CN113374543A - Aeroengine part maintenance method based on time-varying fault rate model - Google Patents

Aeroengine part maintenance method based on time-varying fault rate model Download PDF

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CN113374543A
CN113374543A CN202110629185.2A CN202110629185A CN113374543A CN 113374543 A CN113374543 A CN 113374543A CN 202110629185 A CN202110629185 A CN 202110629185A CN 113374543 A CN113374543 A CN 113374543A
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CN113374543B (en
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严如强
杨旭彪
周峥
孙闯
唐亚军
杨波
田绍华
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Xian Jiaotong University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D21/00—Shutting-down of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for
    • F01D21/003—Arrangements for testing or measuring
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D21/00—Shutting-down of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The disclosure discloses a time-varying fault rate model-based maintenance method for an aircraft engine component, which comprises the following steps: establishing a fault rate model according to historical fault statistical data of the aircraft engine component; constructing a fault risk function based on the actual detection of the detection error term on the actual recession of the aeroengine component, wherein the influence of different maintenance behaviors and times on the component fault risk in the maintenance process is realized by adding a fault rate increasing factor and a working age decreasing factor; adding the effect of the maintenance cost on performance recovery to a work-age decrementing factor to reflect the overall performance change under the effect of the investment cost; considering economy and safety, constructing an objective function with the aim of minimizing long-term expense rate and failure rate including maintenance economy cost and downtime loss cost; and solving the optimal detection time interval of the objective function.

Description

Aeroengine part maintenance method based on time-varying fault rate model
Technical Field
The disclosure belongs to the field of maintenance strategy optimization of an aircraft engine multi-component system, and particularly relates to an aircraft engine component maintenance method based on a time-varying fault rate model.
Background
The rapid development of aerospace technology puts higher and higher requirements on maintenance of an aircraft engine system, so that the maintenance investment cost needs to be reduced economically, the operation safety of equipment needs to be ensured, and major accidents are avoided. Therefore, the method has important research significance on the sustainability research of the maintenance cost and the operation state of the single-component system of the aircraft engine.
The traditional maintenance of the aircraft engine parts is mostly carried out according to regular maintenance, so that the maintenance cost is greatly increased, the problems of excessive maintenance or serious fault shutdown and the like are caused, the current maintenance situation of the aircraft engine is improved by adopting a state-based maintenance scheme, an actual degradation model of the parts is established by carrying out statistical analysis on fault data of the aircraft engine parts, and the change of maintenance behaviors to the performances of the parts can be effectively simulated by introducing a fault rate increasing factor and a working age decreasing factor. By adopting the optimized maintenance parameters, the overall maintenance cost can be reduced while the fault damage caused by high failure rate of the airplane is avoided. Therefore, the proposed method has great application potential in the actual operation and maintenance process.
The above statements are provided to enhance an understanding of the background of the present invention and may, therefore, contain no prior art information known to those of ordinary skill in the art.
Disclosure of Invention
In view of the deficiencies of regular maintenance, it is an object of the present disclosure to provide a method for servicing an aircraft engine component based on a time-varying failure rate model.
In order to achieve the above object, the present disclosure provides the following technical solutions, and a time-varying fault rate model-based aircraft engine component maintenance method includes the following steps:
step 1, establishing a fault rate model according to historical fault statistical data of an aircraft engine component, wherein fault probability distribution of the component along with operation time is established according to the historical fault statistical data of the aircraft engine component, and the fault rate model is established by fitting the fault probability distribution;
step 2, introducing a detection error term to construct a fault risk function based on a fault rate model so as to reflect the real detection of the actual decline of the aero-engine component;
and 3, adding a fault rate increasing factor and a work life decreasing factor into the fault risk function to characterize the performance improvement level of the part, wherein the performance improvement level of the i-th incomplete maintenance is as follows: lambda [ alpha ][i+1] M(t)＝biλ[i] M(t+aiΔTi)(0＜t＜ΔTi+1) Wherein b isiAnd aiRespectively a fault rate increasing factor and a service age decreasing factor, and bi＞1，0＞ai＞1，ΔTiFor the time interval of i-th and i-1-th incomplete maintenance, lambda[i] M(t) the fault risk level at time t after the ith maintenance;
step 4, comprehensively establishing a cost function based on the detection cost, the maintenance cost and the downtime;
step 5, calculating the expense rate and the risk rate based on the cost function and the fault risk function, and constructing a target function;
and 6, solving the optimal detection time interval of the objective function.
