Performance sharing series-parallel hybrid polymorphic system reliability analysis method

Abstract

The invention belongs to the technical field of system reliability analysis, and discloses a performance sharing series-parallel hybrid polymorphic system reliability analysis method, which comprises the following steps: S1, constructing a performance sharing series-parallel hybrid polymorphic system, the total performance surplus S, the total performance loss F, the probability of being in a specific state, the total redistributable performance surplus amount and the sum of the weighted performance loss of the performance sharing series-parallel hybrid polymorphic system are obtained, the performance sharing series-parallel hybrid polymorphic system is composed of m subsystems connected through a common bus, each subsystem comprises k components which are configured in parallel; according to the method, the reliability model of the performance sharing series-parallel hybrid system can be established, and performance defect fault tolerance, transmission loss and different weights of subsystems are considered; moreover, by establishing the MDD model of the system, the method can be repeatedly used for evaluating the reliability of the system under different parameters, thereby facilitating the optimization and adjustment of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of system reliability analysis, and more specifically, to a reliability analysis method for a performance-sharing serial-parallel hybrid polymorphic system. Background Art

[0002] In computer systems and polymorphic systems, performance sharing mechanism as a redundancy mechanism has been widely used to improve system reliability. Traditional performance sharing mechanism mainly uses a common bus to achieve the transmission of performance surplus to meet the needs of other components or subsystems with insufficient performance. After performance sharing, as long as the sum of weighted performance defects of all subsystems is greater than the threshold (pre-designed value), the system will be judged as unreliable.

[0003] However, when analyzing the reliability of a performance sharing system, some practical factors may affect the accuracy of the evaluation of system reliability, among which transmission loss is an issue that cannot be ignored;

[0004] There is currently no research on constrained series-parallel hybrid systems affected by performance sharing and transmission losses, and in which the subsystems have different weights; however, these problems do exist in many actual series-parallel hybrid systems with performance sharing mechanisms.

[0005] In view of this, the present invention proposes a reliability analysis method for a performance-sharing serial-parallel hybrid multi-state system to solve the above problems. Summary of the invention

[0006] In order to overcome the above-mentioned defects of the prior art and to achieve the above-mentioned purpose, the present invention provides the following technical solution: a reliability analysis method for a performance-sharing serial-parallel hybrid multi-state system, comprising the following steps:

[0007] S1. Construct a performance-sharing serial-parallel hybrid polymorphic system, and obtain the total performance surplus S, the total performance loss F, the probability of being in a specific state, the total redistributable performance surplus, and the sum of the weighted performance loss of the performance-sharing serial-parallel hybrid polymorphic system, wherein the performance-sharing serial-parallel hybrid polymorphic system is composed of m subsystems connected by a common bus, and each subsystem includes k parallel-configured components;

[0008] S2. constructing an MDD model of a performance-sharing serial-parallel hybrid polymorphic system, wherein the process of constructing the MDD model of a performance-sharing serial-parallel hybrid polymorphic system includes: constructing a tree-like MDD model of the performance-sharing serial-parallel hybrid polymorphic system layer by layer, and designing and applying multiple simplification rules to obtain a simplified MDD model;

[0009] S3. Calculate the reliability of the performance-sharing serial-parallel hybrid polymorphic system based on the MDD model, wherein the process of calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system includes: obtaining the state classification rules and reliability calculation rules of the performance-sharing serial-parallel hybrid polymorphic system, and calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system using the MDD model based on the reliability calculation rules.

[0010] Furthermore, in S1, the method of obtaining the total performance surplus S and the total performance loss F of the performance sharing serial-parallel hybrid multi-state system is as follows:

[0011] Set the i-th subsystem U i It is composed of k heterogeneous components connected in parallel and is represented by N (i-1)k+1 ,N (i-1)k+2 ,...,N ik , each component consists of a random performance variable and random demand variables express;

[0012] Set a component N j Own r j The performance level of the degradation and k j demand level, for performance g jp and demand jq Component N j , preset X j For component N j The state random variable is denoted as X j ='g jp ,d jq ';

[0013] Setting G i Represents subsystem U i Performance, G i It is calculated from the total performance of k components from (i-1)k+1 to ik, and its expression is:

[0014]

[0015] Furthermore, subsystem U i Demand D i is calculated by the sum of the component requirements, and its expression is:

[0016]

[0017] Default H i is a performance G corresponding to the state of the i-th subsystem i and demand D i A random variable, namely H i ='G i ,Di ';

[0018] If G i ≥D i , then the subsystem U i The performance surplus Si that satisfies the demand is expressed as S i =G i -D i , but failed to fully satisfy the subsystem U i The required performance loss is F i = 0, otherwise, the performance surplus is S i =0, performance loss is F i =G i -D i ;

[0019] Furthermore, the total performance surplus S of the performance-sharing serial-parallel hybrid polymorphic system is the sum of the performance surpluses of all subsystems, that is:

[0020]

[0021] The total performance loss F can be calculated as the sum of the performance losses of all subsystems, that is:

[0022]

[0023] Furthermore, in S1, the method of obtaining the probability that the performance sharing serial-parallel hybrid multi-state system is in a specific state is:

[0024] Set X = (X 1 ,X 2 ,...,X mk ) represents the state vector of the random system, and x=(x 1 ,x 2 ,...,x mk ) is a state of variable X, where x j ='g jp ,d jq 'Represented as component N j state, and thus, there is different states;

[0025] For X j ='g jp ,d jq 'State component N j The probability of Right now

[0026] Furthermore, the probability that the performance-sharing serial-parallel hybrid multi-state system is in a specific state can be expressed as:

[0027]

[0028] Furthermore, in S1, the method for obtaining the total amount of redistributable performance surplus of the performance-sharing serial-parallel hybrid multi-state system is as follows:

[0029] Assuming θ is the loss percentage of the total performance surplus S, the performance surplus after the loss is (1-θ)*S;

[0030] Assume that the common bus has a discrete transmission capacity represented by a random variable C with a given PMF, then the random variable C is selected from the set {c 1 ,c 2 ,...,c v} with the corresponding probability Pr(C=c b ) value;

[0031] Furthermore, the total amount of redistributable performance surplus Q of the performance-sharing serial-parallel hybrid polymorphic system is:

[0032]

[0033] Preset (F 1 ,F 2 ,...,F m ) represents the performance defect vector of all subsystems, and introduces the performance loss vector according to the descending order of subsystem weights The total amount of performance surplus Q will be redistributed in an orderly manner to the subsystems with insufficient performance;

[0034] Presets is the maximum number of subsystems that can be satisfied by the performance surplus, and the range of the total performance surplus Q is expressed as:

[0035]

[0036] Furthermore, in S1, the method of obtaining the sum of weighted performance losses of the performance-sharing serial-parallel hybrid multi-state system is:

[0037] Preset W = (w 1 ,w 2 ,...,w m ) is the subsystem weight vector, and w i is the weight of the ith subsystem;

[0038] After redistributing the total performance surplus Q, the remaining performance deficit of all subsystems will be represented by the new vector Indicates, set represents the remaining performance loss of the ith subsystem after performance sharing, then for:

[0039]

[0040] Furthermore, the sum of weighted performance losses WF of the performance-sharing serial-parallel hybrid multi-state system is:

[0041]

[0042] Furthermore, in S2, a tree-like MDD model of a performance-sharing serial-parallel hybrid multi-state system is constructed layer by layer, and a simplified MDD model is obtained by designing and applying multiple simplification rules:

[0043] Firstly, a tree-like MDD model of performance-sharing serial-parallel hybrid multi-state system is constructed layer by layer, which includes;

[0044] Establish an MDD model, which contains multiple non-terminal nodes and is used to represent the logical reliability expression of a constrained serial-parallel hybrid polymorphic system with heterogeneous components and a common bus.

