efficient genetic algorithm for aerodynamic design of business jet aircraft b.epstein # and s.peigin...
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Efficient Genetic Algorithm Efficient Genetic Algorithm for Aerodynamic Design of for Aerodynamic Design of
Business Jet AircraftBusiness Jet Aircraft
B.Epstein# and S.Peigin*
#Academic College of Tel-Aviv-Yaffo *Israel Aircraft Industries
Major stages of the Major stages of the aircraft design processaircraft design process
Conceptual designPreliminary design stage Final detailed design
Optimization to minimum Optimization to minimum dragdrag
Major drag-related objectives of thepreliminary design:
To develop the minimum drag configuration in cruise conditions subject to various geometrical and aerodynamic constraints
To increase the payload To achieve a good off-design
aerodynamic performance
Why this is so Why this is so difficult?difficult?
Accurate estimates of drag are difficult to attain Global geometrical representation of aerodynamic shapes is an open problem High-dimensional search spaces are needed Efficient handling of non-linear constraints is required Huge overall computational cost
Why this is so Why this is so important?important?
)ln(0
0
W
WW
SFC
a
D
ML fRangeRange
Breguetrange equation
MM – Mach
L & DL & D – lift and drag
aa – acoustic speed
SFCSFC – fuel consumption
WW00 – landing weight
WWff – fuel weight
Typical ratio:WWff=2/3W=2/3W0 0 WWpayloadpayload=1/6W=1/6W00
To keep the range:To keep the range:1% 1% increase in dragincrease in dragleads toleads to7.6% 7.6% decrease in decrease in payload payload
MotivationMotivation To increase the contribution of CFD to
the overall aerodynamic design (at expense of wind tunnel and flight tests)
To reduce the preliminary design stage in the development of commercial aircrafts
To improve the quality of aerodynamic design
To reduce the overall design costs
Automatic Optimization Automatic Optimization Tool OPTIMAS: Main Tool OPTIMAS: Main
FeaturesFeatures
A new strategy for handling non-linear constraints in the framework of Genetic Algorithms (GAs)
The search space is scanned by a combination of high accuracy Navier-Stokes computations with a Reduced Order Method
Multi-domain prediction-correction iterative algorithm ensures the accuracy, robustness and globality of optimal search
A multilevel parallelization efficiently makes use of computational power supplied by MPP
Single-point drag Single-point drag minimization problemminimization problem
The objective is to minimize CD subject to the following classes of constraints: Aerodynamic constraints:
* prescribed constant CL * maximum allowed CM
Geometrical constraints:
* relative thickness (t/c)i * radius of leading
edge (RL)i
* trailing edge angle (i* beam constraints
(y/t)ij
i=1,…,Nws - number of span sections
j=1,…,Nbs(i) – number of beams number of constraints Ncs – 20-25 per wing
A multi-point drag A multi-point drag minimization problem for minimization problem for aerodynamic 3D wingsaerodynamic 3D wings
The objective is to minimize a weighted combination of drag values at several design points
Uniform geometrical constraints are placed upon the solution
Aerodynamic constraints are imposed separately at each of the design points which make the multipoint objective
Optimization Method:Optimization Method:Genetic AlgorithmsGenetic Algorithms
GAs are based on coupling deterministic and probabilistic strategies in search of optimum
They have drawn much attention in the last two decades
The basic idea behind GAs is to imitate evolution process using “genetic”operators:
* selection * crossover * mutation
Floating-point GAFloating-point GA Tournament selection Single-point crossover Non-uniform distant-dependent
mutation Elitism principle
Treatment of Non-Linear Treatment of Non-Linear Constraints by GAs: Constraints by GAs: New Approach New Approach
Change of the conventional search strategy: to employ search paths through bothto employ search paths through both
feasible and infeasible pointsfeasible and infeasible points
The idea: the information from infeasible sub-domains can be very important and a path to a path to the optimal point via infeasible ones can the optimal point via infeasible ones can be essentially shorterbe essentially shorter