In the method, in the step 1, the fault rate model is a two-parameter Weibull model:
Figure BDA0003101134610000021
where t is the aircraft runtime, β and η are the shape parameter and the scale parameter, respectively, and λ0And (t) is the probability of the component failing at time t. Lambda [ alpha ]0(t) refers to a two-parameter weibull model, which can calculate the failure probability of a component at a certain moment, namely: the failure rate. When the model parameter is explained, the lambda is directly explained0(t) is specified as the probability of a component failing at time t.
In the method, in step 2, the detection error term is a gaussian error E, and the fault risk function after adding the gaussian error term is as follows:
Figure BDA0003101134610000022
wherein, beta and eta are Weibull fault rate model parameters, E is a detection error term, N (-) is Gaussian distribution, and sigma is2Is the variance of the error term, lambdaM(t) is a fault risk function that takes into account detection errors.
In the method, in step 3, the effective working age of the ith incomplete maintenance is as follows:
Figure BDA0003101134610000023
wherein, CIPM jFor the jth incomplete maintenance cost, CPRTo replace the cost, a is a cost adjustment parameter, and
Figure BDA0003101134610000031
b is a time adjustment parameter, and 0 < b < 1, the effective work-age replacement work-age decrementing factor yields a performance improvement level that takes into account cost impact:
Figure BDA0003101134610000032
where T is the total operating time of the component since the last replacement, Δ TiThe time interval for the i-th and i-1-th incomplete maintenance.
In the method, in step 4, the constructed cost function includes a detection cost CmAfterward maintenance cost CaPredictive maintenance cost CpAnd cost of shutdown loss Cd。
In the method, in step 5, the objective function includes a charge rate CuAnd risk ratio psiuWherein, in the step (A),
Figure BDA0003101134610000033
wherein M is the total maintenance times, TmAs total flight time of the aircraft, Cm、Ca、Cp、CdCost of maintenance process, tiFor the ith maintenance time, λ[i+1] M(t) is the composite fault risk function followed before the i +1 th maintenance action.
In the method, in step 6, the optimal detection time interval is solved by taking the expense rate and the risk rate of long-term operation as fitness functions through a genetic algorithm.
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FIG. 1 is a schematic representation of the steps of the present invention;
FIG. 2 is a threshold maintenance graph based on risk of failure of the present invention;
FIG. 3 is a flow chart of the simulation of the present invention;
FIG. 4 is a flow chart of the genetic algorithm optimization of the present invention;
FIG. 5 is a maintenance simulation diagram of the invention without the detection error term;
FIG. 6 is a maintenance simulation diagram of the present invention with the addition of a detection error term.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 6. While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present disclosure is to be determined by the terms of the appended claims.
To facilitate an understanding of the embodiments of the present disclosure, the following detailed description is to be considered in conjunction with the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present disclosure.
In one embodiment, as shown in fig. 1, the present disclosure provides a time-varying failure rate model-based aircraft engine component repair method comprising the steps of:
step 1, establishing a fault rate model according to historical fault statistical data of an aircraft engine component;
step 2, establishing a fault risk function for the actual detection of the actual decline of the aero-engine component based on the detection error term;
and 3, adding a fault rate increasing factor and a working age decreasing factor to characterize the performance improvement level of the part, wherein the performance improvement level of the i-th incomplete maintenance is as follows: lambda [ alpha ][i+1] M(t)＝biλ[i] M(t+aiΔTi)(0＜t＜ΔTi+1) Wherein b isiAnd aiRespectively a fault rate increasing factor and a service age decreasing factor, and bi＞1，0＞ai＞1，ΔTiFor the time interval of the i-th and i-1-th incomplete maintenance,
step 4, establishing a cost model;
step 5, constructing an objective function by taking economy and safety as targets;
and 6, solving the optimal detection time interval of the objective function.
In a preferred embodiment of the method, in step 1, the fault rate model is a two-parameter weibull model:
Figure BDA0003101134610000051
where t is the aircraft runtime and β and η are the shape parameter and the scale parameter, respectively.
In a preferred embodiment of the method, in step 2, the detection error term is a gaussian error:
Figure BDA0003101134610000052
wherein E is a detection error term, N (-) is Gaussian distribution, and lambdaM(t) is a fault rate function that takes into account detection errors.