[0045] In the lth level of the MDD model, each non-terminal node has r l *k l branches to represent component N l any possible state;

[0046] A special non-terminal node is introduced at the mk+1 layer, which corresponds to the random variable C of the common bus, where each MDD node at the mk+1 layer has v branches;

[0047] There are two different termination nodes in the mk+2 layer, marked as "0" or "1", "0" or "1" respectively representing the failure or normality of the performance sharing serial-parallel hybrid multi-state system;

[0048] Enumerate all system states of performance-sharing serial-parallel hybrid polymorphism, and the MDD model will present a tree structure with From non-terminal node X 1 The path leading to the terminal node of the mk+2 layer;

[0049] Arrange all subsystems in descending order of weight to obtain a tree-like MDD model, in which the nodes representing the components of the subsystems with the largest weights are constructed in the first k layers of the MDD model, while the nodes representing the components of the subsystems with smaller weights are constructed in the (m-1)*k to m*k layers;

[0050] Then, a number of simplification rules are designed and applied to obtain a streamlined MDD model, which includes:

[0051] The partial system state is represented by a three-variable array T, which is associated with the cumulative performance surplus of the subsystems contained in the partial system, the performance loss vector of the subsystems contained in the partial system, and the total performance surplus or loss of the remaining components, and the partial system state is updated by calculating a new three-variable array T;

[0052] By integrating the partial system states with all possible states of the remaining system, the state of the entire system can be determined, that is, the state of the entire system is derived from the partial system states through truncation operations;

[0053] Set the remaining system by Subsystems and numbers l to Several components, set Represents the performance loss vector of the subsystem. For the non-terminal nodes of the first mk layers in the MDD model, set rules one, two, three, four, five, six and seven to truncate and merge the branches in the MDD model. Set rules eight and nine to reduce the non-terminal nodes of the mk+1 layer. Apply multiple simplification rules to the tree-like MDD model to obtain a streamlined MDD model.

[0054] Furthermore, the preset RT is the maximum weighted performance loss value allowed by the system;

[0055] Rule 1: If the sum of weighted performance losses of subsystems can satisfy WF after performance sharing 1 ≤RT, that is, before subsystem and There is performance surplus in all subsystems, number The minimum performance loss of the subsystem to m is compensated when the calculated weighted performance loss sum WF 1 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node of the lth layer, where

[0056] Rule 2: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 2 ≤RT, that is, before There is performance surplus in the subsystem. Performance loss and number of subsystems The minimum performance loss of the subsystem to m is compensated when the calculated weighted performance loss sum WF 2 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node in the lth layer, where

[0057] Rule 3: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 3≤RT, that is, before The subsystem has performance loss, while the There is performance surplus in each subsystem. Performance loss and number of subsystems When the minimum performance loss of the subsystem to m is compensated, if the calculated weighted performance loss sum WF 3 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node in the lth layer, where

[0058] Rule 4: If the sum of the weighted performance losses of the subsystems can satisfy WF after performance sharing 4 >RT, that is, front The performance loss of each subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 4 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0059] Rule 5: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 5 >RT, that is, front subsystem and The performance losses of each subsystem are numbered When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 5 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0060] Rule 6: If the sum of the weighted performance losses of the subsystems can satisfy WF after performance sharing 6 >RT, that is, when the The performance loss of the subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 6 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0061] The rule seven is: for non-terminal MDD nodes representing different partial system states at the same level, if the ternary arrays T of the partial system states corresponding to these non-terminal nodes are the same, then they have the same subgraph.

[0062] Furthermore, the eighth rule is: under the minimum transmission capacity, if the sum of the weighted performance losses of the subsystems is redistributed, the accumulated performance surplus After that, if it still does not exceed the pre-designed RT value, that is, WF≤RT, then the terminal node marked as "1" can be connected to the branch from the non-terminal MDD node of the nth layer;

[0063] The ninth rule is: Under the maximum transmission capacity, if the sum of the weighted performance losses of the subsystems is redistributed to the cumulative performance surplus After that, it still does not exceed the pre-designed RT value, that is, WF>RT, then the terminal node marked as "0" can be connected to the branch from the non-terminal MDD node of the nth layer.

[0064] Furthermore, in S3, the state classification rule and reliability calculation rule of the performance sharing serial-parallel hybrid multi-state system are obtained as follows:

[0065] A Boolean function A is preset to classify the operation or failure of the system, and the expression of the classification rule is:

[0066]

[0067] In the formula, A(x) is a Boolean function with only two outputs: 0 and 1. 0 indicates that the system works normally, and 1 indicates that the system fails.

[0068] Then the probability of normal operation of the performance-sharing serial-parallel hybrid multi-state system, that is, the system reliability R, can be calculated according to the following reliability calculation rule:

[0069]

[0070] In the formula, For any internal b, any possible value c of C b , For any external x, it is any possible value x of X.

[0071] Furthermore, in S3, the reliability of the performance-sharing serial-parallel hybrid multi-state system is calculated using the MDD model based on the reliability calculation rule as follows:

[0072] Based on the correspondence between the MDD model and the reliability calculation rules of the performance-sharing serial-parallel hybrid multi-state system, it is found that the system reliability R of the performance-sharing serial-parallel hybrid multi-state system is equal to the sum of the path probabilities leading to the terminal node "1" in the MDD model, where the path probability is obtained by multiplying the probabilities of all edge edges appearing in the path, and any edge probability is equal to the probability that a component is in a specific state.

[0073] The sum of all path probabilities leading to the terminal node "1" in the MDD model is calculated recursively as follows;

[0074]

[0075] Where, Pr(MDD b ) represents the non-terminal node MDD of the lth layer b Node probability; Pr(MDD b .Edge) indicates that the node is connected to the child node MDD through the Edge edge. b The probability of Represents component N l The probability that the layer l component represented by the Edge is in a specific state.

[0076] Technical effects and advantages of the reliability analysis method of the performance-sharing serial-parallel hybrid multi-state system of the present invention:

[0077] 1. This invention attempts to establish a reliability model for a performance-sharing serial-parallel hybrid system for the first time, and takes into account performance defect tolerance, transmission loss, and different weights of subsystems;

[0078] 2. By establishing the MDD model of performance-sharing serial-parallel hybrid multi-state system, it can be repeatedly used to evaluate the system reliability under different parameters, thus facilitating system optimization and adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a schematic flow chart of the reliability analysis method of the performance sharing serial-parallel hybrid multi-state system of the present invention;

[0080] Figure 2 Schematic diagrams of a case structure of a non-terminal node of a component of the present invention (a), a case structure of a non-terminal node of a common bus (b), and a path leading to a terminal node '1' in an MDD model (c);

[0081] Figure 3 This is a schematic diagram of the truncation operation described in Rule 1 of the present invention;

[0082] Figure 4 This is a schematic diagram of the truncation operation described in Rule 2 of the present invention;

[0083] Figure 5 This is a schematic diagram of the truncation operation described in Rule 3 of the present invention;

[0084] Figure 6 This is a schematic diagram of the truncation operation described in Rule 4 of the present invention;

[0085] Figure 7 This is a schematic diagram of the truncation operation described in Rule 5 of the present invention;

[0086] Figure 8 This is a schematic diagram of the truncation operation described in Rule 6 of the present invention;

[0087] Fig. 9 This is a schematic diagram of the merging operation described in Rule 7 of the present invention;

[0088] Fig.10 It is a schematic diagram of a more compact MDD model in the exemplary system of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] Example 1

[0091] See also Figure 1 to Figure 2 As shown, the reliability analysis method of the performance sharing serial-parallel hybrid multi-state system described in this embodiment includes the following steps:

[0092] S1. Construct a performance-sharing serial-parallel hybrid polymorphic system, and obtain the total performance surplus S, the total performance loss F, the probability of being in a specific state, the total redistributable performance surplus, and the sum of the weighted performance loss of the performance-sharing serial-parallel hybrid polymorphic system, wherein the performance-sharing serial-parallel hybrid polymorphic system is composed of m subsystems connected by a common bus, and each subsystem includes k parallel-configured components;

[0093] S2. constructing an MDD model of a performance-sharing serial-parallel hybrid polymorphic system, wherein the process of constructing the MDD model of a performance-sharing serial-parallel hybrid polymorphic system includes: constructing a tree-like MDD model of the performance-sharing serial-parallel hybrid polymorphic system layer by layer, and designing and applying multiple simplification rules to obtain a simplified MDD model;

[0094] S3. Calculate the reliability of the performance-sharing serial-parallel hybrid polymorphic system based on the MDD model, wherein the process of calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system includes: obtaining the state classification rules and reliability calculation rules of the performance-sharing serial-parallel hybrid polymorphic system, and calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system using the MDD model based on the reliability calculation rules.

