Timing failure system preventive maintenance method based on state transition monte carlo method

Abstract

The application discloses a timing failure system periodic inspection maintenance method based on a state transition Monte Carlo method. According to a state transition process of the timing failure system, a state set and a decision set of the system are given; a calculation method of state transition probability of different actions in a periodic inspection interval is proposed; based on the state transition Monte Carlo method, each maintenance strategy is simulated to obtain an average maintenance cost rate and an average safety level of the system in a life cycle under a specified maintenance strategy; and according to the average safety level requirement, an optimal maintenance strategy of the timing failure system is determined. The application can be applied to the maintenance strategy formulation of the timing failure system in a civil aircraft, and has important theoretical significance and application value for improving the safety and maintenance efficiency of the timing failure system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of preventive maintenance, and particularly relates to a timing failure system periodic inspection maintenance method based on a state transition Monte Carlo method. BACKGROUND

[0002] In the aircraft maintenance outline formulated based on the MSG-3 idea, aircraft maintenance tasks are divided into four parts of system, structure, area, lightning / high-intensity radiation field protection, wherein the system part is the main body of the civil aircraft, and the maintenance of the airborne system has a significant influence on the economy and safety of the civil aircraft. The European Aviation Safety Agency (EASA) indicates in the guidance material proposed by it that the failure of the airborne system has become the second largest cause of aviation accidents next to human error, and in addition, through the statistics of the A320, CRJ200, B737 and other main force aircraft models of the airlines, it is known that the number of airborne system maintenance tasks accounts for more than 40% of the total maintenance tasks of the civil aircraft. Therefore, the research on the maintenance strategy of the airborne system of the civil aircraft has very important significance.

[0003] The airborne system of the civil aircraft usually adopts redundancy technology in the design to improve its reliability and safety, for example, various redundancy design structures such as parallel connection, cold backup, warm backup, hot backup and multi-mode redundancy are adopted for key components in the design stage of the airborne system. When a single component in the system fails, the standby component is put into work, so that the system continues to run. Such design makes there be a lot of connections between the internal components of the system. The airborne redundancy system contains a special redundancy system, i.e. a redundancy system with timing failure characteristics. The failure state of the system depends not only on the combination of component failures, but also on the time of component failures and the order of component failures. The failure of a single component may affect the life of the remaining components, and different component failure orders may cause significant differences in system failure modes, which is also called timing failure system.

[0004] Typical redundancy structures with timing failure characteristics include warm backup structure, cold backup structure, priority AND gate structure, sequential gate structure, function-dependent gate structure, etc. Among the above structures with timing failure characteristics, the cold and warm backup structures and the load sharing structure are mostly used in the airborne redundancy system. Such design method greatly improves the safety level of the airborne system, but at the same time, it increases the correlation of the components in the system. For a given component, its maintenance decision may be affected by the performance state or maintenance of other components, and the complexity of system maintenance is also increased.

[0005] The existing technical method still has the following problems:

[0006] (1) Existing complex system maintenance model is mostly considered in series-parallel system, voting system and other static systems, ignoring the influence of time sequence failure on system maintenance decision, at this time, the measurement of system safety is not accurate, and the minimization of maintenance cost cannot be realized under the condition of ensuring system safety. For example, in cold backup system, the failure rate of components in backup state is lower than that in working state, if it is approximated as a parallel system, the system safety obtained at this time will be low, so the maintenance strategy will be conservative, and the maintenance cost of the aircraft will also be increased.

[0007] (2) The existing research on time sequence failure system mostly focuses on the research on time sequence failure system safety analysis method, and the research on its maintenance strategy is less, and in the few researches on time sequence failure system maintenance strategy, there is little research on maintenance strategy based on component state, and different components are not maintained according to different system states. Most of them are based on the overall state of the system or the service life of the system, and the cold backup system considering switching factor and maintenance service station factor is modeled, which has strong particularity and is not suitable for the research on maintenance strategy of other time sequence failure systems.

