An FG-DBN-based reliability analysis method for an airborne system of a more-electric aircraft

Abstract

The embodiment of the application discloses a kind of based on FG-DBN's multi-electric aircraft airborne system reliability analysis method, it is related to reliability design field, can be in fuzzy uncertain condition, to the complex polymorphic system in multi-electric aircraft airborne equipment is carried out dynamic reliability analysis.This application includes: the DBN model of complex polymorphic system in airborne equipment is established, the node in DBN model corresponds the failure state of component in complex polymorphic system;Fuzzy gradient function model containing fuzzy support radius is established, fuzzy gradient function model includes: fuzzy membership model of node in corresponding time slice and state transition matrix corresponding to failure mode;The conditional probability table is established for the failure relationship between nodes in DBN model;The output result of fuzzy gradient function model containing fuzzy support radius and the conditional probability table established are used, the node of weak link in complex polymorphic system is identified and reliability is analyzed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of reliability design, and in particular to a multi-electric aircraft airborne system reliability analysis method based on a fusion of fuzzy mathematics and grey system dynamic Bayesian network (FG-DBN). BACKGROUND

[0002] With the continuous rapid development of the automation and intelligentization of aviation equipment systems, the systems have high electrification and high integration characteristics. However, this also increases the safety risk of aviation equipment systems. On the one hand, the complex system of aviation equipment presents a diversified fault state. On the other hand, the reliability evaluation method for the complex multi-state system of aviation equipment is not perfect. Both of them together greatly increase the difficulty of reliability analysis for the complex system of aviation equipment, especially for the complex multi-state system of aviation equipment which generally has multiple failure modes, dynamic changes and uncertain characteristics of basic support. In recent years, the reliability analysis of complex multi-state equipment systems has attracted widespread attention from scholars. Typical BN (Bayesian Network) methods include dynamic Bayesian networks and BN methods based on fault tree analysis. Dynamic Bayesian networks perform well in dealing with time series changes of time systems, but are difficult to handle complex system failure analysis problems due to high requirements for models and data. BN methods based on fault tree analysis have advantages in structured analysis and uncertainty reasoning, but have high model complexity and computational complexity. Moreover, when facing complex systems, there are challenges such as data uncertainty, low dynamic evaluation feasibility, and poor description of system inter-department multiple failure states. In summary, the existing schemes are difficult to cope with the difficulties caused by the difficulties of complex multi-state systems, especially the running state of complex multi-state systems is generally in a fuzzy and uncertain condition, and changes dynamically over time. This has become a difficulty and pain point for reliability analysis of complex multi-state systems.

[0003] Therefore, how to perform dynamic reliability analysis on complex multi-state systems under fuzzy and uncertain conditions has become a research topic. SUMMARY

[0004] Embodiments of the present application provide a multi-electric aircraft airborne system reliability analysis method based on FG-DBN, which can perform dynamic reliability analysis on complex multi-state systems in multi-electric aircraft airborne equipment under fuzzy and uncertain conditions. To achieve the above purpose, embodiments of the present application adopt the following technical solutions, such as Figure 11The method comprises the following steps: S1, a DBN (Dynamic Bayesian Network) model is established for a complex polymorphic system in an airborne device, wherein nodes in the DBN model correspond to components and fault states in the complex polymorphic system; S2, a fuzzy gradient function model with a fuzzy support radius is established; wherein the enhanced fuzzy gradient function model is composed of a fuzzy membership degree and a state transition matrix, the model comprises a fuzzy gradient function with a fuzzy support radius, which is used to obtain the fuzzy membership degree of a node in a corresponding time slice, and a state transition matrix of a discrete time Markov chain, which is used as a state transition matrix corresponding to a fault mode; S3, a conditional probability table is established for fault relationships between nodes in the DBN model; and S4, the node of a weak link in the complex polymorphic system is identified and reliability is analyzed by using an output result of the fuzzy gradient function model with the fuzzy support radius and the established conditional probability table.

[0005] In S2, the following steps are included: a fault state of a root node of the DBN model in a time slice is recorded , t j represents that a time slice currently reached by the DBN model is t j , j is a positive integer, and m represents a total number of time slices t j in a task time T; the fuzzy gradient function model with the fuzzy support radius (FSR) comprises:

[0006] , or, , or, ;

[0007] wherein, , , , and respectively represent fuzzy membership degrees of fault states of a node in a time slice corresponding to 0, 0.33, 0.5, 0.66 and 1.

[0008] To address the challenge of describing dynamic multi-fault states in complex polymorphic systems, a model based on FSR and E-TrMF (Enhanced Trapezoidal Membership Function) is proposed. The model characterizes the fault states of system nodes based on the fuzzy membership degrees of FSR corresponding to different fault modes, and introduces a discrete-time Markov chain to describe the dynamic system. Considering common-cause failures, a DBN model for complex polymorphic systems is used to analyze the uncertainties in the fault states of key system components. Component fault states are classified into three different fault modes: two-mode failures: Normal and Tloss, represented by fuzzy numbers 0 and 1, respectively; three-mode failures: Normal, Ploss, and Tloss, represented by fuzzy numbers 0, 0.5, and 1, respectively; and four-mode failures: Normal, Mistake, Ploss, and Tloss, represented by fuzzy numbers 0, 0.33, 0.66, and 1, respectively. The fuzzy membership degree of time slice t1 is calculated using a fuzzy gradient function model. Based on this, the fuzzy membership degrees of other time slices are calculated using the state transition matrix of a discrete-time Markov chain. The output of the fuzzy gradient function model containing FSR includes:

[0009] , , ,in, Represents node x i In time slice t j Fuzzy membership degree, Represents node x i In time slice t j+1 Fuzzy membership degree, H S This represents the state transition matrix of a node under a three-state failure mode, where S represents the state transition matrix at time slice t. j Time node x i The current failure mode.

