optimization based on evolutionary algorithms for ... - ORBEL

mustardarchaeologistΜηχανική

22 Φεβ 2014 (πριν από 3 χρόνια και 5 μήνες)

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Rajan FILOMENO COELHO


OPTIMIZATION BASED ON
EVOLUTIONARY ALGORITHMS
FOR AERONAUTICS


With support of the Walloon Region and European
Structural Funds ERSF, ESF

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

2

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


I.

Introduction


II.

Brief overview of CENAERO activities


III.

Optimization algorithms


IV.

New trends in structural optimization for aeronautics


V.

Conclusions

Outline

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

3

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

I. Introduction


Since the sixties:


outgrow of numerical methods for structural mechanics,
fluid dynamics, etc. (e.g. finite element, boundary element,
finite volume methods, …)


parallely, development of novel and efficient optimization
algorithms





structural optimization

:
“collection of methods
designed to optimize (mechanical) structures, by means of
optimization algorithms & numerical models”



In aeronautics:


mostly: shape optimization (e.g. wing design optimization)


several physics are involved (


multidisciplinary
)


expensive simulations (CFD, CSM, …)


I. Introduction

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

4

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

I. Introduction


Multi
-
disciplinary shape optimization


objectives: optimal aerodynamic performances


constraints: mechanical integrity, …



State of the art:


expert designers with know
-
how and trial / error procedure


numerical optimization starts to be used in the real design
process, but in general:


limited number of design variables


one physic at a time


the uncomputable functions must be tackled


robustness of the whole design process


link / access to the CAD systems


efficient shape parameterization


I. Introduction

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

5

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

II. CENAERO


Private Non
-
Profit Research Centre


3 universities (ULB, UCL, ULg)


1 research center (VKI)


50 industry members


incorporated in 2002 in Gosselies


35 employees



Activities & Competences


development of simulation softwares for multidisciplinary
problems in aeronautics


R&D in supercomputing, advanced numerical methods,
parallel computing


advanced engineering studies for the industry


High Performance Computing (HPC) center


II. Cenaero

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

6

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

II. CENAERO


Four R&D groups:



Virtual manufacturing


Multiscale Material Modelling


CFD
-
multiphysics


Multidisciplinary Optimization

II. Cenaero

Electron beam
welding

Crack
propagation

Aeroelasticity

Optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

7

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

II. CENAERO



Virtual Manufacturing


Welding (Friction Stir, Laser, Electron Beam)


Metal forming, Machining, Hot forging



Multiscale Material Modelling


Fatigue analysis


Micro
-
macro


Composites



CFD
-
multiphysics


Simulation of large scale turbulent unsteady flows


Aeroacoustics


Heat pipes modelling



Numerical methods and Optimization


Multidisciplinary optimization


Parallelization


II. Cenaero

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

8

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

III. Optimization algorithms


Optimization problems can be written as follows:

min {
f
(
x
) }


s.t.:

g(x)


0

栨砩‽ 0

f
(
x
)
T

= { f
1
(
x
) f
2
(
x
) … f
m
(
x
)

}

g
(
x
)
T

= { g
1
(
x
) g
2
(
x
) … g
k
(
x
)

}

h
(
x
)
T

= { h
1
(
x
) h
2
(
x
) … h
l
(
x
)

}

x
T

= { x
1

x
2

… x
n
}


X



x

: vector of the variables


f

: objective function(s)


g

: inequality constraints


h

: equality constraints


Once an optimization problem is correctly formulated, a
suitable
optimization algorithm

has to be chosen

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

9

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


Optimization problems are classified following …



the nature of the variables :


continuous: e.g. geometrical dimensions


discrete: e.g. sections from a catalogue


integer : e.g. number of holes in a plate


mixed variables


the differentiability (or not) of the functions


the presence of explicit or implicit functions (with respect


to the variables)


the size of the problem


the analytical properties of the functions (linearity,


convexity, …)


one or several objectives (


single
-

or multi
-
objective


optimization)