[0008] (3) In the existing research on maintenance strategy of time sequence failure system, the overall state of the system or the limited maintenance time is taken as the maintenance threshold, and the maintenance threshold is taken as the optimization target, and fixed maintenance measures or replacement of the system are implemented after the maintenance threshold is reached, different components are not maintained according to different system states, and the maintenance action of the system is not flexible enough. SUMMARY

[0009] The purpose of the application is to solve the problems existing in the prior art, and a time sequence failure system periodic maintenance method based on state transition Monte Carlo method is provided.

[0010] Technical scheme: The application discloses a time sequence failure system periodic maintenance method based on state transition Monte Carlo method, and specifically comprises the following steps:

[0011] Step 1: set the periodic inspection interval T and the inspection times N FC ;

[0012] Step 2: perform the N sim th simulation;

[0013] Step 3: when the set inspection time interval is met, the tth inspection is performed, the state probability vector P t of the system is calculated, P t =[p1, p2, L, p n ], p n represents the probability that the system is in the nth state, n represents the total number of system states, and P tjudging the state of the system; if the system is in failure state, then the failure state times is added by 1;

[0014] Step 4: according to the state of the system obtained in step 3, the maintenance strategy is carried out, and then the state probability vector of the system is updated;

[0015] Step 5: the maintenance cost after the tth inspection is calculated;

[0016] Step 6: if t is less than N FC , the inspection times is added by 1, and step 3 is turned to; otherwise, step 7 is turned to;

[0017] Step 7: the total maintenance cost and the total state failure times of the system in this simulation are calculated;

[0018] Step 8: whether the average value of the total maintenance cost and the average value of the state failure times of the system after y simulations are converged is judged, if yes, the simulation is stopped, and the optimal maintenance strategy is selected according to the average value of the total maintenance cost and the average value of the state failure times, otherwise, the simulation times is added by 1 and step 2 is turned to.

[0019] Further, the state probability vector P of the system in step 3 is calculated according to the following formula t :

[0020] P t =P t-1 ×P (pC)

[0021] Wherein, P (pC) represents the comprehensive state transition probability matrix of the system when the strategy p is adopted, and the expression of the element in the ith row and the jth column of the matrix P (pC)

[0022]

[0023] Wherein, represents the comprehensive probability that the system transits from the ith state to the jth state when the maintenance strategy p is adopted, i=1, 2, …, n; k=1, 2, …, n, p=1, 2, …, N, wherein N represents the total number of maintenance strategies; represents the probability that the system transits from the ith state to the kth state when the maintenance strategy p is adopted, represents the probability that the system transits from the kth state to the jth state in the natural degradation process, The expression of is as follows:

[0024]

[0025] Wherein, λ kj ​The transition rate of the system from state k to state j.

[0026] Further, the step 3 includes simulating the state probability vector P 0 of the system at the initial time.

[0027] Further, the step 3 includes simulating the state probability vector P t of the system at the initial time. If u < P , the system is determined to be in the rth state.

[0028] Further, the step 4 includes updating the state probability vector P t of the system. t-1 If the state of the system obtained by the tth check is the same as the state of the system obtained by the (t-1)th check, P t is set to P t-1 , otherwise, the state of the system obtained by the tth check is set to 1, and the states of the system obtained by the tth check are set to 0.

[0029] Further, the step 7 includes calculating the total maintenance cost C of one simulation. T The total maintenance cost C M includes a detection cost C T and a direct cost C M caused by maintenance of components. The expression of the total maintenance cost C is as follows:

[0030]

[0031] An electronic device / system for implementing the method for scheduled maintenance of a time-sequential failure system, including a processor and a memory, the memory storing execution instructions of the processor, and the processor being configured to execute the execution instructions to implement the method for scheduled maintenance.

[0032] A computer-readable storage medium for storing a program, and executing the program to implement the method for scheduled maintenance.

[0033] Advantages:

[0034] (1) Compared with the prior art, the present application considers the influence of the failure sequence of components on the failure of the system, and is suitable for maintenance strategy simulation of time-sequential failure airborne systems such as warm standby, cold standby, and load sharing.

