Abstract—The paper investigates two advanced Computational

Intelligence Systems (CIS) for a morphing Unmanned Aerial Vehicle (UAV) aerofoil/wing shape design optimisation. The first CIS uses Genetic Algorithm (GA) and the second CIS uses Hybridized GA (HGA) with the concept of Nash-Equilibrium to speed up the optimisation process. During the optimisation, Nash-Game will act as a pre-conditioner. Both CISs; GA and HGA, are based on Pareto optimality and they are coupled to Euler based Computational Fluid Dynamic (CFD) analyser and one type of Computer Aided Design (CAD) system during the optimisation.

For the practical test case, one type of morphing techniques; Leading and Trailing Edge Deformation (LTED) is considered to control flow over the aerofoil/wing. LTED to a Natural Laminar Flow (NLF) aerofoil is applied to maximise the lift coefficients (Cl) at both the take-off and landing conditions. Two applications on LTED with low/middle and high design complexities are optimised using GA and HGA. The optimisation efficiency for GA and HGA are compared in terms of computational cost and design quality.

Numerical results clearly show that Nash-Game helps a GA based CIS to accelerate the optimisation process and also to produce higher performance solutions in solving both the low/middle and high complex design optimisation problems. In addition numerical CFD study demonstrates that the implementation of morphing technique on the aerofoil/wing significantly improves the lift coefficients at both the take-off and landing conditions when compared to the baseline design.

Keywords—Shape design optimisation, Hybrid-Game, Nash Equilibrium, Evolutionary Algorithm, Active Flow Control, Morphing Aerofoil/Wing.

I. INTRODUCTION OMPUTATIONAL Intelligence Systems (CIS) have been developed for solving many engineering design problems.

CIS are intrinsically capable of dealing with imprecise context problems and producing a set of feasible solutions [1 -3]. However, due to the increment of design problem complexity in engineering, innovation of CIS is crucial for both solution

DongSeop Lee is with International Center for Numerical Methods in Engineering (CIMNE) as a senior scientist, 08860 Castelldefels Spain. And also he is with Deloitte Analytics – Deloitte Consulting LLC as a senior consultant, Seoul Korea. (e-mail: ds.chris.lee@gmail.com).

Luis Felipe Gonzalez is with the Queensland University of Technology and Australia Research Center Aerospace Automation (ARCAA) as a lecturer. (e-mail: felipe.gonzalez@qut.edu.au).

Jacques Periaux is with CIMNE and UPC as a professor and UNESCO chair, Barcelona 08034, Spain. (e-mail: jperiaux@gmail.com).

Gabriel Bugeda is with CIMNE and UPC as a professor, Barcelona 08034 Spain. (e-mail: bugeda@cimne.upc.edu).

accuracy and computational efficiency [4, 5]. One alternative method to achieve such improvement is Game Strategies which can save CPU usage while producing accurate solutions due to their efficiency in design optimisation [6 -8].

The paper investigates the application of an advanced CIS based on Genetic Algorithms (GA) coupled to Game strategies for the efficient aerodynamic shape design optimisation. For CIS, an optimisation tool; RMOP developed in CIMNE is considered. RMOP has two different CI engines; Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO). In this paper, GA in RMOP is used and denoted as RMOGA. RMOGA uses a standard Genetic Algorithm based on Global-Game and Pareto tournament [9, 10]. In addition, the concept of Hybrid-Game (Pareto/Global-Game and Nash-Game) [11 -13] is applied to RMOGA to accelerate the CIS process and it is denoted as HRMOGA.

Hybridised RMOGA (HRMOGA) with the concept of Nash-Game consists of one Global/Pareto-Player and several Nash-players. Nash-Game will decompose a design problem to several simpler design problems respect to the number of Nash-Players to have their own objective and search space (strategy profile). During the optimisation, a Nash-Game acting as a pre-conditioner provides dynamic elite information to the Global algorithm and hence CIS can have faster convergence while producing high accurate solution simultaneously [11 -13].

Recent advances in design tools, smart materials, electronics, and actuators offer implementation of morphing technologies to improve aerodynamic efficiency by adapting its shape [14 -17]. Such aerodynamic improvement saves mission operating cost (extension of aircraft range and endurance) while reducing aircraft emissions.

