CN111506962A - Complex system reliability calculation method based on BN and UGF - Google Patents

Complex system reliability calculation method based on BN and UGF Download PDF

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CN111506962A
CN111506962A CN202010235660.3A CN202010235660A CN111506962A CN 111506962 A CN111506962 A CN 111506962A CN 202010235660 A CN202010235660 A CN 202010235660A CN 111506962 A CN111506962 A CN 111506962A
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周炜恩
姚雯
朱效洲
沈嘉男
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National Defense Technology Innovation Institute PLA Academy of Military Science
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
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    • G06F30/15—Vehicle, aircraft or watercraft design
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Abstract

The invention discloses a complex system reliability calculation method based on BN and UGF, which comprises the following steps: analyzing a system hierarchical structure, establishing a multi-layer system model, numbering each layer of the system from the bottom layer to the top layer according to an ascending order, wherein each layer is represented as level-i, and i is a natural number; adopting UGF to analyze level-1, taking the obtained probability distribution as the input of level-2, and obtaining the probability distribution of each node in level-2; taking the probability distribution of each node of level-2 as the probability distribution of a root node, and establishing a BN-based complex system reliability model; and calculating the system reliability according to the complex system reliability model based on the BN. The complex system reliability calculation method based on BN and UGF considers the situation that the sub-system layer relationship is difficult to describe, namely the display expression is difficult to obtain, and also considers the situation that the number of bottom layer components is very large, so that a model capable of rapidly obtaining the accurate reliability of the system is established, and a new thought is provided for analyzing the reliability improvement efficiency of the complex system.

