CN106951707B - Method for constructing Bayesian network of reconfigurable system - Google Patents

Method for constructing Bayesian network of reconfigurable system Download PDF

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CN106951707B
CN106951707B CN201710168449.2A CN201710168449A CN106951707B CN 106951707 B CN106951707 B CN 106951707B CN 201710168449 A CN201710168449 A CN 201710168449A CN 106951707 B CN106951707 B CN 106951707B
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张士刚
李洋洋
杨拥民
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National University of Defense Technology
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Abstract

本发明提供了一种可重构系统的贝叶斯网构建方法。包括以下步骤：(1)对可重构系统故障和测试的相关性建立模型；(2)对可重构系统故障和测试的相关性进行表征；(3)确定可重构系统贝叶斯网结构；(4)确定重构系统贝叶斯网参数并采用树形结构进行表征。本发明的有益效果是：提出了一种程序化的可重构系统贝叶斯网构建方法，对贝叶斯网参数存储和检索进行了优化，为解决可重构系统贝叶斯网构建问题提供了一条新的解决途径，可促进贝叶斯网在故障诊断领域的应用。

Figure 201710168449

The invention provides a Bayesian network construction method for a reconfigurable system. It includes the following steps: (1) establish a model for the correlation between the fault and the test of the reconfigurable system; (2) characterize the correlation between the fault and the test of the reconfigurable system; (3) determine the Bayesian network of the reconfigurable system (4) Determine the Bayesian network parameters of the reconstruction system and use a tree structure to characterize it. The beneficial effects of the invention are as follows: a programmatic reconfigurable system Bayesian network construction method is proposed, and the Bayesian network parameter storage and retrieval are optimized, so as to solve the problem of reconfigurable system Bayesian network construction A new solution is provided, which can promote the application of Bayesian network in the field of fault diagnosis.

