Civil aircraft key system preventive maintenance method considering operation process

Abstract

The invention discloses a civil aircraft key system preventive maintenance method considering an operation process, and the method comprises the steps: obtaining an updating function, an operation time distribution function and a maintenance cost parameter through the historical fault data, flight information data and maintenance data of a civil aircraft key system, and constructing a civil aircraft key system preventive maintenance basic model considering the operation process; obtaining a first type of preventive maintenance strategy; obtaining a second type of preventive maintenance strategy according to the civil aircraft key system preventive maintenance optimization model based on the first replacement criterion; obtaining a third type of preventive maintenance strategy through a civil aircraft key system preventive maintenance optimization model based on a post-replacement criterion; and comparing and analyzing the three types of preventive maintenance strategies according to the principle of minimum expected cost rate, and determining the optimal preventive maintenance strategy of the civil aircraft key system. According to the method, the reliability and safety of the civil aircraft key system in the operation process are effectively improved, and a scientific basis is provided for engineers to maintain the civil aircraft key system.

Description

Technical Field

[0001] The present invention relates to the technical field of preventive maintenance, and particularly to a preventive maintenance method for key civil aircraft systems considering the operation process. Background Art

[0002] Developing civil aircraft with high technological content, stable performance and high reliability is of great significance. The reliability and safety of civil aircraft have attracted much attention. Once an accident occurs, the losses are often heavy. Therefore, how to prevent the key systems of civil aircraft from failing during operation has very important practical significance and theoretical research value.

[0003] As a technology that can improve the reliability and safety of systems, preventive maintenance has gradually received attention. However, in real life, the purpose of system design and manufacturing is to complete a certain type of task. For example, an aircraft needs to perform flight tasks, a production system needs to perform manufacturing tasks, a radar system needs to perform reconnaissance tasks, a missile system needs to perform strike tasks, etc. But most of the current preventive maintenance methods ignore the task execution process of the system and do not consider the operation period of the system, resulting in the possibility that the pre-established preventive maintenance strategy may not conform to the actual situation. On the other hand, when the system operation time is short, scholars often consider static costs, that is, the system replacement cost, maintenance cost, etc. remain unchanged. However, for a system with long-term operation, the realization problem of costs needs to be considered because the value of money changes over time.

[0004] Using the existing preventive maintenance technology for the maintenance of key civil aircraft systems has the following problems: 1) Most of the existing preventive maintenance technologies do not focus on in-depth analysis of the system operation process. However, the flight time of civil aircraft has strong randomness and unpredictability. The planned maintenance time obtained by using the existing preventive maintenance model is very likely to occur during the system operation process. If preventive maintenance is carried out by interrupting the task, the task will fail. If the planned maintenance time is postponed, it is difficult to ensure high reliability of the system during operation; 2) Most of the existing related technologies consider static maintenance costs, while for civil aircraft with a long service time, their maintenance costs often change dynamically. It is difficult to determine the maintenance budget by using the existing technologies to maintain civil aircraft systems; 3) Most of the existing related technologies consider the situation where the system executes a single task, while for civil aircraft, they often need to perform multiple flight tasks. It is difficult to determine the operation cycle of civil aircraft systems by using the existing related technologies to maintain civil aircraft systems.

[0005] Therefore, it is necessary to fully consider the operation of key civil aircraft systems and the changes in maintenance costs, and develop a preventive maintenance method for key civil aircraft systems to improve the reliability and safety of key civil aircraft systems during operation. Summary of the Invention

[0006] The problem to be solved by the present invention is to provide a preventive maintenance method for civil aircraft key systems considering the operation process, which can effectively improve the reliability and safety of civil aircraft key systems during operation and provide a scientific basis for engineers to maintain civil aircraft key systems.

[0007] The present invention adopts the following technical solutions: A preventive maintenance method for civil aircraft key systems considering the operation process, comprising the following steps:

[0008] Step 1: Collect civil aircraft key system data, including: historical failure data, flight information data, and maintenance data;

[0009] Step 2: According to the obtained civil aircraft key system data, construct a basic preventive maintenance model for civil aircraft key systems considering the operation process, and obtain the first type of preventive maintenance strategy;

[0010] Step 3: According to the basic preventive maintenance model for civil aircraft key systems considering the operation process, construct an optimized preventive maintenance model for civil aircraft key systems based on the first replacement criterion, and obtain the second type of preventive maintenance strategy;

[0011] Step 4: According to the basic preventive maintenance model for civil aircraft key systems considering the operation process, construct an optimized preventive maintenance model for civil aircraft key systems based on the second replacement criterion, and obtain the third type of preventive maintenance strategy;

[0012] Step 5: Calculate the maintenance costs according to the first, second, and third types of preventive maintenance strategies respectively, and determine the optimal maintenance strategy for civil aircraft key systems according to the principle of the minimum expected cost rate.