In this paper, one type of morphing technique; Leading and Trailing Edge Deformation (LTED) on a Natural Laminar Flow (NLF) aerofoil (RAE 5243) [18] is investigated in order to maximise the lift coefficients at both the take-off and landing conditions. Especially, it is crucial for Short Take-Off and Landing (STOL) of Unmanned Aerial System (UAS).

It is shown in this paper how the Hybrid-Game can accelerate the optimisation process to capture a desired design model using Nash-Game. Both CI systems are coupled with a Partial Differential Equations (PDEs) based FEA tool and a Computer Aided Design system; GiD. They are implemented to solve two morphing aerofoil/wing design optimisations with

Multi-Objective Design Optimization of Morphing UAV Aerofoil/Wing Using Hybridised

MOGA DongSeop Lee, Luis Felipe Gonzalez, Jacques Periaux, and Gabriel Bugeda

C

U.S. Government work not protected by U.S. copyright

WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia IEEE CEC

low/middle and high design complexity that require high computational cost.

The rest of paper is organised as follows: Section II describes optimisation method. Aerodynamic analysis tools and Computer Aided Design (CAD) system are demonstrated in Section III. Section IV conducts two practical test cases for morphing UAV aerofoil/wing design optimisation using RMOGA and Hybridised RMOGA. Section V provides conclusions and addresses several future research.

II. METHODOLOGY

A. Robust Multi-Objective Optimisation Platform (RMOP) RMOP is a computational intelligence framework which is a

collection of population based algorithms including Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO) [9, 10, 19]. As shown in Figure 1, RMOP consists of the eight following modules including a new module named as ELIU (Elitism Unit for Game Strategies);

Fig. 1. Robust Multi-objective Optimisation Platform (RMOP).

EVAU (Evaluation Unit) is a module for evaluation and

collecting results from analysis tools. IOPU (In/Output Unit) is a module for handling input,

output data and also plotting convergence history, initial random population (with/without buffer population), total populations, and Pareto optimal front.

IRPU (Initial Random Population Unit) is a module to produce randomly the first generation.

MEAU (Memory Allocation Unit) is a module for allocating/dis-allocating memory for population and also to provide parallel/distributed computation.

NDOU (Non-Dominated Optimal Unit) is a module for computing Pareto-tournament, non-dominated sorting solutions.

RANU (Random Number Unit) is a module for generating pseudo random number module.

SSOU (Searching/Selection Objective Unit) is a searching module; selection, mutation, crossover for GA and also it produces velocity, positioning module for PSO.

In this paper, RMOP uses GA searching method (denoted as RMOGA). A new module; ELIU (Elitism Unit for Game Strategies) is developed to hybridise RMOGA with a non-cooperative Nash-Game Strategy. ELIU produces elite information from Nash-Game and seeds Nash elite design information to a Global/Pareto-Game population.

B. Non-cooperative Game Strategy: Nash-Game In the Game strategies implemented the ELIU module each

Nash Player is in charge of one objective and uses its own strategy set, a subset of design space. During the game, each player looks for the best strategy in its search space (strategy profile) in order to improve its own objective while the set of elite design variables obtained by other players are fixed. In other words, Nash-Game will decompose a problem (total design domain) into several simpler problems (sub design domains) corresponding to the number of Nash-Players. The Nash-equilibrium is reached after a series of strategies tried by players in a rational set until none of players can improve its objective by changing its own best strategy.

Details and examples of Nash-Game can be found in references [6 -8, 11 -13].

C. Hybrid-Game via ELIU Module Traditionally, Pareto and Nash games are considered

independently when solving a design problem. In this research, a coalition game between Pareto and Nash is considered and developed to improve optimisation efficiency.

A module ELIU (Elitism Unit) is developed to provide a bridge between Pareto/Global-Game and Nash-Game. ELIU generates several populations for Nash-Game and controls elite design information transfer between Pareto-Player and Nash-Players and also between Nash-Players.