Figure 201710168449

Description

Method for constructing Bayesian network of reconfigurable system
Technical Field
The invention relates to a Bayesian network construction method for a reconfigurable system, which is suitable for Bayesian network construction of the reconfigurable system and further can support fault diagnosis and reasoning of equipment.
Background
Fault diagnosis is critical to the proper safe operation of the equipment. The Bayesian network has strong capability in the fields of uncertain knowledge expression and reasoning as a credibility network, and has been successfully applied to fault diagnosis. However, the construction of the bayesian network has been a very difficult task, requires a great deal of expert knowledge, is a very time-consuming and labor-consuming task, and limits the application thereof in large-scale systems. Currently, the construction of the bayesian network is mainly manual, mainly aims at a single-mode small-scale system, and lacks a systematic automatic method. Particularly, for a reconfigurable system, because the system structure changes in the application process, the expression of the bayesian network is difficult, and a bayesian network construction method applicable to engineering is lacking at present.
Disclosure of Invention
The invention aims to provide a Bayesian network construction method suitable for a reconfigurable system, and provides support for fault diagnosis based on a Bayesian network.
To achieve the above object, the present invention provides the following solutions: 1. a method for constructing a Bayesian network of a reconfigurable system comprises the following steps:
(1) establishing a model for the correlation of reconfigurable system faults and tests;
(2) representing the correlation between the reconfigurable system fault and the test;
(3) determining a Bayesian network structure of a reconfigurable system;
(4) and determining Bayesian network parameters of a reconstruction system and representing by adopting a tree structure.
Further, the model in the step (1) comprises four elements, namely a fault, a switch, a test point and a connecting line for connecting the fault, the test point and the switch; the working mode of the model is as follows: when a connection path exists between the fault and the test, the fault is related to the test point, otherwise, the fault is not related; a switch can be arranged between the fault and the test, and the correlation between the fault and the test is influenced by the opening and closing of the switch, so that the reconstruction of the system is realized.
Further, the correlation between the fault and the test in step (2) is represented by a matrix D1, D1＝[dij]m×nWherein d isijThe element belongs to {0,1}, the value of 0 indicates that the ith fault cannot be detected by the jth test in any mode, and the value of 1 indicates that the ith fault can be detected by the jth test; the correlation of the test and the switch is represented by a matrix D2, D2＝[rij]n×kWherein r isijThe element belongs to {0,1}, the value of 0 represents that the correlation of the jth test and the fault is not influenced by the state of the ith switch, and the value of 1 represents that the correlation of the jth test and the fault is correlated with the state of the ith switch; where m represents the number of faults, n represents the number of tests, and k represents the number of switches.
Further, the bayesian network in the step (3) comprises a two-layer structure, wherein the first layer comprises fault and switch nodes, and the second layer comprises test nodes.
Further, the connection relationship between the nodes of the bayesian network in the step (3) corresponds to the matrix in the step (2), and the matrix D is aimed at1＝[dij]m×nIf d isijAdding a connection relation between the ith fault and the jth test, wherein the direction is fiPoint of direction tj(ii) a For matrix D2＝[rij]n×kIf r isijAdding a connection relation between the jth test and the ith switch, wherein the direction is siPoint of direction tj(ii) a Wherein the i-th fault is defined by fiDenotes the jth test with tjDenotes that the ith switch is used as siAnd (4) showing.
Further, the Bayesian network parameters of the test nodes in the step (4) are expressed by a binary tree and generated in an optimization mode.
Further, the optimization method comprises the following steps:
the method comprises the steps that I, for a certain test node, an initial candidate node set is represented by a set E ═ { F, S }, wherein F represents a fault node relevant to the initial candidate node set, and S represents a switch node relevant to the initial candidate node set;
II, selecting the switching node with the largest number of related fault nodes and not being 0 from the set E as the next tree node; removing the switch node from E for the switch closed branch; for the branch with the switch disconnected, removing the switch node and a fault node related to the switch from E, and updating E; if the set E has no switching node, turning to the step III;
III, selecting a fault node with the highest fault rate as a next tree node, removing the fault node from the E, and updating the E; storing a parameter 1 aiming at the branch with the fault, and stopping expanding the branch; if the fault does not have the branch, if the E does not contain other fault nodes, the parameter 0 is stored, otherwise, the step II is continuously selected, and the parameter expression tree is expanded;
and IV, the finally obtained binary tree is the parameter of the test node.
The invention has the beneficial effects that: a method for constructing a programmed reconfigurable system Bayesian network is provided, the Bayesian network parameter storage and retrieval are optimized, a new solution is provided for solving the problem of constructing the reconfigurable system Bayesian network, and the application of the Bayesian network in the field of fault diagnosis can be promoted.
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For ease of illustration, the invention is described in detail by the following detailed description, examples and figures.