[0013] Preferably, in step 2, the method for constructing the basic preventive maintenance model for civil aircraft key systems considering the operation process is as follows:

[0014] Step 201: Fit the reliability distribution function F(t) of the civil aircraft key system according to the historical failure data, and obtain the system renewal function by using the convolution method:

[0015]

[0016] where M(t) is the renewal function, indicating the number of replacements of the civil aircraft key system within the time [0, t], F (j) (t) is the j-fold convolution of the reliability distribution function F(t) of the civil aircraft key system, t is the time, j is the lower bound of the summation, and u is the differential parameter;

[0017] Step 202: Obtain the operating time distribution function according to the flight information data:

[0018] According to the flight information data, record the time interval X1 between the installation of the civil aircraft's key system and the start time Y1 of its first operation, and the start time Yi of the i-th operation i and the start time Yi+1 of the (i + 1)-th operation i+1 with a time interval Xi i+1 . The time distribution function of the N-th start of operation of the system is G (N) (t);

[0019] where G (N) (t) is the N-fold convolution of G(t), and G(t) is the distribution function of X i ;

[0020] Step 203: Determine the basic maintenance strategy of the civil aircraft's key system according to the preventive maintenance theory:

[0021] It is stipulated that the preventive replacement of the civil aircraft's key system is carried out after N operations, and the preventive replacement time is Y N +t x . Before preventive replacement, if a failure occurs, corrective replacement is carried out;

[0022] where t x is the average operation period;

[0023] Step 204: According to the basic maintenance strategy, construct a preventive maintenance basic model for the civil aircraft's key system considering the operation process, expressed as:

[0024]

[0025] where C b (α, t x ; N) is the expected cost rate function of the civil aircraft's key system under long-term operation, C b1 (α, t x ; N) is the expected cost within the first cycle starting from the installation time, T b1 (α, t x ; N) is the time of the first cycle, and α is the discount rate.

[0026] Preferably, in step 2, obtain the first type of preventive maintenance strategy as follows:

[0027] Step 211: Solve the optimal number of operations of the civil aircraft's key system The principle is:

[0028] C b (α, t x ; N + 1) - C b (α, t x ; N) ≥ 0;

[0029] Step 212. According to the optimal number of operations Formulate the first type of preventive maintenance strategy for the preventive maintenance basic model of civil aircraft critical systems considering the operation process: After the civil aircraft critical system runs for the th time, preventive replacement is immediately carried out.

[0030] Preferably, in step 3, an optimization model for preventive maintenance of civil aircraft critical systems based on the first replacement criterion is constructed as follows:

[0031] Step 301. According to the preventive maintenance basic model of civil aircraft critical systems considering the operation process, determine the preventive maintenance optimization strategy for civil aircraft critical systems based on the first replacement criterion:

[0032] According to the planned replacement time T and the moment Y after completing N operations N +t x , taking the earlier arrival moment as the criterion, conduct preventive replacement on the civil aircraft critical system. If the system fails before preventive replacement, corrective replacement is carried out;

[0033] Step 302. According to the preventive maintenance optimization strategy of the civil aircraft critical system, construct an optimization model for preventive maintenance of civil aircraft critical systems based on the first replacement criterion, expressed as:

[0034]

[0035] Among them, C fb (α,t x ; N,T) is the expected cost rate function under the long-term operation of the civil aircraft critical system, and C fb1 (α,t x ; N,T) is the expected cost within the first cycle starting from the installation moment, and T fb1 (α,t x ; N,T) is the time of the first cycle.

[0036] Preferably, in step 3, the second type of preventive maintenance strategy is obtained as follows:

[0037] Step 311. Solve the optimal number of operations The principle is:

[0038] C fb (α,t x ; N+1; T)-C fb (α,t x ; N; T)≥0;

[0039] Step 312. Solve the optimal planned replacement time The principle is:

[0040]

[0041] Among them, is the integral symbol for partial derivative, representing the partial derivative of the numerator after the symbol with respect to the denominator;

[0042] Step 313. According to the optimal operation times and the optimal planned replacement time formulate the second type of preventive maintenance strategy for the preventive maintenance optimization model of civil aircraft key systems based on the first replacement criterion:

[0043] For the planned replacement time T and the completion time of the th operation, take the earlier arrival time as the standard, and conduct preventive replacement of the key system; for and the specified completion time of the Nth operation, take the earlier arrival time as the standard, and conduct preventive replacement of the key system.

[0044] Preferably, in step 4, construct a preventive maintenance optimization model for civil aircraft key systems based on the later replacement criterion, and the method is as follows:

[0045] Step 401. According to the basic model of preventive maintenance of civil aircraft key systems considering the operation process, determine the preventive maintenance optimization strategy for civil aircraft key systems based on the later replacement criterion:

[0046] According to the planned replacement time T and the time Y N +t x after N operations are completed, take the later arrival time as the standard, and conduct preventive replacement of the civil aircraft key system. If the system fails before preventive replacement, conduct corrective replacement;

[0047] Step 402. According to the preventive maintenance optimization strategy for civil aircraft key systems based on the later replacement criterion, construct a preventive maintenance optimization model for civil aircraft key systems based on the later replacement criterion, expressed as:

[0048]

[0049] Among them, C lb (α, t x ; N, T) is the expected cost rate function under long-term operation, and C lb1 (α, t x ; N, T) is the expected cost within the first cycle starting from the installation time, and T lb1 (α, t x ; N, T) is the time of the first cycle.