[0035] (2) The components of the system are considered as the smallest unit, and the state of the system is determined by the failure conditions of the components, and different combinations of failures of different components reflect different states of the system.

[0036] (3) The maintenance decision is refined, so that the minimum maintenance unit of the system is specific to the components constituting the system, and more effective maintenance decisions are made for airborne redundant systems with time-dependent failure characteristics such as temperature reserve, cold reserve, load sharing, etc. considering the average safety level and maintenance economy. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a flowchart of the present application;

[0038] Figure 2 is a flowchart of the condition transfer Monte Carlo method-based maintenance simulation provided by the present application;

[0039] Figure 3 is a state transition process diagram of the engine control system provided by example one;

[0040] Figure 4 is a simulation process diagram of the optimal maintenance strategy of the engine control system provided by example one;

[0041] Figure 5 is a state transition process diagram of the AC power supply system provided by example two;

[0042] Figure 6 is a simulation process diagram of the optimal maintenance strategy of the AC power supply system provided by example two. DETAILED DESCRIPTION

[0043] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application, illustrate the preferred embodiments of the application, and assist in explaining the application. It is not intended that the application be limited in any way by the details of the preferred embodiments, but rather that the application be understood to include any

[0044] As shown in Figure 1 , the present application provides a time-dependent failure system maintenance simulation method based on the state transition Monte Carlo method, comprising the following steps:

[0045] 1. According to the state transition process of the time-dependent failure system, the state set of the system, the maintenance action set, and the feasible maintenance strategy are given.

[0046] The model assumes that the life of the component obeys the exponential distribution, and the state of the component only considers normal and failure. The system state is composed of the state of each component. A system composed of m components has a total of 2 m states in theory, but for airborne redundant systems with time-dependent failure characteristics, the failure process is affected by the order of component failure, for example, the components of the backup system have a specific failure order, so the actual number of states n of the system satisfies n≤2 m , S={s1,s2,...,s n} represents the state set of the system, and the i-th element s i(i = 1, 2, L, n) represents the i-th state of the system, in particular, s1= {l1, l2,..., ln} represents the initial state of the system, m} represents the state in which all components of the system are normal, represents the state in which all components are failed, l i (i = 1, 2, L, m) represents the i-th component is normal, represents the i-th component is failed.

[0047] At each decision point, different maintenance actions a e A can be selected, and the set of maintenance actions a constitutes the decision set. Different maintenance actions represent maintenance of different combinations of components. In the entire operation process of the system, the total number of optional maintenance actions is 2 m , A = {a1, a2, a3,..., a 2m}, wherein a1represents no maintenance on any component, represents maintenance on all components. When the system is in state i, if the number of failed components is k (k≤m), then there are 2 k optional maintenance actions in this state. In addition, when the system fails, the system is completely maintained, that is, the system is replaced.

[0048] When the system is in different states, different maintenance actions can be taken on the system, and the combination of different maintenance actions taken in different states is referred to as a maintenance strategy p. If the system is in state s i , the number of failed components in the system is , and there are optional maintenance actions in this state, in theory, there are maintenance strategies in the entire operation and maintenance process of the system. At this time, some unreasonable (incomplete) maintenance strategies in the maintenance strategy need to be excluded. If maintenance action a1is taken when the system is in state s n , the system moves to state s n-1 after maintenance, but in this maintenance strategy, it is stipulated that maintenance action is continued when the system is in state s n-1 , so this maintenance strategy is incomplete, and therefore this maintenance strategy is excluded in the subsequent simulation.

[0049] 2. The state transition probability between adjacent decision points is composed of the state transition probability caused by different maintenance strategies p and the state transition probability under natural degradation of the system.

[0050] 1) State transition probability of the maintenance process

[0051] At each decision point, maintenance action is taken according to the maintenance strategy p, if maintenance action a is taken, the probability that the designated maintenance component returns to the normal state at the end of maintenance is 1, and the state transition probability of maintenance according to the maintenance strategy p is denoted as Pik represents the probability of the system moving from state i to state k after maintenance with maintenance strategy p, k = 1, 2, …, n.