FIG. 1 is a correlation model of a reconfigurable system in an embodiment of the invention;
FIG. 2 is a Bayesian network constructed by a reconfigurable system in an embodiment of the present invention;
FIG. 3 is a binary node parameter tree of Bayesian network t1 constructed in the embodiment;
FIG. 4 is a binary node parameter tree of Bayesian network t2 constructed in the embodiment.
Detailed Description
The invention comprises the following steps:
step one, modeling a fault-test correlation relation of the reconfigurable system.
Unlike a general single mode system, the reconfigurable system may be changed according to a change in environment due to a system configuration during use. This means that the relationship between faults and tests will also vary. Here, the characterization is performed by means of a multimode, multi-signal model. The model contains the following four elements: the device comprises a fault, a switch, a test point and a connecting line, wherein the connecting line is used for connecting the fault, the test and the switch. The meaning of the model is: if the connection path exists between the fault and the test, the fault and the test are related, otherwise, the fault and the test are not related. A switch can be arranged between the fault detection device and the test device, and the correlation relationship between the fault and the test can be influenced by opening and closing the switch, so that the system reconfiguration is achieved.
Step two, representing the correlation of the reconfigurable system
And analyzing the system based on the model in the step one. A set of two correlation matrices is obtained. Assume that the system has a total of m failure modes, n tests, and k switches. Matrix one is the correlation between fault and test, i.e. D1＝[dij]m×nWherein d isijThe element is {0,1}, and the value of 0 indicates that the jth test cannot detect the ith fault in any mode; a value of 1 indicates that the jth test can detect the ith fault. Matrix two is the correlation between the switch and the test, using D2＝[rij]n×kIs represented by the formula (I) in which rijThe element belongs to {0,1}, and the value of 0 represents that the correlation of the jth test and the fault is not influenced by the ith switch state; a value of 1 indicates a j-th test and fault correlationSex is related to the state of the ith switch.
Step three, determining the structure of the Bayesian network of the reconfigurable system
According to the definition of the Bayesian network, the structure of the Bayesian network comprises two parts of nodes and connection relations among the nodes. The Bayesian network of the reconfigurable system constructed by the invention consists of three types of nodes including two layers. The first layer is the fault and switch layer, represented by the fault node and switch node, respectively. The second layer is a test layer, represented by test nodes. The failure nodes correspond to the failure modes in the step two, and the number of the failure nodes is m. The switch nodes correspond to the switches in the step two, and the total number of the switch nodes is k. The test nodes correspond to the test in the step two, and the number of the test nodes is n.
And after the number and the type of the nodes are determined, adding connection relations among the nodes. The adding mode is carried out according to the two correlation matrixes in the second step. The method specifically comprises the following steps: for matrix D1＝[dij]m×nIf d isijAt the ith fault (using f) when 1iDenoted by t) and the jth test (with t)jRepresented) in a direction of fiPoint of direction tj(ii) a For matrix D2＝[rij]n×kIf r isijTest at jth (with t) 1jDenoted) and ith switch (by s)iRepresented) in a direction of siPoint of direction tj。
Step four, determining parameters of the Bayesian network of the reconfigurable system and representing by adopting a tree structure
(1) And setting normal and abnormal states aiming at the fault node, wherein the abnormal probability represents the fault rate.
(2) And setting two states of on and off aiming at the switch node, wherein the probability is respectively set to be 0.5.
(3) And for one test node, representing an initial candidate node set by using a set E ═ { F, S }, wherein F represents a fault node related to the initial candidate node set, and S represents a switch node related to the initial candidate node set. And selecting the switch node with the largest number of related fault nodes and not being 0 from the set E as the next tree node. Removing the switch node from E for the switch closed branch; e is updated for the branch with the switch open, removing the switch node and the fault node associated with the switch from E. And if no switching node exists, selecting the fault node with the highest fault rate as the next tree node, removing the fault node from the E, and updating the E. Storing a parameter 1 aiming at the branch with the fault, and stopping expanding the branch; and aiming at the fault, if the fault does not have the branch, if the E does not contain other fault nodes, storing the parameter 0, otherwise, continuously selecting the nodes and expanding the parameter expression tree until a stop condition is reached. And finally obtaining the binary tree which is the parameter of the test node.
Examples
Step one, as shown in fig. 1, a correlation model is established for a certain reconfigurable system. The system comprises three fault modes of f1, f2 and f3, two switches of s1 and s2 and two tests of t1 and t 2. Through the change of the switch state, the reconfiguration of the system can be realized.
And step two, characterizing the reconfigurable system.
In this system, m is 3, n is 2, and k is 2.
Figure BDA0001250405030000051
Figure BDA0001250405030000052
Step three, determining the structure of the Bayesian network of the reconfigurable system
The resulting bayesian network structure is shown in fig. 2, according to the bayesian network structure determination rule.
Step four, determining parameters of the Bayesian network of the reconfigurable system