[0050] Preferably, in step 4, obtain the third type of preventive maintenance strategy, and the method is as follows:

[0051] Step 411. Solve the optimal operation times The principle is:

[0052] C lb (α, t x ; N + 1; T) - C lb (α, t x ; N; T) ≥ 0;

[0053] Step 412, Solve for the optimal planned replacement time The principle is:

[0054]

[0055] Step 413, According to the optimal number of runs And the optimal planned replacement time Formulate the third type of preventive maintenance strategy for the preventive maintenance optimization model of the civil aircraft critical system based on the post - replacement criterion:

[0056] For the planned replacement time T and the completion time of the th run, based on the time arrived later, conduct preventive replacement on the critical system; for the optimal planned replacement time And the specified completion time of the Nth run, based on the time arrived later, conduct preventive replacement on the critical system.

[0057] Preferably, in step 5, to determine the optimal maintenance strategy of the civil aircraft critical system, the method is as follows: For the three cases where N and the planned replacement time T are not specified, N is not specified, and the planned replacement time T is not specified, calculate the maintenance costs according to the first, second, and third types of preventive maintenance strategies respectively, conduct comparative analysis, and obtain the optimal maintenance strategy of the civil aircraft critical system with the minimum expected cost rate, and conduct preventive maintenance on the civil aircraft critical system.

[0058] The technical solution of the present invention also provides: An electronic device, including:

[0059] One or more processors;

[0060] A storage device, on which one or more programs are stored;

[0061] When the one or more programs are executed by the one or more processors, the one or more processors implement the preventive maintenance method of the civil aircraft critical system considering the operation process as described in any of the above.

[0062] The technical solution of the present invention also provides a computer - readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the steps in any of the above preventive maintenance methods of the civil aircraft critical system considering the operation process.

[0063] The present invention adopts the above - mentioned technical solution, compared with the prior art, has the following technical effects:

[0064] 1. The preventive maintenance method for civil aircraft critical systems of the present invention fully considers the operating conditions of civil aircraft critical systems and the changes in maintenance costs, obtains the renewal function, operating time distribution function, and maintenance cost parameters using the historical failure data, flight information data, and maintenance data of civil aircraft critical systems, constructs the basic preventive maintenance model for civil aircraft critical systems, obtains three types of preventive maintenance strategies, conducts comparative analysis, and determines the optimal preventive maintenance strategy for civil aircraft critical systems.

[0065] 2. The preventive maintenance method for civil aircraft critical systems of the present invention can further improve the reliability and safety of civil aircraft critical systems during operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a flowchart of the preventive maintenance method for civil aircraft critical systems considering the operation process of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the application will be further elaborated in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments of other researchers in this field belong to the protection scope of the present invention. At the same time, for the step numbers in the embodiments of the present invention, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0068] In an embodiment of the present invention, a preventive maintenance method for civil aircraft critical systems considering the operation process is as follows:

[0069] Step 1: Collect the historical failure data, flight information data, and maintenance data of civil aircraft critical systems;

[0070] In this embodiment, the flight information data includes the start time and arrival time of each flight of the civil aircraft, and the maintenance data includes the preventive replacement cost c of the critical system p and the corrective replacement cost c f .

[0071] Step 2: Obtain the renewal function according to the historical failure data:

[0072] Specifically, fit the reliability distribution function F(t) of the civil aircraft critical system according to the historical failure data, and obtain the renewal function of the system using the method of convolution:

[0073]

[0074] Among them, M(t) is the renewal function, representing the number of replacements of the system within the time interval [0, t], F (j) (t) is the j-fold convolution of the system reliability distribution function F(t), t is time, j is the lower bound of the summation, u is the differential parameter, and d is the differential operator.

[0075] In this embodiment, the density function of M(t) is m(t) ≡ dM(t) / dt.

[0076] Step 3: Obtain the running time distribution function according to the flight information data:

[0077] Specifically, according to the flight information data, record the time interval X1 between the start time Y1 of the first run of the system since installation, the start time Y i of the i-th run and the start time Y i+1 of the (i + 1)-th run, and the time distribution of the N-th start of the system operation is G i+1 (t); (N) where G

[0078] (t) is the N-fold convolution of G(t), and G(t) is the distribution function of X (N) . i

[0079] In this embodiment, the distribution function G(t) is fitted from the data X i .

[0080] Step 4: Determine the basic maintenance strategy of the civil aircraft critical system according to the preventive maintenance theory:

[0081] Specifically, to effectively prevent the failure of the civil aircraft critical system during operation, it is stipulated that the system undergoes preventive replacement after N runs, that is, the preventive replacement time is Y N + t x . Before this time, once a failure occurs, corrective replacement is carried out.

[0082] where t x is the average operation period.

[0083] Step 5: Construct a basic preventive maintenance model for the civil aircraft critical system considering the operation process according to the basic maintenance strategy:

[0084] Specifically, the basic preventive maintenance model for the civil aircraft critical system considering the operation process is:

[0085]

[0086] where C b (α, t x ; N) is the expected cost rate function under long-term operation, Cb1 (α, t x ; N) is the expected cost within the first cycle starting from the installation time, T b1 (α, t x ; N) is the time of the first cycle, and α is the discount rate.