[0095] Furthermore, in S1, the method of obtaining the total performance surplus S and the total performance loss F of the performance-sharing serial-parallel hybrid multi-state system is as follows:

[0096] Set the i-th subsystem U i(1≤i≤m) consists of k heterogeneous components connected in parallel and is represented by N (i-1)k+1 ,N (i-1)k+2 ,…,N ik , each component consists of a random performance variable and random demand variables express;

[0097] Set a component N j Own r j The performance level of the degradation and k j demand level, for performance g jp and demand jq Component N j , preset X j For component N j The state random variable is denoted as X j ='g jp ,d jq '(1≤p≤r j , 1≤q≤k j );

[0098] Specific, performance variables From the set g j = {g j1 ,g j2 ,…,g jrj} Take the value of a given probability mass function (PMF); set Represents component N j The level of demand that may be met, where d jkj Demand variables Take the given PMF value; for the i-th subsystem, it consists of k components numbered from (i-1)k+1 to ik; preset (X (i-1)k+1 ,X (i-1)k+2 ,…,X ik ) is a subsystem U i The random state vector (x (i-1)k+1 ,x (i-1)k+2 ,…,x ik ) is a specific instance (state) of the subsystem state vector, so the subsystem U i The number of states of the subsystem U is equal to the number of combinations of states of different components connected in parallel, that is, i have status.

[0099] Setting G i Represents subsystem U i Performance, G i It is calculated from the total performance of k components from (i-1)k+1 to ik, and its expression is:

[0100]

[0101] Furthermore, similarly, subsystem U i Demand D i is calculated by the sum of the component requirements, and its expression is:

[0102]

[0103] Default H i is a performance G corresponding to the state of the i-th subsystem i and demand D i A random variable, namely H i ='G i ,D i ';

[0104] If G i ≥D i , then the subsystem U i The performance surplus Si that satisfies the demand is expressed as S i =G i -D i , but failed to fully satisfy the subsystem U i The required performance loss is F i = 0, otherwise, the performance surplus is S i =0, performance loss is F i =G i -D i ;

[0105] Therefore, the total performance surplus S of the performance-sharing series-parallel hybrid multi-state system is the sum of the performance surpluses of all subsystems, that is:

[0106]

[0107] The total performance loss F can be calculated as the sum of the performance losses of all subsystems, that is:

[0108]

[0109] Furthermore, in S1, the method for obtaining the probability that the performance sharing serial-parallel hybrid multi-state system is in a specific state is:

[0110] Set X = (X 1 ,X 2 ,...,X mk ) represents the state vector of the random system, and x=(x 1 ,x 2 ,...,x mk ) is a state (specific instance) of variable X, where x j ='gjp ,d jq 'Represented as component N j Therefore, there is a state in the system The number of different states or possible values ​​of x;

[0111] For X j ='g jp ,d jq 'State component N j The probability of Right now

[0112] Furthermore, the probability that the performance-sharing serial-parallel hybrid multi-state system is in a specific state can be expressed as:

[0113]

[0114] Furthermore, in S1, the method for obtaining the total amount of redistributable performance surplus of the performance-sharing serial-parallel hybrid polymorphic system is as follows:

[0115] Assuming θ is the loss percentage of the total performance surplus S, the performance surplus after the loss is (1-θ)*S;

[0116] Assume that the common bus has a discrete transmission capacity represented by a random variable C with a given PMF, then the random variable C is selected from the set {c 1 ,c 2 ,...,c v}(There are v possible values ​​of C) with corresponding probability Pr(C=c b ) value;

[0117] Furthermore, the total amount of redistributable performance surplus of the performance-sharing serial-parallel hybrid polymorphic system is:

[0118]

[0119] Specifically, since all subsystems are connected through a public bus, the performance sharing mechanism only occurs between subsystems. When the performance of a subsystem exceeds its demand, the excess performance can be reallocated to other subsystems with insufficient performance. Considering the impact of transmission loss, the total performance surplus S transmitted to the subsystem with insufficient performance will decrease. This paper sets the transmission performance loss to be proportional to the total performance surplus transmitted. In addition, the amount of performance surplus allowed to be transmitted is limited by the capacity of the public bus.

[0120] It should be noted that the limited series-parallel hybrid polymorphic system can tolerate a certain degree of performance deficiency. The subsystems in the system are set to have different weights, among which the subsystems with higher weights are more important; therefore, the performance sharing mechanism preferentially transfers the performance surplus to the subsystems with higher weights and insufficient performance; further, if the sum of the weighted performance losses of all subsystems after redistributing the performance surplus is not greater than the pre-specified threshold, the limited series-parallel hybrid system is determined to be reliable, and the preset value represents the maximum weighted performance loss value allowed by the entire system, represented by RT.

[0121] Preset (F 1 ,F 2 ,…,F m ) represents the performance defect vector of all subsystems, and introduces the performance loss vector according to the descending order of subsystem weights The total amount of performance surplus Q will be redistributed in an orderly manner to subsystems with insufficient performance;

[0122] Presets is the maximum number of subsystems that can be satisfied by the performance surplus, and the range of the total performance surplus Q is expressed as: In the formula, d' is an indicator, which means from 1 to

[0123] Furthermore, in S1, the sum of the weighted performance losses of the performance-sharing serial-parallel hybrid multi-state system is obtained as follows:

[0124] Preset W = (w 1 ,w 2 ,...,w m ) is the subsystem weight vector, and w i is the weight of the ith subsystem;

[0125] After redistributing the total performance surplus Q, the remaining performance deficit of all subsystems will be represented by the new vector Indicates, set represents the remaining performance loss of the ith subsystem after performance sharing, then for:

[0126]

[0127] Furthermore, the sum of weighted performance losses WF of the performance-sharing serial-parallel hybrid multi-state system is:

[0128]

[0129] Firstly, a tree-like MDD model of performance-sharing serial-parallel hybrid multi-state system is constructed layer by layer, which includes;

[0130] The MDD model contains multiple non-terminal nodes, which are used to represent the logical reliability expression R of a constrained serial-parallel hybrid multi-state system with heterogeneous components and a common bus;

[0131] In the lth layer of the MDD model (1≤l≤mk), each non-terminal node has r l *k l branches to represent component N l Any possible state of node X l The'g l1 ,d l1 '-edge represents component N l With performance l1 and demand l1 , which can be expressed as X l ='g l1 ,d l1 ';Node X l of -Edge represents component N l With performance and demand It can be expressed as Therefore, these non-terminal MDD nodes can be represented by case structures, such as Figure 2 (a)

[0132] A special non-terminal node is introduced in the mk+1 layer, which corresponds to the random variable C of the public bus, such as Figure 2 (b), where each MDD node at the mk+1 layer has v branches, each of which represents a possible transmission capacity of the public bus. mk+1 'c 1 '-edge indicates that the maximum performance surplus of the public bus transmission does not exceed the capacity c 1 , similarly, node X mk+1 'c v '-edge indicates that the maximum performance surplus of the public bus transmission does not exceed the capacity c v ;

[0133] There are two different termination nodes in the mk+2 layer (the last layer), marked as "0" or "1", "0" or "1" respectively representing the failure or normality of the performance sharing serial-parallel hybrid multi-state system;

[0134] It should be noted that from the non-terminal node X 1 The path to the terminal node contains the component state and the transmission capacity of the common bus. The path represents a specific system state x under the capacity constraint of the common bus. 1 ,x 2 ,...,x mk), where component N j The state x j By node X j x j -edges. Therefore, for a specific system state x and common bus capacity, if the sum of weighted performance losses of all subsystems is not greater than the predetermined value after performance sharing, that is, WF≤RT or A(x)=1, then the path leads to the terminal node marked as "1", otherwise the path leads to the terminal node marked as "0";

[0135] In the above example, the states of the four components are "5, 3", "4, 4", "1, 2" and "2, 3". Therefore, the system MDD model contains a path from the non-terminal node X 1 The path leading to the terminal node "1" is composed of node X 1 "5,3"-edge, node X 2 "4,4"-edge, node X 3 "1,2"-edge, node X 4 The "2,3"-edge of node A and the "2"-edge of node C. Figure 2 As shown in (c), this path means that the system under consideration is in a state x = ('5,3','4,4','1,2','2,3') with capacity C = 2 limitation, so the sum of weighted performance defects of the subsystems is WF = 1, that is, A(x) = 1.

