A method for evaluating task reliability of airborne equipment in complex and changeable environment

Abstract

The application discloses a kind of complex and changeable environment under airborne equipment task reliability evaluation method, it is related to the research field of aviation airborne equipment task reliability evaluation.This application is aimed at the deficiency of existing complex and changeable environment under aviation airborne equipment multi-stage task reliability evaluation, establishes a set of system-level task reliability evaluation method based on Markov chain for the multi-stage task of aviation airborne equipment execution, and introduces finite state machine, the equipment operation rule and environmental influence factor when the system state of adjacent two stages is switched are judged and analyzed, so that reliability analysis is closer to actual situation.

Description

Technical Field

[0001] This invention patent relates to the research field of mission reliability assessment of airborne equipment, specifically a system-level mission reliability assessment method based on Markov chains. Background Technology

[0002] When aircraft perform missions, the mission reliability of airborne equipment is fundamental to their operation and safety, directly affecting the mission modes and scale, as well as the ability to sustain missions, and directly impacting mission effectiveness. The operating environment of airborne equipment is complex and variable. Systems are not only affected by conventional environmental factors such as temperature, load, and vibration, but also by extreme environments such as lightning, snow, ice, hail, fog, smog, and harmful gases. These environmental factors also lead to multiple operating modes for airborne equipment. Airborne equipment such as electro-optical reconnaissance platform systems, signal transmission cables, and power systems have varying adaptability to different environmental factors. For example, an aircraft engine, after a failure of its oxygen supplementation system, is no longer suitable for operation in the hypoxic environment of high altitudes; an airborne electro-optical reconnaissance platform, after a failure of its vibration suppression module, will experience low clarity or even blurry video images output by the platform under strong vibration. However, traditional mission reliability assessments often simply describe the transition probability of operating modes, neglecting the impact of complex and variable environments and the conditions for equipment operating mode transitions, resulting in inaccurate mission reliability assessments. Meanwhile, for multi-stage missions, there is a stage-related relationship between the missions. The system units required for different stages and the working modes and working environments of the system units are all different, which further increases the complexity and difficulty of airborne equipment mission reliability assessment.

[0003] Currently, there is a lack of research on the reliability of multi-stage missions in complex and variable environments. Most studies do not consider environmental constraints such as temperature, load, vibration, and lightning, and do not pay attention to the switching conditions of system operating modes and the environmental adaptability of equipment, resulting in inaccurate mission reliability assessment results. Summary of the Invention

[0004] This invention addresses the shortcomings of existing multi-stage mission reliability assessment methods for airborne equipment in complex and variable environments. For airborne equipment that is highly susceptible to environmental influences, this invention proposes a system-level mission reliability assessment method based on Markov chains. This method combines the system working principle of airborne equipment with environmental constraints and introduces a finite state machine model to improve the accuracy of mission reliability assessment.

[0005] The technical solution of this invention is: a method for assessing the mission reliability of airborne equipment under complex and variable environments, the method comprising the following steps:

[0006] Step 1: Obtain the task profile;

[0007] Step 1.1: Divide the task into stages according to the process of the system executing the task, and determine the system units, system working mode, working time and working environment required for each stage;

[0008] Step 1.2: Determine the success metrics for the task;

[0009] Step 2: Finite state machine modeling;

[0010] Step 2.1: Define the state machine and the data structure of each state node;

[0011] Step 2.2: When a triggering event is passed to the state machine, determine the current state of the state machine, and then query the state transition function of the state response;

[0012] Step 2.3: If the same triggering event is found, call the corresponding state transition function and set the state flag to the corresponding next state node; otherwise, the state machine cannot respond to the triggering condition normally, and directly set the state flag to the task failure state.

[0013] The failure rate λ of the working unit for each state node under different environmental conditions is calculated as follows:

[0014] λ=K1·K2·……·K n ·λ G

[0015] Where, λ G K represents the inherent failure rate of the working unit. n The environmental correction factor for the work unit under different environmental conditions is determined based on engineering experience, where n represents the total number of work environment categories.