[0087] In this embodiment,

[0088]

[0089]

[0090]

[0091] Among them, the base e represents the natural base;

[0092] Step Six: According to C b (α, t x ; N + 1) - C b (α, t x ; N) ≥ 0, solve for the optimal number of operation times N b *;

[0093] Specifically, according to C b (α, t x ; N + 1) - C b (α, t x ; N) ≥ 0, we can obtain

[0094]

[0095] Among them, L b (α, t x ; N) ≡ lim T→∞ L b (T, α, t x ; N) and

[0096]

[0097] In this embodiment, for 0 < T ≤ ∞, α > 0, t x > 0, and N = 1, 2, 3, …, if m(t) is strictly monotonically increasing with respect to t, then ) is strictly monotonically increasing with respect to T from m(t x ) / α to L b (∞, α, θ, t x ; N), and is strictly monotonically increasing with respect to N from L b (T, α, θ, t x ; 1) to m(T + t x ) / α.

[0098] Let in the formula For Z b (α, t x ; N), then Z b (α, t x ; N) is strictly monotonically increasing with respect to N to Z b (α, t x ; ∞).

[0099] At this time, there are two cases for the optimal number of operations :

[0100] When Z b (α, t x ; ∞) > c p / c f , there exists a unique optimal solution such that the expected cost rate C b (α, t x ; N) is the lowest; if Z b (α, t x ; ∞) ≤ c p / c f , then

[0101] At this time, the corresponding expected cost rate is which means that the task situation does not need to be considered, and only the after - failure replacement is considered.

[0102] Step Seven: According to formulate the first - type preventive maintenance strategy of the preventive maintenance basic model of civil aircraft key systems considering the operation process;

[0103] Specifically, the first - type preventive maintenance strategy is: after the civil aircraft key system runs for the N b * th time, it needs to be immediately replaced preventively to make it have high reliability and safety during the operation process.

[0104] Furthermore, to verify the scientificity and effectiveness of the preventive maintenance basic model of civil aircraft key systems considering the operation process, the following numerical example 1 is given:

[0105] When G(t) = 1 - e -4t , F(t) = 1 - (1 + 0.25t)e -0.25t , c f = 400.0, through the calculation of the preventive maintenance basic model of civil aircraft key systems considering the operation process, Tables 1 and 2 are obtained.

[0106] Table 1 When t x = 0.5, the and

[0107]

[0108] Table 1 shows the optimal number of operations and the corresponding minimum expected cost rate under different discount rates and preventive replacement costs when the running time t x = 0.5. It can be seen from Table 1 that with respect to c p is strictly monotonically increasing and non-strictly monotonically increasing with respect to α; with respect to c p is strictly monotonically increasing. When α > 0, is strictly monotonically decreasing with respect to α.

[0109] It is not difficult to find that when the replacement cost is the same, the expected cost rate obtained considering the discount rate is generally greater than the case without considering the discount rate. If the decision-maker does not consider the cost discount rate when formulating the preventive maintenance strategy, it will cause a serious shortage of the budget, making it difficult to guarantee the later preventive maintenance measures of the system.

[0110] Table 2 shows the and

[0111]

[0112] Table 2 shows the optimal number of operations and the corresponding minimum expected cost rate under different running times and preventive replacement costs when the discount rate α = 0.1. It can be seen from Table 2 that with respect to c p is strictly monotonically increasing and non-strictly monotonically decreasing with respect to t x ; with respect to c p is strictly monotonically increasing. Table 2 reveals that if the decision-maker does not fully consider the running time of the system, that is, t x = 0, an overestimated optimal number of operations is often obtained. In reliability theory, frequent use of the system will gradually increase the risk of its failure. If it is not repaired in time at the moment of repair, it is difficult to ensure high reliability of the system during subsequent operation.

[0113] In addition, it can be seen from Table 2 that if the running time is not considered, the actual maintenance cost is generally higher than the maintenance cost under the method of the present invention. Therefore, compared with the existing methods, the new method proposed by the present invention is more effective and scientific.

[0114] Step 8: Determine the preventive maintenance optimization strategy for the civil aircraft critical system based on the first replacement criterion according to the basic maintenance basis of the civil aircraft critical system:

[0115] Specifically, for the planned replacement time T and the moment Y after N runs N +t x , taking the earlier-arriving moment as the criterion, the system is preventive replaced. If the system fails before the preventive replacement, corrective replacement is carried out.

[0116] Step Nine: Construct a preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion according to the preventive maintenance optimization strategy for civil aircraft critical systems based on the first replacement criterion described above:

[0117] Specifically, the preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion is:

[0118]

[0119] Among them, C fb (α, t x ; N, T) is the expected cost rate function under long-term operation, and C fb1 (α, t x ; N, T) is the expected cost within the first cycle starting from the installation moment, and T fb1 (α, t x ; N, T) is the time of the first cycle.