[0136] Enumerate all system states of performance-sharing serial-parallel hybrid polymorphism, and the MDD model will present a tree structure with From non-terminal node X 1 The path leading to the terminal node of the mk+2 layer;

[0137] Specifically, the partial system state corresponding to the non-terminal MDD node at the lth layer consists of two parts: subsystem state and component state. Given that the number of components contained in a subsystem is k, the number of subsystems contained in the partial system is Therefore, some system states can be set as This shows that part of the system is composed of Subsystem and number to l-1 components. For example, Figure 2 As shown in (c), from node X 1 The path to the level 4 node includes not only node X 1 (5,3)-edge, node X 2 The (4,4)-edge and node X 3The (1,2)-edge also represents that the partial system state is y = ('5,3','4,4','1,2') = ('9,7','1,2'). At the same time, the root node of the first layer indicates that the system is in an empty state, that is, y = null.

[0138] Arrange all subsystems in descending order of weight to facilitate the construction of the MDD model of the restricted series-parallel hybrid multi-state system, where the nodes representing the components contained in the subsystem with the largest weight are constructed in the first k layers of the MDD model, and the nodes representing the components contained in the subsystem with smaller weight are constructed in the (m-1)*k layer to the m*k layer;

[0139] Then, a number of simplification rules are designed and applied to obtain a streamlined MDD model, which includes:

[0140] The partial system state is represented by a three-variable array T, which is associated with the cumulative performance surplus of the subsystems contained in the partial system, the performance loss vector of the subsystems contained in the partial system, and the total performance surplus or loss of the remaining components, and the partial system state is updated by calculating a new three-variable array T;

[0141] Specifically, for the i ='G i ,D i 'Subsystem U of the state i , can be represented by a three-variable array T as follows:

[0142]

[0143] And the three-variable array T can also be used to represent the state x j ='g jp ,d jq ' components can be expressed as follows:

[0144] T(x j ='g jp ,d jq ')=(0,null,g jp -d jq ),

[0145] Therefore, some system states It is represented by a three-variable array T, which is associated with the cumulative performance surplus of the subsystems contained in the partial system, the performance loss vector of the subsystems contained in the partial system, and the total performance surplus or loss of the remaining components, which is expressed as follows:

[0146]

[0147] in, and They represent the cumulative performance surplus of the subsystem and the total performance surplus or deficit of the remaining components, respectively. Represents the performance loss vector of the subsystem (may include zero values). In particular, when y = null, the corresponding ternary array is T(Y = y) = (0, null, 0). The non-terminal nodes of the MDD model can be represented as part of the system state during the model generation process.

[0148] For the node X l (g lp ,d lq )-edge-guided l+1th layer non-terminal nodes, the new three-variable array T′ can be further calculated as:

[0149]

[0150] By integrating the partial system states with all possible states of the remaining system, the state of the entire system can be determined, that is, the state of the entire system is derived from the partial system states through truncation operations;

[0151] Specifically, set is the remaining system state corresponding to the partial system state Y, which indicates that the remaining system is composed of Subsystems and numbers l to It is composed of several components. represents a specific remaining system state. Therefore, the three-variable array T of the remaining system state can be expressed as:

[0152]

[0153] The maximum cumulative performance surplus of the subsystem and the maximum total performance surplus of the component corresponding to the remaining system state Z are used instead of all possible states of the remaining system, which are specifically expressed as follows:

[0154]

[0155] in,

[0156] Similarly, the minimum performance loss vector of the subsystem and the minimum total performance loss vector of the component corresponding to the remaining system state Z can be obtained by the following formula:

[0157]

[0158] in, and

[0159] For the ternary array T corresponding to the partial system state, the elements of the performance loss vector should be satisfied in turn by the cumulative performance surplus of each subsystem under the limitation of transmission capacity, and the total performance surplus or loss of each component is used to generate the performance loss vector through the numbers l to All possible states of the remaining components of The performance surplus or loss of each subsystem.

[0160] Specifically, set Q 1 It is to redistribute the performance surplus under the minimum transmission capacity After that, number 1 to The remaining performance surplus or loss of the subsystem is Then, let the vector is the residual performance loss vector of the partial system, where F i ′ represents the redistribution of performance surplus After that, subsystem U i The remaining performance loss is calculated as follows:

[0161]

[0162] where k′ can be obtained by Considering the minimum total performance loss corresponding to the expression Min{T(Z)}, the The performance surplus or loss of a subsystem can be expressed as

[0163] If Q 1 ≥0 and Q 2 ≥0, then the minimum performance loss vector in the expression Min{T(Z)} The elements in can be represented by the remaining performance surplus Q 1 and The performance surplus Q of each subsystem 2 , fully or partially satisfied at all possible transmission capacities. The vector Can be used to indicate that the subsystem is redistributing redundant performance The remaining performance loss after It can be obtained as follows:

[0164]

[0165] in, and can be Conclude.

[0166] Therefore, if the numbering changes from If the sum of weighted performance losses of subsystems up to m does not exceed the maximum tolerable threshold RT, the states of non-terminal MDD nodes in layers l, l+1, l+2, …, n can be ignored. This means that the states of the remaining non-terminal nodes have no effect on system reliability. Therefore, the MDD model can be made more compact by the following rules:

[0167] Set the remaining system by Subsystems and numbers l to Several components, set Represents the performance loss vector of the subsystem. For the non-terminal nodes of the first mk layers in the MDD model, set rules one, two, three, four, five, six and seven to truncate and merge the branches in the MDD model. Set rules eight and nine to reduce the non-terminal nodes of the mk+1 layer. Applying these simplified rules to the tree-like MDD model can obtain a streamlined MDD model.

[0168] Furthermore, rule 1 is: if the sum of the weighted performance losses of the subsystems can satisfy WF after performance sharing 1 ≤RT, that is, before subsystem and There is performance surplus in all subsystems, number The minimum performance loss of the subsystem to m is compensated when the calculated weighted performance loss sum WF 1 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node of the lth layer, where

[0169] Rule 2: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 2 ≤RT, that is, before There is performance surplus in the subsystem. Performance loss and number of subsystems The minimum performance loss of the subsystem to m is compensated when the calculated weighted performance loss sum WF 2 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node in the lth layer, where

[0170] Rule 3: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 3 ≤RT, that is, before The subsystem has performance loss, while the There is performance surplus in each subsystem. Performance loss and number of subsystems When the minimum performance loss of the subsystem to m is compensated, if the calculated weighted performance loss sum WF 3 Within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node in the lth layer, where

[0171] Rule 4: If the sum of the weighted performance losses of the subsystems can satisfy WF after performance sharing 4 >RT, that is, forward The performance loss of each subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 4 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0172] Rule 5: If the sum of weighted performance losses of the subsystems can satisfy WF after performance sharing 5 >RT, that is, forward subsystem and The performance losses of each subsystem are numbered When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 5 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0173] Rule 6: If the sum of the weighted performance losses of the subsystems can satisfy WF after performance sharing 6 >RT, that is, when the The performance loss of each subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF 6 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where

[0174] Specifically, consider two non-terminal nodes on the same level with different partial system states y 1 and 2 ; In this case, each possible remaining system state z corresponding to these two non-terminal nodes satisfies the equation T(Y=y 1 )+T(Z=z)=T(Y=y 2 )+T(Z=z); therefore, we can derive the following rules:

[0175] Rule seven is: For non-terminal MDD nodes representing different partial system states at the same level, if the ternary arrays T of the partial system states corresponding to these non-terminal nodes are the same, then they have the same subgraph.

[0176] For the mk+1 layer non-terminal MDD nodes connected to the mk layer node branches, they contain information about the entire system state, such as the cumulative performance surplus and performance loss vectors of all subsystems, which can be found in the ternary array T of the entire system state. represents the cumulative performance surplus of all subsystems, (F 1 ,F 2 ,…,F m ) represents the performance loss vector of all subsystems. In addition, the branches of the non-terminal nodes of the mk+1 layer represent the capacity of the public bus. Under all possible transmission capacities, if the non-terminal nodes of the mk+1 layer can meet the following rules, a more compact MDD model can be constructed through further pruning.

