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A method for flight test subject allocation on multiple test aircrafts based on improved genetic algorithm

  • Yibo LiuEmail author
  • Gang Xiao
  • Miao Wang
  • Tao Li
Review
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Abstract

The civil aircraft flight test technology is complex and related to many systems. The efficiency and rationality of the flight test task planning has become one of the key factors affecting the flight test duration and cost. In the initial planning process of the flight test task, the allocation of a large amount of flight test subjects on multiple test aircrafts is a key issue. There are many shortcomings in manual planning based on work experience. However, the information about the existence of related automated assist algorithms or tools has not been found in the public information. Through the research on the workflow of the current civil flight test and the communication with the relevant departments, the main influencing factors and constraints related to the allocation of flight test subjects were summarized in this paper. The allocation process was simplified, and the core mathematical problem extracted and modeled. A method based on improved genetic algorithm to generate the flight test subject allocation scheme was designed. The superiority of the algorithm was proven by comparing with the research results of related reference literature. The case simulation of several engineering practical application scenarios was carried out, which demonstrated the prospect of this method being put into practical engineering applications.

Keywords

Flight test Flight test subject Genetic algorithm Flight test subject allocation Combination optimization problem 

1 Introduction

1.1 Allocation of flight test subjects

The civil aircraft flight test refers to the process of indicating the conformity of the civil aircraft model and obtaining the airworthiness certificate during the design and development process of the civil aircraft. This is the last and most important part of the civil aircraft model before it is put into commercial operation. In this session, the civil aircraft design and manufacture company must pass a series of flight tests to show that it meets the current airworthiness requirements of the Bureau for Civil Aircraft [1].

The civil aircraft flight test technology is complex and related to many systems. The efficiency and rationality of the flight test planning has become one of the key factors affecting the flight test duration and cost. In the initial planning process of the flight test task, the allocation of a large amount of flight test subjects on multiple test aircrafts is a key issue, which requests considering both cost and flight test duration, as well as various constraints related to subjects and test aircrafts. In public information, the relevant automation assist algorithms or tools was not found. Due to the changes in various conditions and the predictability of planning, it is impossible for the initially determined flight test plans to completely cover subsequent changes, so the flight test plan will be continuously adjusted as the flight test progresses [2]. If it is adjusted manually, due to the complicated constraint relationship between the subject and the flight test aircrafts, even a small adjustment of the subject allocation scheme will bring a huge workload. An automated assist algorithm can greatly reduce the workload. With the development of digital technology, the modern plane design and manufacture has been improved to a new level, then the digital flight test is inevitable trend in the future [3]. Therefore, it is necessary to develop corresponding digital assistant planning methods.

The allocation problem of a large amount of flight test subjects on multiple test aircrafts is a combinatorial optimization problem and a task planning problem. Typical combination optimization problems include BPP (bin packing problem) [4], TSP (traveling salesman problem) [5], JSP (job-shop scheduling problem) [6],etc., task planning problems such as multi-agent collaborative task assignment [7], personnel collaborative task planning [8], drone multi-target task planning problem [9], weapon target allocation [10], etc.

However, research specifically on the flight test subject allocation problem, which is a combination optimization problem under special constraints, is rare.

Due to the complexity of test aircraft constraints and subject constraints, this problem is different from the classical combinatorial optimization problem. It is difficult to apply mature methods, and the research results of similar problems are very rare. The problem that we find closest to the constraint of it is multi-seats collaborative task planning [7]. The task priority constraint proposed by this paper is very consistent with the requirements of the flight test subject, but still there are no corresponding constraints to the window period or the test aircraft deployment time.

In summary, the allocation problem of a large amount of flight test subjects on multiple test aircrafts is a combination optimization problem under a new application scenario.

Generally speaking, there are two methods for solving combinatorial optimization problems, the exact solution method and the approximate solution method. More use in the combinatorial optimization problem is an approximate solution method that achieves better solutions as far as possible, including heuristics and meta-heuristics [11].

1.2 Genetic algorithm

The genetic algorithm simulates the problem to be solved into a process of biological evolution. After evolution for many generations, it is very likely that individuals with high fitness score will evolve.

Genetic algorithm provides a general framework for solving complex system optimization problems. It does not depend on the specific field of the problem, so it is widely used in many disciplines [12]. For problems like JSP, traditional graph theory search methods often encounter combinatorial explosion problems. Genetic algorithms are an effective way to solve such problems. The algorithm can obtain the optimal solution or suboptimal solution of the problem without traversing the solution space [13].