[0120] In this embodiment,

[0121]

[0122]

[0123]

[0124] Step Ten: Solve for the optimal number of runs according to C fb (α, t x ; N + 1; T) - C fb (α, t x ; N; T) ≥ 0

[0125] Specifically, according to C fb (α, t x ; N + 1; T) - C fb (α, t x ; N; T) ≥ 0, it can be obtained that

[0126]

[0127] In this embodiment, let the left part of the above formula be Z fb1 (α, t x ; N; T), when L fb1 (α, tx ; N; T) is strictly monotonically increasing with respect to N, then Z fb1 (α, t x ; N; T) is strictly monotonically increasing with respect to N, and there exists a unique optimal number of operation times

[0128] Among them,

[0129]

[0130] Step Eleven: According to Solve for the optimal planned replacement time

[0131] Specifically, take the derivative of C fb (α, t x ; N; T) with respect to T and set it to zero, we can get:

[0132]

[0133] Among them,

[0134]

[0135] And

[0136] In this embodiment, for 0 < T ≤ ∞, α > 0, t x > 0, and N = 1, 2, 3,..., if m(T) / r(N; T) is not strictly monotonically decreasing with respect to T, then L fb2 (α, t x ; N; T) is strictly monotonically increasing from 0 to L fb2 (α, t x ; N; ∞).

[0137] Let the left part of the formula be Z fb2 (α, t x ; N; T), then Z fb2 (α, t x ; N; T) is strictly monotonically increasing from 0 to Z fb2 (α, t x ; N; ∞).

[0138] At this time, there are two cases for the optimal planned replacement time : When Z fb2 (α, t x ; N; ∞) > c p / c f , there exists a unique optimal solution such that the expected cost rate C fb (α, t x; N; T) is the lowest, and the minimum cost rate is If Z fb2 (α, t x ; N; ∞) ≤ c p / c f , then

[0139] Step Twelve: According to the described and formulate the second type of preventive maintenance strategy for the preventive maintenance optimization model of civil aircraft critical systems based on the first replacement criterion;

[0140] Specifically, the second type of preventive maintenance strategy is: for the specified T and the th run completion time, take the earlier arrival time as the criterion to conduct preventive replacement of the critical system; and for and the specified Nth run completion time, take the earlier arrival time as the criterion to conduct preventive replacement of the critical system.

[0141] Furthermore, to verify the scientificity and effectiveness of the preventive maintenance optimization model of civil aircraft critical systems based on the first replacement criterion, the parameters of Example 1 are continued, and the following Example 2 is given.

[0142] Through the calculation of the preventive maintenance optimization model of civil aircraft critical systems based on the first replacement criterion, Tables 3 and 4 are obtained. By comparing Table 2, Table 3 and Table 4, it can be found that under the same parameters, using the preventive maintenance optimization model of civil aircraft critical systems based on the first replacement criterion can further reduce the maintenance cost on the basis of ensuring the high reliability of the system operation process compared with using the basic preventive maintenance model of civil aircraft critical systems considering the operation process.

[0143] Table 3 When α = 0.1, t x = 1.5 and

[0144]

[0145] Table 4 When α = 0.1, t x = 1.5 and

[0146]

[0147] Step Thirteen: Determine the preventive maintenance optimization strategy of civil aircraft critical systems based on the later replacement criterion according to the basic maintenance basis of the civil aircraft critical systems:

[0148] Specifically, for the planned replacement time T and the time Y N + tx The system is preventively replaced based on the subsequent arrival time. Before preventive replacement, if the system fails, corrective replacement is carried out.

[0149] Step 14: Construct a preventive maintenance optimization model for civil aircraft critical systems based on the subsequent replacement criterion according to the preventive maintenance optimization strategy for civil aircraft critical systems based on the subsequent replacement criterion:

[0150] Specifically, the preventive maintenance optimization model for civil aircraft critical systems based on the subsequent replacement criterion is:

[0151]

[0152] Among them, C lb (α, t x ; N, T) is the expected cost rate function under long-term operation, and C lb1 (α, t x ; N, T) is the expected cost within the first cycle starting from the installation time, and T lb1 (α, t x ; N, T) is the time of the first cycle.

[0153] In this embodiment,

[0154]

[0155]

[0156]

[0157] Step 15: Solve for the optimal number of operating times according to C lb (α, t x ; N + 1; T) - C lb (α, t x ; N; T) ≥ 0

[0158] Specifically, according to C lb (α, t x ; N + 1; T) - C lb (α, t x ; N; T) ≥ 0, we can obtain

[0159]

[0160] Among them,

[0161]

[0162] In this embodiment, for 0 < T ≤ ∞, α > 0, t x> 0, and N = 1, 2, 3, …, if m(t) is strictly monotonically increasing with respect to t, then L lb1 (α, t x ; N; T) is strictly monotonically increasing from N to m(∞) / α.