In a preferred embodiment of the method, in step 3, the effective working age of the i-th incomplete maintenance:
Figure BDA0003101134610000053
wherein, CIPM jFor the jth incomplete maintenance cost, CPRTo replace the cost, a is a cost adjustment parameter, and
Figure BDA0003101134610000054
b is a time adjustment parameter, and 0 < b < 1, the effective work-age replacement work-age decrementing factor yields a performance improvement level that takes into account cost impact:
Figure BDA0003101134610000055
where T is the total run time of the part since the last replacement.
In a preferred embodiment of the method, in step 4, the constructed cost function includes a detection cost CmAfterward maintenance cost CaPredictive maintenance cost CpAnd cost of shutdown loss Cd。
In a preferred embodiment of the method, in step 5, the objective function includes a charge rate CuAnd risk ratio psiuWherein, in the step (A),
Figure BDA0003101134610000061
wherein M is the total detection times, TmIs the total flight time of the aircraft.
In the preferred embodiment of the method, in step 6, the optimal detection time interval is solved by using the cost rate and the risk rate of long-term operation as fitness functions through a genetic algorithm.
In one embodiment, the repair method comprises the steps of:
in step 1, firstly, a two-parameter Weibull fault rate model is established according to historical fault statistical data of aeroengine components, such as formula (1).
Figure BDA0003101134610000062
In the formula: t is the aircraft runtime, and β and η are the shape parameter and the scale parameter, respectively.
In step 2, a detection error term is introduced to describe the actual detection condition of the actual decline of the component, a comprehensive fault risk function is constructed, and the detection error term adopts a Gaussian error:
Figure BDA0003101134610000063
wherein E is a detection error term, N (-) is a Gaussian distribution, and lambdaM(t) is a decay function that takes into account detection errors.
In step 3, taking into account the effect of different maintenance actions and maintenance times on the part property change, a factor increasing the failure rate and a factor decreasing the service life, such as the performance boost level for the i-th incomplete maintenance:
λ[i+1] M(t)＝biλ[i] M(t+aiΔTi)(0＜t＜ΔTi+1) (4)
in the formula: biAnd aiRespectively a fault rate increasing factor and a service age decreasing factor, and bi＞1，0＞ai＞1，ΔTiThe time interval for the i-th and i-1-th incomplete maintenance.
Since different cost investments for incomplete maintenance will also affect the level of current maintenance, the effective age for the i-th incomplete maintenance, is introduced:
Figure BDA0003101134610000071
wherein, CIPM jFor the jth incomplete maintenance cost, CPRTo replace the cost, a is a cost adjustment parameter, and
Figure BDA0003101134610000072
b is a time adjustment parameter, and b is more than 0 and less than 1.
Thus, replacing the working age decrement factor with a valid working age, one can get a level of performance improvement that takes into account the cost impact:
Figure BDA0003101134610000073
where T is the total run time of the part since the last replacement.
In step 4, a detection cost C is establishedmAfterward maintenance cost CaPredictive maintenance cost CpAnd cost of shutdown loss CdThe composite cost function of (2).
In step 5, an objective function is constructed with the economic efficiency and the safety as main targets, and the objective function mainly comprises the charge rate CuAnd risk ratio psiuAs shown in formula (7).
Figure BDA0003101134610000074
In the formula: m is the total number of detections, TmIs the total flight time of the aircraft.
In step 6, the optimal detection time interval of the objective function is solved.
Examples
To further illustrate the invention, FIG. 1 is a flow chart of a method for optimizing a time-varying failure rate model-based aircraft engine component-level maintenance strategy according to the invention. Firstly, acquiring failure time statistical information from historical data of engine components, and further establishing a two-parameter Weibull failure rate model; and introducing performance change caused by detection error and maintenance into a fault risk model by adopting a Gaussian error term and a performance change factor, finally constructing a comprehensive cost model including detection cost, post-maintenance cost, predictive maintenance cost and shutdown loss cost, and solving model parameters by using a genetic algorithm to obtain an optimized detection interval.
FIG. 2 is a threshold maintenance diagram based on risk of failure according to the present invention, by setting a state maintenance threshold D1、D2And a fault threshold F to realize threshold maintenance, wherein the maintenance scheme mainly comprises two incomplete maintenance means of maximum maintenance and minimum maintenance, and the method is implemented as follows:
Figure BDA0003101134610000081
in the formula: m (t) is the maintenance scheme at this moment, LM is the maximum maintenance, MM is the minimum maintenance.
In practical application, the cost model is constructed as follows:
and (3) detection cost:
detection cost CmIs generated for detecting the state of the component:
Cm＝Nm·Csm (9)
in the formula: n is a radical ofmFor the number of detections, CsmThe cost of a single test.
