initial state probability distribution, W i represents the set of all working states of subsystem i, The transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |'s one-step transfer rate matrix, I i represents the identity matrix corresponding to the number of working states of subsystem i, and T represents the transpose; In the step S3, the i-th subsystem has |W i | possible transition states, the yth i Among the possible states, the number of parts in state b is The function getnum(W,l) is used to get the lth element in the vector W, (l=1,2,...,u i ), matrix B i,b Indicates the transition from state b to state u in subsystem i i The number of all components with a given threshold k i,b The relationship between B i,b Size is |W i |×1, is the matrix B i,b yth i elements, where (y i =1,2,...,|W i |), The value of is shown in formula (2): The probability of the subsystem i being in each transition state is shown in formula (3): in, represents the probability that subsystem i is in each transition state, The probability of the subsystem i being in each state is shown in formula (4): in, represents the probability of subsystem i being in each state, r1 represents the state of subsystem i, r1∈(1,2,...,u i ), Indicates the transition from state b to state u in subsystem i i -1 the number of all components with a given threshold k i,b The relationship between B i,1 Represents the number of all components in subsystem i from state b to state 1 and the given threshold k i,b the relationship between; In step S4, the demand satisfaction of the subsystem i in each state is shown in formula (5): Among them, it means Indicates the demand satisfaction of subsystem i in state r1, represents the supply of subsystem i in state r1, The supply quantity of subsystem i in state r1 is β i represents the total number of all possible requirements for subsystem i, represents the probability corresponding to the r2th possible demand in subsystem i, represents the r2th possible demand in subsystem i, The difference between the supply and the possible demand of subsystem i in state r1 is represents the r0th difference between the supply and demand of subsystem i, represents the probability corresponding to the r0th difference between the supply and demand of subsystem i, The probability of undersupply of subsystem i is shown in formula (6): in, represents the probability of insufficient supply of subsystem i, when When true, is 1, When it is false, is equal to 0, The probability that the requirements of subsystem i are met is shown in formula (7): in, represents the probability that the requirements of subsystem i are met, The probability function of the subsystem i's demand satisfaction is shown in formula (8): in, The probability function of subsystem i's requirement satisfaction, z r Indicates the satisfaction of demand, z 0 It means that supply is less than demand, z 1 Indicates that supply is greater than or equal to demand.

2. The reliability calculation method of a multi-state system equipped with a protection device according to claim 1, characterized in that: In step S1, the source impact includes source I and source II, the impact of source I affects the state of the component, and the effective impact of source II affects the state of the protection device; The degradation rules include degradation rules of components and degradation rules of protection devices; The degradation rule of the component includes failure of the component due to internal degradation or external impact from source I. The impact from source I includes type A impact, type B impact and type C impact according to the intensity. The type A impact has no effect on the component state, the type B impact causes the component state to deteriorate, and the type C impact causes the component to fail. The degradation rules of the protection device include that the protection device ensures the normal operation of the subsystem by isolating the failed components from the subsystem. The protection device will undergo state transition due to internal degradation or external effective impact from source II. When the cumulative number of effective impacts received by the protection device reaches a threshold, the internal degradation rate of the protection device will accelerate. The startup errors of the protection device include startup failure and erroneous startup.

3. The reliability calculation method of a multi-state system equipped with a protection device according to claim 2, characterized in that: In step S1, the impact arrival rate of the source I is The impact arrival rate of source II is The probability of the type A shock from source I is The probability of the type B shock from source I is The B-type impact causes the component condition to deteriorate The probability of the C-type impact is The probability that the source II shock is a valid shock is The components in the polymorphic system are polymorphic components. The components in different subsystems are different. There are n components in subsystem i. i components, the normal internal degradation rate of the components is When the cumulative B-type shock reaches the threshold Internal degradation rate increases to in It represents the multiple of the internal degradation rate of the component in subsystem i based on the initial normal internal degradation rate; The state of the subsystem i is divided according to the number of components in different states. The state space of the components in the subsystem i is Ω i ={0,1,...,u i }, where 0 is the failure state, u i Is the perfect working state, vector Contains the subsystem i in 0,1,...,u i The number of parts in each state, where Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components mistakenly isolated by protection devices in the subsystem i. When the number of components in state 0 in subsystem i reaches k i When Subsystem failure k i represents the failure threshold of subsystem i, The status of the components in the subsystem i is When , the state of the subsystem i, the working state of the subsystem i is divided into the following: (1) When subsystem i is in u i The number of parts is not less than hour, Equal to u i ; (2) When the number of components in subsystem i that is greater than or equal to state l is less than k i,l , where (j+1≤l≤u i ), and there are at least k i,j When the state of the components is not less than j, the state of the subsystem is j; (3) When the number of components in subsystem i that are greater than or equal to state l is less than k i,l When (l=1,2,…,u i ), subsystem i fails; In order to ensure that all possible component state combinations in subsystem i have corresponding subsystem states and avoid repeated state divisions in subsystem i, k i,1 =n i -k i +1, The state space of the protection device in the multi-state system is Where 0 is the failure state, g i is the optimal working state of the i-th protection device. The protection device ensures the normal operation of the subsystem by isolating the failed components from the subsystem. The internal degradation rate of the protection device is The protective device degrades after receiving an effective impact When the cumulative number of effective impacts received by the protection device reaches When the internal degradation rate of the protection device becomes in It represents the multiple of the internal degradation rate of the protection device in subsystem i increased on the basis of the initial normal internal degradation rate, and the protection device is in state o during operation. i The probability Successful start, with probability Failed to start, o i Indicates the status of the i-th protection device, o i ∈{0,1,...,g i }, the protection device is in state o i The maximum number of startup attempts under The protection device is in state o i The probability of being started incorrectly is When the shock to the subsystem is type A, the probability that the protection device mistakenly isolates a normally functioning component in the subsystem is When the subsystem is subjected to a Type B shock, the state of the component will be degraded but will not fail, and the component with the degraded state will be mistakenly isolated by the protection device.