[0052] 2) State transition probability under natural deterioration process

[0053] The state transition probability under natural deterioration process is represented as:

[0054]

[0055] Pjk: the transition probability of state k to state j in the natural deterioration process of the system; d: is the abbreviation of the English word deterioration; T: the inspection interval; f(x): the probability density function; λ kj Pjk: the transition rate of the system from state k to state j, j = 1, 2, …, n.

[0056] The state transition probability under natural deterioration process is determined by the transition rate between states and the flight segment time. The state transition probability is different when the flight segment time or the inspection interval of the system is different. Therefore, when the inspection intervals are not equal, multiple probability matrices need to be set to describe the state transition probability of the natural deterioration process of the system under different inspection intervals.

[0057] 3) Comprehensive state transition probability

[0058] The comprehensive state transition probability considers the state transition probability of the system in the maintenance process and the state transition probability under the natural deterioration process.

[0059] The comprehensive state transition probability is represented as:

[0060]

[0061] wherein, Pijk represents the comprehensive probability of the system moving from the i-th state to the j-th state when maintenance strategy p is adopted, p = 1, 2, …, N, wherein N represents the total number of maintenance strategies; at each maintenance decision-making moment, maintenance actions are taken according to a certain maintenance strategy, and the state transition probability of the corresponding maintenance process is obtained; according to the length of the next inspection interval, the state transition probability of the system under natural deterioration from the end of the inspection maintenance to the next maintenance decision-making moment is obtained; and according to the above formula, the state transition probability of adjacent decision points can be obtained.

[0062] If Pijk represents the state transition probability matrix under natural state, and Pijk represents the state transition probability matrix when maintenance strategy p is adopted, the state transition probability matrix Pijk of the system adopting different maintenance strategies can be represented as (d) (pR) (pR) that is, the matrix Pijk​​​(pR) consisting of elements ; the comprehensive state transition probability matrix P of taking maintenance strategy p (pC) may be expressed as:

[0063] P (pC) = P (pR) * P (d) (3)

[0064] is an element in the matrix P (pC) .

[0065] 3. The failure and maintenance process of the system is simulated by state occurrence probability random number, and the average maintenance cost rate and the average safety level of the system during long-term operation under the specified maintenance strategy are obtained by simulation.

[0066] Under a certain specified maintenance strategy, the total maintenance cost and the number of failure state occurrences N sim of the system during long-term operation time T can be obtained after each simulation. The average total maintenance cost of the system after a plurality of simulations and the average number of failure state occurrences of the system can be expressed as:

[0067]

[0068] When and converge, the simulation is completed, and the final average total maintenance cost C F of the system and the average number of failure state occurrences N F of the system are obtained, and then the failure state frequency of the system during long-term operation under the specified maintenance strategy is obtained, which represents the average safety level of the system, and the expression of the failure state frequency of the system is shown in formula (5), and the average maintenance cost rate of the system is shown in formula (6). Different maintenance strategies are simulated in turn, and the maintenance strategy corresponding to the minimum total maintenance cost under the condition of meeting the requirement of the average safety level of the system is the optimal strategy.

[0069]

[0070] The maintenance simulation process based on the state transition Monte Carlo method provided by the application is shown in Figure 2 , and specifically comprises the following steps:

[0071] Step 1: Known conditions are given

[0072] The periodic inspection interval T of the system and the number of inspections N of the aircraft in the long-term operation time are given FCList all the possible states S in the system and the transition probability matrix P between each state under each maintenance policy (pC) and the cost matrix C of each policy, and select a maintenance policy.

[0073] After this step, go to Step 2.

[0074] Step 2: Initialize global variables

[0075] The global variables include the current simulation number N sim , the average number of occurrences of failure states of the system in the life cycle of the aircraft, and the average maintenance cost.

[0076] After this step, go to Step 3.

[0077] Step 3: Determine whether the program can be terminated

[0078] When the average maintenance cost of the system over a long period of time and the average number of occurrences of failure states converge, the program is terminated. That is, when formula (7) is satisfied, the program is terminated. And and Otherwise, go to Step 4.