1.3 Main content of this article

Based on the research of the current flight test task planning process and the characteristics of flight test subject, the main influencing factors and constraints related to the allocation of flight test subjects are summarized, The allocation process is simplified, and the core mathematical problem is extracted and modeled. A method based on improved genetic algorithm to generate the flight test subject allocation scheme is designed, which is used to solve the problem of reasonable allocation of flight test subjects on multiple test aircrafts.

Based on the established mathematical model, a simple coding method is designed to represent the assignment of subjects on the test aircraft; sorting all subjects by batch activation, all the constraints are satisfied, a fitness score calculation model adapted to the coding mode is established; the screening process is improved to avoid population deterioration; an adaptive genetic operator is designed to optimize the crossover and mutation processes.

Based on the data of Ref. [7], the simulation was carried out with the flight test duration as the fitness score. When the constraint setting is the same as in Ref. [7], the comparison of the simulation results proves the superiority of the method.

Then, considering the requirements in the actual flight test engineering, the constraints are added based on the original model, the simulations are carried out under various initial conditions, and satisfactory results are obtained, which shows the effectiveness of this method.

This method has been recognized by professional flight test engineers and is considered to have broad engineering application prospects.

2 Key factors extraction and mathematical modeling

2.1 Key factors of flight test subject allocation

One of the main tasks in the initial planning phase of the flight test is to develop an allocation scheme to distribute flight tests subjects to several test aircrafts. The test missions undertaken on each test aircraft have different mission execution priorities, and the implementation of the subjects should consider different pre-subject requirement, aircraft test modifications, aircraft configuration and ground support constraints [3].

The factors that need to be considered in the preparation of the flight test plan are: the distribution of tasks on the test aircraft, the logical relation of the subjects, the configuration requirement of the subject, the aircraft system configuration plan, the flight test aircraft modification plan, the special flight test window period and related ground test plans, etc. It is also necessary to sort out the subjects that can be considered together.

Through the communication with the civil aircraft flight test department, combined with the actual engineering requirements, the factors related to the allocation of the flight test subjects on test aircrafts are simplified. The attributes that must be considered in the flight test subjects and the constraints in the subject allocation process are summarized in this section.

The subject attributes are: subject name, subject flight test duration, pre-test subjects (Fig. 1);
Fig. 1

The key influencing factors

Allocation constraints The number of test aircrafts, the deployment time of test aircraft, special flight test window period, and test aircraft limitation. These terms are introduced separately below.

2.1.1 Subject flight test duration

In this paper, by default, in the initial planning stage, the flight test department can give an estimate value of subject flight test duration based on experience for the initial flight test preparation. In fact, there are many factors that need to be considered when estimating the duration, including test aircraft modification, configuration change, installation of parameter acquisition equipment, the duration of the flight period and the flight delays, delays due to uncertainties, repeated flight duration of the same subject, etc.

2.1.2 Pre-execution subject

According to the flight test requirements, when planning the flight test and developing a detailed flight test plan, it is necessary to consider the constraint relationship between various task requirements. One of the most important constraints is the existence of pre- and post-constraints between different subjects.

For example, the flight test subjects such as stall speed and pole curve, they must be performed after subjects such as airspeed system calibration and atmospheric temperature calibration [14]. Therefore, each flight test subject has a collection of pre-execution subjects. This subject can only be executed after all flight test subjects in the pre-execution subjects are completed.

2.1.3 The deployment time of test aircraft

The test aircrafts are not manufactured at the same time, and their deployment time needs to be considered in the subject allocation process.

2.1.4 Special flight test window period

Some flight test subjects, such as natural icing, require special modifications, meteorological conditions or geographical conditions. The window period for these special subjects is determined at the beginning of the flight test plan. These subjects cannot be executed outside the window period; some other subjects need to wait for the completion of aircraft configuration, so these subjects have an earliest execution time which means that they cannot be executed until this time. For the above two types of special subjects, the window period constraints must be considered during the planning.

2.1.5 Test aircraft limitation

Subjects in one subject group can only be tested on specified test aircrafts. The test aircraft task assignment has a defined process. Generally, the flight test subjects (such as stall, flutter, envelope extension, control law adjustment) closely related to the verification of the aircraft platform are prioritized, and these subjects are usually arranged on the first two flight test aircrafts.

Flight test tasks with clear pre-requisite requirements (such as engine thrust determination flight test is the predecessor of most performance flight tests) are arranged on the corresponding aircraft according to test modification requirements, flight mechanism requirements and flight test tasks. Some special flight test tasks will be arranged on the test aircraft with relevant test modification conditions and corresponding configuration.

2.2 Mathematical modeling

Because the main purpose of this study is to extract the core mathematical problems in the process of subject allocation and try to solve it, temporarily we do not consider the test aircraft limitation and the subject name is represented by S plus account number such as S{3}.

