Efficient Genetic Algorithm for Aerodynamic Design of Business Jet Aircraft B.Epstein # and S.Peigin * # Academic College of Tel-Aviv-Yaffo * Israel Aircraft

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


Original Case_GBJ_1




Original Case_GBJ_4 Case_GBJ_5



Original Case_GBJ_5

2Y/b = 0.442Y/b = 0.44




Original Case_GBJ_6 Case_GBJ_7



-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


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


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


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.

Documents

Efficient Genetic Algorithm for Aerodynamic Design of Business Jet Aircraft B.Epstein # and S.Peigin * # Academic College of Tel-Aviv-Yaffo * Israel Aircraft