[0079]

[0080] In the formula and are the average number of occurrences of failure states obtained by N sim times of simulation and N sim -1 times of simulation, respectively, and are the average maintenance cost of the system obtained by N sim times of simulation and N sim -1 times of simulation, respectively. ε is a very small positive real number, and for the first simulation not to be terminated, it is taken as

[0081] Step 4: Start a new simulation and initialize local variables

[0082] The local variables include the current check number t, the number of occurrences of failure states in this simulation the system maintenance cost in this simulation the state probability vector P of the system t , and the state s of the system.

[0083] P t is represented as a vector composed of the probabilities of being in each state after the tth check:

[0084] P t= [p1, p2...p n ]

[0085] where p i (i = 1, 2,..., n) is the probability of the system being in the ith state, where 0 ≤ p i ≤ 1, at the beginning of each simulation, all components are normal, the system is in a brand new state, so the initial state distribution of the system is P 0 = [1, 0,... 0], at this time s = 1, t = 0, and the number of system failure states (unacceptable states) at this time is 0, i.e.

[0086] After this step, go to step 5.

[0087] Step 5: Determine the state of the system after this flight cycle

[0088] The system state transition probability matrix is obtained from equations (1), (2), and (3), and the state probability vector P t at the end of the tth inspection is calculated by applying equation (9):

[0089] P t = P t-1 × P (pC)

[0090] A uniformly distributed random number u is generated in (0, 1), and u is compared with P t to simulate the state i at the end of the tth inspection. The specific method is as follows: if u < p , then the system is in state r.

[0091] If the simulated state is a system failure state, then let s = s + 1.

[0092] After this step, go to step 6.

[0093] Step 6: Maintenance of the system according to the specified maintenance strategy

[0094] According to the simulated state of the system, maintenance is performed according to the specified maintenance strategy, and the corresponding inspection and maintenance costs are added, and P If the simulated state i at the tth inspection is the same as the simulated state at the t-1th inspection, let P t = P t-1 ; if the simulated state i at the tth inspection is different from the simulated state at the t-1th inspection, let P t The probability value of state r in P

[0095] The maintenance cost of the system mainly includes three parts, namely, detection cost C T , direct cost C M of maintenance parts (including replacement cost). The total maintenance cost of the system obtained by each simulation is the sum of the detection cost and the direct maintenance cost of the system within the specified inspection times N FC (long-term running time). The total maintenance cost of the system obtained by each simulation can be expressed as:

[0096]

[0097] After this step, go to step 7.

[0098] Embodiment 1

[0099] The simplified engine control system provided in the embodiment is composed of an engine control unit (ECU), a hydro mechanical unit (HMU) and an alternator winding (AW) unit. The ECU includes two channels (ECU Channel). When ECU Channel 1 fails, ECU Channel 2 works, and ECU Channel 1 and ECU Channel 2 form a warm backup structure. The AW unit is composed of AW 1 and AW 2. When AW 1 fails, AW 2 works, and AW 1 and AW 2 also form a warm backup structure. The failure rates of the units of the alternating current power supply system are as follows. For convenience of representation, the ECU is denoted as A, the AW is denoted as B, and the HMU is denoted as C. Wherein, λ A is the failure rate of ECU Channel in the working state, is the failure rate of ECU Channel in the backup state. λ B is the failure rate of AW in the working state, is the failure rate of ECU Channel in the backup state. λ C is the failure rate of HMU, wherein λ A = 0.9 x 10 -5 / h, λ B = 0.9 x 10 -5 / h, λ C = 2 x 10 -6 / h.

[0100] 1) System state

[0101] ​The deterioration process of the engine control system is described according to the failure development of its components, and the system is divided into 10 states during its entire life cycle, and the state transition process of the engine control system is shown in Figure 3 FIG. 1, wherein state 10 represents the failure state.

[0102] Figure 3 A1 and A2 represent two ECUs of the main power supply being normal, B1 and B2 represent two AWs being normal, and C represents the HMU being normal. represent the corresponding components being failed.