The default game strategy of RMOP is a Pareto-Game. RMOP will use either GA or PSO based on Pareto-optimality (only one type of population). If the user defines more than one population then RMOP via one of functions in ELIU generates one population for Pareto-Game and Nash-Game for the rest populations. For instance, if the number of population types is set as four by the user then RMOP employs one Pareto-Game and three Nash-Players as shown in Figure 2. In other words, ELIU in RMOP decomposes a design problem into several simpler design problems. The followings are the key mechanism of Hybrid-Game;

Pareto-Game handles the original single or multi-objective and multidisciplinary design problem by considering all objectives and design variables,

Nash-Game splits the design search space and the original problem into three simpler single-objective design problems corresponding to the number of Nash-Players.

ELIU module collects elite designs obtained by Nash-Players and adds them into the next candidate list of the Pareto-Player at every pre-defined function evaluations (Hybrid-Game I).

ELIU module also compares the best values between Pareto and Nash games so far. ELIU adds the best design obtained by Pareto-Game into the next candidate list for Nash-Players if fitness values (Pareto non-dominated solutions) of Pareto-Player are better than the elite design obtained by Nash-Players (Hybrid-Game II). This process is to force Nash-Players to generate better elite designs when compared to the non-dominated solutions obtained by the Pareto-Player.

Fig. 2. Example shape of Hybrid Game topology controlled by ELIU. (Note: ParetoP and NPi represent Pareto Player and ith Nash-Player.)

III. AERODYNAMIC ANALYSIS TOOL AND PRE-POST PROCESSOR

In this paper, the GiD and PUMI software are utilized as a pre/post CAD processor and an unstructured mesh Euler finite element solver [20, 21], respectively. Both software were developed in International Center for Numerical Methods for Engineering (CIMNE). GiD can generate a mesh for finite element, finite volume or finite difference analysis and write the information for a numerical simulation program in its desired format. PUMI uses Euler based finite element approach with Galerkin approximation method. The validation of PUMI compared to the wind tunnel data can be found in reference [22]. GiD generates an unstructured mesh/grid for each candidate’s model based on the design parameters obtained by the RMOGA and HRMOGA. PUMI evaluates the unstructured model and generates aerodynamic outputs in the format for GiD for post processing.

IV. MORPHING AEROFOIL/WING DESIGN OPTIMISATION USING RMOGA AND HRMOGA

In this section, the Leading and Trailing Edge Deformation (LTED) morphing technique is applied to a Natural Laminar Flow aerofoil (RAE 5243) and its shape is optimised using RMOGA and HRMOGA. The results obtained by RMOGA and HRMOGA are compared in terms of computational cost and solution quality.

A. Parameterisation of Morphing Technique: Leading & Trailing Edge Deformation (LTED) The LTED can be defined by four control parameters as

shown in Figure 3; leading edge actuator position (xLE), trailing edge actuator position (xTE), deformation angle for leading edge (θLE), and deformation angle for trailing edge (θTE).

Deformation angle follows the right-hand rule. Figure 4 shows a morphing technique mechanism consisting four steps;

• Step1: Find actuator positions for leading and trailing

edges; xLE, yLE, xTE, yTE (marked as crosses), • Step2: Deform leading edge by θLE, • Step3: Deform trailing edge by θTE, • Step4: Smooth sharp joints (marked as circles shown in

Figure 4) using Bezier Spline Curves; BSC1, BSC2, BSC3, and BSC4.

B. Formulation of Design Problem For the baseline design, a natural laminar flow aerofoil RAE

5243 is selected as shown in Figure 5. The baseline design has the maximum thickness ratio (t/c) of 0.14 at 41% of the chord and the maximum camber of 0.018 at 54 % of the chord.

Fig. 5. Baseline design (RAE 5243) geometry (Note: max t/c = 0.14 at 41%c and max camber = 0.018 at 54%c).

Figure 6 shows the computational mesh of 14,301 vertexes

and 27,317 elements generated by using GiD software. The mesh conditions on the suction and pressure sides of the aerofoil are set by constant ratio. In other words, there will be the same mesh conditions around aerofoil even though the

Fig. 3. Control parameters for morphing technique at fixed leading and trailingedge actuator positions.