[0016] Step 3: Markov chain modeling requires establishing state transition relationships and calculating the system's state probability vector at time t based on the initial state;

[0017] Step 3.1: Determine the equipment state transition relationships;

[0018] Step 3.2: Establish the transition probability matrix of the continuous-time Markov chain, denoted as:

[0019]

[0020] in,

[0021] The Markov chain {X} n The state transition density of} is constituted by the following state transition density matrix M:

[0022]

[0023] A state transition graph is constructed based on the "reachability" and "connectivity" of the state set, and transition probabilities exist in the link relationships;

[0024] Step 3.3: For the state transition density matrix M in Step 3.2, the system state equation is expressed as:

[0025]

[0026] P(t) is the state vector of the system at time t; the Laplace transform of the system's state equation yields:

[0027] L[P'(t)]=SP(S)-P(0)=MP(S)

[0028] (SM)P(S)=P(0)

[0029] Where P(0) is the initial state vector of the system, S is the complex variable in the Laplace transform, P(S) is the complex function after the Laplace transform of P(t), P'(t) is the derivative function of P(t) with respect to t, and L[P'(t)] represents the Laplace transform of P'(t);

[0030] Let D = SM. Using Cramer's rule to solve, since D ≠ 0, we get:

[0031] P(S)=P(0) / D

[0032] p i (S)=|D i | / |D|

[0033] Among them, D i A matrix is ​​obtained by replacing the elements in the i-th column of matrix D with elements of column vector P(0), while keeping the elements in the remaining columns unchanged; p i (S) represents the solution to the state equation;

[0034] For p i (S) Performing an inverse Laplace transform yields the probability p of the system at time t when it is in state i. i (t);

[0035] Step 3.4: The system's state probability vector P(t) at time t is:

[0036] P(t)=(p1(t),p2(t),…,p i (t),…)

[0037] Where, p i (t) represents the probability that the system is in state i at time t;

[0038] Step 4: Mission reliability assessment;

[0039] Step 4.1: Initial Parameter Setting: Assume the task is divided into Z stages, with task stage m representing one of these stages; the device has N states, with state i representing one of these states. Then, the system probability vector for task stage m is represented as:

[0040] P m =(p1,p2,…,p i ,…)

[0041] Where m = 1, 2, ..., Z; i = 1, 2, ..., N; the initial value of m is 1, and the initial state of the system in task phase 1 is assumed to be the normal state, that is, the initial probability vector of the system is P0 = (1, 0, 0, ...).

[0042] Step 4.2: Parameter input for the m-th task stage: the probability vector P of the system's state at the end of the previous task stage. m-1 Triggering condition a: Task time t during this phase m System status required for the task;

[0043] Step 4.3: Calculate the initial state vector for stage m;

[0044] Step 4.4: Calculate the equipment failure rate λ under the current task environment. m ,Right now

[0045] λ m =K1·K2·……·K n ·λ G

[0046] Where, λ G K represents the inherent failure rate of the working unit. n The environmental correction factor for the working unit under different environmental conditions is determined based on engineering experience; λ has been set in the finite state machine. G and K n The value;

[0047] Step 4.5: Calculate the Markov state transition time t based on the Markov chain model defined in Step 3. m The system's state probability vector at the end:

[0048] P(t m )=(p1(t m ),p2(t m ), ...,p i (t m ),...)

[0049] Where, p i (t m ) represents time t mThe probability that the system is in state i at the end;

[0050] Step 4.6: When m < Z, it means there is a next-stage task, then let m = m + 1 and enter Step 4.1 to continue the calculation; if m = Z, the task execution is completed, and the task reliability calculation is as follows:

[0051]

[0052] where I' is the set of states where the device operates normally.