Allocation constraints: number of test aircrafts, the deployment time of test aircraft, and special flight test window period. These terms are introduced separately below.

Flight test subject parameters: subject name, subject flight test duration, and pre-execution subjects. The definition of each attribute is as follows:
  • Subject name The name of the flight test subject should be unique and should be used as one of the distinguishing marks between different subjects.

  • Subject flight test duration In the algorithm development phase, the specific time can be converted to a value from 0 to 20.

  • Pre-execution subjects Represented by an array, the elements in the array are the account number of the subject, and each number uniquely corresponds to a flight test subject. If there is no pre-execution subject, the array is empty. In particular, the account number of the predecessor subjects must be bigger than the subject account number.

  • The deployment time of test aircraft Suppose there are N test aircraft, the deployment time is represented by an N-dimensional array, and each element represents the deployment time of the corresponding aircraft

  • Special flight test window period We use an array to represent. Each element is a three-dimensional array representing the account number, the earliest execution time and the latest execution time. For example: {[3 5 inf], [11 12 15]} means there are two special subjects, the earliest executable time of the subject no. 3 is 5, for subject no. 11, the earliest execution time is 12 and the latest execution time is 15.

3 Improved genetic algorithm design

3.1 Genetic algorithm workflow

The genetic algorithm begins with a population that represents a potential set of solutions to a problem; a population consists of a certain number of individuals coded by genes. After the initial generation of the population, according to the principle of “survival of the fittest”, the evolution of generations produces more and better approximate solutions. In each generation, the individual is selected according to the individual’s fitness value; crossover and mutation are performed with a certain probability to generate a new population. This process will make the offspring population more adaptable to the environment than the previous generation. The optimal individual in the last generation population is decoded and can be used as the approximate optimal solution of the problem [12] (Fig. 2).
Fig. 2

Traditional genetic algorithm flow

The problem of the allocation of a large amount of test subjects on multiple test aircrafts is a combinatorial optimization problem. As the scale of the problem expands, the search space for combinatorial optimization problems expands dramatically. Sometimes, it is difficult or even impossible to obtain an accurate optimal solution using the enumeration method on current computers. For such complex problems, people have realized that they should focus on finding a satisfactory solution, and genetic algorithm is one of the best tools for seeking such a satisfactory solution.

3.2 Improved genetic algorithm design

In this paper, a simple yet unique coding method is proposed, matching process of crossover and mutation is designed, and genetic operators are designed to vary linearly, rather than being fixed in traditional algorithm. The traditional screening method is improved, too. In traditional algorithm, excellent individuals have a high chance of being retained, but may still be screened out. In this paper, the best 1% of individuals in every generation will not be eliminated. The total flight test duration is used as the fitness score. A fitness score calculation model which can automatically satisfy the constraints is established. In the calculation model, all the constraints are met by arranging the subjects in batches in the order of activation.

3.2.1 Coding process

Coding is to compile the solution of the problem into a form like a biological chromosome, to mimic the chromosome of the organism, thereby facilitating operations such as crossover and mutation. The coding method depends on the specific constraints of the problem.

The coding method of this paper is: suppose there are N test aircrafts, the amount of flight test subjects is Sn, and the code of each chromosome is an Sn dimension array, each element randomly takes an integer from 1 to N. That is, all subjects are randomly assigned to all test aircraft. The specific arrangement on each aircraft is confirmed by the fitness function calculation model. Due to the limitation of the pre-execution subjects’ account number and the activation order, the uniqueness correspondence between the code and the corresponding planning scheme can be guaranteed.

3.2.2 Initial population generation

For a given subject group, codes can be randomly generated as different individuals and many such individuals can be used as the initial population.

3.2.3 Fitness score calculation model

The total flight test duration is used as the fitness score and the duration is calculated according to the code:
$$D = {\text{Duration}}\;({\text{code}}).$$
(1)

Calculating the total flight test duration, there are many constraints to consider. It is difficult to derive a fitness score in the form of a mathematical formula; therefore, a separate fitness score calculation model needs to be established. In the process of calculating the flight test duration D, it is necessary to consider the various constraints mentioned above.

The process of calculating the flight test duration corresponding to the code is as follows: the subjects are activated in batches according to the requirements of the pre-execution subject, and only the activated batch of subjects is arranged on the aircraft each time (Fig. 3).
Fig. 3

Decoding process

The activation requirement is defined as condition, and the first batch of activated subjects is the subject with no pre-execution subject. These subjects are arranged according to their code to the corresponding test aircraft, and then the account number of these subjects is added to the condition.