[0010] Indicates time slice t j Time node x i Under normal conditions and at time slice t j+1 The conditional probability that the state is still in a normal state. Indicates time slice t j Time node x i It is in a normal state;

[0011] Indicates time slice t j Time node xi Under normal conditions and at time slice t j+1 The conditional probability of being in a partially failed state. Indicates time slice t j+1 Time node x i It is in a partially failed state;

[0012] Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a normal state. Indicates time slice t j Time node x i It is in a completely inoperable state;

[0013] Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a completely ineffective state.

[0014] The rows of the conditional probability table are used to record the data in time slice t. j Given a parent node in a specific failure state, the probability that a child node is in the corresponding failure mode is given. Then the parent node in time slice t j It is in a normal state at that time, among which, The gray number in the interval is used to quantize the child node y. i The probability of being in a normal state. , Indicates time slice t j Corresponding x i child nodes, Indicates y i The parent node, Indicates time slice t j Time node Node y in normal state i The gray number of the interval of the probability of a complete failure state, where S represents the probability at time slice t. j Time node x i The current failure mode.

[0015] The process of identifying weak nodes in the complex polymorphic system and analyzing their reliability includes: analyzing the probability of node failure in the complex polymorphic system; and analyzing the importance of nodes in the complex polymorphic system. The analysis of the probability of node failure in the complex polymorphic system includes:

[0016] Get leaf nodes in the time dimension At time slice t j In a fault state Gray fuzzy possibility ; Then get the leaf node In a fault state Gray fuzzy possibility . Specifically:

[0017] , , ,

[0018] ;

[0019] Wherein, the established DBN model corresponds to a task time T, T is divided into m time slices, when the complex polymorphic system is in time slice t j All nodes represent , p represents the total number of nodes, all child nodes represent , q represents the total number of child nodes, represents the current fault state of each root node from 1 to p, represents the fault state of node x i In time slice t j ; represents the fault state of each intermediate node from 1 to q.

[0020] And respectively represent the parent node set of leaf node and child node y q In time slice t j , represents the fuzzy membership degree of node In time slice t j When the current fault state is , represents the current fault state of each child node from 1 to q, represents the fault state of child node y i In time slice t j , represents the parent node set of child node y1 in time slice t j , represents the fuzzy membership degree of node In time slice t j When the current fault state is , represents the fuzzy membership degree of node In time slice t j When the current fault state is The fuzzy membership degree of time.

[0021] The conditional probability value of the node corresponding to the interval gray at time slice t j , The lower limit of the conditional probability value of the node corresponding to the interval gray at time slice t j , The upper limit of the conditional probability value of the node corresponding to the interval gray at time slice t j , and r represents the number of the conditional probability value containing the interval gray number.

[0022] The importance of the node in the complex polymorphic system is analyzed, including: obtaining the probability importance of the root node x i and the intermediate node y i corresponding to the task time T, and the probability importance of the root node x i and the intermediate node y i corresponding to each time slice in the task time T; further obtaining the critical importance of each node.

[0023] In this embodiment, FSR is combined with discrete time Markov chain to establish a model based on FSR and E-TrMF, to dynamically quantify multiple failure states, and at the same time, a gray conditional probability table GCPT (grey conditional probability table) method based on interval gray numbers is used to represent uncertainty, to provide more accurate input for reliability analysis of complex polymorphic systems. The FG-DBN scheme can effectively represent multiple failure states of complex multi-electric aircraft systems, and reduce the influence of uncertainty on system reliability. Through failure analysis of the complex polymorphic system, the system failure mode under the current running state is judged; on this basis, the probability importance and the critical importance are combined to analyze the short-term impact and long-term deficiency of the system, to provide a basis for maintenance support of the system. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The BN model structure diagram based on FSR, wherein, Figure 1 Part (a) of FIG. 1 is a schematic diagram of the BN structure; Figure 1 Part (b) of FIG. 1 is a schematic diagram of the DBN structure;

[0025] Figure 2 The corresponding relationship diagram of the fuzzy support radius variable d and the membership function of the complex polymorphic system, wherein, Figure 2 Part (a) of FIG. 2 is a double-mode failure; Figure 2 Part (b) of FIG. 2 is a three-mode failure; Figure 2 Part (c) of FIG. 2 is a four-mode failure;

[0026] Figure 3This is a schematic diagram of GCPT for a complex multimorphic system, where, Figure 3 Part (a) is a schematic diagram of the DBN structure of a complex polymorphic system; Figure 3 Part (b) is time slice t j A schematic diagram of the GCPT structure at time node y1; Figure 3 Part (c) is time slice t j A schematic diagram of the GCPT structure at time node y2;