Fig. 4. Morphing mechanism.

shape of aerofoil is changed. Figure 7 shows the pressure and Mach contour obtained by the baseline design at both the take-off (M∞ = 0.2, α = 15.0°) and landing (M∞ = 0.12, α = 17.18°) conditions.

Fig. 6. Mesh conditions for the baseline design obtained by GiD.

Fig. 7. Cp contours obtained by the baseline design at the take-off (top) – CpTakeOff range [-14:1.3] and landing (bottom) – CpLanding range [-15:2] conditions.

In the following Sections, the shape of the baseline design will be adapted to control the transonic flow especially to maximise the lift coefficient. For the optimisation, the

population size of Pareto-Game and Nash-Game is set as twenty and the probabilities of mutation and crossover are set as 1/n and 0.9 respectively (where n is the number of design variables). For Pareto-Game, n is the total number of design variables that is the sum of design variable numbers for Nash players. In other words, Nash-Game will have higher mutation probability so Nash-Game can have better exploration when compare to Pareto-Game. At every twenty function evaluations, the elite designs obtained by either Pareto-Game or Nash-Game will be seeded to Nash-Game or Pareto-Game if only if its fitness value dominates other game’s fitness value that is strictly based on the concept of survival of the fittest.

C. Low/Middle Design Complex Morphing UAV Aerofoil/Wing Optimisation of using RMOGA and HRMOGA Problem Definition This test case considers a multi-objective optimisation of a

LTED morphing method with low/middle design complexity using RMOGA and HRMOGA. The objectives of this optimisation are to maximise lift coefficients (Cl) at both the take-off (M∞ = 0.2, α = 15.0°) and landing (M∞ = 0.12, α = 17.18°) conditions. Hybrid-Game (HRMOGA) consists of three players; one Pareto-Player (PP), two Nash-Players (NP1 and NP2). The fitness functions for Pareto-Player (f1 and f2) and Nash-Game (fNP1 and fNP2) are shown in Equations (1) –(4).

f1 xLE ,xTE ,θLE ,θTE( ) = min 1 ClTakeOff( )( ) (1)

f2 xLE , xTE ,θLE ,θTE( ) = min 1 ClLanding( )( ) (2)

fNP1 xLE , xTE* ,θLE ,θTE

*( ) = min 1 ClTakeOff( )( ) (3)

fNP2 xLE* ,xTE ,θLE

* ,θTE( ) = min 1 ClLanding( )( ) (4)

where design variables with * are the elite designs obtained by Nash-Players; xLE

* and θLE* are the elite designs obtained by

Nash-Player 1, and xTE* and θTE

* are the elite designs from Nash-Player 2. The Pareto-Player will optimise both leading and trailing edge deformation parameters to maximise Cl at both the take-off and landing conditions. In contrast, Nash-Player 1 will optimise only leading edge deformation parameters with an elite design of trailing edge deformation obtained by Nash-Player 2 at the take-off conditions. Nash-Player 2 optimises trailing edge deformation with elite design parameters for leading edge obtained by Nash-Player 1 at the landing conditions.

The stopping criterion is set by the pre-defined elapse time (25 hours) for both RMOGA and HRMOGA.

Design Variables The design variable bounds for a morphing geometry with low/middle design complexity are illustrated in Table I. All Bezier Spline Curves (BSC) shown in Figure 4; BSC1, BSC2, BSC3, and BSC4, have a constant length of 20% of aerofoil chord length. BSC1 and BSC2 have the same x-axis Bezier control points (starting, peak, finishing points) and both BSC3

and BSC4 have the same Bezier control points. So four design parameters are considered in total.

Table II shows design variable distribution for HRMOGA. It can be seen that the Nash-Players 1 and 2 consider only 2 design variables for leading edge deformation parameters (xLE, θLE) and trailing edge deformation parameters (xTE, θTE) respectively while the Pareto-Player for RMOGA and HRMOGA considers 4 design variables (xLE, θLE, xTE, θTE).

Numerical Results

Two optimisation algorithms; RMOGA and HRMOGA have run 25 hours of computer time (613 and 260 function evaluations respectively) using a single 4 × 2.8 GHz processor. Figure 8 compares the Pareto optimal front obtained by RMOGA and HRMOGA with the baseline design. Even though both RMOGA and HRMOGA produce better solutions when compared to the baseline design, the optimal solution obtained by HRMOGA dominates the Pareto solutions obtained by RMOGA and the baseline design. In other words, HRMOGA has better convergence for both the objectives 1 and 2.