[0163] Let the left - hand side of the formula part be Z lb1 (α, t x ; N; T), then Z lb1 (α, t x (α, t

[0164] At this time, there are two cases for the optimal number of operations . When Z lb1 (α, t x ; ∞; T)> c p / c f , there exists a unique optimal solution such that the expected cost rate C lb (α, t x ; N; T) is minimized; if Z lb1 (α, t x (α, t p / c f , then

[0165] Step Sixteen: According to Solve for the optimal planned replacement time

[0166] Specifically, take the derivative of C lb (α, t x ; N; T) with respect to T and set it to zero, we get

[0167]

[0168] Let the left - hand side of the above formula be Z lb2 (α, t x ; N; T). When m(T) is a strictly monotonically increasing function of T, then Z lb1 (α, t x ; N; T) is strictly monotonically increasing from Z lb1 (α, t x ; N; t x ) to Z lb1 (α, t x ; N; ∞).

[0169] Therefore, there are three cases for the optimal solution of the planned replacement time . If Z lb1 (α, t x ; N; tx ) ≥ c p / c f , then If Z lb1 (α, t x ; N; t x ) < c p / c f < Z lb1 (α, t x ; N; ∞), then there exists a unique optimal planned replacement time such that C lb (α, t x ; N; T) is minimized, and the minimum cost rate is:[[]]

[0170]

[0171] If Z lb1 (α, t x ; N; ∞) < c p / c f , then

[0172] Step 17: According to the and formulate the third type of preventive maintenance strategy for the preventive maintenance optimization model of civil aircraft critical systems based on the later replacement criterion;

[0173] Specifically, the third type of preventive maintenance strategy is: for the specified T and the th operation completion time, with the subsequent arrival time as the reference, perform preventive replacement on the critical system; and for and the specified Nth operation completion time, with the subsequent arrival time as the reference, perform preventive replacement on the critical system.

[0174] In this embodiment, to verify the scientificity and effectiveness of the preventive maintenance optimization model of civil aircraft critical systems based on the later replacement criterion, the parameters of Example 1 are continued to be used, and the following Example 3 is given.

[0175] Through the calculation of the preventive maintenance optimization model of civil aircraft critical systems based on the later replacement criterion, Tables 5 and 6 are obtained.

[0176] It can be concluded from Table 5 that Regarding c p is non-strictly monotonically increasing and non-strictly monotonically decreasing with respect to T. It reveals that when the planned replacement time is longer, the decision maker should try to reduce the number of system operations

[0177] Table 5 When α = 0.1, t x = 1.5 and

[0178]

[0179] It can be concluded from Table 6 that Regarding c p and N are not strictly monotonically increasing. It reveals that when the number of runs increases, the decision maker should delay the preventive replacement time as much as possible.

[0180] Table 6 When α = 0.1, t x = 1.5 and

[0181]

[0182] Step Eighteen: For the three cases where N and T are not specified, N is not specified, and T is not specified, obtain the optimal maintenance strategy for the civil aircraft critical system with the minimum expected cost rate.

[0183] In this embodiment, according to the actual situation, when F(t) = 1 - (1 + 0.125t)e -0.125t , G(t) = 1 - e -0.5t , t x = 0.2, α = 0.2, c f = 8000000.00, c p = 1000000.00, for the three cases where N and T are not specified, N is not specified, and T is not specified, illustrate the optimal maintenance strategy for the civil aircraft critical system with the minimum expected cost rate through Example Four.

[0184] (1) N and T are not specified.

[0185] First, according to the basic preventive maintenance model of the civil aircraft critical system considering the operation process, calculate that the optimal number of runs is 9 times, and the corresponding expected cost is 1386770.00.

[0186] When the optimal number of runs is 9 times, according to the preventive maintenance optimization model of the civil aircraft critical system based on the first replacement criterion, the optimal planned replacement time is 12.289, and the corresponding expected cost is 1384260.00.

[0187] According to the preventive maintenance optimization model of the civil aircraft critical system based on the second replacement criterion, the optimal planned replacement time is 12.346, and the corresponding expected cost is 1385840.00.

[0188] By comparing the expected costs under the three models, it can be concluded that the expected cost of the preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion is the lowest. Therefore, the optimal maintenance strategy for civil aircraft critical systems is as follows: For the planned replacement time of 12.289 and the moment after 9 operations are completed, the system is preventively replaced based on the earlier arrival time. If the system fails before the preventive replacement, corrective replacement is carried out.

[0189] (2) N is not specified.

[0190] When the decision maker gives the planned replacement time of 16.000 in advance, according to the preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion, the optimal number of operations is 12, and the corresponding expected cost is 1,384,970.00.

[0191] According to the preventive maintenance optimization model for civil aircraft critical systems based on the second replacement criterion, the optimal number of operations is 1, and the corresponding expected cost is 1,385,030.00.

[0192] By comparing the expected costs under the two models, it can be concluded that the expected cost of the preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion is the lowest. Therefore, the optimal maintenance strategy for civil aircraft critical systems is as follows: For the planned replacement time of 16.000 and the moment after 12 operations are completed, the system is preventively replaced based on the earlier arrival time. If the system fails before the preventive replacement, corrective replacement is carried out.

[0193] (3) T is not specified.

[0194] When the decision maker gives the number of operations of 5 in advance, according to the preventive maintenance optimization model for civil aircraft critical systems based on the first replacement criterion, the optimal planned replacement time is 13.495, and the corresponding expected cost is 1,414,450.00.