[0027] Figure 4 A schematic diagram of the reliability analysis process for a Dynamic Bayesian Network (FG-DBN) model that integrates fuzzy mathematics and grey systems;

[0028] Figure 5 This section explains the operating mechanism and key component relationships of a typical SG system. Figure 5 Part (a) is a schematic diagram of the typical SG system start-up mode; Figure 5 Part (b) is a schematic diagram of a typical SG system power generation mode; Figure 5 The English abbreviations in the text are as follows: BR represents rectifier bridge, CEC represents generator excitation contactor, EXG represents exciter, RR represents rotating rectifier, SG represents starter generator, SC represents starter contactor, CMSC represents general motor starter controller, GCB represents generator control circuit breaker, ATRU represents autotransformer rectifier, APB represents auxiliary power circuit breaker, EPC represents external power contactor, APU represents auxiliary power unit, GEN represents generator, and ATU represents autotransformer unit.

[0029] Figure 6 This is a schematic diagram illustrating the working mechanism and relationships between key components of a typical SG system. Figure 6 The English abbreviations in the text are as follows: SFS represents signal feedback sensor, SLS represents starting law calculation sensor, SCSG represents starting control signal generation component, PWR represents power supply, DCU represents computer control system, SCU represents starting controller, APU represents auxiliary power unit, EXG represents exciter, SG represents starter generator, BR represents rectifier bridge, RR represents rotating rectifier, VR represents voltage regulating circuit, ENG represents engine, and OE represents airborne equipment.

[0030] Figure 7 A schematic diagram of the DBN model for an SG system considering common-cause failure, where, Figure 7 Part (a) is a schematic diagram of the DBN model structure; Figure 7 Part (b) is a schematic diagram of the dynamic process of the DBN model; Figure 7The English abbreviations in the table below represent: SFS represents a signal feedback sensor, SLS represents a start law calculation sensor, SCSG represents a start control signal generation part, PWR represents a power source, DCU represents a computer control system, SCU represents a start controller, EXG represents an exciter, SG represents a starting generator, ER represents an engine rotor, RR represents a rotating rectifier, BR represents a rectifier bridge, VR represents a voltage regulator circuit, ENG represents an engine, SM represents a start mode, GM represents a generation mode, SGS represents a starting generation system.

[0031] Figure 8 Fig. 4 is a graph showing the change of the average value of the gray fuzzy possibility of the leaf node Y and the variable d for the time slice t1;

[0032] Figure 9 Fig. 5 is a graph showing the quantification of the gray fuzzy possibility of the leaf node Y for different fault states;

[0033] Figure 10 Fig. 6 is a graph showing the distribution of the probability importance and the criticality importance of the node during the task time T, wherein, Figure 10 the (a) part of Fig. 6, Figure 10 the (c) part of Fig. 6 and Figure 10 the (e) part of Fig. 6 are the probability importance of the SG system; Figure 10 the (b) part of Fig. 6, Figure 10 the (d) part of Fig. 6 and Figure 10 the (f) part of Fig. 6 are the criticality importance of the SG system.

[0034] Figure 11 Fig. 7 is a flow chart of the method according to an embodiment of the present application. DETAILED DESCRIPTION

[0035] A Bayesian network (BN) is a directed acyclic graph consisting of nodes and directed edges. The nodes represent random variables, and the directed edges represent conditional dependencies or causal relationships between these variables. Bayesian network analysis enables probabilistic reasoning by calculating the posterior probabilities of variables based on prior knowledge and observed evidence.

[0036] In Bayesian network analysis, a directed acyclic graph (DAG) is used to describe the conditional dependencies between variables. The basic BN model structure is shown in the (a) part of Fig. 1. Figure 1

[0037] ​DBN is an extension of BN in temporal logic, which consists of an initial BN and a transition network. By adding a time dimension, the static BN model becomes a probability distribution model that can handle temporal information. DBN can be constructed by expanding multiple time slices, where each slice corresponds to a static BN model. The structural dependencies between adjacent time slices are preserved to ensure temporal consistency, as shown in part (b) of Figure 1. Figure 1

[0038] (1) Dynamic Bayesian Network Framework

[0039] The establishment method of Bayesian network can be divided into the following steps: 1) Determine the variables, first need to determine the variables involved in modeling, which can be continuous variables or discrete variables. 2) Build network structure, in Bayesian network, nodes represent random variables, and edges represent conditional dependencies between two variables. Therefore, it is necessary to determine the conditional dependencies between variables and build the network structure. 3) Determine the probability distribution of variables, after determining the network structure, it is necessary to determine the probability distribution of each variable, which can be discrete distribution or continuous distribution. The method of determining the probability distribution can be subjective assignment method, maximum likelihood method, Bayesian method, etc. 4) Model evaluation, after establishing the model, it needs to be evaluated to determine its prediction performance. Common methods include cross-validation, information criterion, error evaluation, etc. 5) Model application, after establishing the Bayesian network, it can be used to infer the conditional dependencies between variables, and can be used for probability inference, decision analysis, data mining, etc.