Fig. 8. Pareto optimal front obtained by RMOGA and HRMOGA. Figure 9 compares the convergence history obtained by RMOGA and HRMOGA in terms of the normalised function evaluations and the best fitness value for objective 1. Even though the optimal from HRMOGA has lower fitness value when compared to the optimal design of RMOGA, two non-dominated solutions (less than 1% fitness value difference)

are selected to compare the computational efficiency of both methods; HRMOGA (146 function evaluations (14 hours): f1 = 0.3349 and f2 = 0.3526) and RMOGA (465 function evaluations (18.9 hours): f1 = 0.3344 and f2 = 0.3557). It can be seen that HRMOGA reduces the computational cost of RMOGA by 5 hours. In other words, applying Nash-Game improves the optimisation efficiency of RMOGA by 26%. The main reason why HRMOGA has faster convergence is that Nash-Game acts as a pre-conditioner.

Fig. 9. Convergence history (f1 vs. normalised function evaluation) obtained by RMOGA and HRMOGA. Table III compares the fitness values obtained by RMOGA, HRMOGA and the baseline design (RAE 5243) for objectives 1 and 2. It can be seen that the optimal solutions obtained by RMOGA and HRMOGA have higher lift coefficient for both take-off and landing missions when compared to the baseline design. Pareto member 1 obtained by RMOGA and HRMOGA are selected for further investigation. The optimal morphing configurations obtained by RMOGA (Pareto member 1) and HRMOGA (Pareto member 1) are described in Table IV. Figure 10 compares the geometry of the baseline design and with the optimal morphing configurations from RMOGA and HRMOGA.

The optimal morphing solutions from both RMOGA and HRMOGA have the same maximum thickness ratio (t/c) of 0.14 at 41% of the chord, as the baseline design while increasing the maximum camber; RMOGA (max camber = 0.159 at 59.5%c and c = 0.917) and HRMOGA (max camber =

TABLE I DESIGN BOUNDS OF MORPHING TECHNIQUE WITH LOW/MIDDLE DESIGN

COMPLEXITY DVs xLE θLE xTE θTE

Lower Bound 15.0 - 25.0° 65.0 - 5.0° Upper Bound 25.0 + 10.0° 75.0 + 35.0°

Note: DVs represents design variables. xLE, xTE are in the baseline chord length (%c) [0:100] and deformation angle follows right-hand rule.

TABLE II DESIGN VARIABLE DISTRIBUTION FOR HYBRID-GAME

Types Hybridised RMOGA (HRMOGA) RMOGA GP NP1 NP2 Leading Edge √ √ √Trailing Edge √ √ √

Note: GP, NP1 and NP2 represent global player and Nash-Players 1 and 2.

TABLE III FITNESS VALUES OBTAINED BY RMOGA AND HRMOGA. Aerofoil 1/ClTakeOff 1/ClLanding Baseline 0.5906 0.4589

RMOGA (PM1) 0.3344 (- 43.4%) 0.3557 (- 22.5%) RMOGA (PM2) 0.3427 (- 42.0%) 0.3537 (- 23.0%)

HRMOGA (PM1) 0.3315 (- 44.0%) 0.3417 (- 25.5%) Note: PMi represents the ith Pareto optimal member.

TABLE IV OPTIMAL MORPHING CONFIGURATIONS WITH LOW/MIDDLE COMPLEXITY

Variables xLE (%c) θLE xTE (%c) θTE RMOGA (PM1) 20.37 -22.36° 66.29 35.00°

HRMOGA (PM1) 21.87 -24.34° 66.71 34.85° Note: PMi represents the ith Pareto optimal member.

0.163 at 59.4%c and c = 0.912). Both optimal solutions have higher camber by 14%c and lower chord length by 8.5%c.

Fig. 10. Baseline design with the optimal morphing configurations obtained by RMOGA (max t/c = 0.14 at 41%c and max camber = 0.159 at 59.5%c) and HRMOGA (max t/c = 0.14 at 41%c and max camber = 0.163 at 59.4%c).