[0053] Furthermore, the specific method of Step 2.1 is as follows:

[0054] The finite state machine is defined as a five-tuple V;

[0055] V = (q, ∑, δ, q0, F)

[0056] Q is a non-empty finite set of states. q ∈ Q is called a state of the finite state machine. The state information includes the device failure rate and working power. Different working environments and working powers will have different failure rates; Σ is the triggering event, and the triggering events include temperature, load, vibration, and device function switching; q0 is the initial state of the finite state machine, which is the initial state of the device in the first task stage; F is the set of termination states. q ∈ F is called the termination state of the state machine; δ is the state transition function, in the form: δ(i, a) = j means that the state machine reads the triggering event a in state i and turns to state j.

[0057] Furthermore, the specific method of Step 3.1 is as follows:

[0058] The device state transition relationship satisfies the Markov chain {X n , n ≥ 0}, and the state space composed of all possible values of its corresponding X <000003​​​​​​​​​​​​​​​​​​For a non-zero state i, according to the finite state machine defined in step 2, the probability p(j|i) of state i transitioning to state j after reading the trigger condition a is obtained, that is:

[0063] p(j|i)=p i

[0064] After all states are transitioned by the finite state machine, the probability p of the system being in state j can be obtained according to the law of total probability. j ,Right now:

[0065]

[0066] Then the initial state vector P of stage m is obtained. m :

[0067] P m =(p1,p2,p3,…,p j ,…)

[0068] Where j = 1, 2, ..., N.

[0069] This invention establishes a system-level mission reliability assessment method based on Markov chains for multi-stage missions performed by airborne equipment. It also introduces a finite state machine to determine and analyze the equipment operation rules and environmental influencing factors when the system state switches between two adjacent stages, making the reliability analysis closer to the actual situation. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating a specific implementation of the method of the present invention.

[0071] Figure 2 Flowchart of the method for modeling finite state machines.

[0072] Figure 3 Flowchart of the method for modeling Markov chains.

[0073] Figure 4 This is a flowchart for reliability assessment. Detailed Implementation

[0074] This invention addresses the shortcomings of existing multi-stage mission reliability assessment methods for airborne equipment in complex and variable environments by proposing a system-level mission reliability assessment method based on Markov chains. This method includes the following steps:

[0075] Step 1: Mission profile analysis. The mission environment is complex and variable, including not only conventional environmental factors such as temperature, load, and vibration, but also extreme environments such as snow, ice, hail, fog, smog, and harmful gases.

[0076] Step 1.1: Divide the task into stages according to the process of the system executing the task, and determine the system units, system working mode, working time and working environment required for each stage.

[0077] Step 1.2: Determine the success criteria for the task. In complex and ever-changing environments, the successful execution of a task depends not only on the integrity of the equipment itself, but also on the equipment's adaptability to the environment. In particular, the adaptability will decrease after partial equipment failure.

[0078] Step 2: Finite state machine modeling. The modeling process needs to consider the unrepairable characteristics of the airborne equipment during the execution of the mission. Based on the equipment's operating rules and environmental adaptability, it is determined whether the equipment function can be switched normally. Based on the equipment status and working environment such as temperature, load, and vibration, the inherent failure rate and environmental correction coefficient of the equipment are set.

[0079] Step 2.1: Define the state machine and the data structure of each state node.

[0080] A finite state machine is defined as a quintuple.

[0081] M=(q,∑,δ,q0,F)

[0082] Q: A non-empty finite set of states. q∈Q is called a state of a finite state machine. State information includes equipment failure rate, operating power, etc. Different operating environments and operating power will result in different failure rates.

[0083] Σ: Triggering events, including working environment such as temperature, load, vibration, and equipment function switching;

[0084] q0: The initial state of the finite state machine, which is the initial state of the device in the first task phase;

[0085] F: The set of termination states. q∈F is called the termination state of the state machine. There can be multiple termination states, including states that cannot meet the task requirements, such as equipment failure or inability to switch equipment functions.