[0195] According to the preventive maintenance optimization model for civil aircraft critical systems based on the second replacement criterion, the optimal planned replacement time is 12.273, and the corresponding expected cost is 1,383,760.00.

[0196] By comparing the expected costs under the two models, it can be concluded that the expected cost of the preventive maintenance optimization model for civil aircraft critical systems based on the second replacement criterion is the lowest. Therefore, the optimal maintenance strategy for civil aircraft critical systems is as follows: For the planned replacement time of 12.273 and the moment after 5 operations are completed, the system is preventively replaced based on the later arrival time. If the system fails before the preventive replacement, corrective replacement is carried out.

[0197] An embodiment of the present invention further provides an electronic device, including: one or more processors; a storage device storing one or more programs thereon; when the one or more programs are executed by the one or more processors, the one or more processors implement the preventive maintenance method for civil aircraft key systems considering the operation process as described above.

[0198] In an embodiment of the present invention, a computer-readable storage medium is further provided, having a computer program stored thereon, and when the program is executed by a processor, the steps in the preventive maintenance method for civil aircraft key systems considering the operation process as described above are implemented.

[0199] In summary, for the preventive maintenance method for civil aircraft key systems considering the operation process proposed by the present invention, historical failure data, flight information data, and maintenance data of civil aircraft key systems are used to obtain an update function, an operation time distribution function, and maintenance cost parameters. The basic model of preventive maintenance for civil aircraft key systems considering the operation process is adopted to obtain the first type of preventive maintenance strategy; according to the preventive maintenance optimization model for civil aircraft key systems based on the first replacement criterion, the second type of preventive maintenance strategy is obtained; through the preventive maintenance optimization model for civil aircraft key systems based on the second replacement criterion, the third type of preventive maintenance strategy is obtained; according to the principle of minimizing the expected cost rate, a comparative analysis is performed on the three types of preventive maintenance strategies to determine the optimal preventive maintenance strategy for civil aircraft key systems. The comparison result with the existing method shows that the method of the present invention can further improve the reliability and safety of civil aircraft key systems during operation.

[0200] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A preventive maintenance method for key civil aircraft systems considering the operation process, characterized in that, It includes the following steps: Step 1: Collect data of the key systems of civil aircraft, including historical failure data, flight information data, and maintenance data; Step 2: According to the obtained data of the key systems of civil aircraft, construct a basic preventive maintenance model of the key systems of civil aircraft considering the operation process, and obtain the first type of preventive maintenance strategy; Step 3: According to the basic preventive maintenance model of the key systems of civil aircraft considering the operation process, construct an optimized preventive maintenance model of the key systems of civil aircraft based on the pre-replacement criterion, and obtain the second type of preventive maintenance strategy; Step 4: According to the basic preventive maintenance model of the key systems of civil aircraft considering the operation process, construct an optimized preventive maintenance model of the key systems of civil aircraft based on the post-replacement criterion, and obtain the third type of preventive maintenance strategy; Step 5: Calculate the maintenance costs according to the first, second, and third types of preventive maintenance strategies respectively, and determine the optimal maintenance strategy of the key systems of civil aircraft according to the principle of the minimum expected cost rate.

2. The preventive maintenance method for a key civil aircraft system considering the operation process according to claim 1, characterized in that In Step 2, the method for constructing the basic preventive maintenance model of the key systems of civil aircraft considering the operation process is as follows: Step 201: Fit the reliability distribution function F(t) of the key systems of civil aircraft according to the historical failure data, and obtain the system renewal function by using the convolution method: Among them, M(t) is the renewal function, representing the number of replacements of the key civil aircraft systems within the time interval [0, t], and F (j) (t) is the j-fold convolution of the reliability distribution function F(t) of the key civil aircraft systems, t is the time, j is the lower bound of the summation, and u is the differential parameter; Step 202: Obtain the operation time distribution function according to the flight information data; According to the flight information data, record the time interval X1 between the installation of the key systems of the civil aircraft and the start time Y1 of the first operation, and the start time Y i of the i-th operation and the start time Y i+1 of the (i + 1)-th operation, with the time interval X i+1 . The time distribution function of the N-th start of the system operation is G (N) (t); Among them, G (N) (t) is the N-fold convolution of G(t), and G(t) is the distribution function of X i . Step 203: Determine the basic maintenance strategy of the key systems of civil aircraft according to the preventive maintenance theory; It is stipulated that preventive replacement of key civil aircraft systems shall be carried out after N operations, and the preventive replacement time is Y N +t x , and in case of failure before preventive replacement, corrective replacement shall be carried out; where t x is the average operation period; Step 204: According to the basic maintenance strategy, construct a basic preventive maintenance model of the key systems of civil aircraft considering the operation process, expressed as: Among them, C b (α, t x ; N) is the expected cost rate function under the long-term operation of the civil aircraft key system, C b1 (α, t x ; N) is the expected cost within the first cycle starting from the installation moment, T b1 (α, t x ; N) is the time of the first cycle, and α is the discount rate.

