CN109033569B - Method for optimizing strength and times of preventive maintenance threshold of shipboard aircraft sensor system - Google Patents
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Abstract
The invention relates to a method for optimizing the intensity and times of a preventive maintenance threshold of a ship-based aircraft sensor system. The method comprises the steps of firstly generating a probability density function for preventing the residual degradation amount of maintenance, resolving to obtain the service life cycle and the total maintenance cost of the shipboard aircraft sensor system according to the replacement probability and the invalidation replacement probability of the prevention maintenance, resolving to obtain the long-term expected cost rate, and optimizing to obtain the optimal prevention maintenance threshold strength and the limitation of the prevention maintenance times. The method has the advantages that the service life cycle prediction model of the shipboard aircraft sensor system is described by adopting a nonlinear degradation process, the influence of two main variables of preventive maintenance threshold strength and preventive maintenance frequency limit on the long-term maintenance cost rate is considered in the optimization model, the optimal long-term maintenance cost rate is lower, and meanwhile, reference is provided for parameter setting during maintenance and repair. The reliability and the effectiveness of the method are verified through simulation experiments.
Description
(I) technical field
The invention relates to a method for optimizing the strength and times of a preventive maintenance threshold of a ship-borne aircraft sensor system.
(II) background of the invention
The main operational weapons of aircraft carriers are carrier-based aircraft. Because the number of the carrier-based aircraft carried by the aircraft carrier is limited, in order to ensure that the number of the available carrier-based aircraft meets the action requirement, the availability of the carrier-based aircraft needs to be ensured to be higher. The availability of the carrier-based aircraft mainly depends on the life cycle of each sensor, so that the method has important significance for researching factors influencing the life cycle of the sensors. The prediction and health management technology can fully utilize the state monitoring information of the system, estimate the reliability of the system in the life cycle and reduce the risk of system failure events through maintenance activities. Accurate prediction of remaining life is central and fundamental, enabling determination of appropriate maintenance opportunities. The preventive maintenance is an important component of the prediction and health management technology, so that the safety and reliability of the shipboard aircraft sensor system can be improved, and the probability of failure events is reduced. Thus, preventive maintenance is a hot issue in current research.
With the development of modern information acquisition technology, it becomes relatively easy to acquire degraded signals. In practical engineering, the degraded signal has non-linear and random characteristics. Currently, for modeling of the degradation process, a linearized model or an approximately linearized model is generally employed. Ke x.j. 2015 proposes a piecewise model of a linear-drift-based wiener process, in which two different degenerated drifts are introduced as hidden states. For nonlinear degradation processes which exist in large quantities in engineering practice, tracking estimation cannot be effectively carried out by using a linear modeling method. Sun l.w. 2015, the reliable life of the coating was studied with an accelerated degradation model, and the test data was fitted with a linear regression model, which is only suitable for analysis of the linear degradation process, with nonlinear characteristics in practice, so this method has limitations. Zio e, 2011 estimates the remaining lifetime of the nonlinear degradation process using a monte carlo method and a particle filtering method, but such methods can only obtain an approximate numerical solution and cannot obtain an analytic solution of the probability density function required for health management. Lan s., 2014 proposes a lifetime extrapolation method based on an internal circuit degradation mechanism, deduces a relationship between a degradation model parameter and an external stress, and predicts lifetimes under different voltage stresses. Peng c.y, 2009 proposes a general linear degradation path, derives an implicit expression of the product lifetime distribution, and by using contour likelihood, maximum likelihood estimates of parameters, and their confidence intervals, can be easily obtained. The linearization or approximately linearization degradation models adopted in the researches have certain limitations and are difficult to meet the requirements of actual engineering.
And the research for describing a preventive maintenance model from a degradation angle is poor. Sun f.q., 2016 proposed a new model of accelerated degradation with multiple parameters using the general wiener process, and analyzed the dependency between different degradation metrics using the Copula method. This non-linear degradation model ignores the role of preventive maintenance in the degradation process. Wang z.q., 2014 proposes a wiener process with negative jumps to predict the remaining life of a device under maintenance activity intervention, but does not involve the problem of maintenance decision. Hu J.F., 2013 provides a method for predicting the residual life of an on-site pump impeller by combining a correlation vector machine and the sum of two exponential functions, and provides a new characteristic extraction process for processing on-site vibration data so as to obtain characteristics changing along with damage of the pump impeller. Zhang x.h., 2015 proposes a residual life prediction model based on a dynamic window neural network, which mainly comprises three steps: increasing window size, changing point detection, and rolling prediction. Lassera f.s. 2015 describes a data-driven hybrid model for successful prediction of remaining useful life of an aircraft engine that combines multivariate adaptive regression spline techniques with principal component analysis and classification regression trees, elements extracted from sensor signals are used to train the hybrid model, representing different health levels of the aircraft engine, and using the hybrid algorithm to predict trends in these elements, the future health status of the system can be determined and its remaining useful life accurately estimated. These methods do not take into account the effect of preventive maintenance on the remaining life. Lei y.g., 2016 proposes a new mechanical residual life prediction method based on a stochastic process model, which constructs a new stochastic process model while considering a plurality of variables of the stochastic degradation process of the machine, and then estimates the system state by using a kalman particle filter algorithm, wherein the method only considers the influence of preventive maintenance on the residual life and does not consider the influence of preventive maintenance on the maintenance cost. There are also studies to study the impact of preventive maintenance on residual life and maintenance decisions based on linear degradation models, but real-world degradation models tend to have non-linear characteristics, and these methods need to be improved and studied in combination with non-linear degradation models.
