An optimization method for condition based maintenance (CBM) of aircraft fleet considering prognostics uncertainty is proposed. The CBM and dispatch process of aircraft fleet is analyzed first, and the alternative strategy sets for single aircraft are given. Then, the optimization problem of fleet CBM with lower maintenance cost and dispatch risk is translated to the combinatorial optimization problem of single aircraft strategy. Remain useful life (RUL) distribution of the key line replaceable Module (LRM) has been transformed into the failure probability of the aircraft and the fleet health status matrix is established. And the calculation method of the costs and risks for mission based on health status matrix and maintenance matrix is given. Further, an optimization method for fleet dispatch and CBM under acceptable risk is proposed based on an improved genetic algorithm. Finally, a fleet of 10 aircrafts is studied to verify the proposed method. The results shows that it could realize optimization and control of the aircraft fleet oriented to mission success.
Prognostic and health management (PHM) technology has a rapid development and been widely used in aeronautical equipment in recent years. The failure position and remain useful life (RUL) of equipment could be predicted by PHM. Further, it can be used in aircraft condition based maintenance (CBM) [
The aircraft usually performs mission in fleet manner and shares limited support resource. So, there will be a tradeoff range for fleet CBM. This means each aircraft can choose strategy among dispatching strategy, standby strategy, and maintenance strategy or their combination when the RUL has been obtained, and the synthetic strategy for fleet (combination of each aircraft’s strategy) should meet the mission requirement.
There are three forms of RUL in PHM, and each form includes some uncertainty. First is the point value of the time of potential failure. Second is the interval value of the time of potential failure [
Two methods can be used in reducing the impact of prognostics uncertainty on CBM decision. One is to reduce the uncertainty of failure prediction directly so that the decision risk will decrease [
Most research about RUL for CBM is about the life cycle maintenance optimization decisions on single aircraft and researchers would rather consider the maintenance decisions than think about the mission requirements and the dispatched strategy. The research on fleet CBM oriented to mission successes is few. Agent technology and the heuristic algorithm are used to fleet CBM in article [
An optimal aircraft fleet CBM method for aviation unit maintenance is proposed in the paper considering dispatch, mission, and resource constraints. Moreover, the RUL distribution of the key LRM has been transformed into the failure probability of the aircraft, and the calculation method of the costs and risks for mission is given. Then, an optimization decision making method for fleet dispatch and CBM under acceptable risk is proposed based on an improved genetic algorithm.
Consider an aircraft fleet containing
CBM for aircraft fleet.
The basic assumptions of the problem are listed below in order to define the problem.
The aircraft fails when any key LRM fails.
The RUL distribution of LRM which is given at the time
Assume the maintenance method of the LRM is renew, which means the LRM will be as good as new after maintenance, considering the field maintenance of aviation unit maintenance.
Only one aircraft can be repaired in each ISS simultaneously. But the total number of the aircraft maintenance may be more than one from the time
Different LRM in the same aircraft can be replaced at the same time for renew is served as a maintenance method.
The maintenance cost of the different LRM varied while the same LRM cost is the same. The maintenance cost of the LRM on
Each aircraft malfunction will cause the mission to fail when the fleet is on mission. The consequences of the economic loss will not be taken into consideration.
Spare parts are plentiful.
The main work of the optimization decision making method for fleet CBM considering prognostics uncertainty includes the following steps:
Modeling framework for CBM of aircraft fleet.
Assume the distribution of the
Considering an aircraft fleet containing
Maintenance program considers whether a certain LRM should be maintained and the selection of the ISSs.
The maintenance matrix
According to the assumption
Assume repairing the
There may be more than one aircraft that should be repaired at ISS
The total maintenance cost of all aircrafts can be got as
Whether the aircraft is “dispatching” or “dispatching after maintenance” should be taken into consideration when calculating the mission risk of the fleet. The status of the aircraft should be updated if the single strategy of the fleet is “dispatching after maintenance.” Then, the modified health status matrix
The failure probability of the single aircraft could be estimated after modifying the health matrix of the fleet. According to the first assumption, “the aircraft fails when any key LRM fails”; the failure probability
Formula (
Then,
Suppose
Assume the serious consequences of the mission that failed are similar without taking the economic losses into account. The failure probability of the fleet mission can be calculated by the following according to (
The optimization problem in the paper is to find a fleet CBM strategy with acceptable risk and lowest cost considering prognostics uncertainty.
Thus, describe the objective of the optimization as
The constraints that should be considered about involve the maintenance ability constraint
For first constraint
All maintenance of site
Assume that the total number of the aircraft which maintained at site
It will not be allowed to dispatch if the failure probability is too high for security risk existing in single aircraft. Consider a mission need
According to (
The variable constraint, which means that the variables should be in a certain range, is described as
The conceptual model for aircraft fleet condition based maintenance and dispatch is given as follows:
The optimization problem cannot meet the KKT (
The optimization model can be simplified as
The problem has more variables and constraints, so the solution quality of problem and the convergence rate could not be satisfied. Therefore, the improvement strategy of the genetic algorithm is given in Figure
Improved strategies for genetic algorithm.
According to the multifactor and 2level orthogonal experimental design in order to cover widely, define the initial population of the maintenance matrix
It is necessary to find a set of feasible solutions which meet the constraint of the ability of ISS
According to formula (
Consider that there are
The maintenance time
Initialize the matrix
Set the value of the matrix
Calculate the value of
Remove the line in which the aircraft
Compare the
The matrix
Some matrix
The energy function for every
The fitness function is given as follows in order to minimize the objective function:
Proportional selection, singlepoint crossover, and the basic alleles can be used in solving this problem.
This problem can be dealt with by some method written in the article [
Simulate the annealing stretching for fitness before selecting the operator as follows:
Consider a fleet containing 10 aircrafts and each aircraft includes 4 LRM (A, B, C, D) of which life can be predicted. Assume the RUL following Gaussian distributions
The RULs of the LRM.
Number  1  2  3  4  5  6  7  8  9  10 