The after repair cost:
afterward maintenance cost CaIs the result of maintenance activity following a fault, typically determined by setting a fault threshold. In this case, the failure is already serious, and the maintenance timing is delayed, so the maintenance means mainly includes: replacement, and the risk of failure of the component after maintenance is returned to 0:
Ca＝Na·Csa (10)
in the formula: n is a radical ofaFor the number of failures, CamFor the cost of maintenance after a failure.
To and haveRisk function lambdaM(t) the number of times of occurrence of failure in the i-th detection interval:
Figure BDA0003101134610000091
predictive maintenance cost:
predictive maintenance cost CpIndicating the economic cost incurred when the component is subject to state-based maintenance.
Assuming that the component replacement is performed at the N +1 th maintenance, the maintenance cost:
Figure BDA0003101134610000092
in the formula, NMMAnd NLMRespectively minimum and maximum maintenance times, CMMAnd CLMSingle economic cost, C, of minimum and maximum maintenance, respectivelyPRFor a single replacement cost.
Shutdown loss cost:
when an unexpected fault occurs or maintenance of a component is performed, the whole airplane needs to be shut down, and the airplane is late, tasks are delayed and even safety accidents occur due to overlong shutdown time. The assumed cost of downtime per unit time is CsdTotal down time of TdMainly comprises the following steps: predictive maintenance time and post-maintenance down time, ignoring the time taken for instantaneous detection.
Figure BDA0003101134610000093
In the formula, MTTR is the mean post-failure repair time of the component, and M is the total number of detections.
FIG. 3 is a flow chart of a simulation by which T is obtained according to the present inventionmOverall economic cost and reliability over time, using cost rate CuAnd risk ratio psiuThe realization is as follows:
Figure BDA0003101134610000101
FIG. 4 is a flow chart of genetic algorithm optimization according to the present invention, interacting with the simulation process in the individual evaluation phase, and simultaneously optimizing a comprehensive objective function (as formula (15)) considering economy and safety by using the cost rate and risk rate of long-term operation as fitness functions, wherein the parameter λ can be taken from experience, thereby solving the optimal detection time interval Δ T of the objective function*。
Figure BDA0003101134610000102
In the specific implementation process, the maintenance data of the external casing component of a certain type of aircraft engine are obtained as shown in tables 1 to 3.
TABLE 1 shutdown duration of external casing part of aircraft engine
Figure BDA0003101134610000103
TABLE 2 maintenance cost of external casing parts of aircraft engines
Figure BDA0003101134610000104
TABLE 3 maintenance parameters for external casing parts of aircraft engines
Figure BDA0003101134610000111
Setting the variance of the error term during detection to be 0, and carrying out simulation with the time length of 1000h to obtain the maintenance process shown in FIG. 5, wherein the prism mark points in the graph are detection points. It can be seen that the degradation trajectory of the part changes after each maintenance, subject to the increasing factor of the failure rate and the decreasing factor of the working life, the more the number of maintenance times, the greater the tendency of the degradation process. The detection time interval Δ T is solved to obtain an optimal value of 151h, i.e., maintenance is performed at a detection interval of 151h, and meanwhile, regular maintenance is compared under the same simulation duration, as shown in table 4. The results in the table show that compared with regular maintenance, the maintenance strategy optimization based on the detection state formulated by the method can effectively reduce the occurrence frequency of faults, reduce the maintenance cost and improve the overall reliability of the component operation process.
TABLE 4 aeroengine part maintenance comparison
Figure BDA0003101134610000112
FIG. 6 is a maintenance process diagram with a detection error term added and a variance of 1e-6, and the variance of the detection error term is set to study the influence of errors caused by human factors or equipment factors on a maintenance decision process in the detection process. The results are shown in table 5, and compared with the error item without detection, the addition of the error item will result in the increase of the number of faults during detection, which corresponds to the fact that the number of false alarms is often increased in practice, and meanwhile, the larger the variance of the error item, the more significant the detection error is, which will result in the increase of the maintenance cost per unit time. Therefore, in the maintenance process of the actual aircraft engine component, the improvement of the detection capability and the reduction of the detection error of manpower or equipment are important measures for truly reflecting the degradation state of the component and reducing the maintenance cost.