Disclosure of the invention
The invention aims to provide a method for optimizing the intensity and times of a preventive maintenance threshold of a ship-borne aircraft sensor system.
The purpose of the invention is realized as follows:
the invention discloses a method for optimizing the intensity and times of a preventive maintenance threshold of a ship-borne aircraft sensor system, which comprises the following stepsThe method comprises a shipboard aircraft sensor system (1), a shipboard aircraft sensor system model simplification (2), a shipboard aircraft sensor system preventive maintenance degradation amount generator (3), a shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4), and a shipboard aircraft sensor system first reaching preventive maintenance threshold strength time
Generator (5), shipboard aircraft sensor system first reach the invalidation threshold strength time Ln,εA generator (6) for generating a voltage,
a probability density solver (7),
cumulative distribution function solver (8), Ln,εProbability density solver (9), Ln,εCumulative distribution function solver (10), cnThe system comprises a T moment preventive maintenance and replacement probability solver (11), (i +1) a T moment preventive maintenance and replacement probability solver (12), a K time preventive maintenance and replacement probability solver (13), an obsolete replacement probability solver (14), a shipboard aircraft sensor system life cycle solver (15), a shipboard aircraft sensor system maintenance total cost solver (16), a shipboard aircraft sensor system maintenance long-term expected cost rate target (17), and a preventive maintenance threshold strength and preventive maintenance frequency optimizer (18).
The method for optimizing the intensity and times of the preventive maintenance threshold of the shipboard aircraft sensor system comprises the following steps:
1) the shipboard aircraft sensor system (1) provides the composition of the shipboard aircraft sensor system, the shipboard aircraft sensor system (1) is simplified according to the simplification rule of the shipboard aircraft sensor system model simplification (2), and then the shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4) is used for generating the probability density function according to the intermediate variable omega (r)n) Preventing overhaul threshold strength epsiloncGenerating probability density function f (r) for preventing maintenance residual degradation amount by using the hyper-parameters omega and mun) The data are transmitted to a generator (3) for preventing overhaul degeneration of the sensor system of the shipboard aircraft, and diffusion coefficient beta and standard are combinedQuasi Brown movement B (t), drift coefficient alpha (t, theta), number of preventive maintenance times n experienced by the sensor before time t and nth preventive maintenance time tnAnd generating a preventive maintenance degradation amount Y (t).
2) The preventive maintenance degradation quantity Y (t) is transmitted to a ship-borne aircraft sensor system for reaching the preventive maintenance threshold intensity time
The generator (5) calculates the first-arrival preventive maintenance threshold intensity time
Is transmitted to
A probability density solver (7) and
the cumulative distribution function solver (8) respectively calculates the probability density of the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
3) The first invalidation threshold strength time L is transmitted to a ship-borne aircraft sensor system by preventing overhaul degeneration quantity Y (t)n,εThe generator (6) calculates the first arrival voiding threshold intensity time Ln,εIs transmitted to Ln,εProbability density solver (9) and Ln,εThe cumulative distribution function solver (10) respectively calculates the probability density f of the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn)。
4)cnThe preventive maintenance replacement probability solver (11) at the T moment has the probability density according to the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
Is solved to obtain cnProbability P (c) of preventive maintenance and replacement at time Tn) The (i +1) T moment preventive maintenance replacement probability is transmitted to an (i +1) T moment preventive maintenance replacement probability solver (12) to be solved to obtain an (i +1) T moment preventive maintenance replacement probability Pc(i +1, K), transmitting to a preventive maintenance replacement probability solver (13) for K times of preventive maintenance, and then calculating to obtain a preventive maintenance replacement probability P for K times of preventive maintenancec(T,εc)。
4) The invalidation replacement probability solver (14) has a probability density f based on the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn) Resolving to obtain a revocation replacement probability PI(T,εc)。
5) The life cycle resolver (15) of the shipboard aircraft sensor system utilizes Pc(T,εc) And PI(T,εc) Resolving to obtain the service life cycle L of the shipboard aircraft sensor system, and resolving the total maintenance cost (16) of the shipboard aircraft sensor system according to Pc(T,εc)、PI(T,εc) Expected value N of number of detectionsdAnd the cost of each detection cdExpected value N for preventing overhaul frequencymAnd each time of preventive maintenance cost cmEach time, the maintenance and replacement cost c is preventedcAnd replacement costs of each invalidation cIAnd calculating to obtain the total maintenance cost T _ C.