(1) For the failed nodes (i.e., f1, f2, f3), each node has two states: failure and normal. The probability of failure, i.e., failure rate, assumes three failure rates of 0.1, 0.3, and 0.6, respectively.
(2) For the switch nodes (i.e., s1, s2), each node has two states: open and close. The occurrence probability of both was set to 0.5.
(3) For test node t1, the initial candidate node is E ═ { f1, f2, s1, s2 }. The number of failed nodes associated with s1 is 1 and the number of failed nodes associated with s2 is 2, for which s2 is selected as the next tree node. For the switch closing branch, updated E' ═ { f1, f2, s1 }; for the switch open branch, E ″ { f1, s1 }. Then, by analogy, a parameter expression tree of t1 is obtained as shown in FIG. 3.
For test node t2, the initial candidate node is E ═ { f3}, and its binary parameter tree is shown in fig. 4.
The foregoing shows that the basic principles and essential features of the invention, as well as features of the invention, are described. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which shall fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1.一种可重构系统贝叶斯网构建方法，其特征在于：包括以下步骤：1. a reconfigurable system Bayesian network construction method, is characterized in that: comprise the following steps: (1)对可重构系统故障和测试的相关性建立模型；(1) Model the correlation between faults and tests of reconfigurable systems; (2)对可重构系统故障和测试的相关性进行表征；故障和测试的相关性用矩阵D1表示，D1＝[dij]m×n，其中dij∈{0,1}，取值为0表示第j个测试在任意模式下均无法检测到第i个故障，取值为1表示第j个测试可检测到第i个故障；所述测试和开关的相关性用矩阵D2进行表示，D2＝[rij]n×k，其中rij∈{0,1}，取值为0表示第j个测试和故障的相关性不受第i个开关状态的影响，取值为1表示第j个测试和故障的相关性和第i个开关的状态相关；其中，m表示故障的个数，n表示测试的个数，k表示开关的个数；(2) Characterize the correlation between the fault and the test of the reconfigurable system; the correlation between the fault and the test is represented by a matrix D1, D 1 =[d ij ] m×n , where d ij ∈{0,1}, take A value of 0 means that the jth test cannot detect the ith fault in any mode, and a value of 1 means that the jth test can detect the ith fault; the correlation between the test and the switch is carried out by matrix D2 represents, D 2 =[r ij ] n×k , where r ij ∈{0,1}, the value of 0 indicates that the correlation between the j-th test and the fault is not affected by the i-th switch state, and the value is 1 represents the correlation between the jth test and the fault and the state of the ith switch; where m represents the number of faults, n represents the number of tests, and k represents the number of switches; (3)确定可重构系统贝叶斯网结构；所述贝叶斯网包括两层结构组成，第一层由故障和开关节点组成，第二层由测试节点组成，贝叶斯网节点之间的连接关系和步骤(2)中的矩阵对应，针对矩阵D1＝[dij]m×n，如果dij＝1，则在第i个故障和第j个测试之间添加连接关系，方向由fi指向tj；针对矩阵D2＝[rij]n×k，如果rij＝1，则在第j个测试和第i个开关之间添加连接关系，方向由si指向tj；其中，所述第i个故障用fi表示，所述第j个测试用tj表示，所述第i个开关用si表示；(3) Determine the Bayesian network structure of the reconfigurable system; the Bayesian network includes a two-layer structure, the first layer is composed of fault and switch nodes, the second layer is composed of test nodes, and the Bayesian network node is composed of two layers. The connection relationship between is corresponding to the matrix in step (2). For the matrix D 1 =[d ij ] m×n , if d ij =1, then add the connection relationship between the ith fault and the jth test, The direction points from fi to t j ; for the matrix D 2 =[r ij ] n×k , if r ij =1, then a connection relationship is added between the jth test and the ith switch, and the direction points from si to t j ; wherein, the i -th fault is represented by fi, the j-th test is represented by t j , and the i-th switch is represented by si ; (4)确定重构系统贝叶斯网参数并采用树形结构进行表征。(4) Determine the Bayesian network parameters of the reconstruction system and use the tree structure to characterize it. 2.根据权利要求1所述的方法，其特征在于，所述步骤(1)中的模型包含四种元素，分别为故障、开关、测试点以及用来连接故障、测试点及开关的连接线；该模型的工作方式为：当故障和测试之间有连接通路，则故障和测试点之间相关，否则不相关；所述故障和测试之间可设置开关，通过开关的启闭影响故障和测试之间的相关性，进而实现系统的重构。2. method according to claim 1, is characterized in that, the model in described step (1) comprises four kinds of elements, respectively is fault, switch, test point and the connecting line that is used to connect fault, test point and switch ; The working method of this model is: when there is a connection path between the fault and the test, the fault and the test point are related, otherwise they are not related; a switch can be set between the fault and the test, and the fault and test points can be affected by the opening and closing of the switch. The correlation between tests, and then the reconstruction of the system. 3.根据权利要求1所述的方法，其特征在于：步骤(4)中测试节点贝叶斯网参数采用二叉树表达，并采用优化方式生成。3. The method according to claim 1, wherein: in step (4), the Bayesian network parameters of the test node are expressed by a binary tree, and are generated by an optimization method. 4.根据权利要求3所述的方法，其特征在于，所述优化方法包括以下步骤：4. method according to claim 3, is characterized in that, described optimization method comprises the following steps: Ⅰ，针对某一个测试节点，用集合E＝{F,S}表示初始备选节点集，其中F表示与其相关的故障节点，S表示与其相关的开关节点；I, for a certain test node, the initial candidate node set is represented by the set E={F,S}, where F represents the fault node related to it, and S represents the switch node related to it; Ⅱ，从集合E中选择相关故障节点数目最多且不为0的开关节点作为下一步的树节点；针对开关闭合分枝，从E中去除该开关节点；针对开关断开这一分枝，从E中去除该开关节点以及和该开关相关的故障节点，更新E；若集合E中无开关节点，转步骤Ⅲ；II, select the switch node with the largest number of relevant fault nodes and not 0 from the set E as the next tree node; for the switch closed branch, remove the switch node from E; for the switch open branch, from Remove the switch node and the faulty node related to the switch from E, and update E; if there is no switch node in set E, go to step III; Ⅲ，选择故障率最高的故障节点作为下一步的树节点，从E中去除该故障节点，更新E；针对故障存在这一分枝，存储参数1，停止扩展该分枝；针对故障不存在这一分枝，若E中不包含其它故障节点，存储参数0，否则，继续选择步骤Ⅱ，扩展参数表达树；Ⅲ. Select the faulty node with the highest failure rate as the next tree node, remove the faulty node from E, and update E; for the existence of this branch, store parameter 1, and stop expanding the branch; One branch, if E does not contain other faulty nodes, store parameter 0, otherwise, continue to select step II to expand the parameter expression tree; Ⅳ，最终所得的二叉树即为测试节点的参数。IV, the final binary tree is the parameter of the test node.
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