[0177] Furthermore, Rule 8 is: Under the minimum transmission capacity, if the sum of the weighted performance losses of the subsystems is redistributed to the cumulative performance surplus After that, if it still does not exceed the pre-designed RT value, that is, WF≤RT, then the terminal node marked as "1" can be connected to the branch from the non-terminal MDD node of the nth layer;

[0178] Rule 9: Under maximum transmission capacity, if the sum of weighted performance losses of subsystems is redistributed to the cumulative performance surplus After that, it still does not exceed the pre-designed RT value, that is, WF>RT, then the terminal node marked as "0" can be connected to the branch from the non-terminal MDD node of the nth layer.

[0179] Further, in S3, the state classification rule and reliability calculation rule of the performance sharing serial-parallel hybrid multi-state system are obtained as follows:

[0180] A Boolean function A is preset to classify the operation or failure of the system, and the expression of the classification rule is:

[0181]

[0182] Where WF represents the sum of weighted performance losses, RT represents the maximum weighted performance loss value, i.e., the predetermined threshold, and A(x) represents a Boolean function with only two outputs, 0 and 1. 0 represents the normal operation of the system, and 1 represents the system failure.

[0183] Then the probability of normal operation of the performance-sharing serial-parallel hybrid multi-state system, that is, the system reliability R, can be calculated according to the following reliability calculation rule:

[0184]

[0185] In the formula, the calculation order is from inside to outside, For any internal b, any possible value c of C b , For any external x, it is any possible value x of X.

[0186] Further, in S3, the reliability of the performance-sharing serial-parallel hybrid multi-state system is calculated using the MDD model based on the reliability calculation rule as follows:

[0187] Based on the correspondence between the MDD model and the reliability calculation rules of the performance-sharing serial-parallel hybrid polymorphic system, it is found that the system reliability R of the performance-sharing serial-parallel hybrid polymorphic system is equal to the sum of the probabilities of all paths leading to the terminal node "1" in the MDD model, where the path probability is obtained by multiplying the probabilities of all edge edges appearing in the path. Any edge probability is equal to the probability that a component is in a specific state or the probability that node C has a specific capacity.

[0188] The sum of all path probabilities leading to the terminal node "1" in the MDD model is calculated recursively as follows;

[0189]

[0190] Where, Pr(MDD b ) represents the non-terminal node MDD of the lth layer b Node probability; Pr(MDD b .Edge) indicates that the node is connected to the child node MDD through the Edge edge. b probability; Represents component N l The probability that the layer l component represented by the Edge is in a specific state or the probability that node C has a specific capacity.

[0191] Specifically, in the constructed MDD model, the path leading to the terminal node "1" indicates that under the capacity limit of the common bus, the sum of the weighted performance losses of each subsystem in the considered system does not exceed the pre-designed threshold RT, that is, WF≤RT. Conversely, the path leading to the terminal node "0" indicates that under the capacity limit of the common bus, the sum of the weighted performance losses of each subsystem in the considered system is greater than the pre-designed threshold RT, that is, WF>RT. However, according to the Shannon decomposition expression, the actual calculated system reliability R is obtained by recursively calculating the node probability from the terminal node to the first-level root node, rather than automatically summarizing the occurrence probability. Therefore, using this recursive calculation method, the system reliability R is equal to the node probability of the first-level root node.

[0192] Example 2

[0193] See also Figures 3 to 10 As shown, the reliability analysis method of the performance sharing serial-parallel hybrid multi-state system described in this embodiment, an example system, is as follows;

[0194] In a performance-sharing serial-parallel hybrid multi-state system, every two heterogeneous components with different performance levels and demand levels are configured in parallel to form a subsystem, and each subsystem is connected to a common bus that can be used to transmit redundant performance. When a subsystem cannot meet its needs, the total performance surplus of other subsystems can be transmitted to the subsystem with insufficient performance through the common bus. The performance loss of subsystems with higher weights is preferentially met by the system. Therefore, the common bus capacity and the corresponding random probability are set to c = {7, 6, 5} and γ = {0.8, 0.1, 0.1} respectively. The weight distribution of the two subsystems is W = (4, 3). In addition to the influence of the common bus capacity, the amount of redundant performance allowed to be transmitted through the common bus is also affected by the performance loss rate. The loss rate is set to θ = 0.5.

[0195] In addition, the fault-tolerant system can tolerate a certain degree of performance loss. If the sum of the weighted performance losses of all subsystems does not exceed the pre-designed critical value, the system under consideration is considered to be working properly. The maximum performance loss that the example system can tolerate (i.e., the pre-designed value or preset value) is set to RT = 2. Table 3 provides the configuration of each component: performance level, demand level, corresponding performance and demand probability.

[0196] Table 3 Performance levels and requirements of components in the system considered

[0197]

[0198] Without any truncation or restoration operations, the traditional MDD model with a tree structure can be constructed by enumerating all system states. Specifically, the MDD root node X 1represents the empty partial system state y = null and is created at the first level by the corresponding ternary array T(Y = y) = (0, null, 0). 1 With 3 performance levels and 2 demand levels, each node has 6 different states: '5,5', '5,0', '3,5', '1,5' and '1,0', represented by 6 branches.

[0199] At layer 2, from node X 1 To Node X 2 The new partial system state represented by the path is equal to node X 1 The branch state of node X 1 The partial system state guided by the branch of can be represented as the corresponding branch state. For example, node X 1 The partial system state guided by the (5,5)-edge is y = ('5,5'), and the node X 1 The partial system state led by the (1,0)-edge of is y = ('1,0'). According to the non-terminal node X 1 The branch state of non-terminal node X 2 The corresponding three-variable tuple T of the partial system state can be calculated by the formula corresponding to the new three-variable array. 1 The triplet T guided by the (5,5)-edge is T = (0,null,5-5) = (0,null,0), which is composed of node X 1 The (1,0)-edge-guided triplet T is T = (0, null, 1-0) = (0, null, 1). Since the component N 2 There are 3 performance levels and 2 demand levels, each non-terminal node X 2 There are 6 different states: '6,6', '6,4', '5,6', '5,4', '2,6' and '2,4', represented by 6 branches.

[0200] At layer 3, by inserting node X into the partial system state vector created at layer 2 2 The corresponding branch state of node X is created 2 The new partial system state guided by the branch. For example, in the leftmost path, since the partial system state vector created by layer 2 is y = ('5,5'), node X 2 The new partial system state led by the (6,6)-edge of the node X is obtained by inserting the corresponding branch state into the partial system state vector, which can be expressed as y = ('5,5','6,6'). Similarly, in the rightmost path, the partial system state vector created by layer 2 is y = ('1,0'), so node X 2The new partial system state led by the (2,4)-edge is y = ('1,0','2,4'). 2 The branch state of non-terminal node X 3 The corresponding ternary array T of the partial system state can also be calculated by the formula corresponding to the new three-variable array. For example, in the leftmost and rightmost paths, the node X 2 The new triplet T introduced by the (6,6)-edge is T = (0 + (6-6), (0), 0) = (0, (0), 0), which is composed of the node X 2 The new triplet T guided by the (2,4)-edge is T = (0+0, (1+(2-4)), 0) = (0, (-1), 0). Since the component N 3 There are 3 performance levels and 2 demand levels, each non-terminal node X 3 It has 6 different states: '4,3', '4,1', '3,3', '3,1', '1,3' and '1,1', represented by 6 branches.

[0201] Similarly, at level 4, by adding node X 3 The branch state of is inserted into the partial system state vector created in layer 3 to create node X 4 The new partial system state, and node X 4 The corresponding new three-element array T of partial system state can also be calculated by the formula corresponding to the new three-variable array. For example, in the leftmost path, since the partial system state vector created by layer 3 is y = ('5,5','6,6'), by inserting the corresponding branch state into the vector ('5,5','6,6'), node X 3 The new partial system state guided by the (4,3)-edge can be expressed as y = ('5,5','6,6','4,3'); and the node X 3 The triplet T guided by the (4,3)-edge is T = (0, (0), 0 + (4-3)) = (0, (0), 1). In the rightmost path, the partial system state vector created by layer 3 is y = ('1, 0', '2, 4'). Therefore, the 3 The new partial system state guided by the (1,1)-edge can be expressed as y = ('1,0', '2,4', '1,1'), and the node X 3 The (1,1)-edge-guided ternary array T can be expressed as T = (0, (-1), 0 + (1-1)) = (0, (-1), 0). Since the component N 4 There are 3 performance levels and 2 demand levels, each non-terminal node X 4It has 6 different states: '4,4', '4,3', '3,4', '3,3', '2,4' and '2,3', and is represented by 6 branches. In addition, the new partial system state and the corresponding three-variable tuple of the 5th level non-terminal node are calculated in the same way as for the node X 4 For example, since the partial system state vector created at layer 3 in the leftmost path is y = ('5,5','6,6','4,3'), node X 4 The partial system state guided by the (4,4)-edge is y = ('5,5','6,6','4,3','4,4'), and the node X 4 The corresponding ternary array T is T = (0 + (1 + (4-4)), (0,0), 0) = (1, (0,0), 0). Note that the new ternary array T now represents the ternary array of the entire system state.