6) The long-term expected cost rate min (epsilon) is obtained by resolving a target device (17) for maintaining the long-term expected cost rate of the shipboard aircraft sensor system according to the life cycle L and the total maintenance cost T _ CcK) is transmitted to a preventive maintenance threshold intensity and preventive maintenance frequency optimizer (18), and the optimal preventive maintenance threshold intensity is obtained through optimization
And preventing maintenance frequency limitation K*。
The method has the advantages that the service life cycle prediction model of the shipboard aircraft sensor system is described by adopting a nonlinear degradation process, and meanwhile, the influence of two main variables of preventive maintenance threshold strength and preventive maintenance frequency limit on the long-term maintenance cost rate is considered in the optimization model. Compared with other optimization methods which aim at a variable independently, the method disclosed by the invention has the advantages that the optimal long-term maintenance cost rate is lower, the optimal preventive maintenance threshold strength and the optimal preventive maintenance frequency limit are obtained, better economic benefits can be realized, the maintenance expense is reduced on the premise of ensuring the service life cycle of the shipboard aircraft sensor system, the cost is saved, and meanwhile, a reference is provided for parameter setting during maintenance and maintenance. The reliability and the effectiveness of the method are verified through simulation experiments.
(IV) description of the drawings
FIG. 1 is a general block diagram of a method for optimizing preventive maintenance threshold strength and times for a ship-based aircraft sensor system;
FIG. 2 is a ship-based aircraft sensor fault interval time quantile graph;
FIG. 3 is a graph of accumulated failure times of a shipboard aircraft sensor;
FIG. 4 is a long term maintenance cost optimization curve.
The devices represented by the numbers in fig. 1 are as follows: 1-shipboard aircraft sensor system; 2, simplifying a ship-borne aircraft sensor system model; 3, a maintenance-preventing degradation amount generator of the shipboard aircraft sensor system; 4, a probability density function generator for preventing and repairing the residual degradation amount of the shipboard aircraft sensor system; 5-time for preventing overhaul threshold intensity of shipboard aircraft sensor system
A generator; 6-first-arrival invalidation threshold strength time L of shipboard aircraft sensor systemn,εA generator; 7- (E) -E
A probability density solver; 8- (E) -acetic acid
A cumulative distribution function solver; 9-Ln,εA probability density solver; 10-Ln,εA cumulative distribution function solver; 11- (E) -acetic acidcnThe probability solver is prevented, maintained and replaced at the moment T; a preventive maintenance replacement probability solver at the time of 12- (i +1) T; carrying out preventive maintenance and replacement probability solver after 13-K preventive maintenance; 14-invalidation replacement probability solver; 15-a life cycle resolver of a shipboard aircraft sensor system; 16-a total maintenance cost resolver of the shipboard aircraft sensor system; 17, maintaining a target of long-term expected cost rate by a ship-based aircraft sensor system; and 18, an optimizer for preventing maintenance threshold intensity and preventing maintenance times.
(V) detailed description of the preferred embodiments
The present invention is described in detail below:
as shown in figure 1, the method for optimizing the intensity and times of the preventive maintenance threshold of the shipboard aircraft sensor system comprises a shipboard aircraft sensor system (1), a shipboard aircraft sensor system model simplification (2), a shipboard aircraft sensor system preventive maintenance degradation amount generator (3), a shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4), and a shipboard aircraft sensor system firstly reaching the time of the intensity of the preventive maintenance threshold
Generator (5), shipboard aircraft sensor system first reach the invalidation threshold strength time Ln,εA generator (6) for generating a voltage,
a probability density solver (7),
cumulative distribution function solver (8), Ln,εProbability density solver (9), Ln,εCumulative distribution function solver (10), cnThe system comprises a T moment preventive maintenance and replacement probability solver (11), (i +1) a T moment preventive maintenance and replacement probability solver (12), a K times preventive maintenance is carried out and then a preventive maintenance and replacement probability solver (13), an obsolete replacement probability solver (14), a shipboard aircraft sensor system life cycle solver (15), a shipboard aircraft sensor system maintenance total cost solver (16), a shipboard aircraft sensor system maintenance long-term expected cost rate target (17), and a preventive maintenance threshold strength targetAnd a preventive maintenance times optimizer (18). The shipboard aircraft sensor system (1) provides the composition of the shipboard aircraft sensor system, the shipboard aircraft sensor system (1) is simplified according to the simplification rule of the shipboard aircraft sensor system model simplification (2), and then the shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4) is used for generating the probability density function according to the intermediate variable omega (r)n) Preventing overhaul threshold strength epsiloncGenerating probability density function f (r) for preventing maintenance residual degradation amount by using the hyper-parameters omega and mun) The data are transmitted to a ship-borne aircraft sensor system preventive maintenance degradation amount generator (3), and diffusion coefficient beta, standard Brown motion B (t), drift coefficient alpha (t, theta), preventive maintenance times n of the sensor before the time t and nth preventive maintenance time t are combinednAnd generating a preventive maintenance degradation amount Y (t). The preventive maintenance degradation quantity Y (t) is transmitted to a ship-borne aircraft sensor system for reaching the preventive maintenance threshold intensity time