LRM_{A}  (25, 7.7)  (19, 4.4)  (29, 8.3)  (29, 9.1)  (13, 3.8)  (20, 5.7)  (21, 6.3)  (20, 6.2)  (9, 2.5)  (21, 5.9) 
LRM_{B}  (28, 7.4)  (3, 0.7)  (29, 6.6)  (15, 3.3)  (28, 8.5)  (2, 0.5)  (23, 5.6)  (6, 1.3)  (2, 0.5)  (10, 2.8) 
LRM_{C}  (4, 1.0)  (9, 2.9)  (5, 1.2)  (25, 5.7)  (24, 7.1)  (26, 7.9)  (23, 6.1)  (22, 7.2)  (3, 0.8)  (29, 9.1) 
LRM_{D}  (28, 7.5)  (17, 5.6)  (30, 7.9)  (5, 1.2)  (29, 7.9)  (29, 7.1)  (12, 3.5)  (1, 0.3)  (25, 6.4)  (2, 0.6) 
The mission requires dispatch 8 aircrafts one hour later and lasting two hours.
Assume there are 3 ISSs, of which ability of the maintenance are the same, being in charge of all aircrafts’ maintenance. The maintenance time and cost of each LRM is given in Table
The maintenance time of the LRM.
LRM  A  B  C  D 

Maintenance time  20 min  25 min  11.6 min  16.6 min 
Maintenance cost  2348.2  2843  1297.3  1009.2 
Consider that there are 100 individuals in populations, and one of these individuals is described as follows:
Set up the
Result of calculation.
The total cost of the maintenance is 14439.3 and the mission risk is 8.95
Then, optimal maintenance program can be written as Table
The optimal scheme for aircraft fleet CBM and dispatching.
Aircraft number  1  2  3  4  5  6  7  8  9  10 

ISS 1  LRM_{C}  /  /  /  /  LRM_{B}  /  /  /  / 
ISS 2  /  /  LRM_{C}  /  /  /  /  LRM_{B/D}  /  / 
ISS 3  /  /  /  LRM_{D}  /  /  /  /  /  LRM_{B/D} 


Dispatch?  Yes  No  Yes  Yes  Yes  Yes  Yes  Yes  No  Yes 
Then, the optimal scheme of aircraft CBM and dispatching are described completely in Table
This paper researches optimization decision method for aircraft fleet CBM oriented to mission success considering prognostics uncertainty and the resource constrain. The CBM and dispatch process of fleet is analyzed; the modeling method and an improved genetic algorithm for the problem are given, and the method is verified by case about fleet with 10 aircrafts.
The main advantages of this method are shown as follows.
The alternative strategy sets for single aircraft are defined; then, the optimization problem of fleet CBM is translated to the combinatorial optimization problem of single aircraft strategy. The relationship between maintenance strategy and mission risk is established, and the problem becomes easier to solve.
This paper used the RUL distribution, which has the maximum information and the highest in prognostics. It has more accurate description of the uncertainty compared with others.
The optimization decision with risk for fleet CBM is realized. The fleet mission risk is quantitatively assessed, and the optimal CBM strategy for fleet could satisfy the requirement of lowest maintenance cost and acceptable risk.
This paper presents a theoretical approach for fleet CBM considering prognostics uncertainty. Some factors have been simplified, such as the cost of risk, the consequences of risk mission, the effect of the CBM process form ability of maintenance personnel, and the effect of random failures. The focus of further work is a more detailed and comprehensive model considering all above factors.
The authors declare that there is no conflict of interests regarding the publication of this paper.