[0202] Since the common bus has three capacity levels, each non-terminal MDD node C at the 5th layer has three branches: (3)-edge, (2)-edge, and (1)-edge. Under the capacity constraints of the common bus guided by the branches of node C, the redistributable performance surplus should give priority to satisfying the performance losses of subsystems with higher weights. If the sum of the weighted performance losses of all subsystems in the example system is not greater than the pre-designed RT value, the branch corresponding to the non-terminal node at the 5th layer should be connected to the terminal node marked with '1', otherwise it should be connected to the terminal node marked with '0'. Therefore, the polymorphic decision tree model used to analyze the reliability of the example system is constructed according to the above process, and the number of nodes at each layer is shown in Table 4.

[0203] Table 4. Number of nodes at each level in the example MDD model

[0204]

[0205] Because all possible states of components need to be enumerated, the computational efficiency of system reliability assessment methods based on decision tree models is poor or even impractical, especially when the number of components is large. Therefore, in order to avoid a large number of useless or redundant extensions in decision tree models, some rules can be used to build a more compact MDD model.

[0206] By performing the truncation operations described in rules 1, 2, and 3, some non-terminal MDD nodes can be directly connected to the terminal node '1' instead of the non-terminal node. For example, based on the operation described in rule 1, the node X represented as T = (3, (0), 0) can be directly connected to the terminal node '1' instead of the non-terminal node. 3The (4,2)-edge guided by the corresponding branch is truncated, where the ternary array T guided by the corresponding branch is T = (3, (0), 2). Since the performance loss of subsystems with larger weights is satisfied first, the accumulated performance surplus of subsystems in some systems can be used to compensate the elements of the performance loss vector in an orderly manner. Under the constraints of minimum capacity and transmission loss, the total remaining performance surplus of the subsystems after redistribution of the performance surplus is Q 1 =1.5. In addition, the sum of the minimum performance losses of the components in the remaining system is -1, so the remaining performance surplus of each component is calculated as Q 2 = 0. The remaining performance surplus Q in the subsystem 1 = 1.5 and the remaining performance surplus Q of each component 2 = 0, which meets the condition of Rule 1. Therefore, considering all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the minimum performance deficit vector of the subsystem in the remaining system state is actually a null vector, and the remaining performance surplus Q of the available subsystem is 1 and the remaining performance surplus Q of the component 2 To compensate. In view of this, the sum of the weighted performance losses of all subsystems is 0, which is within the tolerable performance loss range of the system, that is, WF=0<RT. Figure 3 As shown, the terminal node '1' and the node X 3 The (4,2)-edges of the nodes are directly connected, instead of regenerating a non-terminal MDD node. Similarly, according to Rule 1, there are 5 other cases where truncation is allowed.

[0207] Since the node X represented by T = (5, (0), 0) 3 The calculation of the triple array T guided by the (2,4)-edge is T = (5, (0), -2), and the corresponding edges can be truncated according to the description of Rule 2. The performance loss of the subsystem with larger weight is satisfied first, so under the influence of the minimum capacity constraint and transmission loss, the total performance surplus of the subsystem after redistribution of the performance surplus is Q 1 =2.5. In addition, the sum of the minimum performance defects of the components in the remaining system is -1, so the calculated remaining performance loss of the components is Q 2 = -3. The remaining performance surplus in the subsystem is Q 1 = 2.5 and the remaining performance loss of the component is Q 2 = -3, which meets the condition of Rule 2. Therefore, under the constraint of all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the remaining performance loss Q 2 The minimum performance loss vector of the remaining system states can be given by the remaining performance surplus Q 1Orderly compensation. In view of this, the sum of the weighted performance losses of all subsystems is 1.5, which is within the tolerable performance loss range of the system, that is, WF=1.5<RT. Figure 4 As shown, the terminal node '1' and the node X 3 The (2,4)-edges of the nodes are directly connected, instead of regenerating a non-terminal MDD node. Similarly, according to the description of Rule 2, there are 12 other allowed truncation situations.

[0208] The truncation operation described in Rule 3 is used only once, that is, the non-terminal node X represented by T = (0, (-1), 0) 3 The (4,2)-edge of the corresponding edge is calculated as T = (0, (-1), 2). Since the performance loss of the subsystem with higher weight is satisfied first, affected by the minimum capacity constraint and transmission loss, the remaining total performance loss of the subsystem after redistributing the performance surplus is Q 1 = -1. In addition, the sum of the minimum performance defects of each component in the remaining system is -1, so the remaining performance surplus of each component is Q 2 = 1. The remaining performance loss in the subsystem is Q 1 = -1 and the remaining performance surplus of each component is Q 2 = 1, which satisfies the condition of Rule 3. Therefore, considering all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the remaining performance loss Q 1 The minimum performance loss vector of the remaining system can be obtained by the remaining performance surplus Q 2 Orderly compensation. In view of this, the sum of the weighted performance losses of all subsystems is 2, which is within the tolerable performance loss range of the system, that is, WF=2≤RT. Figure 5 As shown, the terminal node '1' and the node X 3 The (4,2)-edges of the two nodes are directly connected, instead of regenerating a non-terminal MDD node.

[0209] In addition to performing the truncation operations described in rules 1, 2, and 3, existing non-terminal MDD nodes can be directly connected to the terminal node '0' through the truncation operations described in rules 4, 5, and 6. For example, a node X represented by T = (0, null, -2) 2 The (2,5)-edge can be truncated according to the description of Rule 4, where the calculation of the triple array T guided by the corresponding edge is T = (0, (-5), 0). Since the performance loss of the subsystem with higher weight is satisfied first, after redistributing the performance surplus under the maximum capacity constraint and transmission loss, the total remaining performance loss of the subsystem is calculated as Q′ 1 = -5. In addition, the sum of the maximum performance surplus of each component in the remaining system is 0, so the remaining performance surplus of each component is Q'2 = 0. The remaining performance defect in the subsystem is Q' 1 = -5 and the remaining performance surplus of each component is Q′ 2 = 0, which meets the condition of Rule 4. Therefore, under the constraints of all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the residual performance loss vector of the subsystem in the partial system can be obtained by the residual performance surplus Q′ of the component 2 The maximum performance surplus of the subsystem is compensated in order. In view of this, the sum of the weighted performance losses of all subsystems is 12, which exceeds the tolerable performance loss range of the system, that is, WF=12>RT. Figure 6 As shown, the terminal node '0' and the node X 2 Instead of regenerating a non-terminal MDD node, the (2,5)-edge of the 3rd layer is connected. Similarly, some non-terminal nodes of the 3rd layer can also be truncated according to the description of rule 4, such as the node X represented by T = (0, (-1), 0) 3 The (2,4)-edge and (0,2)-edge of the MDD model. The truncation operation described in Rule 4 was used 5 times in the process of building the MDD model.

[0210] Since the node X represented by T = (0, (-1), -4) 3 The calculation of the triple array T guided by the (0,4)-edge is T = (0, (-1), -4), so the corresponding edge can be truncated according to the description of Rule 5. The performance loss of the subsystem with higher weight is satisfied first, so under the maximum capacity constraint and transmission loss, the remaining total performance loss of the subsystem calculated after redistributing the performance surplus is Q′ 1 = -1. In addition, the sum of the maximum performance surplus of each component in the remaining system is 2, so the remaining performance loss of each component is Q′ 2 = -2. The remaining performance loss in the subsystem is Q' 1 = -1 and the remaining performance loss of the component is Q′ 2 = -2, which meets the conditions of Rule 5. Therefore, considering all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the remaining performance loss vector of the subsystem and the remaining performance loss of the component can be compensated in order by the maximum performance surplus of the subsystem in the remaining system. In view of this, the sum of the weighted performance losses of all subsystems is 10, which exceeds the tolerable performance loss range of the system, that is, WF = 10 > RT. Figure 7 As shown, instead of regenerating a non-terminal MDD node, the terminal node '0' is connected to the node X 3 The truncation operation described in Rule 5 is only used once when constructing the MDD model.