The generator (5) calculates the first-arrival preventive maintenance threshold intensity time
Is transmitted to
A probability density solver (7) and
the cumulative distribution function solver (8) respectively calculates the probability density of the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
The first invalidation threshold strength time L is transmitted to a ship-borne aircraft sensor system by preventing overhaul degeneration quantity Y (t)n,εThe generator (6) calculates the first arrival voiding threshold intensity time Ln,εIs transmitted to Ln,εProbability density solver (9) and Ln,εThe cumulative distribution function solver (10) respectively calculates the probability density f of the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn)。cnThe preventive maintenance replacement probability solver (11) at the T moment has the probability density according to the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
Is solved to obtain cnProbability P (c) of preventive maintenance and replacement at time Tn) The (i +1) T moment preventive maintenance replacement probability is transmitted to an (i +1) T moment preventive maintenance replacement probability solver (12) to be solved to obtain an (i +1) T moment preventive maintenance replacement probability Pc(i +1, K), transmitting to a preventive maintenance replacement probability solver (13) for K times of preventive maintenance, and then calculating to obtain a preventive maintenance replacement probability P for K times of preventive maintenancec(T,εc). The invalidation replacement probability solver (14) has a probability density f based on the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn) Resolving to obtain a revocation replacement probability PI(T,εc). The life cycle resolver (15) of the shipboard aircraft sensor system utilizes Pc(T,εc) And PI(T,εc) And resolving to obtain the service life cycle L of the shipboard aircraft sensor system. A total maintenance cost resolver (16) of the shipboard aircraft sensor system according to Pc(T,εc)、PI(T,εc) Expected value N of number of detectionsdAnd the cost of each detection cdExpected value N for preventing overhaul frequencymAnd each time of preventive maintenance cost cmEach time, the maintenance and replacement cost c is preventedcAnd replacement costs of each invalidation cIAnd calculating to obtain the total maintenance cost T _ C. The long-term expected cost rate min (epsilon) is obtained by resolving a target device (17) for maintaining the long-term expected cost rate of the shipboard aircraft sensor system according to the life cycle L and the total maintenance cost T _ CcK). The data is transmitted to a preventive maintenance threshold intensity and preventive maintenance frequency optimizer (18) to obtain the optimal prevention through optimizationStrength of service threshold
And preventing maintenance frequency limitation K*。
The shipboard aircraft sensor system (1) comprises a plurality of sensors, and the degradation performance of each sensor influences the usability of the shipboard aircraft, so that a degradation performance model of the sensor needs to be researched to determine the remaining life of the shipboard aircraft. The 9 most prone sensors of F-14 were selected as the study subjects. The degradation data for the first sensor includes a fault interval time decitex map and an accumulated fault times map, as shown in fig. 2 and 3, respectively. The y-axis in FIG. 2 represents the quantile and the x-axis represents the time between two failures of the sensor. The y-axis of FIG. 3 represents cumulative sensor failure times and the x-axis represents cumulative time of flight.
Simplifying a model of the shipboard aircraft sensor system (2) and giving a simplifying assumption of the shipboard aircraft sensor system:
1) because the carrier-based aircraft executes tasks according to the fixed beat of the flight plan, the average flight time of each carrier-based aircraft in the air is 2 hours, the minimum detection time interval of each carrier-based aircraft is 2 hours, the detection can completely reflect the degradation level of the sensor, and the detection time is ignored.
2) Because the spare parts of the sensors carried by the aircraft carrier during the aircraft carrier is limited, in order to ensure that the usability of the carrier-based aircraft meets the quantity required by the operation, the reliability of the sensors is improved by adopting a maintenance mode as much as possible after the sensors break down, and the sensors are only replaced when the sensors are completely useless or reach the limited times of preventive maintenance.
3) It is assumed that sensor failures can be timely discovered by personnel.
4) All composite faults of a single sensor are considered to be individual faults of each sensor.
5) It is assumed that in the standby mode, the operation of the sensor is continuous.
6) It is assumed that the time required for overhaul and replacement of the sensor is negligible.