4. A reliability calculation method for a multi-state system equipped with a protection device according to claim 3, characterized in that: In step S1, a random point process {X i (t),t≥0}, y i =1,2,...,Y i , X i (t) represents the state of subsystem i at time t, represents the yth subsystem i i possible states, Y i represents the total number of possible states of subsystem i, where Contains(u i +4) random variables, among which Used to record status 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components incorrectly isolated by the protection device. The cumulative number of B-type shocks suffered by the subsystem i is given by Indicates that i represents the state of the i-th protection device, is the total number of effective impacts received by the protection device. The multi-state system consists of m subsystems. When the number of subsystems whose requirements are not met reaches k, the multi-state system fails. The transition rules between the states of the subsystem i are as follows: Scenario 1: Degradation of the i-th protection device: (1) For i = 1, 2, ..., m, if 0 <o1≤o i ≤g i , The state transition is: The state transition rate is: (2) For i = 1, 2, ..., m, if 0<o1≤o i ≤g i , The state transition is: The state transition rate is: (3) For i = 1, 2, ..., m, if The state transition is; The state transition rate is (4) For i = 1, 2, ..., m, if The state transition is: The state transition rate is: Scenario 2: Component degradation without component failure: (5) For i = 1, 2, ..., m, if 0<α<β≤u i , α represents the state of the component after degradation, and β represents the state of the component before degradation. represents the cumulative B-type shock threshold that causes an increase in the internal degradation rate of components in subsystem i; The state transition is: The state transition rate is: represents the number of components in subsystem i in state β before state transition; (6) For i = 1, 2, ..., m, if 0<α<β≤u i , The state transition is: The state transition rate is: (7) For i = 1, 2, ..., m, if 0<o i ≤g i ; The state transition is: The state transition rate is: Scenario 3: The number of components in state 0 increases due to internal degradation, external shocks, and false activation of protection devices: (8) For i = 1, 2, ..., m, if 0<o i ≤g i ; The state transition is: The state transition rate is: (9) For i = 1, 2, ..., m, if 0<o i ≤g i ; The state transition is: The state transition rate is: (10) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ; The state transition is: The state transition rate is: represents the internal degradation rate of the component in subsystem i from state β to state 0; (11) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ; The state transition is: The state transition rate is: Scenario 4: Since the number of components in state 0 reaches the failure threshold k i The subsystem i fails as a result of: (12) For i = 1, 2, ..., m, if 0<o i ≤g i ; The state transition is: F i represents the failure state of subsystem i; The state transition rate is: (13) For i = 1, 2, ..., m, if 0<o i ≤g i ; The state transition is: The state transition rate is: Scenario 5: Failure of the i-th subsystem due to failure of the protection device to activate and isolate the failed component: (14) For i = 1, 2, ..., m, if 0 <o i ≤g i ; The state transition is: The state transition rate is: (15) For i = 1, 2, ..., m, if 0<β≤u i , 0<o i ≤g i ; The state transition is: The state transition rate is: Scenario 6: In the case of failure of both the component and the protection device, the subsystem i fails: (16) For i = 1, 2, ..., m, if 0<β≤u i ,0<β≤u i , o i =0; The state transition is: The state transition rate is: (17) For i = 1, 2, ..., m, if 0<β≤u i , o i =0; The state transition is: The state transition rate is:

5. The reliability calculation method of a multi-state system equipped with a protection device according to claim 1, characterized in that: In step S5, the probability function of the polymorphic system's demand satisfaction is shown in formula (9): in, The probability function of the polymorphic system's demand satisfaction is expressed as follows: H represents the maximum number of subsystems whose demands are satisfied, H = m, h represents the number of subsystems whose demands are satisfied, h∈(0,1,…,H), π h represents the probability of the number of subsystems whose requirements are met, z h The number of subsystems whose requirements are met is h, The reliability of the multi-state system is shown in formula (10): Among them, R s (t) represents the reliability of the polymorphic system, and k represents the failure of the system when the number of subsystems whose requirements are not met reaches k.

6. An electronic device, characterized in that: The method comprises a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the processor implements the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute the method according to any one of claims 1 to 5.

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