Method for calculating reliability of polymorphic system with protection device

Abstract

The invention provides a reliability calculation method for a polymorphic system equipped with a protection device, and the method comprises the steps: determining the arrival rates of impacts from different sources during the operation of the polymorphic system according to the historical information of the polymorphic system; the method comprises the following steps of: obtaining a degradation rule through internal degradation rates of parts in each subsystem in a polymorphic system and a protection device and degradation conditions after effective impact of an external environment, and obtaining a state transition rate matrix when each subsystem runs in different states of the protection device; the reliability function of each subsystem in the polymorphic system and the probability of each subsystem in each state are obtained; according to the probability of each subsystem in each state, obtaining a probability function of a demand satisfaction condition of each subsystem through a general generation function method; and obtaining the number of subsystems meeting the requirements in the polymorphic system through a general generation function method, and obtaining the reliability of the polymorphic system through the number of the subsystems. According to the invention, the reliability of the polymorphic system equipped with the protection device can be calculated more accurately.

Description

Technical Field

[0001] The invention belongs to the field of system reliability calculation, and specifically 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 may lead to serious consequences, such as mission interruption and economic losses. In order to improve the reliability of the system and extend its life, protection devices are usually equipped to slow down the degradation of the system. Protection devices are currently used in various systems, such as protection devices for pumping discharge pipelines, accumulator buffers for hydraulic systems, and protective relays for power systems. Depending on the actual situation, protection devices have different protection mechanisms. For example, under the influence of impact, auxiliary components can partially protect the main components from external impact; in multi-state systems, protection devices can reduce external damage to the system through defense factors; multi-state protection devices can improve the reliability of the system by protecting the system from external impacts, and their protection capabilities are related to their states; in a multi-component protection device system, the protection device can reduce the probability of effective impacts, which will have benefits for system recovery, and the protection level of the protection device is related to the number of protection components it works on.

[0004] In addition to the effects of shocks, the system 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 the degradation of the critical subsystem. The system protected by the protection device may also be affected by both internal degradation and external shocks. In addition, 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 may have direct and indirect performance damage, reflected in a shortened state transfer time. In addition to the protection mechanism 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 the faulty components, such as overload protection relays in motors, protection relays in substations, etc.

[0005] The prior art provides a reliability analysis method for a system equipped with a protection device under the mechanism of isolating faulty components, and at the same time models the degradation process of the system when the impact and degradation are independent of each other, and considers the error situation of the failure of the protection device to start, which is reflected by a certain probability of startup failure. When the number of failed components and isolated components in the system reaches a threshold or the failed components are not successfully isolated, the system fails. However, in actual engineering systems, the protection device of the isolation fault component protection system may be triggered by mistake, and the prior art ignores this failure mode of the protection device. In addition, the internal degradation and external impact of the system equipped with a protection device will affect each other, and the relevant prior art ignores the relationship between the internal degradation and external impact of the system. In addition, there is no relevant reliability modeling for the system for the purpose of modeling the engineering examples of the system protected by the protection device to meet the demand. Therefore, it is necessary to consider a system reliability analysis method composed of multiple polymorphic demand-based subsystems, in which the protection device considers two startup errors. In view of the above-mentioned problems, it is necessary to study and design a new reliability calculation method for polymorphic systems equipped with protection devices to overcome the problems existing in the reliability analysis method of systems equipped with protection 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 the reliability analysis method of the system equipped with protection devices, such as incomplete research on the protection mechanism of the system equipped with protection devices, inability to solve the reliability of the system composed of multiple polymorphic subsystems equipped with protection devices based on demand, and failure to consider the relationship between internal degradation and external impact in the existing model.

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

[0008] S1. Determine the arrival rate of impacts from different sources when the multi-state system is running according to the historical information of the multi-state system, obtain the degradation rule through the internal degradation rate of the components and protection devices in each subsystem of the multi-state system and the degradation after being effectively impacted by the external environment, and obtain the state transition rate matrix of each subsystem when the protection device is running in different states through the degradation rule and Markov process embedding method;

[0009] S2. Obtain the reliability function of each subsystem in the multi-state system 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 of the subsystems obtained in step S2 and the state division criteria of the subsystems, the probability of each of the subsystems being in each state is obtained;

[0011] S4. According to the probabilities of each of the subsystems being in each state obtained in step S3, the supply level of each of the subsystems in each state and the demand of each of the subsystems in each state are obtained, and the probability function of the satisfaction of the demand of each of the subsystems is obtained by the general generating function method;