[0040] Fuzzy mathematics is a discipline that focuses on dealing with complex fuzzy problems, and its core is to provide a quantitative analysis framework for things that are difficult to define accurately. In fuzzy mathematics, fuzzy sets introduce the concept of "membership degree", which allows elements to belong to a set to different degrees (between 0 and 1). This feature enables fuzzy mathematics to better handle qualitative knowledge, language variables in complex systems, and provide effective tools for uncertain information, while building a flexible mathematical framework for problems that are difficult to model accurately.

[0041] Under the background of fuzzy comprehensive evaluation, choosing the right membership function is crucial to accurately reflect the characteristics of the research topic. Common membership functions include triangular functions and trapezoidal functions. The choice of these functions depends on the specific characteristics of the problem being considered, and the purpose is to ensure that fuzzy concepts can be reasonably quantified.

[0042] (2) Fuzzy Logic (Fuzzy Logic)

[0043] ​Extended Boolean logic is an advanced tool for fuzzy reasoning that deals with fuzzy propositions by introducing fuzzy operators. One key difference of extended Boolean logic is that it allows variables to take values in the interval (0, 1), rather than the traditional boundaries of 0 and 1. This extension enhances the effectiveness of the logic in dealing with fuzziness and uncertainty.

[0044] Based on the above mathematical algorithms and model tools, the main design goal of the present embodiment is to effectively describe the diversified fault states caused by complex polymorphic systems, the fuzziness of basic data, and the dynamic changes of working states. The main design idea is to realize dynamic reliability analysis of complex polymorphic systems under fuzzy and uncertain conditions by introducing the theories of grey system and fuzzy mathematics, combined with the DBN reliability analysis method, to evaluate the failure probability, short-term weak links and long-term weak links of complex polymorphic systems, and to ensure the effectiveness and universality of the method.

[0045] Specifically, to solve the problem of describing dynamic multi-fault states in complex polymorphic systems, an enhanced trapezoidal membership function (E-TrMF) method based on fuzzy support radius (FSR) and Markov chain is proposed. This method is based on FSR fuzzy membership corresponding to different failure modes to characterize the fault state of system nodes, and introduces a discrete-time Markov chain to describe the dynamic system. Considering common cause failure, the DBN model of complex polymorphic systems is used to analyze the uncertainty in the fault state of key system components. The component fault state is divided into three different failure modes:

[0046] 1) Two-state failure: normal operation (Normal) and complete failure (Tloss), represented by fuzzy numbers 0 and 1, respectively;

[0047] 2) Three-mode failure: normal operation (Normal), partial failure (Ploss), and complete failure (Tloss), represented by fuzzy numbers 0, 0.5, and 1, respectively;

[0048] 3) Four-mode failure: normal operation (Normal), abnormal operation (Mistake), partial failure (Ploss), and complete failure (Tloss), represented by fuzzy numbers 0, 0.33, 0.66, and 1, respectively.

[0049] As shown in Figure 2 , first, the fault state of the DBN model root node in a specific time slice is defined as state . Then, let the fuzzy support radius variable be d (0≤d≤0.165) to satisfy:

[0050] , or, , or, ;

[0051] The fuzzy support radius d is combined with the trapezoidal membership function to realize the description of the node failure state at the current time slice. Among them, 、 、 、 and respectively represent the fuzzy membership degree of the node failure state corresponding to 0, 0.33, 0.5, 0.66 and 1 when the E-TrMF method is at time slice . Secondly, the fixed region and the uncertain region of the proposed E-TrMF method will be adaptively determined according to the value of variable d, and dynamically adjusted with the change of d. As shown in Figure 2 , there are three different failure modes. In the proposed E-TrMF method, the calculation of each failure state of the root node under the corresponding failure mode is realized by integrating the three failure state types, as shown in Table 1 and Table 2.

[0052] Table 1 Membership of node under two / three-state failure mode

[0053]

[0054] Table 2 Membership of node under four-state failure mode

[0055]

[0056] Node failure state At time slice j i , it is any value within the interval (0, 1) to meet the fuzzy gradient function model containing fuzzy support radius (Fuzzy support radius, FSR). For example, the failure state of four-mode failure node x i is , where .

[0057] Assuming that node x i is in one of the three failure states, according to Table 1, the calculation result of the node at time slice t j can be obtained according to the state transition matrix (TPM) combined with the discrete-time Markov chain. Thus, the fuzzy membership degree of the node at time slice t j+1 is calculated, and the specific calculation process is as follows: , ,

[0058] where represents the fuzzy membership degree of node x i at time slice t j , Represents node x i In time slice t j+1 Fuzzy membership degree, H S This represents the state transition matrix of a node under a three-state failure mode, where S represents the state transition matrix at time slice t. j Time node x i The current failure mode Indicates time slice t j Time node x i Under normal conditions and at time slice t j+1 The conditional probability that the state is still in a normal state; Indicates time slice t j Time node x i Under normal conditions and at time slice t j+1 The conditional probability of being in a partially failed state; Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a normal state; Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a completely ineffective state.