Constrained Constrained OptimizationOptimization Problems Problems
Feasible region
Infeasible region
Conventional approach
Presentapproach
Implementation of the Implementation of the constraints handlingconstraints handling
The modified objective function Q was defined as follows
5.0 ] [0.3
][ 0.15
b]-[125.0
][2.0)]/()/[(1.0
T*T
*
*
*
*
D
MM
LL
C
CC
b
RRctct
Q
*)/()/( if ctct * if LL RR
)()( if tyty lu otherwise
*TT if
* if bb * if MM CC
ComputationalComputational Efficiency Efficiency Motivation Motivation
The major weakness of GAs lies in their poor computational efficiency An algorithm with population M=100 requires (for the case of 200
iterations) at least 20000 evaluations of the cost function (CFD solutions)
This is practically unacceptable
ROM-LAM methodROM-LAM method
Reduced-Order Models approach in form of Local Approximation Method (ROM-LAM):(ROM-LAM):
cost function is approximated by a local data local data basebase to ensure accuracy and robustness of the method a multi-domain prediction-verification prediction-verification principleprinciple is used prediction stageprediction stage: GAs search on a set of domains verification stageverification stage: the whole set of optima is verified via full Navier-Stokes computations to ensure the global character of search - iterationsiterations
Computational efficiency:Computational efficiency:How to improve?How to improve?
Fast grid generation automatic transformation of the initial grid using
topological similarity of geometrical configurations
Grid coarsening
Massive Massive parallelizationparallelization
preservation of the hierarchy of fitness function
Typical Computational Effort Typical Computational Effort required for one optimizationrequired for one optimization
10 10 optimization steps to reach reasonable optimum
50-150 CFD runs50-150 CFD runs per optimization step Hence approx. 500-1500 CFD500-1500 CFD runs
required to achieve desired design optimum.
Intensive parallelization technology is essential to realize optimization in industrial environment.
Multilevel Parallelization Multilevel Parallelization StrategyStrategy
Five levels of parallelization are to be implemented:
Level 1Level 1 – Parallelization of the NES code Level 2Level 2 – Parallel CFD scanning of multiple
geometries Level 3Level 3 – Parallelization of GAs search Level 4Level 4 – Parallel search on multiple
domains Level 5Level 5 – Parallel grid generation
CONSTRAINTS ON (per CONSTRAINTS ON (per section):section): (t/c)(t/c)maxmax
Leading edge radiusLeading edge radius Trailing edge angleTrailing edge angle Pitching moment CPitching moment CMM
Beams at 2 locationsBeams at 2 locations
3D Test-cases3D Test-casesOptimization by OPTIMAS Optimization by OPTIMAS
DESIGN POINTS ARE DETERMINED DESIGN POINTS ARE DETERMINED BY:BY: Mach valueMach value CCLL value value
Wing geometry :Wing geometry : ParameterizationParameterization
Wing planform is fixed Root profile is not changed Wing surface is generated by linear interpolation in span direction The number of sectional airfoils is fixed Shapes of sectional airfoils are determined by Bezier Splines Locations of sectional airfoils are
determined by twist and dihedral
List of test casesList of test casesDescriptionDescription List of List of
casescasesMach Mach rangerange
CCLL rangerange
1 point 1 point optimizatiooptimizationsns
Case_GBJ_1-Case_GBJ_1-
Case_GBJ_5Case_GBJ_50.75 –0.75 –0.800.80
0.4 -0.4 -0.520.52
2 point 2 point optimizatiooptimizationsns
Case_GBJ _6Case_GBJ _6 0.2 – 0.2 – 0.800.80
0.4 -0.4 -1.211.21
3 point 3 point optimizatiooptimizationn
Case_GBJ_7Case_GBJ_7 0.2 – 0.2 – 0.820.82
0.4 -0.4 -1.211.21
Generic Business Jet Design Generic Business Jet Design M=0.75 CL=0.52M=0.75 CL=0.52
317.5 317.5 countscounts
304.1 304.1 countscounts
Original Case_GBJ_1
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
292.0 292.0 countscounts
275.7 275.7 countscounts
Original Case_GBJ_4 Case_GBJ_5
276.1 276.1 countscounts
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
Original Case_GBJ_5
2Y/b = 0.442Y/b = 0.44
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
292.0 292.0 countscounts
276.1 276.1 countscounts
Original Case_GBJ_6 Case_GBJ_7
275.6 275.6 countscounts
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
-0.1
-0.05
0
0.05
0.1
0 0.2 0.4 0.6 0.8 1
y/c
x/c
Tip shape.