[0012] S5. According to the probability function of the satisfaction of the requirements of each subsystem obtained in step S4, the number of subsystems whose requirements are met in the polymorphic system is obtained by the general 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 of source I, and the impact of 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 state of the component, the type B impact causes the state of the component 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 impact 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 The normal internal degradation rate of a component is When the cumulative B-type shock reaches the threshold The 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 It is a perfect working state, vector Contains the subsystem i in 0,1,...,u i The number of parts in each state, where Used to record states 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components mistakenly 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 state 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 is 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 is degraded 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 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 launch, with probability Failed to start, o i represents the state 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 subsystem is subjected to a type A shock, 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 reliability calculation method for 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 states 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components that are incorrectly isolated by the protection device. The cumulative number of type B 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 on 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, 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: Increase in the number of components in state 0 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: As 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: It represents the value of the component state degradation in subsystem i caused by type B 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 the failure of the protection device to start 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 reliability calculation method for 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, It means that the transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |The one-step transition 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 reliability calculation method for 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 The 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.

[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 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 in 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 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 insufficient supply 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 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 demand 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 the supply is less than the demand, and the demand is not met. 1 It means that supply is greater than or equal to demand, and the 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, 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,

[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 multi-state system, and k means that the system fails 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 used 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 reliability calculation method for a polymorphic system equipped with a protection device. The polymorphic system of the present invention is composed of polymorphic subsystems under multiple protection devices. The method fully considers the situation of failure to start the protection device, and considers the relationship between the internal degradation and external impact of the polymorphic system. It is used to solve the problems in the existing reliability calculation method, that is, in the system equipped with a protection device, the protection mechanism is not fully studied, and the reliability of the system composed of multiple demand-based polymorphic subsystems equipped with protection devices cannot be solved, and the relationship between internal degradation and external impact is not considered in the existing model. The method can more accurately calculate the reliability of the polymorphic system equipped with protection 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 Embodiment 3 of the present invention;

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

[0134] Figure 4 is a reliability function diagram of the system under different failure thresholds of subsystem 1 in embodiment 3 of the present invention;

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

[0136] Figure 6 It is a multi-state system reliability function diagram of the 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 the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0138] It should be noted that the terms "including" and "having" and any variations thereof in the embodiments of the present application and the accompanying drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device including 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 these processes, methods, products or devices.

[0139] Embodiment 1, this embodiment provides a reliability calculation method of a multi-state system equipped with a protection device, such as Figure 1 As shown, the following steps are included:

[0140] S1. Determine the arrival rate of impacts from different sources when the multi-state system is running according to the historical information of the multi-state system, obtain the degradation rules through the internal degradation rates of the components and protection devices in each subsystem of the multi-state system and the degradation conditions after being effectively impacted by the external environment, and obtain the state transition rate matrix of each subsystem when the protection device is running in different states through the degradation rules and Markov process embedding method;

[0141] S2. Obtain the reliability function of each subsystem in the multi-state system 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. According to the probability 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 the probability function of the satisfaction of the demand of each subsystem is obtained by 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 met in the polymorphic system is obtained by the general generating function method, and the reliability of the polymorphic system is obtained by the number of subsystems.

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

[0146] S1. Determine the arrival rate of impacts from different sources when the multi-state system is running according to the historical information of the multi-state system, obtain the degradation rules through the internal degradation rates of the components and protection devices in each subsystem of the multi-state system and the degradation conditions after being effectively impacted by the external environment, and obtain the state transition rate matrix of each subsystem when the protection device is running in different states through the degradation rules and Markov process embedding method;

[0147] Specifically, 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 protective device;

[0148] The degradation rules include the degradation rules of components and the degradation rules of protection devices;

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

[0150] 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 the threshold, the internal degradation rate of the protection device will accelerate. The startup errors of the protection device include startup failure and incorrect startup. When the protection device has a startup error, the subsystem may still fail even if the corresponding protection device of the subsystem is running. 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 The normal internal degradation rate of a component is When the cumulative B-type shock reaches the threshold The 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 It is a perfect working state, vector Contains the subsystem i in 0,1,...,u i The number of parts in each state, where Used to record states 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 as follows:

[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 is 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 is degraded after receiving an effective impact When the cumulative number of effective impacts received by the protective device reaches When the internal degradation rate of the protection device becomes in It indicates 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 launch, with probability Failed to start, o i represents the state 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 subsystem is subjected to a type A shock, 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 state of the component will degrade but will not fail, and the component with the degraded state will be mistakenly isolated by the protection 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 states 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components that are incorrectly isolated by the protection device. The cumulative number of type B 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 impacts on 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, 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: Increase in the number of components in state 0 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: As 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: It represents the value of the component state degradation in subsystem i caused by type B 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 the failure of the protection device to start 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. Obtain the reliability function of each subsystem in the multi-state system 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, It means that the transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |The one-step transition rate matrix, I i represents the unit matrix corresponding to the number of working states of subsystem i, and T represents 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 The 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. According to the probability 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 the probability function of the satisfaction of the demand of each subsystem is obtained by 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 in 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 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 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 subsystem i's demand satisfaction is shown in formula (8):

[0255]

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

[0257] S5. According to 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 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 It means that the supply is less than the 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, represents 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 of the satisfaction of subsystem i, HΩ∪i represents the maximum number of subsystems whose requirements are met after incorporating subsystem i into the set Ω, π Ω∪i,h represents the probability that the demand is satisfied when the number of subsystems is h after the 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 demand satisfaction of the polymorphic system is shown in formula (10):

[0264]

[0265] in, The probability function of the polymorphic system's demand satisfaction, H represents the maximum number of subsystems whose demands are satisfied, h represents the number of subsystems whose demands are satisfied, h∈(0,1,...,H), π h 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 multi-state system, and k means that the system fails 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 used to execute the computer program in the memory to implement the above method.

[0270] This embodiment also 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] Embodiment 3, this embodiment provides a reliability calculation method for a polymorphic system equipped with a protection device, the polymorphic system is composed of multiple demand-based polymorphic subsystems, to solve the problems in the existing reliability calculation method, that the protection mechanism in the system equipped with a protection device is not comprehensively studied, and the reliability of the polymorphic system composed of multiple demand-based polymorphic subsystems equipped with protection devices cannot be solved, and the relationship between internal degradation and external impact is not considered in the existing model. The reliability calculation method of this embodiment is a method for determining the state of the subsystem based on the number of components in each state in the subsystem, and then determining the supply of the subsystem and the satisfaction of the subsystem demand, and finally obtaining the reliability of the polymorphic system, while considering the situation that the internal degradation of the components and the protection device is affected by the external impact, as well as the two startup errors of the protection device.

[0272] This embodiment mainly uses the Markov process embedding method to describe the operation process of the subsystem, calculates the probability index related to the subsystem, and uses the general generating function method to obtain the subsystem demand satisfaction and the 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), and 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 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 type A shock, Indicates that the shock to subsystem i is the threshold of type B shock. 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 impact 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 starting errors. The relay state spaces in the three subsystems of the wind turbine system are and The arrival rate of the source II shock is Impact strength For all three relays, the internal degradation rate accelerates 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 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, It indicates the parameter of the protection device's state decline 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 impact effects

[0278]

[0279] In addition, the parameters of the two starting errors of the relay are listed in Table 3, where: It indicates the probability of successful startup in state 3 during the operation of the protection device. It indicates the probability of successful startup of the protection device in state 2 during operation. It indicates 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 erroneously activated in state 3, represents the probability of the protection device being erroneously activated in state 2, represents the probability of the protection device being erroneously activated in state 1, It represents the probability that a protective device mistakenly isolates 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 2Through analysis, we can draw the following conclusions: when the false-touch probability of the relay is different, the reliability of the three subsystems, by comparison, 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 false-touch probability 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 Figure 3 As shown. Figure 3 It can be observed that as the probability of relay start failure in each subsystem decreases, the survival time of the corresponding subsystem increases. In addition, the increase in the probability of relay start failure has a stronger marginal effect on the decrease in wind turbine system reliability. This is because the probability of relay start failure is the base of the power function, and the derivative of the 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 that it can meet the 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, probably 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: Analyze the change of the reliability of the multi-state system when the threshold of the wind turbine system failure changes, such as Figure 5 shown. Figure 5 Explains when the need to meet Figure 3 As the threshold value shown becomes larger, the reliability of the entire multi-state system decreases. When k = 3, it means that the normal operation of the entire system can only be achieved if the needs of all generator systems are met. Therefore, the reliability curve of the multi-state system is the same as the curve of the generator system that fails first. Similarly, when k = 1, the reliability function of the multi-state system is consistent with the reliability function of the generator system that fails 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 of the i-th generator system, and the corresponding values ​​are shown in Table 4. When j = 1, the probability of the three generator systems being the maximum demand is 1. Obviously, the demand for the generator system can only be met when the generator system is in the best state, 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 taking the minimum demand value gradually increases. Therefore, the demands of the three generator systems are easier to be met, which leads to an increase 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, and when the instructions are executed by the electronic device, the electronic device executes the method provided in the above embodiments.