III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

10

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


Characteristics of optimization problems in aeronautics:




global optimum


multiple objectives and constraints


robust


multi
-
physics implies at least


no access to objective function derivatives


need of a generic optimization method


high CAE computational time (> 1h)


must be parallelized


uncomputable functions have to be tackled


several type of design variables: real, integer, …


non
-
differentiable objectives and constraints


noisy objective functions


III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

11

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


To handle those requirements,
evolutionary algorithms

combined with
approximation methods
have been
selected



Main instances of EAs:


Genetic algorithms, genetic programming, evolution
strategies



Principle:


a.

Creation of a random population of potential designs


b.

Selection of the best individuals (through a fitness fct.)


c.

Recombination of the individuals (by crossover and



mutation) in order to generate new ones


d.

Go back to step b and repeat the procedure until a



convergence criterion is reached


III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

12

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

III. Optimization algorithms

initial population

selection of the best

crossover

mutation

initial population

Termination criterion

reached ?

STOP

yes

no

Illustration of a standard GA

(2
-
variable design space)

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

13

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


Example of design optimization with EAs



aero
-
engine liner optimization:

Liners

Approach Condition

M

= 0.21

Noise Frequency = 2500 Hz

[Credits: Dr. Paul Ploumhans (FFT)]

III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

14

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


Problem definition



Design Variables


Liner 1 Impedance Z


1 < Re(Z) / (

0
c
0
) < 4


-
2 < Im(Z) / (

0
c
0
) < 0.5


Liner 2 Impedance Z


1 < Re(Z) / (

0
c
0
) < 4


-
2 < Im(Z) / (

0
c
0
) < 0.5


Design Objectives


Minimize acoustic pressure


Simulation


Actran


FFT


Simulation time: 1 h

III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

15

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


Reduction of the noise for both liners


III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

16

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization


In CENAERO, MAX optimization software is developed


(C++ object
-
oriented code)



Properties of the optimization algorithms in MAX:



based on evolutionary algorithms with advanced genetic
operators


multiobjective optimization


optimization combined with meta
-
models


“in
-
house” tools to perform multidisciplinary optimization
and allow access to CAD design geometries



Future developments considered:



robust optimization


III. Optimization algorithms

III. Optimization
algorithms

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

17

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


Advanced optimization strategies in aeronautics


involve:




Multiobjective optimization


Optimization combined


with meta
-
models


Multidisciplinary optimization


Robust optimization


Collaborative design


& optimization



IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

18

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


Multiobjective optimization:


ex.: optimizing a heat pipe for satellite


objectives:

1. maximize the power






2. minimize the room occupied



IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

19

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


definition of the multiobjective problem:


Design Variables


D = internal diameter [5, 30 mm]


G = groove count [5, 20]


d = hydraulic diameter [0.8, 2.5 mm]

D

Objectives


maximize power


minimize external diameter

D
ext

Credits: S. Rossomme & C. Goffaux

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

20

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

21

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization



«

if
f
i

:
m

criteria to be minimized;

x
is a Pareto (or non
-



dominated solution if there exists no other solution
x
*




such that
f
i
(
x
)



f
i
(
x
*
)


i

and


i

|
f
i
(
x
)

>

f
i
(
x
*
)

»





Concept of Pareto solution:

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

22

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


3 approches are available [Horn, 1997]:



a posteriori

methods:





1 run of the algorithm


overview of the front de Pareto (PF)






so far: lack of reliable convergence criterion







difficulty to visualize the Pareto front when the number of




criteria exceeds 3



a priori

methods:





interesting for more than 3 criteria, because the search is




directly oriented towards a specific region of the Pareto front





only one point for each run of the algorithm





what is the exact interpretation of the weights given to each




objective ?



IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

23

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization



interactive

methods:







the choice of a solution is guided by an interaction






with the user








usually : only one point by run of the algorithm








requires from the user a good knowledge of the problem








most common approach in aeronautics:






-


use an
a posteriori
method to find the Pareto front






-


use a multicriteria decision aid method to choose a






solution (or a set of solutions)





a posteriori
multiobjective algorithms: often based on




evolutionary algorithms (based on a population)








in MAX: Strength
-
Pareto Evolutionary Algorithms 2 (SPEA2)




due to Zitzler & Thiele




IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

24

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


Optimization combined with meta
-
models


MAX software developed at CENAERO combines


evolutionary algorithms with approximation models

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

25

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


initial accurate points are used to build the first
approximated model


the optimization is executed on this approximated model


the optimized point is computed with the accurate model

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

26

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


the new accurate point is added to the initial database


and a new approximated model is built


the process is repeated until a convergence criterion is


reached

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

27

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

initial design

control points

IV. New trends in structural optimization


example:
design optimization of a blade from VKI
-
LS89


highly loaded transonic turbine



1. Building the blade design geometry:




the algorithm
generates points in
order to minimize the
distance between the
points created and the
initial design


these points play the
role of the control
points of B
-
splines





the variables are:


y
-
coordinates of 16 control points

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

28

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization



2.

Constructing the viscous mesh (TRAF)




3.

Computing the flow (TRAF quasi
-
3D analysis)





For the optimizer, the objective is defined as follows ...



for each operating point, the loss coefficient
z
2

is to be minimized


practically, a weighted sum approach is followed






minimize
z
2
op1

+
z
2
op2




... and the constraint:



the outlet flow angle
a

must remain between
-
74.8
°

and
-
74.7
°



4.

Post
-
processing: for each operating point, the loss coefficient




z
2

is computed:

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

29

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


density


for the initial design:

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

30

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization




convergence history (200 design cycles):

iteration

loss coefficient sum

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

31

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


Multidisciplinary optimization: application to boosters



commercial aircraft turbofan engines are complex


systems involving several engineering sciences


the compression system of the turbofan is generally


composed of three elements:


a fan


a multistage low


pressure compressor


(LPC =
booster
)


a multistage high


pressure


compressor (HPC)


IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

32

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


The design of a LPC (booster) is a challenging task:



from a mechanical point of view:


ensuring the static viability of the compressor


preventing any dangerous dynamical modes from


aerodynamical and mechanical excitations


from an aerodynamical point of view:


satisfy a set of critical performances in terms of mass


flow rate, total pressure ratio and efficiency


typical LPC maps show wide variations of mass flow and



rotational speed during their operating lines:


these large variations influence significantly the blade inlet


conditions (Mach number, airflow incidence)





the design of LPC turbomachinery blades requires
multi
-
disciplinary

optimization (on multiple operating points)




IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

33

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


The methodology followed to optimize turbomachinery


blade design is described schematically:











CFD code: TRAF (A. Arnone, University of Florence)


FEM Structural Analysis code: SAMCEF (Samtech)

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

34

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


3D representation of the optimized blade design:

IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

35

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

IV. New trends in structural optimization


Advantage of multidisciplinary optimization



multidisciplinary = different physics are taken into account



simultaneously


enhanced reliability of the solution


but : problematic of coupling of physics (theoretical




numerical


softwares)



Interest of using meta
-
models



each simulation run takes ~1h40 on 1 processor (on



CENAERO Linux cluster)


the use of meta
-
models enables a reduction of the CPU



time by a factor ~10


IV. New trends
in structural
optimization

Rajan Filomeno Coelho


Optimization based on EAs for Aeronautics

36

I. Introduction

III. Optimization
algorithms

V. Conclusions

II. Cenaero

IV. New trends
in structural
optimization

V. Conclusions


Why optimize structures in aeronautics ?



optimization more and more important, to decrease


time dedicated to design and dimensioning, and


increase the quality of the product


optimization algorithms and simulation tools


are now mature enough to be used in


several aeronautical applications


for the engineer: gain of knowledge about the problem


(influence of the parameters on a design, …)




improvement of
expertise




V. Conclusions