[0103] 2) Possible maintenance actions

[0104] Since components A1 and A2 in the system are the same components, they form a warm backup structure, and if A1 and A2 fail at the same time, the system fails, at which time the system is replaced as a whole, and there is no action of simultaneously maintaining A1 and A2, so maintenance component A1 and maintenance component A2 are combined into maintenance component A; similarly, maintenance component B1 and maintenance component B2 are combined into maintenance component B; when component C fails, the system fails, at which time the system is replaced as a whole, so there is no maintenance action of separately maintaining component C.

[0105] As can be seen from the above analysis, there are a total of 5 possible maintenance actions in the entire deterioration process of the system, which are a1 (no maintenance of any component), a2 (maintenance of component A), a3 (maintenance of component B), a4 (maintenance of components A and B), and a5 (replacement of the system). The maintenance actions that can be selected in different states are shown in Table 1.

[0106] Table 1

[0107]

[0108]

[0109] 3) Possible maintenance strategies

[0110] When only one ECU (AW) fails in the system, the maintenance measures that can be taken are: maintaining the ECU (AW) and not maintaining the ECU (AW); when one ECU and one AW fail in the system, the maintenance measures that can be taken are: none (not considered), maintaining the ECU, maintaining the AW, and maintaining the ECU and the AW. For convenience of representation,

[0111] That is, there are a total of 2x2x3=12 possible maintenance strategies, and 4 unreasonable maintenance strategies are excluded, leaving 8 feasible maintenance strategies.

[0112] 4) State transition probability matrix

[0113] The state transition probability matrix of the system under natural degradation is:

[0114]

[0115] The state transition probability matrix P of the system under different maintenance strategies (pR) is expressed as that is, the matrix P (pR) is composed of elements , which can be expressed by formula (12) to formula (19), wherein p ∈ p1~p8. The comprehensive state transition probability matrix of the system under different maintenance strategies can be calculated by formula (3). By substituting T1 = 500h, the comprehensive state transition probability matrix of the eight strategies can be obtained.

[0116]

[0117]

[0118] The costs generated in the maintenance process are as follows: the inspection cost is 20000 yuan, the maintenance cost of the ECU is 100000 yuan, the maintenance cost of the AW is 90000 yuan, the replacement cost and the loss cost generated after the system failure are 220000 yuan. The average cost rate and the average safety level of each maintenance strategy obtained by the simulation of the condition-based maintenance based on the state transition Monte Carlo method are shown in Table 2.

[0119] Table 2

[0120]

[0121] As shown in Table 2, when the periodic inspection is performed, the average cost rate of the system in the running process is the smallest when the maintenance according to the strategy 8 is performed, and the maintenance strategy meets the safety level requirement of the engine control system 10 -5 . That is, the optimal strategy is that when the system is inspected and only one ECU fault or only one AW fault is found, no maintenance action is taken, and when the system is inspected and one ECU and one AW faults are found, the AW is maintained. The simulation process of the optimal condition-based maintenance strategy of the engine control system based on the state transition Monte Carlo method is shown in Figure 4 .

[0122] Example Two

[0123] The AC power system provided by the embodiment is composed of a main power source, an auxiliary power source and an emergency power source. The main power source is composed of two integrated drive generators (IDGs). When both of the two IDGs are normal, the two IDGs supply power together, and the failure rates of the two IDGs are the same. When one of the two IDGs fails, the other one can supply power alone, but the failure rate of the other one increases, that is, the two IDGs form a load sharing structure. When the main power source fails, an auxiliary power unit (APU) drives an auxiliary generator (APU GEN) to work, and the APU GEN and the main power source form a warm backup structure. The emergency power source and the main power source and the auxiliary power source form a cold backup structure. Only when the main power source, the auxiliary power source and the emergency power source all fail, the power system fails.