[0291] Based on the above embodiments, the embodiments of the present application further provide 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. For example, but not limited to, a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store the 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 may be provided as methods, systems, or computer program products. Therefore, the present application may 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 may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0294] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate 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 A 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 operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0296] The embodiments of the present invention are given for the purpose 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 of ordinary skill in the art. The embodiments are selected and described in order to better illustrate the principles and practical applications of the present invention and to enable those of ordinary skill in the art to understand the present invention and thereby design various embodiments with various modifications suitable for specific uses.

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 impacts from different sources when the multi-state system is running according to the historical information of the multi-state system, obtain the degradation rule through the internal degradation rate of the components and protection devices in each subsystem of the multi-state system and the degradation after being effectively impacted by the external environment, and obtain the state transition rate matrix of each subsystem when the protection device is running in different states through the degradation rule and Markov process embedding method; S2. Obtain the reliability function of each subsystem in the multi-state system 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 of the subsystems obtained in step S2 and the state division criteria of the subsystems, the probability of each of the subsystems being in each state is obtained; S4. According to the probabilities of each of the subsystems being in each state obtained in step S3, the supply level of each of the subsystems in each state and the demand of each of the subsystems in each state are obtained, and the probability function of the satisfaction of the demand of each of the subsystems is obtained by the general generating function method; S5. According to the probability function of the satisfaction of the requirements of each subsystem obtained in step S4, the number of subsystems whose requirements are met in the polymorphic system is obtained by the general generating function method, and the reliability of the polymorphic system is obtained by the number of subsystems.

2. A reliability calculation method for 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 of source I, and the impact of 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 state of the component, the type B impact causes the state of the component 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. A reliability calculation method for a multi-state system equipped with a protection device according to claim 2, characterized in that: In step S1, the impact arrival rate of 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 impact 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 The normal internal degradation rate of a component is When the cumulative B-type shock reaches the threshold The 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 It is a perfect working state, vector Contains the subsystem i in 0,1,...,u i The number of parts in each state, where Used to record states 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components mistakenly 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 state 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 is 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 is degraded 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 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 launch, with probability Failed to start, o i represents the state 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 subsystem is subjected to a type A shock, 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 states 1, 2, ..., u respectively i number of parts, represents the total number of failed components and components that are incorrectly isolated by the protection device. The cumulative number of type B 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 on 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 The state transition is: The state transition rate is: (2) For i = 1, 2, ..., m, if 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 α represents the state of the component after degradation, 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 The state transition is: The state transition rate is: (7) For i = 1, 2, ..., m, if The state transition is: The state transition rate is: Scenario 3: Increase in the number of components in state 0 due to internal degradation, external shocks, and false activation of protection devices: (8) For i = 1, 2, ..., m, if The state transition is: The state transition rate is: (9) For i = 1, 2, ..., m, if The state transition is: The state transition rate is: (10) For i = 1, 2, ..., m, if 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 The state transition is: The state transition rate is: Scenario 4: As 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 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 The state transition is: The state transition rate is: Scenario 5: Failure of the i-th subsystem due to the failure of the protection device to start and isolate the failed component: (14) For i = 1, 2, ..., m, if The state transition is: The state transition rate is: (15) For i = 1, 2, ..., m, if 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 The state transition is: The state transition rate is: (17) For i = 1, 2, ..., m, if The state transition is: The state transition rate is:

5. A reliability calculation method for a multi-state system equipped with a protection device according to claim 1, characterized in that: In step S2, the reliability function of the subsystem is as 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, It means that the transfer rate between the transition states of subsystem i forms a magnitude of |W i |×|W i |The one-step transition rate matrix, I i It represents the identity matrix corresponding to the number of working states of subsystem i, and T represents the transpose.

6. A reliability calculation method for a multi-state system equipped with a protection device according to claim 5, characterized in that: In 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 The 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.

7. A reliability calculation method for a multi-state system equipped with a protection device according to claim 6, characterized in that: 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 in 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 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 insufficient supply of subsystem i is shown in formula (6): in, represents the probability of insufficient supply of subsystem i, when When true, is 1, When 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, represents the probability function of the satisfaction of the requirements of subsystem i, 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.

8. A reliability calculation method for a multi-state system equipped with a protection device according to claim 1, characterized in that: In step S5, the probability function of the demand satisfaction of the polymorphic system is shown in formula (9): in, The probability function of the polymorphic system's demand satisfaction, 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 multi-state system, and k means that the system fails when the number of subsystems whose requirements are not met reaches k.

9. 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 8.

10. 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 8.

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