7) It is assumed that the replaced sensor has the same failure characteristics as the new sensor.
8) Preventive maintenance cannot reduce the amount of degeneration to 0, but has an effect on both the amount of degeneration and the rate of degeneration.
According to the generator (3) for preventing overhaul degeneration of the shipboard aircraft sensor system, the nonlinear degeneration process of the shipboard aircraft sensor is set as { Y (t), t is more than or equal to 0}, t represents the current time, Y (t) represents the degeneration at the time t, and the expression of Y (t) is
Wherein β represents a diffusion coefficient, B (t) represents a standard Brown motion, α (t, θ) represents a drift coefficient,
is a non-linear function, theta is an unknown parameter, alpha (t, theta) is lambda tau tτ-1τ and λ denote drift parameters, and the initial state Y (0) is set to 0.
After n times of preventive maintenance is carried out on the shipboard aircraft sensor, the shipboard aircraft sensor enters the (n +1) th stage of the life cycle, and the degeneration quantity of the shipboard aircraft sensor is as follows:
n is the number of preventive maintenance times of the shipboard aircraft sensor before the moment t, n is more than or equal to 0 and less than or equal to K, K is the limitation of the total number of preventive maintenance times, and t is the total number of preventive maintenance timesnFor the nth preventive maintenance time, rnFor the residual degradation amount after the nth preventive maintenance, r0＝0。
According to a probability density function generator (4) of the residual degradation quantity of the shipboard aircraft sensor system for preventing and repairing, r is assumednProbability density function f (r)n) Satisfies the following formula:
where ω and μ are hyperparameters, Ω (r)n) Is expressed as
Wherein epsiloncTo prevent threshold intensity of service.
Based on the first arrival time concept, the service life L of the shipboard aircraft sensor is as follows:
L＝inf{t:Y(t)≥ε|Y(0)＜ε}
wherein epsilon represents the invalidation threshold intensity of the ship-borne aircraft sensor, and inf represents the infimum limit.
Preventing the maintenance threshold intensity time according to the first arrival of a shipboard aircraft sensor system
A generator (5) for generating the residual degradation r after the nth preventive maintenance of the shipboard aircraft sensornThe degradation of the sensor is known to reach the preventive maintenance threshold intensity epsiloncTime of
Is defined as
Wherein x isnRepresenting a time increment, tnIndicating the nth preventive maintenance time.
Meanwhile, according to the first-arrival invalidation threshold strength time L of the shipboard aircraft sensor systemn,εThe generator (6) and the shipboard aircraft sensor firstly reach the time L of the invalidation threshold strength epsilonn,εIs defined as:
Ln,ε＝inf{xn:Y(tn+xn)≥ε|rn＞0,xn＞0}
according to
Probability density solver (7) and Ln,εA probability density solver (9),
and Ln,εProbability density function of
And fε,n(xn|rn) Is defined as:
according to
Cumulative distribution function solver (8) and Ln,εA cumulative distribution function solver (10),
and Ln,εCumulative distribution function of
And Fε,n(tn|rn) Is defined as:
where Φ represents a normal distribution function and P represents a probability.
The service life of the shipboard aircraft sensor can be prolonged through preventive maintenance, and the service life cycle of the shipboard aircraft sensor is terminated as follows:
(1) the end of life cycle caused by maintenance and replacement is prevented;
(2) end of life cycle due to obsolete replacement.
According to the shipboard aircraft sensor system life cycle resolver (15), the expectation of the shipboard aircraft sensor life cycle L can be defined as:
wherein T is a detection interval. j represents the jth preventive maintenance, j is more than or equal to 1 and less than or equal to K, and K is the preventive maintenance frequency. i represents the ith detection, i is more than or equal to 1 and less than or equal to N, N is the detection frequency, Pc(i +1, j) is the probability of the shipboard aircraft sensor for preventive maintenance and replacement, PIAnd (i +1, K) is the probability of the carrier-based aircraft sensor for invalid replacement.