[0211] The truncation operation described in Rule 6 is also used only once, to process the node X represented by T = (1, (0), 0) 3 The corresponding edge guides the case of (0,4)-edge. The triple array T guided by the corresponding edge is calculated as T = (1, (0), -4). Since the performance loss of the subsystem with higher weight is satisfied first, the remaining performance surplus of the subsystem is redistributed under the maximum capacity constraint and transmission loss, and is calculated as Q′ 1 = 1. In addition, the sum of the maximum performance surpluses of the components in the remaining system is 2, so the remaining performance loss of the components is Q′ 2 = -2. The remaining surplus in the subsystem is Q' 1 = 1 and the remaining loss of the component is Q′ 2 = -2, which satisfies the condition of Rule 6. Therefore, considering all possible capacities c = {7, 6, 5} and loss rate θ = 0.5, the remaining loss of the components in the partial system can be given by the remaining performance surplus Q′ 1 The sum of the maximum performance surplus of the subsystems in the remaining system is used to compensate. In view of this, the sum of the weighted performance losses of all subsystems is 4.5, which exceeds the tolerable performance loss range of the system, that is, WF=4.5>RT. Figure 8 As shown, instead of regenerating a non-terminal MDD node, the terminal node '0' is connected to the node X representing T = (1, (0), 0) 3 The (0,4)-edge of .

[0212] To avoid redundant branches, the merge operation described in Rule 7 is applicable to isomorphic non-terminal MDD nodes. The key to the merge operation is to identify isomorphic nodes on the same layer, which can be achieved by comparing MDD nodes with the same triple array T. For example, a node X represented by T = (0, null, 4) 2 The triple array T = (3, (0), 0) of the partial system state guided by the (2, 3)-edge and the node X represented by T = (0, null, 0) 2 The (8,5)-edge and the node X represented by T = (0, null, -2) 2 The (8,3)-edges of the partial system states are the same. Fig. 9 As shown, it is represented by T = (0, null, 0) node X 2 The (2,3)-edge and node X are represented by T = (0, null, -2). 2 The partial system states guided by the (6,5)-edge can also be merged. The merging operation was performed 20 times in total.

[0213] The MDDGeneration algorithm can perform the above six truncation operations and one merging operation. Since the partial system state corresponding to the non-terminal nodes in the fifth layer represents a specific system state, the reduction operation described in Rules 8 and 9 is applicable to the state generated by node X. 4 For example, the non-terminal node X represented by T = (3, (0), -4) can be processed according to the description of rule eight. 4 The (4,2)-edge case. In the 5th layer, node X 4 The ternary array of node C guided by the corresponding edge of is T = (3, (0, -2), 0), which represents the ternary array T of the entire system state. The total performance surplus of all subsystems in the example system is 3, which can be used to compensate the elements in the performance loss vector (0, -2) in order. Considering the transmission loss and all possible capacities, even in the case of the minimum capacity C = 5, the sum of the weighted performance losses of the subsystems is WF = 1.5, which is within the tolerable performance loss range, that is, WF ≤ RT. In other words, regardless of the capacity of the common bus, the example system can work normally after performance sharing. Therefore, the terminal node '1' replaces the non-terminal node C and connects with the node X 4 In addition, according to the description of rule nine, it is represented as T = (1, (0), -2) non-terminal node X 4 The (2,3)-edge case can also be solved. At layer 5, the node X 4 The triple array of node C led by the corresponding edge of is T = (1, (0, -3), 0), which represents the triple array T of the entire system state. The total performance surplus of all subsystems in the example system is 1, which can be used to sequentially compensate for the elements in the performance loss vector (0, -3). Considering the transmission loss and all possible capacities, even in the case of the maximum capacity C = 7, the sum of the weighted performance losses of the subsystems is WF = 7.5, which exceeds the tolerable performance loss range, that is, WF> RT. Therefore, the terminal node '0' replaces the non-terminal node C and connects with the node X 4 The (2,3)-edges of the example are connected. According to the above rules, the reduction operations described by rules 8 and 9 are used 20 and 16 times respectively. Finally, in order to analyze the reliability of the example restricted series-parallel hybrid multi-state system, a more compact and standardized MDD model is constructed, as shown in Fig.10 shown.

[0214] Finally, by recursively evaluating Fig.10 The reliability of the example system is obtained by calculating the probability of the MDD node in the first layer. In other words, the reliability R is equal to the probability of the MDD node in the first layer, that is, Pr(MDD 1 ). Table 5 shows the calculation results of the MDD node probability and gives the probability of normal operation of the example system.

[0215] Table 5 Recursive evaluation process of the constructed MDD model

[0216]

[0217]

[0218] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

Claims

1. A reliability analysis method for a performance-sharing serial-parallel hybrid multi-state system, characterized in that: The following steps are involved: S1. Construct a performance-sharing serial-parallel hybrid polymorphic system, and obtain the total performance surplus S, the total performance loss F, the probability of being in a specific state, the total redistributable performance surplus, and the sum of the weighted performance loss of the performance-sharing serial-parallel hybrid polymorphic system, wherein the performance-sharing serial-parallel hybrid polymorphic system is composed of m subsystems connected by a common bus, and each subsystem includes k parallel-configured components; S2. constructing an MDD model of a performance-sharing serial-parallel hybrid polymorphic system, wherein the process of constructing the MDD model of a performance-sharing serial-parallel hybrid polymorphic system includes: constructing a tree-like MDD model of the performance-sharing serial-parallel hybrid polymorphic system layer by layer, and designing and applying multiple simplification rules to obtain a simplified MDD model; S3. Calculate the reliability of the performance-sharing serial-parallel hybrid polymorphic system based on the MDD model, wherein the process of calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system includes: obtaining the state classification rules and reliability calculation rules of the performance-sharing serial-parallel hybrid polymorphic system, and calculating the reliability of the performance-sharing serial-parallel hybrid polymorphic system using the MDD model based on the reliability calculation rules.

2. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 1 is characterized in that: In S1, the method of obtaining the total performance surplus S and the total performance loss F of the performance sharing serial-parallel hybrid multi-state system is: Set the i-th subsystem U i It is composed of k heterogeneous components connected in parallel and is represented by N (i-1)k+1 ,N (i-1)k+2 ,...,N ik , each component consists of a random performance variable and random demand variables express; Set a component N j Own r j The performance level of the degradation and k j demand level, for performance g jp and demand jq Component N j , preset X j For component N j The state random variable is denoted as X j ='g jp ,d jq '; Setting G i Represents subsystem U i Performance, G i It is calculated from the total performance of k components from (i-1)k+1 to ik, and its expression is: Furthermore, subsystem U i Demand D i is calculated by the sum of the component requirements, and its expression is: Default H i is a performance G corresponding to the state of the i-th subsystem i and demand D i A random variable, namely H i ='G i ,D i '; If G i ≥D i , then the subsystem U i The performance surplus Si that satisfies the demand is expressed as S i =G i -D i , but failed to fully satisfy the subsystem U i The required performance loss is F i = 0, otherwise, the performance surplus is S i =0, performance loss is F i =G i -D i ; Furthermore, the total performance surplus S of the performance-sharing serial-parallel hybrid polymorphic system is the sum of the performance surpluses of all subsystems, that is: The total performance loss F can be calculated as the sum of the performance losses of all subsystems, that is:

3. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 2 is characterized in that: In S1, the method of obtaining the probability that the performance sharing serial-parallel hybrid multi-state system is in a specific state is: Set X = (X1, X2, ..., X mk ) represents the state vector of the random system, and x=(x1,x2,…,x mk ) is a state of variable X, where x j ='g jp ,d jq 'Represented as component N j state, and thus, there is different states; For X j ='g jp ,d jq 'State component N j The probability of Right now Furthermore, the probability that the performance-sharing serial-parallel hybrid multi-state system is in a specific state can be expressed as:

4. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 3 is characterized in that: In S1, the method of obtaining the total amount of redistributable performance surplus of the performance-sharing serial-parallel hybrid multi-state system is as follows: Assuming θ is the loss percentage of the total performance surplus S, the performance surplus after the loss is (1-θ)*S; Assume that the public bus has a discrete transmission capacity represented by a random variable C with a given PMF, then the random variable C is selected from the set {c1, c2, …, c v } with the corresponding probability Pr(C=c b ) value; Furthermore, the total amount of redistributable performance surplus Q of the performance-sharing serial-parallel hybrid polymorphic system is: Preset (F1, F2, ..., F m ) represents the performance defect vector of all subsystems, and introduces the performance loss vector according to the descending order of subsystem weights The total amount of performance surplus Q will be redistributed in an orderly manner to subsystems with insufficient performance; Presets is the maximum number of subsystems that can be satisfied by the performance surplus, and the range of the total performance surplus Q is expressed as:

5. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 4 is characterized in that: In S1, the method of obtaining the sum of weighted performance losses of the performance-sharing serial-parallel hybrid multi-state system is: Preset W = (w1, w2, ..., w m ) is the subsystem weight vector, and w i is the weight of the ith subsystem; After redistributing the total performance surplus Q, the remaining performance deficit of all subsystems will be represented by the new vector Indicates, set represents the remaining performance loss of the ith subsystem after performance sharing, then for: Furthermore, the sum of weighted performance losses WF of the performance-sharing serial-parallel hybrid multi-state system is:

6. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 5 is characterized in that: In S2, a tree-like MDD model of a performance-sharing serial-parallel hybrid multi-state system is constructed layer by layer, and a simplified MDD model is obtained by designing and applying multiple simplification rules: Firstly, a tree-like MDD model of performance-sharing serial-parallel hybrid multi-state system is constructed layer by layer, which includes; Establish an MDD model, which contains multiple non-terminal nodes and is used to represent the logical reliability expression of a constrained serial-parallel hybrid polymorphic system with heterogeneous components and a common bus. In the lth level of the MDD model, each non-terminal node has r l *k l branches to represent component N l any possible state; A special non-terminal node is introduced at the mk+1 layer, which corresponds to the random variable C of the common bus, where each MDD node at the mk+1 layer has v branches; There are two different termination nodes in the mk+2 layer, marked as "0" or "1", "0" or "1" respectively representing the failure or normality of the performance sharing serial-parallel hybrid multi-state system; Enumerate all system states of performance-sharing serial-parallel hybrid polymorphism, and the MDD model will present a tree structure with The path from the non-terminal node X1 to the terminal node of the mk+2 layer; Arrange all subsystems in descending order of weight to obtain a tree-like MDD model, in which the nodes representing the components of the subsystems with the largest weights are constructed in the first k layers of the MDD model, while the nodes representing the components of the subsystems with smaller weights are constructed in the (m-1)*k to m*k layers; Then, a number of simplification rules are designed and applied to obtain a streamlined MDD model, which includes: The partial system state is represented by a three-variable array T, which is associated with the cumulative performance surplus of the subsystems contained in the partial system, the performance loss vector of the subsystems contained in the partial system, and the total performance surplus or loss of the remaining components, and the partial system state is updated by calculating a new three-variable array T; By integrating the partial system states with all possible states of the remaining system, the state of the entire system can be determined, that is, the state of the entire system is derived from the partial system states through truncation operations; Set the remaining system by Subsystems and numbers l to Several components, set Represents the performance loss vector of the subsystem. For the non-terminal nodes of the first mk layers in the MDD model, set rules one, two, three, four, five, six and seven to truncate and merge the branches in the MDD model. Set rules eight and nine to reduce the non-terminal nodes of the mk+1 layer. Apply multiple simplification rules to the tree-like MDD model to obtain a streamlined MDD model.

7. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 6 is characterized in that: The preset RT is the maximum weighted performance loss value allowed by the system; Rule 1: If the sum of weighted performance losses of the subsystems can satisfy WF1≤RT after performance sharing, then subsystem and There is performance surplus in all subsystems, number When the minimum performance loss of the subsystem from 1 to m is compensated, when the calculated weighted performance loss sum WF1 is within the acceptable loss range, the termination node '1' can replace the non-termination MDD node of the lth layer, where, Rule 2: If the sum of weighted performance losses of the subsystems can satisfy WF2≤RT after performance sharing, then There is performance surplus in the subsystem. Performance loss and number of subsystems When the minimum performance loss of the subsystem from to m is compensated, when the calculated weighted performance loss sum WF2 is within the acceptable loss range, the termination node '1' can replace the non-termination MDD node of the lth layer, where Rule 3: If the sum of weighted performance losses of the subsystems can satisfy WF3≤RT after performance sharing, then The subsystem has performance loss, while the There is performance surplus in each subsystem. Performance loss and number of subsystems When the minimum performance loss of the subsystem from to m is compensated, if the calculated weighted performance loss sum WF3 is within the acceptable loss range, the terminal node '1' can replace the non-terminal MDD node of the lth layer, where Rule 4: If the sum of weighted performance losses of subsystems after performance sharing can satisfy WF4>RT, that is, The performance loss of each subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF4 still exceeds the acceptable loss range, the termination node '0' can replace the non-termination MDD node of the lth layer, where Rule 5: If the sum of weighted performance losses of the subsystems after performance sharing can satisfy WF5>RT, that is, subsystem and The performance losses of each subsystem are numbered When the maximum performance surplus of the subsystem m is compensated, if the calculated weighted performance loss sum WF5 still exceeds the acceptable loss range, the termination node '0' can replace the non-termination MDD node of the lth layer, where Rule 6: If the sum of weighted performance losses of the subsystems can satisfy WF6>RT after performance sharing, that is, when the The performance loss of the subsystem is Performance margin and number of subsystems When the maximum performance surplus of the subsystem m is compensated, if the sum of the weighted performance losses calculated is WF6 If the loss is still beyond the acceptable range, the termination node '0' can replace the non-termination MDD node of the lth layer, where The rule seven is: for non-terminal MDD nodes representing different partial system states at the same level, if the ternary arrays T of the partial system states corresponding to these non-terminal nodes are the same, then they have the same subgraph.

8. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 7 is characterized in that: The eighth rule is: Under the minimum transmission capacity, if the sum of the weighted performance losses of the subsystems is redistributed to the cumulative performance surplus After that, if it still does not exceed the pre-designed RT value, that is, WF≤RT, then the terminal node marked as "1" can be connected to the branch from the non-terminal MDD node of the nth layer; The ninth rule is: Under the maximum transmission capacity, if the sum of the weighted performance losses of the subsystems is redistributed to the cumulative performance surplus After that, it still does not exceed the pre-designed RT value, that is, WF>RT, then the terminal node marked as "0" can be connected to the branch from the non-terminal MDD node of the nth layer.

9. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 8 is characterized in that: In S3, the state classification rule and reliability calculation rule of the performance sharing serial-parallel hybrid multi-state system are obtained as follows: A Boolean function A is preset to classify the operation or failure of the system, and the expression of the classification rule is: In the formula, A(x) is a Boolean function with only two outputs: 0 and 1. 0 indicates that the system works normally, and 1 indicates that the system fails. Then the probability of normal operation of the performance-sharing serial-parallel hybrid multi-state system, that is, the system reliability R, can be calculated according to the following reliability calculation rule: In the formula, For any internal b, any possible value c of C b , For any external x, it is any possible value x of X.

10. The reliability analysis method of performance-sharing serial-parallel hybrid multi-state system according to claim 9, characterized in that: In S3, the reliability of the performance-sharing serial-parallel hybrid multi-state system is calculated using the MDD model based on the reliability calculation rule as follows: Based on the correspondence between the MDD model and the reliability calculation rules of the performance-sharing serial-parallel hybrid multi-state system, it is found that the system reliability R of the performance-sharing serial-parallel hybrid multi-state system is equal to the sum of the path probabilities leading to the terminal node "1" in the MDD model, where the path probability is obtained by multiplying the probabilities of all edge edges appearing in the path, and any edge probability is equal to the probability that a component is in a specific state. The sum of all path probabilities leading to the terminal node "1" in the MDD model is calculated recursively as follows; Where, Pr(MDD b ) represents the non-terminal node MDD of the lth layer b Node probability; Pr(MDD b .Edge) indicates that the node is connected to the child node MDD through the Edge edge. b probability; Represents component N l The edge represents the l The probability that a layer component is in a specific state.

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