[0124] IDG 1 and IDG 2 are denoted by M1 and M2 respectively, A denotes the APU, and B denotes the emergency power source. M is the failure rate of the two IDGs in the main power source working together. When one of the two IDGs fails, the failure rate of the other one working alone is λ M + . A is the failure rate of the APU in the working state, λ A - is the failure rate of the APU in the backup state. B is the failure rate of the emergency power source. The failure rates of the units in the power system are as follows, M = 1 × 10 -6 / h, λ A = 2 × 10 -6 / h, λ B = 1 × 10 -5 / h.

[0125] 1) System state

[0126] In the whole life cycle of the AC power system, according to the failure development of the components, the deterioration process of the system is described, and the AC power system is divided into 9 states. The state transition diagram of the deterioration process of the AC power system is shown in Figure 5 .

[0127] Figure 5 M1, M2, A and B in the figure represent that the corresponding components are normal. respectively represent that the corresponding components fail. In the system, when all the components fail, the system fails. The state in which there is only one redundant component in the system is defined as an unacceptable state, that is, state 9 is an unacceptable state, and the system is completely repaired in the state.

[0128] 2) Maintenance actions that can be taken

[0129] There are nine possible maintenance actions during the entire degradation process of the AC power system: a1 (no repair of any component), a2 (repair component M1), a3 (repair component M2), a4 (repair component A), a5 (repair component M1M2), a6 (repair component M1A), a7 (repair component M2A), a8 (repair component M1M2A), and a9 (repair component M1M2AB, i.e., replace the entire power system). The available maintenance actions under different conditions are shown in Table 3.

[0130] 3) Optional maintenance strategies

[0131] When only one IDG fails in the system (corresponding to) Figure 5 In states 2 and 3, the possible maintenance actions are: no maintenance, maintenance of one IDG; when only one APU GEN is faulty in the system (corresponding to...). Figure 5 In state 4, the possible maintenance actions are: no maintenance, maintenance of one APU GEN; when two IDGs in the system fail (corresponding to...). Figure 5 In state 5, the possible maintenance actions are: no maintenance, maintenance of one IDG, or maintenance of both IDGs; when one IDG and one APU GEN fail in the system (corresponding to...). Figure 5 In states 6 and 7, the possible maintenance actions are: no maintenance, maintenance of one IDG, maintenance of one APU GEN, and maintenance of one IDG and one APU GEN.

[0132] Table 3

[0133]

[0134] As mentioned above, there are a total of 2×2×3×4=48 maintenance strategies that can be adopted during the operation and maintenance of this AC power system. After excluding unreasonable (incomplete) maintenance strategies, there are 29 remaining optional maintenance strategies.

[0135] 4) State transition probability matrix

[0136] It can be represented by equations (20) to (48), where p∈p1~p 29 Under different maintenance strategies, the overall state transition probability matrix of the system can be calculated by equation (3). Substituting the values ​​of the failure rates of each unit and the inspection interval T = 800h into the equation, the overall state transition probability matrix of 29 strategies can be obtained.

[0137]

[0138]

[0139]

[0140] The costs of the AC power system during the maintenance process are as follows: the inspection cost is 50,000 yuan, the maintenance cost of one IDG is 70,000 yuan, the maintenance cost of one APU is 80,000 yuan, the replacement cost and the loss cost after the AC power system fails are 270,000 yuan, and the inspection interval is 800 h. The average cost rate and the frequency of unacceptable state (one redundant component remaining) of different maintenance strategies are shown in Table 4. The maintenance strategy corresponding to the lowest average cost rate is strategy 27, that is, no maintenance action is taken when the number of redundant components remaining is greater than or equal to 2, and only the replacement maintenance action is taken when the number of redundant components remaining is 1.