[0059] In practical applications, complex polymorphic systems involve numerous interacting components, intricate internal relationships, and diverse operating environments. The complex interactions between components can lead to common-cause failures and multiple fault states among subsystems, thereby jeopardizing the stability of the entire system. Therefore, describing the fault relationships between critical components and the system using deterministic data within the task timeframe is extremely difficult. To accurately describe the fault relationships between components in complex polymorphic systems, this embodiment proposes a Conditional Probability Table (GCPT) method based on grey system theory, using interval grey numbers to describe the conditional probabilities in the DBN model. The DBN operates in time slice t. j GCPT at that time Figure 3 As shown, each row represents the time slice t. j Given a parent node in a specific failure state, the conditional probability that a child node will also be in a specified failure state. For example, Indicates the parent node in time slice t j It is in a normal state at this time. Therefore, child node y i The probability of being in a normal state is determined by the gray number of the interval. This indicates that... At the same time, it should also meet... .

[0060] Meanwhile, to solve the challenge of dynamic reliability analysis in complex multi-state system, a reliability analysis method based on FG-DBN is designed for the airborne system of More-Electric Aircraft. The method analyzes the dynamic failure of multi-state system and the importance of system nodes, respectively describes the overall failure state of the system and identifies the weak links in the system. It provides important reference value for the reliability evaluation, fault diagnosis and maintenance decision of complex multi-state system. In order to quantitatively analyze the uncertainty problem in complex multi-state system, the E-TrMF method and the GCPT method are used to describe the fault state of system nodes in different time slices. The uncertainty range of system fault state can be dynamically characterized, the influence of subjective factors can be reduced, and the basis for identifying weak links in the system can be provided. For example: assuming that the DBN task time of complex multi-state system is T, which is divided into m time slices. When the system is in time slice t j , the root node is , the intermediate node is , and the leaf node is Y. The current fault state of each root node is , and the gray fuzzy possibility of the leaf node in the time slice t j is in the fault state is . Then, the gray fuzzy possibility of the leaf node in the fault state z' within the task time T is calculated as , and the calculation process is as follows:

[0061] ,

[0062] ,

[0063] , wherein the established DBN model corresponds to the task time T, T is divided into m time slices, when the complex multi-state system is in time slice t j , all nodes represent , p represents the total number of nodes, all child nodes represent , q represents the total number of child nodes, represents the current fault state of each node from 1 to p, represents the fault state of node x i in time slice t j ; and respectively represent the parent node set of leaf node Y and child node y q in time slice t j , represents the current fault state of node in time slice t j , the fuzzy membership degree of the node at time slice t , the current fault state of the node y at time slice t j , the parent node set of the node y i at time slice t j , the current fault state of the node at time slice t j , the fuzzy membership degree of the node at time slice t j , the fuzzy membership degree of the node at time slice t j . the conditional probability value of the node corresponding to the interval grey number at time slice t j , the lower limit of the conditional probability value of the node corresponding to the interval grey number at time slice t j , the upper limit of the conditional probability value of the node corresponding to the interval grey number at time slice t j , r represents the number of conditional probability values containing interval grey numbers.

[0064] Further, in order to identify the weak link in the complex polymorphic system, the importance of the system fault node is quantified to affect the uncertainty, including the probability importance and the critical importance, which respectively reflect the short-term and long-term reliability. The two importance indexes jointly support the identification of the weak link of the system, and provide reliable reference basis for the maintenance decision under the condition of complex uncertainty.

[0065] (1) Probability importance

[0066] The probability importance of the root node or the intermediate node refers to the average influence degree of the node on the leaf node in the specified risk state in the process of the state of the node from 0 to 1. The higher the probability importance, the greater the influence on the corresponding leaf node. Assuming that the leaf node Y is in the fault state j at time slice t , the calculation process of the root node probability importance and the intermediate node probability importance is described as follows:

[0067] , wherein, and respectively represent the fault state of the leaf node in two fault states and 0. The degree of probability; f w It is the corresponding node in the current fault mode S. The fault state; w represents the fault mode number of the node; It is the intermediate node y i In the current time slice t j The probability of a fault state at that time; and The intermediate node y is respectively i The state of failure f w When the leaf node is at time 0, the fault state is: The possibility.

[0068] The probability importance of nodes within task time T is and The task time T is divided into m time slices t. j The probability importance of nodes within task time T is calculated as follows: .in, and Representing the root node x within task time T respectively i and intermediate node y i The probability importance; and For time slice t j Root node x i and intermediate node y i The probability importance.

[0069] (2) Critical importance

[0070] Critical importance is defined as the ratio of the probability of a node occurring to the probability of a leaf node occurring. Calculating critical importance requires probabilistic importance as supporting data. When leaf node Y occurs in time slice t... j In fault state At that time, the root node and intermediate nodes The calculation process for critical importance is as follows:

[0071] , ,in, and For time slice t j The inner leaf node is in a fault state. Root node x i and intermediate node y i The critical importance.

[0072] The critical importance of nodes within task time T is and The task time T is divided into m time slices t. jThe critical importance of the nodes within the task time T is calculated as follows:

[0073] wherein, and respectively represent the critical importance of the root node x i and the intermediate node y i within the task time T.