Case_GBJ_7Case_GBJ_5
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
240 260 280 300 320 340 360 380
CL
CD
Generic BJ. Drag Polars at M=0.80
OriginalCase_GBJ_7Case_GBJ_6
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
240
260
280
300
320
340
360
380
0.6 0.65 0.7 0.75 0.8
CD
Mach
Generic BJ. Mach Drag Divergence at CL=0.4
OriginalCase_GBJ_7Case_GBJ_2
Generic Business Jet Design Generic Business Jet Design M=0.80 CL=0.40M=0.80 CL=0.40
0.8
1
1.2
1.4
1.6
6 8 10 12 14 16 18 20
CL
alpha
Generic BJ. CL vs alpha at M=0.20
OriginalCase_GBJ_7Case_GBJ_6Case_GBJ_2
Computational efforts for one-pointComputational efforts for one-point 3D wing optimization 3D wing optimization
in wing-body configuration in wing-body configuration
Direct application of GA search Direct application of GA search Pop.size=100; 200 generationsPop.size=100; 200 generations 20000 20000 177.2 years177.2 years
+ Hierarchy principle+ Hierarchy principle 11.9 years11.9 years
+ ROM-LAM approach+ ROM-LAM approach
20000 20000
1050 1050 228.7 days228.7 days
+ multilevel parallelization+ multilevel parallelization 1050 1050 16.7 hours16.7 hours
1919
1515
329329
CFD CFD runsruns
CPU CPU timetime
624 processors624 processors
Automatic “discovery” of Automatic “discovery” of knownknown aerodynamic trends aerodynamic trends (1)(1) Supercritical airfoils Supercritical airfoils The phenomenon was found in the 1950’s, The phenomenon was found in the 1950’s,
but the practical design of supercritical but the practical design of supercritical airfoils is highly complicatedairfoils is highly complicated especially in the 3D case of a swept wing where supercritical airfoils must be combined with more conventional aerodynamic profiles.
Thus the optimization can automatically Thus the optimization can automatically “discover” sophisticated aerodynamic “discover” sophisticated aerodynamic shapes.shapes.
Automatic “discovery” of Automatic “discovery” of knownknown aerodynamic trends aerodynamic trends (2)(2) Leading edge droop Leading edge droop
This is a method of introducing a local twist a local twist in the leading edge areain the leading edge area of the airfoil, which
allows to avoid the overloading of the region
at moderate angles of attack.
The optimization method also “discovered” The optimization method also “discovered” this trend in 3D cases.this trend in 3D cases.
Conclusions (1)Conclusions (1)
A new robust tool (code OPTIMAS) (code OPTIMAS) for multipoint multi-constrained design of wing-body aircraft configurations has been developed at IAI.
The capability of the method was illustrated through optimization of transport-type aircraft configuration
Conclusions (2)Conclusions (2)
It was demonstrated that the proposed method allows:
* to ensure a low drag level in cruise regime* to ensure a low drag level in cruise regime * to handle a required number of constraints* to handle a required number of constraints * to achieve good off-design performance at * to achieve good off-design performance at take-off conditions and high Mach zonetake-off conditions and high Mach zone This technology has opened up the
possibility of achieving optimum aerodynamic configuration within a dramatically more competitive design-cycle time.