[0086] δ: State transition function, expressed as:

[0087] δ:Q×∑→Q

[0088] right δ(i,a)=j: The state machine reads the trigger event a in state i and transitions to state j. The design of the state transition function needs to consider the operating rules of the device, its environmental adaptability, and the unrepairable nature of the device during task execution.

[0089] Step 2.2: When a triggering event is passed to the state machine, determine the current state of the state machine, and then query the state transition function of the state response;

[0090] Step 2.3: If the same triggering event is found, call the corresponding state transition function and set the state flag to the corresponding next state node; otherwise, the state machine cannot respond to the triggering condition normally and directly sets the state flag to the task failure state.

[0091] Each state node needs to consider the impact of different environmental conditions on the reliability of equipment tasks. For the corresponding working unit and its failure mode, an environmental correction factor is used to revise the failure rate of the corresponding working unit. The failure rate of the working unit considering different environmental conditions is calculated as follows:

[0092] λ=K1·K2·……·K n ·λ G

[0093] Where, λ G K represents the inherent failure rate of the working unit (in units of 1 / h, where h represents hours). n The environmental correction factor for the working unit under different environmental conditions is determined based on engineering experience.

[0094] Step 3: Markov chain modeling requires establishing state transition relationships and calculating the system's state probability vector at time t based on the initial state.

[0095] Step 3.1: Determine the device state transition relationship, which satisfies the Markov chain {X}. n For each n ≥ 0, the corresponding X n The state space consisting of all possible values ​​is a discrete state set I = {i0, i1, i2, ...}, where the state combinations for normal operation of the device are a subset I' of I. The state transition probabilities satisfy the formula:

[0096]

[0097] Step 3.2: Establish the transition probability matrix of the continuous-time Markov chain: the state transition probability p in the previous step ij (Δt) is the probability that the device will transition to state j at time t+Δt, given that it is in state i at time t; p ii (Δt) is the probability that the device, given that it is in state i at time t, will remain in state i at time t+Δt. This patent considers unrepairable components, therefore the probability can be written in matrix form, denoted as:

[0098]

[0099] in,

[0100] The Markov chain {X} nThe state transition density can be constructed as a matrix of the following form:

[0101]

[0102] A state transition graph is constructed based on the "reachability" and "connectivity" of the state set, and transition probabilities exist in the link relationships.

[0103] Step 3.3: For the state transition density matrix M in Step 3.2, the system state equation can be expressed as:

[0104]

[0105] Taking the Laplace transform of the system's state equations, we get:

[0106] L[P'(t)]=SP(S)-P(0)=MP(S)

[0107] (SM)P(S)=P(0)

[0108] Where P(0) is the initial state vector of the system.

[0109] Let D = SM. Using Cramer's rule to solve, since D ≠ 0, we can obtain:

[0110] P(S)=P(0) / D

[0111] p i (S)=|D i | / |D|

[0112] Among them, D i A matrix is ​​obtained by replacing the elements in the i-th column of matrix D with the elements of column vector P(0), while keeping the elements in the remaining columns unchanged.

[0113] For p i (S) Performing an inverse Laplace transform yields the probability p of the system at time t when it is in state i. i (t).

[0114] Step 3.4: The state probability vector P(t) at time t is expressed as:

[0115] P(t)=(p1(t),p2(t),…,p i (t),…)

[0116] Where, p i (t) represents the probability that the system is in state i at time t.

[0117] Step 4: Mission reliability assessment.

[0118] Step 4.1: Initial Parameter Setting: Assume the task is divided into Z stages, with stage m representing one of these stages; the device has N states, with state i representing one of these states. Then, the system probability vector for stage m can be expressed as:

[0119] P m =(p1,p2,…,p i ,…)

[0120] Where m = 1, 2, ..., Z; i = 1, 2, ..., N.

[0121] The initial value of m is 1. The initial state of the system in task phase 1 is assumed to be the normal state, that is, the initial probability vector of the system is P0 = (1, 0, 0, ...).