[0074] In practical applications, the approximate logic of the reliability analysis process of the fusion of fuzzy mathematics and gray system dynamic Bayesian network (FG-DBN) is as shown in Figure 4 , mainly including 4 steps:

[0075] (1) Step one: DBN model construction of complex polymorphic system:

[0076] Firstly, based on the working mechanism and structural composition of the complex polymorphic system, the typical faults and fault features of the key components are distinguished, and the relationship between the key components and the system fault modes is clarified. Then, based on the working mechanism and typical fault modes of the complex polymorphic system, the network structure of the BN model is constructed to accurately reflect the functional dependence relationship and fault propagation within the system. Finally, the BN model is converted into a DBN model through time slices and task time, and the DBN model of the complex polymorphic system is established.

[0077] (2) Step two: Fuzzy membership degree model construction of dynamic multiple failure state:

[0078] In view of the problems of dynamic change and multiple failure state existing in the complex polymorphic system, this embodiment proposes a method based on fuzzy support radius (FSR) and enhanced trapezoidal membership function (E-TrMF) of Markov chain. Firstly, three types of fault modes are divided to represent the multiple failure state of the system; secondly, fuzzy mathematics and gray system theory are introduced to establish the fuzzy gradient function with FSR corresponding to each fault mode; finally, the fuzzy gradient function is combined with the discrete time Markov chain to associate the dynamic change with the state transition matrix, realizing the representation of dynamic change and multiple failure state.

[0079] (3) Step three: Construction of gray conditional probability table:

[0080] According to the typical fault modes and working mechanism of the complex polymorphic system, the interval gray number of the gray system theory is introduced as the basic support of the DBN model, which is combined with the maintenance manual and fault isolation manual of the complex polymorphic system, so as to realize the expression of the mutual relationship between the nodes in the DBN model, especially for the fuzzy and uncertain mutual relationship existing in the complex polymorphic system, which can effectively represent the content structure relationship of the system.

[0081] (4) Step four: Dynamic reliability analysis and evaluation:

[0082] For the reliability analysis problem of complex multi-state system under fuzzy and uncertain conditions, a dynamic reliability analysis method of FG-DBN is proposed. Firstly, the DBN model of complex multi-state system is taken as the model input; secondly, the system failure probability in the time slice and task time is calculated by combining E-TrMF and GCPT methods as the basic support, and the dynamic reliability analysis of the system failure state is realized; finally, according to the current system failure probability, the weak links of the system in short-term and long-term conditions are identified from the probability importance and critical importance, so as to realize the dynamic reliability evaluation of the current system state.

[0083] In order to verify the effect of the embodiment scheme, the more electric aircraft starting power system is taken as the research object of complex multi-state system. The starting power system is an important part of the power supply system of more electric aircraft, and there are various failure states caused by various factors such as electrical failure, mechanical failure, environmental influence and improper maintenance. At the same time, the starting power system is affected by load change and environmental conditions, resulting in dynamic operation state of system working state, and the key components and working mechanism detailed diagram are as shown in Figure 5 The running process can be divided into two modes: starting mode and power generation mode, as shown in Figure 5 The failure of more electric aircraft starting power system is mainly caused by the failure of key components. Based on the mechanism and main components of more electric aircraft starting power system, the risk causing elements can be determined as the failure of key components, including the failure of main generator, exciter, excitation contactor, starting contactor, rectifier bridge, various sensors, power control unit, rotating rectifier and voltage regulating circuit. Therefore, these main key components are classified, that is, the function execution components responsible for directly controlling the starting / power generation work, the information collection components responsible for collecting the working voltage, power and other information of generator, engine and other components, and the information processing components responsible for summarizing and processing the collected information, as shown in Figure 6

[0084] Combined with the typical failure modes of different types of key components, the failure state of key components is classified into the following categories: normal work, abnormal work, partial failure and complete failure. The classification of system state is based on the actual situation of subsystem, as shown in Table 3.

[0085] Table 3 Classification of typical failure modes of starting power system

[0086]

[0087] ​A DBN model is constructed by analyzing the working mechanism and typical failure modes of the key components of the starter-generator (SG) system, as shown in FIG. 1. Figure 7 The task time T is divided into three time slices, and the GCPT of the DBN nodes is determined according to the aircraft maintenance manual and the fault isolation manual. The DBN model considers the common cause failure problem between key components, represents the interaction between components and the fault propagation path in the system, and effectively reflects the dynamic characteristics of the system in different working states.

[0088] In the DBN model, the nodes represent the key components and working states of the SG system, and the directed edges describe the mutual relationship between the nodes. Therefore, the DBN model of the SG system clearly shows the fault propagation process between components and the influence of the working state change of each component on the system performance and the dynamics between related components. The names of the related key components are shown in Table 4.

[0089] Table 4 Names of key components of SG system

[0090]

[0091] Taking the starter control unit 1 (SCU1) node as an example, when the node fails, the exciter generator 1 (EXG1) and the starter generator 1 (SG1) are identified as two components that may be affected by the common cause failure, and the influence of the failure on the entire system is determined. This DBN-based modeling method can provide strong support for fault diagnosis and maintenance decision-making. In addition, the DBN model can describe the dynamic changes of the system, thereby improving the accuracy and reliability of the evaluation of the working state of the SG system.