[0141] Table 4

[0142]

[0143]

[0144] If the safety level (the frequency of unacceptable state) of the system is considered, the frequency of unacceptable state of the system is less than 10 -9 %, and the maintenance strategy corresponding to the lowest average cost rate is strategy 4, that is, no maintenance action is taken when only one IDG or one APU GEN fails is detected, one IDG is repaired when two IDG failures are detected, the APU GEN is repaired when one IDG and one APU GEN failures are detected, and all the failed components are repaired when two IDG and one APU GEN failures are detected. The simulation process of the optimal inspection and maintenance strategy of the AC power system based on the state transition Monte Carlo method is shown in Figure 6

[0145] In addition, it should be noted that various specific technical features described in the above embodiments can be combined in any appropriate manner without contradiction. In order to avoid unnecessary repetition, various possible combinations are not described again in the present application.​

Claims

1. A method for periodic maintenance of a time-to-failure system based on state transition Monte Carlo method, characterized in that, Specifically includes the following steps shown: Step 1: Set the periodic check interval T, check number N FC ; Step 2: Perform the Nth sim emulation; Step 3: When the set check time interval is met, perform the t-th check and calculate the system's state probability vector P. t P t = [p1, p2, ..., p n ], p n Let P represent the probability that the system is in the nth state, where n represents the total number of system states, and let P be the probability that the system is in the nth state. t Determine the system's current state; if the system is determined to be in a failed state during this check, increment the failure state count by 1. Step 4: according to the state of the system obtained in step 3, maintenance is carried out according to the specified maintenance strategy, and then the state probability vector of the system is updated; Step 5: calculate the maintenance cost after the tth inspection; Step 6: If t is less than N FC , increment the number of checks and go to step 3. Otherwise go to step 7; Step 7: calculate the total maintenance cost and the total state failure times of the simulated system; Step 8: judge whether the average value of the total maintenance cost and the average value of the state failure times of the system after y times simulation are converged, if yes, stop the simulation, and select the optimal maintenance strategy according to the average value of the total maintenance cost and the average value of the state failure times according to the actual situation, otherwise increase the simulation times by 1 and go to step 2; The step 3 calculates the state probability vector P of the system according to the following formula t : P t = P t-1 x P (pC) ; where P (pC) denotes the overall state transition probability matrix of the system when strategy p is adopted, P (pC) The expression of the element in the ith row and jth column of the matrix is: wherein, represents the comprehensive probability of the system moving from the ith state to the jth state when maintenance strategy p is adopted, i = 1, 2, …, n; k = 1, 2, …, n, p = 1, 2, …, N, wherein N represents the total number of maintenance strategies; represents the probability of the system moving from the ith state to the kth state after maintenance is performed on the system in the ith state using maintenance strategy p, represents the probability of the system moving from the kth state to the jth state in the natural degradation process, The expression of is as follows: where λ kj denotes the transition rate of the system from state k to state j.

2. The condition-based maintenance method for a time-varying failure system based on a state transition Monte Carlo method according to claim 1, wherein, The state probability vector P of the system at the initial time of simulation 0 The probability corresponding to the state in which all components of the system are normal is 1, and the probabilities corresponding to the other states are 0.

3. The condition-based maintenance method for a time-varying failure system based on a state transition Monte Carlo method according to claim 1, wherein, The step 3 in accordance with P t The state of the system is determined as follows: a random number μ is generated in the range (0, 1) uniformly, if 1≤r<n; the system is determined to be in the rth state.

4. The condition-based maintenance method for a time-varying failure system based on a state transition Monte Carlo method according to claim 1, wherein, The step 4 of updating the state probability vector of the system is specifically: if the state of the system calculated by the tth check is the same as the state of the system obtained by the t-1th check, then P t =P t-1 , otherwise the probability corresponding to the state of the system obtained by the tth check is 1, and the probabilities corresponding to other states in P t are 0.

5. The condition-based maintenance method for a time-varying failure system based on a state transition Monte Carlo method according to claim 1, wherein, the total repair cost of the one simulation in step 7 including the detection cost C T and the direct cost C M , The expression is as follows:

6. An electronic device for a method of timing out a system maintenance inspection, characterized by The processor and the memory, the memory stores the execution instructions of the processor, and the processor is configured to execute the execution instructions to implement the maintenance method for fixed inspection in any one of claims 1-5.

7. A computer readable storage medium for storing a program, characterized in that, The program is executed to implement the maintenance method for fixed inspection in any one of claims 1-5.

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