Then we activate the remaining subjects whose pre-execution requirement is within the updated condition and repeat the above process until the condition length is the same as Sn. Since the subject account number must be bigger than the number of its pre-execution subjects, the correspondence between the coding and the planning scheme is unique.

The account number and the start time of the arranged subjects will be recorded. When a subject is arranged on the aircraft, the start time correction must be performed first to avoid the overlap of subjects and the violation of the requirements of the pre-execution.

After the decoding process, with all subjects’ start time recorded, the total duration can be calculated as the fitness score of this individual.

3.2.4 Screening

The traditional roulette probability method is improved for screening. Since the solution space is not continuous, small changes in coding are likely to cause large changes in fitness score. Using traditional screening methods tends to cause errors to eliminate the optimal individuals and cause population deterioration, So, the screening rules are improved. The best 1% of individuals will not be eliminated.

3.2.5 Crossover and mutation

To ensure that the best individuals will not change due to the process of crossover or mutation, a linearly varying genetic operator is designed in this paper. Set the crossover probability pc and the mutation probability pm, the probability of crossover, mutation of the best individual is zero and the probability of the worst individual is PC, PM. Sort by fitness score from large to small. For the no. I individual in the population, its probability of mutation is:
$${\text{pm}} = \frac{{\left( {{\text{PM}} \times (i - 1)} \right)}}{{{\text{ps}} - 1}},$$
(2)
where ps represents population scale. The probability calculation of crossover is similar to the mutation one.

4 Application of the improved genetic algorithm

To verify the feasibility and effectiveness of the algorithm, this paper uses MATLAB to carry out simulation calculation based on the case data in Ref. [7]. First, set the condition that there is no test aircraft deployment time constraint or special subject window period constraint, that is, under the same initial condition as in Ref. [7].

The simulation results were calculated, the best results of 23 subjects under the conditions of four test aircrafts were obtained. Then the number of test aircrafts was reduced to three, and the same shortest time as the four test aircrafts was obtained; next, the deployment time constraints and the special subject window period constraints were added in sequence and satisfactory results were obtained.

4.1 Initial condition setting

Use the cell data format in MATLAB to store the information of the flight test subjects. After the data of Ref. [7] is processed according to the requirements of this article, the definition of the subject is as shown in the Table 1.
Table 1

Subject data setting

Subject account number

Subject duration

Account number of pre-execution subject

1

4

[]

2

4

[1]

3

10

[2]

4

2

[3]

5

2

[3]

6

5

[4]

7

4

[5]

8

5

[6]

9

7

[5 8]

10

3

[9]

11

3

[1]

12

3

[1]

13

5

[8]

14

9

[10 12]

15

3

[10]

16

2

[10 11]

17

6

[16]

18

3

[10]

19

3

[10]

20

3

[14 17]

21

3

[13]

22

3

[21]

23

3

[15 18 19 20]

It is important to point out that the duration here does not have a meaningful unit. For ease of understanding, the unit of duration is defined as day.

A subject is represented as S {account number} {flight duration, [pre-execution subjects]}.

S stands for the subject. The number in the braces after S is the account number of the subject in the entire subject set, which acts like a database primary key to determine the location of the subject.

The meaning and requirements of each element are as described in Sect. 2.

4.2 Result display

4.2.1 No special constraint, four aircrafts

The genetic algorithm parameter setting is as shown in Table 2.
Table 2

Genetic algorithm parameter setting (1)

Parameter name

Parameter meaning

Parameter value

PC

Maximum crossover probability

0.8

PM

Maximum mutation probability

0.8

Popsize

Population size

20

slnm

Number of iterations

10

N

Total aircraft number

4

DT

Test aircraft deployment time

[0 0 0]

Reference [7] applies the improved particle swarm optimization algorithm. The relationship between the optimal time and the number of iterations is shown in the Fig. 4. It is necessary to iterate more than 100 times to get the convergence result. Applying the improved genetic algorithm proposed in this paper, under the condition that the population size is set to 20, after many experiments, most of the time, only one time of iteration is needed to find the best arrangement. Two task planning Gantt charts generated by improved genetic algorithm are shown in Figs. 5 and 7. Each rectangle represents a subject, the text in the rectangle represents the account number of the subject, and the length of the rectangle represents the flight duration of the subject. All subjects met its pre-execution constraints (Figs. 6, 7, 8).
Fig. 4

Improved particle swarm optimization iterative process

Fig. 5

Task planning Gantt chart (1)

Fig. 6

Improved genetic algorithm iterative process (1)

Fig. 7

Task planning Gantt chart (2)

Fig. 8

Improved genetic algorithm iterative process (2)