[0122] Step 4.2: Parameter input for the m-th task stage: the probability vector P of the system's state at the end of the previous task stage. m-1 Triggering condition a (environmental factors, equipment function switching, etc. in this stage), task time t in this stage m System status required for the task.

[0123] Step 4.3: Calculate the initial state vector for stage m. Take probability p from the state probability vector. i For a non-zero state i, according to the finite state machine defined in step 2, the probability p(j|i) of state i transitioning to state j after reading the trigger condition a is obtained, that is:

[0124] p(j|i)=p i

[0125] After all states are transitioned by a finite state machine, the probability p of the system being in state j can be obtained according to the law of total probability. j ,Right now:

[0126]

[0127] Furthermore, the initial state vector P of stage m can be obtained. m :

[0128] P m =(p1,p2,p3,…,p j ,…)

[0129] Where, j = 1, 2, ..., N

[0130] Step 4.4: Calculate the equipment failure rate λ under the current task environment. m ,Right now

[0131] λ m =K1·K2·……·K n ·λG

[0132] Among them, λ G is the inherent failure rate (1 / h) of the working unit. K n is the environmental correction factor of the working unit under different environmental conditions, which is determined based on engineering experience. λ G and K n values have been set in the finite state machine.

[0133] Step 4.5: According to the Markov chain model defined in Step 3, calculate the state probability vector of the system at the end of the Markov state transition time t m :

[0134] P(t m ) = (p1(t[[ID=2​​​​​​​​​​​​​​​​

Claims

1. A method for evaluating the mission reliability of airborne equipment in a complex and variable environment, the method comprising the following steps: Step 1: Obtain the mission profile; Step 1.1: Divide the mission phases according to the process of the system executing the mission, and determine the system units, system operating modes, operating times, and operating environments required for each phase; Step 1.2: Determine the mission success criteria; Step 2: Finite state machine modeling; Step 2.1: Define the state machine and the data structures of each state node of the state machine; Step 2.2: When a trigger event is passed to the state machine, determine the current state of the state machine, and then query the state transition function corresponding to the state; Step 2.3: If the same trigger event is found, call the corresponding state transition function, and at the same time set the state identifier to the corresponding next state node; otherwise, the state machine cannot respond to the trigger condition normally, and directly set the state identifier to the mission failure state; The failure rate λ of the working unit considering different environmental conditions for each state node is calculated as follows: λ=K1·K2·……·K n ·l G in, λ G K represents the inherent failure rate of the working unit. n The environmental correction factor for the work unit under different environmental conditions is determined based on engineering experience, where n represents the total number of work environment categories. Step 3: Markov chain modeling, which requires establishing a state transition relationship and calculating the state probability vector of the system at time t according to the initial state; Step 3.1: Determine the state transition relationship of the equipment; Step 3.2: Establish a continuous-time Markov chain transition probability matrix, denoted as: in, The Markov chain {X} n The state transition density of} is constituted by the following state transition density matrix M: Establish a state transition diagram according to the "reachability" and "connectivity" of the state set, and there is a transition probability in the link relationship; Step 3.3: For the state transition density matrix M in Step 3.2, the system state equation is expressed as: P(t) is the state vector of the system at time t; performing the Laplace transform on the system state equation gives: L[P'(t)] = SP(S) - P(0) = MP(S) (S - M)P(S) = P(0) where, P(0) is the initial state vector of the system, S is the complex variable in the Laplace transform, P(S) is the complex function after the Laplace transform of P(t), P'(t) is the derivative function of P(t) with respect to t, and L[P'(t)] represents the Laplace transform of P'(t); Let D = S - M, and use Cramer's rule to solve. Since D ≠ 0, we get: P(S) = P(0) / D p i (S)=|D i | / |D| Among them, D i A matrix is ​​obtained by replacing the elements in the i-th column of matrix D with elements of column vector P(0), while keeping the elements in the remaining columns unchanged; p i (S) represents the solution to the state equation; For p i (S) Performing an inverse Laplace transform yields the probability p of the system at time t when it is in state i. i (t); Step 3.4: The state probability vector P(t) of the system at time t is: P(t)=(p1(t),p2(t),…,p i (t),…) Where, p i (t) represents the probability that the system is in state i at time t; Step 4: Mission reliability evaluation; Step 4.1: Initial parameter setting: Assume that the mission is divided into Z phases, and mission phase m represents one of the phases; the equipment has N states, and state i represents one of the states. Then the system probability vector in mission phase m is expressed as: P m =(p1,p2,…,p i ,…) where, m = 1, 2,..., Z; i = 1, 2,..., N; the initial value of m is 1, and the initial state of the system in mission phase 1 is assumed to be the normal state, that is, the system initial probability vector is P0 = (1, 0, 0,...); Step 4.2: Parameter input for the m-th task stage: the probability vector P of the system's state at the end of the previous task stage. m-1 Triggering condition a: Task time t during this phase m System status required for the task; Step 4.3: Calculate the initial state vector of phase m; Step 4.4: Calculate the equipment failure rate λ under the current task environment. m ,Right now l m =K1·K2·……·K n ·l G Where, λ G K represents the inherent failure rate of the working unit. n The environmental correction factor for the working unit under different environmental conditions is determined based on engineering experience; λ has been set in the finite state machine. G and K n The value; Step 4.5: Calculate the Markov state transition time t based on the Markov chain model defined in Step 3. m The system's state probability vector at the end: P(t m )=(p1(t m ),p2(t m ),…,p i (t m ),…) Where, p i (t m ) represents time t m The probability that the system is in state i at the end; Step 4.6: When m < Z, it means there is a next mission phase, then let m = m + 1, and enter Step 4.1 to continue the calculation; if m = Z, the mission execution is completed, and the mission reliability is calculated as: where, I' is the set of states in which the equipment operates normally.