Description

Complex system reliability calculation method based on BN and UGF
Technical Field
The invention relates to the technical field of complex system reliability calculation, in particular to a complex system reliability calculation method based on BN and UGF.
Background
In a multi-state system, reliability analysis is an important research content, and has significance to design, manufacture, use and maintenance of equipment. The generic generation function (UGF) is an important method in reliability analysis, and can obtain the reliability of the system through fast algebraic operation, thereby being capable of analyzing the time efficiency of the reliability of a complex system.
However, when the structural relationships between subsystems or components are not clear or difficult to describe with a display expression, then the UGF approach may be difficult or not applicable at all. The bayesian network has natural advantages in uncertainty inference, but the method of using the bayesian network alone is too time-consuming to analyze the system once it involves too many parts and cannot obtain the reliability of the system within a suitable time limit.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a complex system reliability calculation method based on BN and UGF. The specific technical scheme is as follows:
a complex system reliability calculation method based on BN and UGF, the method comprising:
analyzing a system hierarchical structure, establishing a multi-layer system model, numbering each layer of the system from the bottom layer to the top layer according to an ascending order, wherein each layer is represented as level-i, and i is a natural number;
adopting UGF to analyze level-1, taking the obtained probability distribution as the input of level-2, and obtaining the probability distribution of each node in level-2;
taking the probability distribution of each node of level-2 as the probability distribution of a root node, and establishing a BN-based complex system reliability model;
and calculating the system reliability according to the complex system reliability model based on the BN.
Alternatively, in a multi-level system model, for level-1,
Figure BDA0002430874850000011
a jth element of L th node representing level-2, the relationship between the elements being determined by
Figure BDA0002430874850000012
Therein is described
Figure BDA0002430874850000013
Representing the component structure function of L th node of level-2, and for level-2, S2L(0≤L≤m2) The numbers in the subscripts indicate that the node is at level-2, and the subscript L indicates the L th node of the level.
Alternatively, using UGF to analyze level-1, the jth element u function is obtained by the following formula:
Figure BDA0002430874850000021
optionally, according to the structure function of the L th node of level-2 and the u-function of each component, obtaining the probability distribution of the L th node of level-2 by the following formula:
Figure BDA0002430874850000022
the technical scheme of the invention has the following main advantages:
the BN and UGF-based complex system reliability calculation method provided by the invention considers the situation that the sub-system layer relationship is difficult to describe, namely the display expression is difficult to obtain, and also considers the situation that the bottom layer components are very many, and combines the BN and UGF, so that a model capable of quickly obtaining the accurate reliability of the system is established, after the UGF method is added, the analysis efficiency of the BN method is improved by dozens of times, and a new thought is provided for analyzing the reliability improvement efficiency of the complex system.
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The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a complex system reliability calculation method based on BN and UGF according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a multi-layer system model according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a multi-layer system of an aircraft according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a BN model of an aircraft according to an embodiment of the present invention;
fig. 5 is a comparison graph of the effect of the calculation method of the present invention and the simple BN algorithm in the prior art according to an embodiment of the present invention;
fig. 6 is a schematic diagram illustrating a time ratio of the calculation method of the present invention and a simple BN algorithm in the prior art according to an embodiment of the present invention, which varies with the number of bottom layers.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme provided by the embodiment of the invention is described in detail below with reference to the accompanying drawings.
The embodiment of the invention provides a complex system reliability calculation method based on BN and UGF, and for facilitating understanding of the technical scheme of the invention, the BN and UGF are explained first.
A complex system reliability model based on a Bayesian network is as follows:
bayesian Network (BN) is a directed acyclic graph combining graph theory and probability theory, expressing the probabilistic relationships between variables graphically, proposed by Pearl in 1986. In the directed acyclic graph, nodes represent random variables, and directed arcs between the nodes represent direct dependency between two random variables; each Node in the directed acyclic graph is attached with a Node Probability Table (NPT), the NPT of the root Node is an edge Probability distribution, and the NPT of the non-root Node is a conditional Probability distribution. The basic definition of BN is as follows:
BN is a tuple X ═ (G, P), and G ═ V, a is a directed acyclic graph.
P＝{P(Vi|π(Vi) 1,2 …, n is the NPT set of all nodes in the directed acyclic graph.
Wherein n represents the number of all nodes in the directed acyclic graph;
Virepresenting the ith node in the directed acyclic graph;
v denotes a set of all nodes in the directed acyclic graph, and V ═ Vi|i＝1,2，…，n}；
A represents a set of directed arcs in a directed acyclic graph;
π(Vi) Represents ViSet of parent nodes of a node, if ViThe point is the root node
Figure BDA0002430874850000031
P(Vi|π(Vi) Denotes V in a directed acyclic graphiThe NPT of the node.
In particular, for further details regarding bayesian networks, see: pearl J. reading in Intelligent Systems of Networks of plant interference [ M ] Morgan Kaufmann publishers,1988: 1022-.
Complex system reliability model based on Universal Generating Function (UGF):
defining the u (z) function of the independent discrete random variable X as a polynomial:
Figure BDA0002430874850000041
where the variable X has K possible values, qkIs variable X ═ XkThe probability of (c).
Binomial form uj(z) the performance distribution of element j in the system can be defined, i.e. the binomial represents all possible states of a part, and the probability of each state is linked to the performance of that part. Note that the performance parameter of component j can be represented by gj＝{gjk，1≤k≤KjAnd pj＝{pjk，1≤k≤KjIs presented.
Figure BDA0002430874850000042
To obtain u (z) which contains two component subsystems, a combination operator is introduced. These operators determine the u-functions of two components connected in parallel and in series, respectively, by performing a simple algebraic operation on the single u-function of the component. All composite operators are derived using these two basic forms.
Series connection:
Figure BDA0002430874850000043
the above formula is changed into
Figure BDA0002430874850000044
Parallel connection:
Figure BDA0002430874850000045
the above formula is changed into
Figure BDA0002430874850000046
The resulting u-function relates the probability of each state of the subsystem (equal to the product of the state probabilities of the individual components) to the performance state of the subsystem at that state. The composite operator representation of the functions par and ser is to relate the entire performance state of a subsystem consisting of two components to the individual performance states of the components in the subsystem. The definition of the functions par and ser depends strictly on the physical property measurements of the system and the interaction relationship between the components.
The u-function for a system containing n components can be described as:
Figure BDA0002430874850000051
therein ΨwConsidered as a subsystem common structure operator, can be replaced by par (-) and ser (-) according to the component relationship w (-).
Further details regarding the general occurrence function may be found, in particular, in A. L isonianski and G. L evitin, Multi-State System Reliability: Assess-ment, Optimization and applications in applications.New York, NY, USA: World Scientific Publishing Co Pte L td,2003.
By combining the characteristics of the complex system and utilizing the respective advantages of the bayesian method and the general occurrence function method, as shown in fig. 1, the embodiment of the present invention provides a complex system reliability calculation method based on BN and UGF, as follows:
hierarchical systems are ubiquitous in engineering systems, with the obvious feature that the output (response) of a low-level component is the input to a high-level subsystem. Taking a complex satellite system as an example, the hierarchical structure of the system is firstly analyzed, and the system comprises a component layer, a subsystem layer and a system layer, wherein subsystems of each layer of the system are regarded as nodes. And numbering the system levels from the bottom layer to the top layer in an ascending order, wherein the bottom layer is the smallest component layer and is numbered as level-1, and the top layer is the system layer and is numbered as level-n. In the case of level-1, the level is,
Figure BDA0002430874850000052
the j component of the L th node of level-2 can be represented, and the relationship between the components can be realized through
Figure BDA0002430874850000053
Therein is described
Figure BDA0002430874850000054
Representing the component structure function of L th node of level-2, and for level-2, S2L(0≤L≤m2) The number 2 in the subscript indicates that the node is at level-2, the subscript L indicates the L th node of the layer, and the specific structure of the multilayer system model is shown in fig. 2.
For the system, the number of system layers is more and more, nodes on each layer are increased, the number of level-1 components is more, and the whole system is analyzed by adopting a BN method, so that the problem of exponential explosion caused by state combination exists, and great difficulty is caused in expression of PNT of system nodes in the Bayesian network; and the method of UGF is adopted to analyze the whole system, and the node relation of the system layer is not clear, thereby causing difficulty for the analysis of the method UGF. Combining the advantages of the BN and UGF methods, UGF is adopted to analyze level-1, the obtained probability distribution is used as the input of level-2, and then the BN method is adopted to analyze.
Firstly, analyzing level-1, taking the component of the L th node of the level-2 layer as an example, and obtaining a u function of a first component by using the probability distribution of the component:
Figure BDA0002430874850000061
reuse the structure function of L th node of level-2
Figure BDA0002430874850000062
Obtaining the probability distribution of L th nodes of level-2:
Figure BDA0002430874850000063
the probability distribution U of each node of level-2LAnd modeling and reasoning by using a BN method as the probability distribution of the root node. It can be understood that the BN complex system is established when modeling and reasoning are carried out by using the BN methodThe bottom layer of the system reliability model is a level-2 layer of the multilayer system model, the layers are the same as the layers above the level-2 layer in the multilayer system model, and the BN complex system reliability model is one less than the multilayer system model.
The pseudo code of the complex system reliability model based on BN and UGF is shown in the following table:
Figure BDA0002430874850000064
to sum up, the BN and UGF-based complex system reliability calculation method provided by the embodiment of the present invention combines BN and UGF, considering not only the situation that a subsystem layer relationship is difficult to describe, i.e., a display expression is difficult to obtain, but also the situation that a number of bottom layer components are very large, thereby establishing a model that can quickly obtain the accurate reliability of the system, and after the UGF method is added, the analysis efficiency of the BN method is improved by several tens of times, thereby providing a new idea for analyzing the reliability improvement efficiency of the complex system.
The beneficial effects of the complex system reliability calculation method based on BN and UGF provided by the implementation of the present invention are explained below with reference to specific examples:
a schematic of the aircraft hierarchy is shown in fig. 3, with aircraft components as shown in the table below.
Figure BDA0002430874850000071
After analyzing level-1 by using UGF algorithm, a BN model as shown in FIG. 4 is established. In order to better compare the analysis efficiency of the algorithm provided by the embodiment of the invention with the analysis efficiency of the BN method, the number of bottom layer components is continuously increased, the comparison graph of the time effect of the BN method and the method provided by the invention is shown in the following figure 5, and the graph of the time ratio of the BN method and the method provided by the invention along with the change of the number of the bottom layers is shown in the following figure 6. It can be seen that when the number of bottom layers is increased, the complex system reliability calculation method based on BN and UGF provided by the embodiment of the present invention can significantly shorten the calculation time and improve the calculation efficiency. And as the number of the bottom layers is increased, the efficiency improvement effect is increased in proportion.
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper" and "lower" in this document are referred to the placement states shown in the drawings.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (5)