If the degradation amount of the carrier-based aircraft sensor subjected to K times of preventive maintenance still does not reach the invalidation threshold strength, the carrier-based aircraft sensor needs to be subjected to preventive maintenance and replacement. The moment of preventive maintenance and replacement is set to be (i +1) T, and i is more than or equal to K. The shipboard aircraft sensor is replaced in the preventive maintenance and replacement activity, so that the safety and the reliability of the shipboard aircraft sensor are ensured. Setting the nth preventive maintenance time as cnT, n is more than or equal to 1 and less than or equal to K. Due to the prevention of the maintenance time cnT is random, so the probability P (c) of preventive maintenance at this moment needs to be determinedn)。
According to cnThe probability solver (11) is replaced in the preventive maintenance at the time T, if the shipboard aircraft sensor is at the time cnT (T denotes a detection interval, c)nIndicating the number of detections) is performed, i.e. (c)n-1) the amount of degradation at time T satisfies Y ((c)n-1)T)＜εcAnd c is and cnThe amount of degeneration at time T satisfies epsilonc≤Y(cnT) < ε, thus cnProbability P (c) of preventive maintenance at time Tn) Expressed as:
P(cn)＝P(Y((cn-1)T)＜εc∩εc≤Y(cnT)＜ε)＝P(Y((cn-1)T)＜εc∩Y(cnT)≥εc)-P(Y((cn-1)T)＜εc∩Y(cnT)≥ε)
using the independent incremental property of Wiener process, namely Y (c)nT)＝Y(T)+Y((cn-1) T), the above formula can be arranged as:
P(cn)
＝P(Y((cn-1)T)＜εc∩Y((cn-1)T)+Y(T)≥εc)-P(Y((cn-1)T)＜εc∩Y((cn-1)T)+Y(T)≥ε)
＝P(Y((cn-1)T)＜εc∩Y(T)≥εc-Y((cn-1)T))-P(Y((cn-1)T)＜εc∩Y(T)≥ε-Y((cn-1)T))
based on independent event theory, when the residual degradation r is not consideredn-1When random of (c)nConditional probability P (c) for preventive maintenance at time Tn|rn-1) Can be expressed as:
consider (c)n-1) amount of degradation Y at time T ((c)n-1) randomness of T), the calculation of terms 1, 2 and 3 in the above formula being:
wherein,
u, v and z represent intermediate variables.
Can obtain cnConditional probability P (c) for preventive maintenance at time Tn|rn-1) Comprises the following steps:
from the formula of total probability, cnProbability P (c) of preventive maintenance at time Tn) Comprises the following steps:
according to the preventive maintenance replacement probability solver (12) at the (i +1) T moment, the shipboard aircraft sensor carries out preventive maintenance replacement probability P at the (i +1) T momentc(i +1, K) is:
and then according to the probability resolver (13) for preventive maintenance and replacement after K preventive maintenance, the probability P for preventive maintenance and replacement of the shipboard aircraft sensor after K preventive maintenancec(T,εc) Comprises the following steps:
replacement probability solver (14), shipboard aircraft sensor according to invalidationProbability of performing a void change PI(T,εc) Can be expressed as:
due to the randomness of the performance degradation of the shipboard aircraft sensor, the shipboard aircraft sensor is possibly invalidated in any stage in the life cycle, and the replacement activities after invalidation are invalidated replacement. If the shipboard aircraft sensor is invalidated in (iT, (i +1) T) time, the invalidation replacement is divided into two situations according to the prevention and maintenance times of the shipboard aircraft sensor before invalidation.
(1) The shipboard aircraft sensor is not prevented and overhauled before being abandoned
The fact that the shipboard aircraft sensor is not subjected to preventive maintenance before being invalidated means that the preventive maintenance cannot prolong the service life of the shipboard aircraft sensor, namely, the degeneration quantity at the moment iT meets the condition that the degeneration quantity is more than epsilon in Y (iT)cIf the amount of degradation at time (i +1) T satisfies Y ((i +1) T) > epsilon, the probability P that the sensor has not been subjected to preventive maintenance before being invalidatedIThe expression of (i +1,0) is:
(2) j (j is more than or equal to 1 and less than or equal to K) preventive maintenance is carried out before the shipboard aircraft sensor is abandoned
The shipboard aircraft sensor enters the j +1 th stage of the life cycle after j times of preventive maintenance, and the shipboard aircraft sensor is invalidated in the (iT, (i +1) T) time, which means that the service life of the shipboard aircraft sensor is prolonged by the preventive maintenance, and the probability of j times of preventive maintenance performed on the shipboard aircraft sensor before invalidation is as follows:
for the maintenance and replacement processes of the shipboard aircraft sensor, the detection time, the invalidation threshold strength, the maintenance cost and the replacement cost are all fixed values. So as to obtain the optimal preventive maintenance threshold intensity epsiloncAnd preventing maintenance frequency limitation K, and selecting the long-term expected cost rate as an optimization target. Maintaining a long-term expected cost rate target (17) according to a shipboard aircraft sensor system, and optimizing a target S (epsilon)cAnd K) is represented as:
wherein, T _ C is the total cost of the life cycle of the shipboard aircraft sensor, including the prevention maintenance cost, the detection cost, the prevention maintenance replacement cost and the obsolete replacement cost. And L is the expectation of the life cycle of the shipboard aircraft sensor.
Maintaining a total cost resolver (16) from the shipboard aircraft sensor system, the total cost T _ C being expressed as:
T_C＝cdNd+cmNm+ccPc(T,εc)+cIPI(T,ε)
wherein, cdThe cost for each detection is saved. c. CmTo prevent maintenance costs each time, ccTo prevent maintenance and replacement costs each time, cIFor replacement costs each time spent, c is usually satisfiedd＜cm＜cc＜cI，NdFor expected number of detections, NmExpected value for number of overhauls.