TABLE 5 maintenance of the added detection error term
Figure BDA0003101134610000121
Aiming at a single-component system of an aircraft engine, a Weibull fault rate model is established by acquiring historical fault information of components; considering human or equipment errors during detection, introducing an error term based on a fault rate model to simulate a component degradation process; the influence of different maintenance behaviors and times on the degradation performance is realized by adding a fault rate increasing factor and a service life decreasing factor; adding the influence of the maintenance cost on the performance recovery into a working life decrement factor to reflect the comprehensive performance change under the influence of the maintenance times and the investment cost; setting the long-term cost rate and the failure rate including the maintenance economic cost and the shutdown loss cost as target functions, and optimizing by adopting a genetic algorithm to obtain the optimal detection interval time. The method can effectively improve the maintenance current situation of the aircraft engine, and reduce the overall maintenance cost while avoiding the fault damage caused by high failure rate of the aircraft.
Although the embodiments of the present disclosure are described above with reference to the drawings, the technical solutions of the present disclosure are not limited to two operating conditions of different rotation speeds and different loads, and include other kinds of operating conditions. The particular embodiments disclosed above are illustrative and explanatory only and are not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the disclosure as set forth in the claims that follow.

Claims (7)

1. An aircraft engine component maintenance method based on a time-varying fault rate model comprises the following steps:
step 1, establishing a fault rate model according to historical fault statistical data of an aircraft engine component, wherein fault probability distribution of the component along with operation time is established according to the historical fault statistical data of the aircraft engine component, and the fault rate model is established by fitting the fault probability distribution;
step 2, introducing a detection error term to construct a fault risk function based on a fault rate model so as to reflect the real detection of the actual decline of the aero-engine component;
and 3, adding a fault rate increasing factor and a work life decreasing factor into the fault risk function to characterize the performance improvement level of the part, wherein the performance improvement level of the i-th incomplete maintenance is as follows: lambda [ alpha ][i+1] M(t)＝biλ[i] M(t+aiΔTi)(0＜t＜ΔTi+1) Wherein b isiAnd aiRespectively a fault rate increasing factor and a service age decreasing factor, and bi＞1，0＞ai＞1，ΔTiFor the time interval of i-th and i-1-th incomplete maintenance, lambda[i] M(t) the fault risk level at time t after the ith maintenance;
step 4, comprehensively establishing a cost function based on the detection cost, the maintenance cost and the downtime;
step 5, calculating the expense rate and the risk rate based on the cost function and the fault risk function, and constructing a target function by taking the lowest expense rate and risk rate as targets;
and 6, solving the optimal detection time interval of the objective function.
2. The method according to claim 1, wherein preferably, in step 1, the fault rate model is a two-parameter weibull model:
Figure FDA0003101134600000011
where t is the aircraft runtime, β and η are the shape parameter and the scale parameter, respectively, and λ0And (t) is the probability of the component failing at time t.
3. The method of claim 1, wherein the detection error term is gaussian error E, and the fault risk function after adding the gaussian error term is:
Figure FDA0003101134600000012
wherein, beta and eta are Weibull fault rate model parameters, E is a detection error term, N (-) is Gaussian distribution, and sigma is2Is the variance of the error term, lambdaM(t) is a fault risk function that takes into account detection errors.
4. The method of claim 1, wherein in step 3, the effective age of the i-th incomplete maintenance:
Figure FDA0003101134600000021
wherein, CIPM jFor the jth incomplete maintenance cost, CPRTo replace the cost, a is a cost adjustment parameter, and
Figure FDA0003101134600000022
b is a time adjustment parameter, and 0 < b < 1, the effective work-age replacement work-age decrementing factor yields a performance improvement level that takes into account cost impact:
Figure FDA0003101134600000023
where T is the total operating time of the component since the last replacement, Δ TiThe time interval for the i-th and i-1-th incomplete maintenance.
5. The method of claim 4, wherein the cost function constructed in step 4 comprises a detection cost CmAfterward maintenance cost CaPredictive maintenance cost CpAnd cost of shutdown loss Cd。
6. The method of claim 5, wherein in step 5, the objective function comprises a charge rate CuAnd risk ratio psiuWherein, in the step (A),
Figure FDA0003101134600000024
wherein M is the total maintenance times, TmAs total flight time of the aircraft, Cm、Ca、Cp、CdCost of maintenance process, tiFor the ith maintenance time, λ[i+1] M(t) is the composite fault risk function followed before the i +1 th maintenance action.
7. The method according to claim 1, wherein in step 6, the optimal detection time interval is solved by using a genetic algorithm and taking the cost rate and the risk rate of long-term operation as fitness functions.
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