4.2.2 No special constraint, three aircrafts

Only the total number of test aircraft was changed from four to three, while the remaining initial conditions were unchanged. The results obtained are shown in Fig. 9. It shows that after reducing the number of test aircrafts, the adoption of a more compact subject arrangement does not result in an increase in the minimum flight duration. This provides a basis for decision making on the number of test aircrafts during the initial planning phase of the flight test (Table 3; Fig. 10).
Fig. 9

Task planning Gantt chart (3)

Table 3

Genetic algorithm parameter setting (2)

Parameter name

Parameter meaning

Parameter value

PC

Maximum crossover probability

0.8

PM

Maximum mutation probability

0.8

Popsize

Population size

20

slnm

Number of iterations

10

N

Total aircraft number

3

DT

Test aircraft deployment time

[0 0 0]

Fig. 10

Improved genetic algorithm iterative process (3)

4.2.3 With deployment time constraint, four aircrafts

Add constraint of aircraft deployment time. As shown in Table 4, the deployment time of the four aircraft is 0, 10, 20, and 30, respectively. Since the constraints are more complex, both the population size and the number of iterations need to be increased to get satisfactory results. The task planning Gantt chart and the iterative process are shown in Figs. 11, 12. The red wireframe represents the deployment preparation phase at which no subjects can be scheduled on the aircraft. It shows that the best time still converges to 55, which proves that the algorithm in this paper can get the best arrangement while satisfying the constraints.
Table 4

Genetic algorithm parameter setting (3)

Parameter name

Parameter meaning

Parameter value

PC

Maximum crossover probability

0.8

PM

Maximum mutation probability

0.8

Popsize

Population size

200

slnm

Number of iterations

100

N

Total aircraft number

4

DT

Test aircraft deployment time

[0 10 20 30]

Fig. 11

Task planning Gantt chart (4)

Fig. 12

Improved genetic algorithm iterative process (4)

4.2.4 With deployment time and special flight test window period, four aircrafts

At the same time, considering the constraints of the aircraft deployment time and the special subject window period. Two special subjects are set, the earliest executable time of the subject No.3 is 15 from the start, for subject No.11, the earliest execution time is 12 and the latest execution time is 15, as shown in Table 5. After the algorithm is modified accordingly, the simulation calculation is performed, the result is shown in Fig. 13 and 14. The blue rectangle in the figure is a subject with window period constraints, it shows that the special subjects are satisfied. Constraint requirements are all satisfied while ensuring the shortest overall flight duration.
Fig. 13

Task planning Gantt chart (5)

Fig. 14

Improved genetic algorithm iterative process (5)

Table 5

Genetic algorithm parameter setting (4)

Parameter name

Parameter meaning

Parameter value

PC

Maximum crossover probability

0.8

PM

Maximum mutation probability

0.8

Popsize

Population size

200

slnm

Number of iterations

100

N

Total aircraft number

4

DT

Test aircraft deployment time

[0 10 20 30]

SP

Special subject window period

{[3 15 inf], [11 12 15]}

5 Conclusion

The technical requirements of the flight test optimization algorithm are complex, involve many disciplines, and require the cooperation of many departments. The factors involved in the preliminary planning phase of the civil aircraft flight test were studied and summarized in this paper. Then the allocation problem of flight test subjects was simplified into a combinatorial optimization problem. Aiming at such a combinatorial optimization problem for civil aircraft flight test, the improved genetic algorithm was used to optimize and automatically generate the allocation scheme. The effectiveness of the algorithm was verified by comparison with other algorithm. Several cases have been used to prove its application prospects in engineering. In the future, based on this algorithm, iterative improvement can be carried out by considering more actual demand of flight test and various special cases. The research in this paper provides a useful exploration for the automation and intelligence of the future flight test task planning.

Notes

Acknowledgements

This paper was sponsored by the Civil Aviation Pre-Research Projects and Shanghai Engineering Research Center of Civil Aircraft Flight Testing.

Author contributions

Conceptualization, YL; data curation, YL and MW; formal analysis, MW; funding acquisition, GX; investigation, MW; methodology, YL; resources, GX; supervision, GX and TL; validation, TL; writing—original draft, YL; writing—review and editing, GX and MW.

Funding

This research was funded by the National Program on Key Basic Research Project (2014CB744903), National Natural Science Foundation of China (61673270), Shanghai Industrial Strengthening Project (GYQJ-2017-5-08), Shanghai Science and Technology Committee Research Project (17DZ1204304).

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

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Copyright information

© Shanghai Jiao Tong University 2019

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Shanghai Aircraft Design and Research InstituteShanghaiChina

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