3. The preventive maintenance method for key civil aircraft systems considering the operation process according to claim 2, characterized in that, In Step 2, the method for obtaining the first type of preventive maintenance strategy is as follows: Step 211, solve the optimal operation times of the key systems of civil aircraft The principle is as follows: C b (α, t x ; N + 1)-C b (α, t x ; N) ≥ 0; Step 212. According to the optimal number of operations Formulate the first type of preventive maintenance strategy for the basic preventive maintenance model of civil aircraft critical systems considering the operation process: After the th operation of the civil aircraft critical system, preventive replacement is immediately carried out.

4. The preventive maintenance method for key civil aircraft systems considering the operation process according to claim 3, characterized in that In Step 3, the method for constructing the optimized preventive maintenance model of the key systems of civil aircraft based on the pre-replacement criterion is as follows: Step 301: According to the basic preventive maintenance model of the key systems of civil aircraft considering the operation process, determine the optimized preventive maintenance strategy of the key systems of civil aircraft based on the pre-replacement criterion; According to the planned replacement time T and the time Y after N runs are completed N +t x , taking the earlier arrival time as the criterion, preventive replacement is carried out on the key systems of civil aircraft. If the system fails before preventive replacement, corrective replacement is carried out; Step 302: According to the optimized preventive maintenance strategy of the key systems of civil aircraft, construct an optimized preventive maintenance model of the key systems of civil aircraft based on the pre-replacement criterion, expressed as: Among them, C fb (α,t x ; N, T) is the expected cost rate function of the key systems of civil aircraft under long-term operation, C fb1 (α,t x ; N,T) is the expected cost in the first cycle starting from the installation time, T fb1 (α,t x ; N, T) is the time of the first cycle.

5. The preventive maintenance method for key civil aircraft systems considering the operation process according to claim 4, characterized in that, In Step 3, the method for obtaining the second type of preventive maintenance strategy is as follows: Step 311, Solve the optimal number of running times The principle is: C fb (α, t x ; N + 1; T)-C fb (α, t x ; N; T)≥0； Step 312, Solve the optimal planned replacement time The principle is: Step 313. According to the optimal operation times and the optimal planned replacement time formulate the second type of preventive maintenance strategy for the preventive maintenance optimization model of the key civil aircraft systems based on the prior replacement criterion: For the planned replacement time T and the completion time of the th run, the key system is preventively replaced based on the earlier arrival time; for and the specified completion time of the Nth run, the key system is preventively replaced based on the earlier arrival time.

6. The preventive maintenance method for civil aircraft critical systems considering the operation process according to claim 4, characterized in that In Step 4, the method for constructing the optimized preventive maintenance model of the key systems of civil aircraft based on the post-replacement criterion is as follows: Step 401: According to the basic preventive maintenance model of the key systems of civil aircraft considering the operation process, determine the optimized preventive maintenance strategy of the key systems of civil aircraft based on the post-replacement criterion; According to the planned replacement time T and the time Y after N runs are completed N +t x , taking the time of subsequent arrival as the standard, preventive replacement is carried out on the key systems of civil aircraft. In case of system failure before preventive replacement, corrective replacement is carried out; Step 402: According to the optimized preventive maintenance strategy of the key systems of civil aircraft based on the post-replacement criterion, construct an optimized preventive maintenance model of the key systems of civil aircraft based on the post-replacement criterion, expressed as: Among them, C lb (α, t x ; N, T) is the expected cost rate function under long-term operation conditions, and C lb1 (α, t x ; N, T) is the expected cost within the first cycle starting from the installation moment, and T lb1 (α, t x ; N, T) is the time of the first cycle.

7. The preventive maintenance method for key civil aircraft systems considering the operation process according to claim 6, characterized in that In Step 4, the method for obtaining the third type of preventive maintenance strategy is as follows: Step 411, Solve the optimal number of operation times The principle is: C lb (α, t x ; N + 1; T)-C lb (α, t x ; N; T)≥0； Step 412, Solve the optimal planned replacement time The principle is: Step 413. According to the optimal number of operation times and the optimal planned replacement time formulate the third type of preventive maintenance strategy for the preventive maintenance optimization model of civil aircraft key systems based on the post-replacement criterion: For the planned replacement time T and the completion time of the th run, and for the subsequent arrival times, preventive replacement of the critical system is carried out; for the optimal planned replacement time and the specified completion time of the Nth run, and for the subsequent arrival times, preventive replacement of the critical system is carried out.

8. The preventive maintenance method for key civil aircraft systems considering the operation process according to claim 6, characterized in that In Step 5, the method for determining the optimal maintenance strategy of the key systems of civil aircraft is as follows: For the three cases where N and the planned replacement time T are not specified, N is not specified, and the planned replacement time T is not specified, calculate the maintenance costs according to the first, second, and third types of preventive maintenance strategies respectively for comparative analysis, and obtain the optimal maintenance strategy of the key systems of civil aircraft with the minimum expected cost rate, and conduct preventive maintenance on the key systems of civil aircraft.

9. An electronic device, characterized in that, It includes: One or more processors; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the preventive maintenance method for civil aircraft critical systems considering the operation process as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, A computer program is stored thereon, and when the program is executed by a processor, the steps in the preventive maintenance method for civil aircraft critical systems considering the operation process as described in any one of claims 1 to 8 are implemented.

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