D. High Design Complex Morphing UAV Aerofoil/Wing Optimisation using RMOGA and HRMOGA Problem Definition This test case considers the same design problem in Section C

where the objective is to maximise the lift coefficient of the aerofoil at both the take-off and landing conditions. The complexity of morphing design problem is increased by considering more design variables; the length of Bezier spline curves for BSC1, BSC2, BSC3, and BSC4.

Both optimisers; RMOGA and HRMOGA, are used. The fitness functions for RMOGA and HRMOGA are shown in Equations (1) –(4). The stopping criterion for both RMOGA and HRMOGA is set by the pre-defined elapse time (25 hours).

Design Variables The design variable bounds for a high complex morphing

geometry are illustrated in Table V. To find more sophisticated morphing shape, the lengths of all Bezier Spline Curves (BSC); BSC1, BSC2, BSC3, and BSC4, are considered as additional design parameters. In total, eight design variables are considered.

The distribution of design variables for each player is shown in Table II. The Nash-Players 1 and 2 consider only four design variables for leading edge deformation parameters (xLE, θLE, LBSC1, LBSC2) and trailing edge deformation parameters (xTE, θTE, LBSC3, LBSC4) respectively while the Pareto-Player of HRMOGA considers all eight design variables (xLE, θLE, LBSC1, LBSC2, xTE, θTE, LBSC3, LBSC4).

Numerical Results

Two optimisation algorithms; RMOGA and HRMOGA were allowed to run for 25 hours of computer time (640 and 285 function evaluations respectively) using a single 4 × 2.8 GHz processor. Figure 11 compares the Pareto optimal front

obtained by RMOGA and HRMOGA and the baseline design. It can be seen that both RMOGA and HRMOGA produce better solutions when compared to the baseline design. The Pareto optimal solutions obtained by HRMOGA dominate the optimal solutions from RMOGA.

Fig. 11. Pareto optimal front obtained by RMOGA and HRMOGA. Figure 12 compares the convergence history obtained by RMOGA and HRMOGA in terms of the normalised function evaluations and the best fitness value for objective 1. Even though RMOGA needs more computational cost or more function evaluations to catch the Pareto optimal solutions obtained by HRMOGA, two similar solutions (less than 3.5% fitness value difference) are selected to compare the computational efficiency; HRMOGA (67 function evaluations (5.8 hours): f1 = 0.3292 and f2 = 0.3695) and RMOGA (560 function evaluations (22.0 hours): f1 = 0.3390 and f2 = 0.3816). It can be seen that HRMOGA reduces the computational cost of RMOGA by 16.1 hours. In other words, applying Nash-Game improves the optimisation efficiency of RMOGA by 73%.

The fact that cannot be ignored here is that HRMOGA has a computational cost reduction by 47% more when compared to the numerical results in Section C. This indicates that the use of Hybrid-Game (ELIU module) will be more beneficial when the problem considers high design complexity.

Table VI compares the fitness values obtained by RMOGA, HRMOGA and the baseline design (RAE 5243) for objectives 1 and 2. The optimal solutions obtained by RMOGA and HRMOGA have higher lift coefficient for both take-off and landing conditions when compared to the baseline design. Pareto member 5 obtained by RMOGA, and Pareto member 2 obtained by HRMOGA are selected for further investigation.

TABLE V DESIGN BOUNDS OF MORPHING TECHNIQUE WITH HIGH DESIGN COMPLEXITY

DVs xLE θLE LBSC1 LBSC2 xTE θTE LBSC3 LBSC4 Lower 15.0 - 25.0° 10.0 10.0 65.0 - 5.0° 10.0 10.0 Upper 25.0 + 10.0° 25.0 25.0 75.0 + 35.0° 30.0 30.0

Note: DVs represents design variables. xLE, xTE are in the baseline chord length (%c) [0:100] and deformation angle follows right-hand rule. LBSCi represents the length of ith BSC (%c).

Fig. 12. Convergence history (f1 vs. normalised function evaluation) obtained by RMOGA and HRMOGA.