[0092] In order to clearly illustrate the relationship between the SG system and its key components, this embodiment proposes a fault state representation method based on the E-TrMF and GCPT methods applied to the DBN model, thereby effectively describing the multi-state and dynamic changes of the SG system. First, the fault states of the DBN nodes are defined. The fault states of each root node at time slice t1 are represented as , , , , and respectively. According to Tables 1 and 2, the fuzzy membership degrees at time slice t1 are obtained using the E-TrMF method, and the specific results are shown in Tables 5 and 6. In addition, the upper and lower bounds of the average value of the gray fuzzy possibility of each fault state of the leaf node Y at time slice t1 are analyzed The relationship with the FSR variable d, such as Figure 8 As shown.

[0093] Table 5 Membership degrees of root nodes in binary / tri-state failure at time slice t1

[0094]

[0095] Table 6 Membership degrees of the four-state failure root node at time slice t1

[0096]

[0097] To ensure the generalizability of the experimental results, based on engineering practice and expert experience, d = 0.1 was chosen to analyze the system's reliability. Under this condition, the fuzzy membership degree of the E-TrMF corresponding to the root node failure state was determined. Two-state, three-state, and four-state failures were calculated using the state transition matrix of the discrete-time Markov chain, and their state transition matrices correspond to... , and The fuzzy membership degree of the root node fault state in each time slice was calculated, as shown in Table 7.

[0098] Table 7. Fuzzy membership degrees of root node fault states at different times.

[0099]

[0100] according to Figure 7 As shown in Table 4, the failure modes of each node in the DBN model are first clarified. The failure modes and working mechanism of the SG system are analyzed, and the power supplies (PWR1 and PWR2) are defined to have two failure modes, denoted as x. i = [0, 1], i = 1, 2. The Signal Feedback Sensor (SFS), Start-up Rule Calculation Sensor (SLS), and Computer Control Unit (DCU) have three fault modes, denoted as x. i y1, y2 = [0, 0.5, 1], i = 3, 4. The remaining nodes exhibit four failure modes, represented as x5, y6, y7, y8, y9, y1, y2 ... i Y = [0, 0.33, 0.66, 1], i = 3, 4, …, 18. The conditional probability table (CPT) for each node is represented using the GCPT method. Taking the CPTs of nodes y1 and Y containing interval gray numbers as examples, as shown in Tables 8 and 9. Each row in the tables represents the value at time slice t. j When the parent node is in different fault states, the conditional probability of the child node failing.

[0101] Table 8 shows the CPT of node y1 containing the gray number of the interval at time slice t1.

[0102]

[0103] Table 9 shows the CPT of node Y containing the gray number of the interval at time slice t1.

[0104]

[0105] Failure analysis of complex multimorphic systems: The probability of different failure states of leaf node Y in the SG system is calculated. The calculation results are as follows: Figure 9 As shown. The FG-DBN method compares the possible outcomes within task time T and finds that its value is... This indicates that the SG system is most likely in the Tloss state, followed by the Normal state, while the Ploss and Mistake states have similar probabilities and are extremely unlikely to occur. Therefore, timely maintenance and adjustments are necessary to mitigate the risk of serious accidents and ensure system reliability. Importance analysis of complex polymorphic systems: Since the importance of a node is affected by both the current component failure state and the FSR variable d, any change in the failure state of a critical component will lead to differences in the corresponding importance interval. Therefore, the analysis identifies different weak links in the system. Assuming the node is in a normal state, the probability of leaf node Y under various failure states is determined. Then, the probabilistic importance of leaf node Y under the current failure state can be obtained, such as... Figure 10 As shown. Figure 10 As shown in sections (a), (c), and (e), the proposed FG-DBN method determines the probabilistic importance of a node under each fault state. Under the current node fault state, for any abnormal state of the SG system, node y... 11 and y 12 It is the weakest link in the system. In a partially failed state, nodes y1, y2, and y3... 15 and y 16 This represents the weakest link in the system. In a completely failed state, nodes x5, y7, y8, and y... 18 It is the weakest link in the system. Similarly, the importance of nodes under different fault states is as follows: Figure 10of (b), (d) and (f) shown in the SG system in the abnormal, partial failure and complete failure state of the key importance of each node analysis shows that the identified weak links and the results obtained in the probability importance assessment, further verify the accuracy of the proposed FG-DBN method. The main advantages and value in practical application of this embodiment are: 1) in order to realize the reliability analysis of complex multi-state system under the condition of multiple sources of uncertainty, this embodiment proposes a FG-DBN method suitable for complex multi-state system. First, the E-TrMF method is combined with FSR and discrete time Markov chain to dynamically quantify the multiple failure states of the key components during task execution. Secondly, the GCPT method based on interval grey number is used for fault analysis under dynamic conditions. Finally, the multi-electric aircraft starting power system (SGS) is taken as a complex multi-state system to verify the effectiveness of the proposed FG-DBN method. 2) in order to solve the problem of inaccurate state and dynamic multiple failure state in reliability analysis of complex multi-state system, this embodiment proposes a method based on E-TrMF and GCPT. By combining fuzzy support radius (FSR) with discrete time Markov chain, an E-TrMF (Enhanced trapezoidal membership function) method based on FSR and Markov chain is proposed to dynamically quantify multiple failure states. At the same time, a GCPT (grey conditional probability table) method based on interval grey number is proposed to represent uncertainty, which provides more accurate input for reliability analysis of complex multi-state system. 3) unlike traditional reliability analysis methods, the proposed FG-DBN method can effectively represent multiple failure states of complex multi-electric aircraft system, reducing the influence of uncertainty on system reliability. Through failure analysis of complex multi-state system, the system failure mode under current operating state is judged; on this basis, combined with probability importance and critical importance, the short-term impact and long-term deficiency of the system are analyzed, which provides basis for system maintenance support. 4) in the case analysis, this method takes the typical complex multi-state system of multi-electric aircraft starting power system as the research object, and constructs the DBN model structure of starting power system through the typical failure fault and working mechanism of starting power system, which serves as the support for subsequent model. For this complex multi-state system DBN model, the FG-DBN reliability analysis method is used to effectively realize the static / dynamic reliability analysis of multi-electric aircraft starting power system under the condition of multiple sources of uncertainty, and combined with the probability and critical importance analysis of the system, the short-term and long-term weak links of complex multi-state system are evaluated.