NdAnd NmThe expressions are respectively:
according to the preventive maintenance threshold intensity and the preventive maintenance frequency optimizer (18), the optimal preventive maintenance threshold intensity is optimized by utilizing a particle swarm algorithm
And preventing maintenance frequency limitation K*A search is conducted.
The simulation parameter is alpha (t, theta) lambda tau tτ-1＝0.01*10*t9，β＝0.006，ε＝10，T＝2，ω＝0.3，μ＝0.005，εc＝8，K＝4，cd＝60，cm＝140，cc＝250，cI＝460。
The simulation results are shown in fig. 4. Optimal preventive maintenance threshold intensity by particle swarm algorithm
And preventing maintenance frequency limitation K*The results of the search were: the optimal preventive maintenance threshold intensity is 3, the number of preventive maintenance times is limited to 14, and the optimal long-term maintenance cost rate is 199 dollars/hour at the lowest. The influence of two main variables on the long-term maintenance charge rate is considered in the optimization model, compared with other methods which are used for independently aiming at the optimization result of a certain variable, the optimal long-term maintenance charge rate is lower, better economic benefit can be realized, the maintenance cost expenditure is reduced on the premise of ensuring the service life cycle of the shipboard aircraft sensor system, the cost is saved, and meanwhile, a reference is provided for parameter setting during maintenance and overhaul.
Claims (10)
1. A method for optimizing the strength and times of a preventive maintenance threshold of a shipboard aircraft sensor system comprises the shipboard aircraft sensor system (1), a shipboard aircraft sensor system model simplification (2), a shipboard aircraft sensor system preventive maintenance degradation amount generator (3), a shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4), and the shipboard aircraft sensor system firstly achieves the time of preventing the maintenance threshold strength
Generator (5), shipboard aircraft sensor system first reach the invalidation threshold strength time Ln,εA generator (6) for generating a voltage,
a probability density solver (7),
cumulative distribution function solver (8), Ln,εProbability density solver (9), Ln,εCumulative distribution function solver (10), cnThe probability solver (11) is changed in the preventive maintenance at T moment, (i +1) the probability solver (12) is changed in the preventive maintenance at T moment, K preventive maintenance back is carried out and is prevented overhauld and change probability solver (13), the probability solver (14) is changed to the abandonment, carrier-borne aircraft sensor system life cycle solver (15), carrier-borne aircraft sensor system maintains total expense solver (16), carrier-borne aircraft sensor system maintains long-term expectation rate of charge target ware (17), preventive maintenance threshold intensity and preventive maintenance number of times optimizer (18), its characterized in that:
the shipboard aircraft sensor system (1) provides the composition of the shipboard aircraft sensor system, the shipboard aircraft sensor system (1) is simplified according to the simplification rule of the shipboard aircraft sensor system model simplification (2), and then the shipboard aircraft sensor system preventive maintenance residual degradation amount probability density function generator (4) is used for generating the probability density function according to the intermediate variable omega (r)n) Preventing overhaul threshold strength epsiloncGenerating probability density function f (r) for preventing maintenance residual degradation amount by using the hyper-parameters omega and mun) The data are transmitted to a ship-borne aircraft sensor system preventive maintenance degradation amount generator (3), and diffusion coefficient beta, standard Brown motion B (t), drift coefficient alpha (t, theta), preventive maintenance times n of the sensor before the time t and nth preventive maintenance time t are combinednGenerating a preventive maintenance degradation amount Y (t);
the preventive maintenance degradation quantity Y (t) is transmitted to a ship-borne aircraft sensor system for reaching the preventive maintenance threshold intensity time
The generator (5) calculates the first-arrival preventive maintenance threshold intensity time
Is transmitted to
A probability density solver (7) and
the cumulative distribution function solver (8) respectively calculates the probability density of the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
The first invalidation threshold strength time L is transmitted to a ship-borne aircraft sensor system by preventing overhaul degeneration quantity Y (t)n,εThe generator (6) calculates the first arrival voiding threshold intensity time Ln,εIs transmitted to Ln,εProbability density solver (9) and Ln,εThe cumulative distribution function solver (10) respectively calculates the probability density f of the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn)；
cnThe preventive maintenance replacement probability solver (11) at the T moment has the probability density according to the first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
Is solved to obtain cnProbability P (c) of preventive maintenance and replacement at time Tn) The (i +1) T moment preventive maintenance replacement probability is transmitted to an (i +1) T moment preventive maintenance replacement probability solver (12) to be solved to obtain an (i +1) T moment preventive maintenance replacement probability Pc(i +1, K), transmitting to a preventive maintenance replacement probability solver (13) for K times of preventive maintenance, and then calculating to obtain a preventive maintenance replacement probability P for K times of preventive maintenancec(T,εc) I represents the ith detection;