1. A complex system reliability calculation method based on BN and UGF, the method comprising:
analyzing a system hierarchical structure, establishing a multi-layer system model, numbering each layer of the system from the bottom layer to the top layer according to an ascending order, wherein each layer is represented as level-i, and i is a natural number;
adopting UGF to analyze level-1, taking the obtained probability distribution as the input of level-2, and obtaining the probability distribution of each node in level-2;
taking the probability distribution of each node of level-2 as the probability distribution of a root node, and establishing a BN-based complex system reliability model;
and calculating the system reliability according to the complex system reliability model based on the BN.
2. The BN and UGF-based complex system reliability computation method of claim 1, wherein, in the multi-layer system model, for level-1,
Figure FDA0002430874840000011
a jth element of L th node representing level-2, the relationship between the elements being determined by
Figure FDA0002430874840000012
Therein is described
Figure FDA0002430874840000013
Representing the component structure function of L th node of level-2, and for level-2, S2L(0≤L≤m2) The numbers in the subscripts indicate that the node is at level-2, and the subscript L indicates the L th node of the level.
3. The BN and UGF-based complex system reliability computation method of claim 2, wherein the UGF analysis level-1 is adopted to obtain the jth component u function by the following formula:
Figure FDA0002430874840000014
。
4. the BN and UGF based complex system reliability calculation method according to claim 3, wherein the probability distribution of L th node of level-2 is obtained by the following formula according to the structure function of L th node of level-2 and the u-function of each component:
Figure FDA0002430874840000015
。
5. the complex system reliability calculation method of claim 4 based on BN and UGF, wherein the probability distributions of level-2 other nodes are obtained by the same method, then the obtained probability distributions of all nodes are used as the input of a BN root node, a BN model is established, BN analysis inference is carried out, and finally the reliability of the whole system is obtained.
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