2. The method for assessing the mission reliability of airborne equipment under complex and variable environments as described in claim 1, characterized in that, The specific method for step 2.1 is as follows: A finite state machine is defined as a quintuple V; V=(q,∑,δ,q0,F) Q is a non-empty finite set of states. q∈Q is called a state of the finite state machine. The state information includes the equipment failure rate and operating power. Different operating environments and operating power will result in different failure rates. Σ is the triggering event. The triggering events include temperature, load, vibration, and equipment function switching. q0 is the initial state of the finite state machine, which is the initial state of the equipment in the first task phase. F is the set of termination states, and q∈F is called the termination state of the state machine; δ is the state transition function, in the form: δ(i,a)=j, indicating that the state machine reads the trigger event a in state i and transitions to state j.

3. The method for assessing the mission reliability of airborne equipment under complex and variable environments as described in claim 1, characterized in that, The specific method for step 3.1 is as follows: The state transition relationships of the devices satisfy the Markov chain {X} n For each n ≥ 0, the corresponding X n The state space consisting of all possible values ​​is a discrete state set I = {i0, i1, i2, ...}, where the state combinations for normal operation of the equipment are a subset I' of I; the state transition probabilities satisfy the formula: p ij (Δt) represents the probability that the device transitions to state j at time t+Δt, given that it is in state i at time t. ii (Δt) is the probability that the device will remain in state i at time t+Δt, given that it is in state i at time t.

4. The method for assessing the mission reliability of airborne equipment under complex and variable environments as described in claim 1, characterized in that, The specific method for step 4.3 is as follows: Take the probability p from the state probability vector i For a non-zero state i, according to the finite state machine defined in step 2, the probability p(j|i) of state i transitioning to state j after reading the trigger condition a is obtained, that is: p(j|i)=p i After all states are transitioned by the finite state machine, the probability p of the system being in state j can be obtained according to the law of total probability. j ,Right now: Then the initial state vector P of stage m is obtained. m : P m =(p1,p2,p3,…,p j ,…) Where j = 1, 2, ..., N.

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