Claims

1. A reliability analysis method for multi-electric aircraft airborne systems based on FG-DBN, characterized in that, include: S1. Establish a DBN model for the complex polymorphic system in airborne equipment, wherein the nodes in the DBN model correspond to the components and fault states in the complex polymorphic system; S2. Establish a fuzzy gradient function model containing fuzzy support radii; S3. Establish a conditional probability table for the fault relationships between nodes in the DBN model; S4. Using the output of the fuzzy gradient function model with fuzzy support radius and the established conditional probability table, identify the weak nodes in the complex polymorphic system and analyze their reliability. Fault states are classified into at least three fault modes, including: Two-state faults: Normal and Tloss, represented by fuzzy numbers 0 and 1 respectively; Three-mode failures: Normal, Ploss (partial failure), and Tloss (complete failure), represented by fuzzy numbers 0, 0.5, and 1, respectively; Four-mode failure: Normal, Mistake, Ploss, and Tloss, represented by fuzzy numbers 0, 0.33, 0.66, and 1, respectively; The fuzzy gradient function model includes: the fuzzy membership degree of the node in the corresponding time slice and the state transition matrix corresponding to the fault mode; in S2, it includes: Record the root node of the DBN model in the time slice node x in i Fault status , t j This indicates the current time slice identifier of the DBN model, where j is a positive integer and m represents the total number of time slices within the task time T; Establish a fuzzy gradient function model containing FSR; The fuzzy gradient function model containing FSR includes: ， or, , or, ; in, , , , and These represent time slices. At that time, node The fault states correspond to fuzzy membership degrees of 0, 0.33, 0.5, 0.66, and 1, respectively; the output of the fuzzy gradient function model containing FSR includes: ， ， ， in, Represents node x i In time slice t j Fuzzy membership degree, Represents node x i In time slice t j+1 Fuzzy membership degree, H S This represents the state transition matrix of a node under a three-state failure mode, where S represents the state transition matrix at time slice t. j Time node x i The current failure mode; Indicates time slice t j Time node x i Under normal conditions and at time slice t j+1 The conditional probability that the state is still in a normal state. Indicates time slice t j Time node x i It is in a normal state; Indicates time slice t j Time node x i Under normal conditions and at time slice t j+1 The conditional probability of being in a partially failed state. Indicates time slice t j+1 Time node x i It is in a partially failed state; Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a normal state. Indicates time slice t j Time node x i It is in a completely inoperable state; Indicates time slice t j Time node x i Under the condition of complete failure and in time slice t j+1 The conditional probability of being in a completely ineffective state; The rows of the conditional probability table are used to record the data in time slice t. j Given a parent node in a specific failure state, the probability that the child node is in the corresponding failure mode. Among them, if Then the parent node in time slice t j It is in a normal state at that time, among which, The gray number in the interval is used to quantize the child node y. i The probability of being in a normal state. , Indicates time slice t j Corresponding x i child nodes, Indicates y i The parent node, Indicates time slice t j Time node Node y in normal state i The gray number of the interval of the probability of a complete failure state, where S represents the probability at time slice t. j Time node x i The current failure mode.

2. The method according to claim 1, characterized in that, The process of identifying weak points in the complex multimorphic system and analyzing their reliability includes: Analyze the probability of node failure in complex polymorphic systems; Analyze the importance of nodes in a complex polymorphic system.

3. The method according to claim 2, characterized in that, The analysis of the probability of node failure in complex polymorphic systems includes: Get leaf nodes in the time dimension In time slice t j When in a fault state gray ambiguity possibility ; Then obtain the leaf nodes. The system is in a fault state during mission time T. gray ambiguity possibility .

4. The method according to claim 3, characterized in that, The analysis of the importance of nodes in a complex polymorphic system includes: Get the root node x corresponding to task time T i and intermediate node y i The probability importance of and , and the root node x corresponding to each time slice within task time T. i and intermediate node y i The probability importance; Further determine the critical importance of each node.

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