the invalidation replacement probability solver (14) has a probability density f based on the first-arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(tn|rn) Resolving to obtain a revocation replacement probability PI(T,εc)；
The life cycle resolver (15) of the shipboard aircraft sensor system utilizes Pc(T,εc) And PI(T,εc) Resolving to obtain the service life cycle L of the shipboard aircraft sensor system, and resolving the total maintenance cost (16) of the shipboard aircraft sensor system according to Pc(T,εc)、PI(T,εc) Expected value N of number of detectionsdAnd the cost of each detection cdExpected value N for preventing overhaul frequencymAnd each time of preventive maintenance cost cmEach time, the maintenance and replacement cost c is preventedcAnd replacement costs of each invalidation cICalculating to obtain total maintenance cost T _ C;
the long-term expected cost rate min (epsilon) is obtained by resolving a target device (17) for maintaining the long-term expected cost rate of the shipboard aircraft sensor system according to the life cycle L and the total maintenance cost T _ CcK) is transmitted to a preventive maintenance threshold intensity and preventive maintenance frequency optimizer (18), and the optimal preventive maintenance threshold intensity is obtained through optimization
And preventing maintenance frequency limitation K*。
2. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: the probability density function f (r) for preventing and repairing residual degradationn) The method comprises the following steps:
where ω and μ are hyperparameters, Ω (r)n) Is expressed as
εcTo prevent threshold intensity of overhaul, rnThe residual degradation amount after the nth preventive maintenance is carried out, and n is the advance experienced by the shipboard aircraft sensor before the moment tAnd (5) preventing maintenance times.
3. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: the first-arrival preventive maintenance threshold intensity time
The method comprises the following steps:
wherein x isnRepresenting a time increment, tnDenotes the nth preventive maintenance time, inf denotes an infimum limit, Y (t) denotes the amount of degeneration at time t, εcTo prevent threshold intensity of overhaul, rnThe residual degradation amount after the nth preventive maintenance is obtained.
4. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: probability density of first-arrival preventive maintenance threshold intensity time
And cumulative distribution function
The method comprises the following steps:
where Φ represents a normal distribution function, P represents a probability, and xnRepresents a time increment, rnThe residual degradation amount after the nth preventive maintenance is obtained.
5. The method for the preventive maintenance threshold intensity and times optimization of the shipboard aircraft sensor system according to the claim 1,the method is characterized in that: probability density f of the first arrival invalidation threshold intensity timeε,n(xn|rn) And cumulative distribution function Fε,n(|) means:
wherein epsilon represents the invalidation threshold strength of the shipboard aircraft sensor.
6. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: k preventive maintenance is carried out and probability P of replacement is maintainedc(T,εc) The method comprises the following steps:
wherein,
t is the detection interval, cnRepresenting the detection times, u representing an intermediate variable, i representing the ith detection, and epsilon representing the invalidation threshold strength of the shipboard aircraft sensor.
7. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: the invalidation replacement probability PI(T,εc) The method comprises the following steps:
wherein, Pc(T,εc) And the preventive maintenance replacement probability is shown after K preventive maintenance.
8. The preventive maintenance threshold strength and secondary maintenance threshold strength for the shipboard aircraft sensor system according to claim 1A method of number optimization, characterized by: the service life cycle L of the shipboard aircraft sensor system is as follows:
wherein T is a detection interval, j represents the jth preventive maintenance, j is more than or equal to 1 and less than or equal to K, K is the preventive maintenance frequency, i represents the ith detection, i is more than or equal to 1 and less than or equal to N, N is the detection frequency, P isc(i +1, j) is the probability of the shipboard aircraft sensor for preventive maintenance and replacement, PIAnd (i +1, K) is the probability of the carrier-based aircraft sensor for invalid replacement.
9. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: the total maintenance cost T _ C refers to: t _ C ═ CdNd+cmNm+ccPc(T,εc)+cIPI(T, ε) wherein cdThe cost for each detection; c. CmTo prevent maintenance costs each time, ccTo prevent maintenance and replacement costs each time, cIFor replacement costs each time spent, c is usually satisfiedd＜cm＜cc＜cI，NdFor expected number of detections, NmExpected value for number of overhauls.
10. The method for preventing the overhaul threshold strength and times optimization of the shipboard aircraft sensor system according to claim 1, wherein the method comprises the following steps: the long-term expected cost rate min (epsilon)cAnd K) means:
t _ C is the total cost of the life cycle of the shipboard aircraft sensor, including the prevention maintenance cost, the detection cost, the prevention maintenance replacement cost and the obsolete replacement cost, and L is the expectation of the life cycle of the shipboard aircraft sensor.
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