The optimal morphing configurations obtained by RMOGA and HRMOGA are described in Table VII. Figure 13 compares the geometry of the baseline design and the baseline with the optimal morphing configurations obtained by RMOGA and HRMOGA.

The optimal solutions have the same maximum thickness ratio (t/c) of 0.14 at 41% of the chord as the baseline design while increasing the maximum camber; RMOGA (max camber = 0.154 at 64.0%c and c = 0.919) and HRMOGA (max camber = 0. 160 at 62.5%c and c = 0.920). Both optimal solutions have higher camber by 14%c and lower chord length by 8.0%c.

Figure 14 compares pressure contours obtained by the

baseline design with the optimal morphing configurations (Pareto member 2) obtained by HRMOGA at take-off and landing conditions. It can be seen that the optimal morphing configurations has a wider high pressure at the pressure side of the aerofoil when compared to the baseline design shown in Figure 7.

Fig. 13. Baseline design with the optimal morphing configurations obtained by RMOGA (max t/c = 0.14 at 41%c and max camber = 0.153 at 63.9%c) and HRMOGA (max t/c = 0.14 at 41%c and max camber = 0.160 at 62.5%c).

Fig. 14. Cp contours obtained by the Pareto member 2 from HRMOGA at take-off (top) – CpTakeOff range [-14:1.3] and landing (bottom) CpLanding range [-15:2] conditions.

To summarise the optimisation test cases shown in Sections IV.C and IV.D, morphing configurations on the baseline design; RAE 5243 are optimised using RMOGA and HRMOGA. It is demonstrated that morphing techniques are useful for the flow control at both the take-off and landing conditions. Design engineer may choose the optimal morphing configurations (Pareto member 2) obtained by HRMOGA (Section IV.D) since it can increase the lift coefficient by 42% at the take-off condition while improving 26% of the lift coefficient at the landing condition.

Figure 15 compares the optimisation efficiency of RMOGA and HRMOGA. It is clearly shown that Hybrid-Game (HRMOGA) significantly reduces the computational cost while generating high quality optimal solution in solving engineering

TABLE VI FITNESS VALUES OBTAINED BY RMOGA AND HRMOGA. Aerofoil 1/ClTakeOff 1/ClLanding Baseline 0.5906 0.4589

RMOGA (PM5) 0.3433 (- 41.8%) 0.3626 (- 21.0%) HRMOGA (PM1) 0.3282 (- 44.4%) 0.3584 (- 22.0%) HRMOGA (PM2) 0.3434 (- 41.8%) 0.3406 (- 25.7%)

Note: PMi represents the ith Pareto optimal member.

TABLE VII OPTIMAL MORPHING CONFIGURATIONS WITH HIGH DESIGN COMPLEXITY

DVs xLE θLE LBSC1 LBSC2 xTE θTE LBSC3 LBSC4 RMOGA 23.7 - 22.4° 23.7 11.4 69.3 34.3° 26.2 15.4

HRMOGA 21.9 - 20.6° 12.3 21.4 66.0 34.4° 20.2 13.6 Note: DVs represents design variables. xLE, xTE are in the baseline chord length (%c) [0:100] and deformation angle follows right-hand rule. LBSCi represents the length of ith BSC (%c).

design problems with both low/middle and high design complexity.

Fig. 15. Optimisation efficiency in terms of computational efficiency obtained by RMOGA and HRMOGA.

V. CONCLUSION In this paper, two advanced optimisation techniques have

been demonstrated and implemented as a methodology for morphing aerofoil/wing design optimisation. Analytical research clearly shows the benefits of using Hybrid-Game in terms of computational cost and design quality for multi-objective design problems with low/middle and high design complexity. In addition, the use of morphing method on current aerofoil increases significantly lift coefficients at both take-off and landing conditions.

Future work will focus on robust multi-objective design optimisation of morphing method (Taguchi method), which can produce a set of design models with better performance and stability at variability of operating conditions.

ACKNOWLEDGMENT The authors would like to thank E. Escolano in GiD team,

and R. Flores and E. Ortega at CIMNE for their support and fruitful discussions on GiD and PUMI.

The third author acknowledges the support of Spanish Ministerio de Ciencia e Innovación through project DPI2011-27834.

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