Evolutionary Algorithms in modefrontier

(1)

1 University of Trieste Dipartimento di Energetica

Evolutionary Algorithms in

modeFRONTIER

Carlo Poloni

Univ. Trieste

Italy

University of Trieste

PRESENTATION OUTLINE

•

• Some concept on OPTIMIZATION

Some concept on OPTIMIZATION

–

what we need and what we can do

•

• Some considerations about Evolutionary

Some considerations about Evolutionary

Algorithms

–

some

hystory

& state of the art

•

• Some examples

Some examples

–

Optimisation

of a composite

wing

-

Fluid

/

Structure

interaction

•

• Marc

Marc

,

StarCD

,

Nastran

–

Optimisation

of Gas Turbine performance

•

• Tascflow

Tascflow

–

Optimisation

of hot

-

stamping process

•

(2)

3

University of Trieste Dipartimento di Energetica

Design Office Needs

Today Product Development:

Pre-design

CAE for verification

Testing

_Production

Analyst work often frustrating: usless information,

criticism for inaccuracies, cost of computing not visible in

product innovation

Modification after CAE are costly

The design is almost frozen after Pre-design

CAD use

4

Design Office Needs

• Build

parametric models

• Make

rational design data-flow

• USE

all

best company skills

from the beginning

• Optimise the product and

produce innovation

Pre-design

Parametric CAD

Extensive CAE

FRONTIER

Testing

Production

(3)

IT infrastructure

(Intranet)

Logic and

Optimisation

Algorithms

The

The use

use

of Design

Optimisation means

:

Execute simulations or

experiments efficiently

Archive in an organized

way “sensible” data in an

easyly accessible way

(through a web browser)

Take rational decisions on the

best compromise between

“cost”

and

“performances”

Formulate a logic

analysis process

Optimisation needs

An Optimisation task:

• requires several repetition of the complete computation cycle

–

parameterise all computation flow

• involving commercial software and/or in-house utilities

• need of flexible utilities to extract relevant information

– control parameters input files

– objectives to optimise output files

• needs to control the global computation time

–

use the best optimisation approach among several (

RMS, DOE,

MOGA, ANN

…)

–

send and control many jobs on a hybrid network

–

parallelise optimisation steps

• needs to get insight on system behaviour (N-dimension space),

allowing the designer to ”make the right decision”

”make the right decision”

–

contribution of parameters

–

Pareto dominance

(4)

7

Global Optimisation Strategy

• Multi Objective

Genetic Algorithm

for

global exploration

• Local Hill Climbing

for improvements

• Interpolation techniques

for data synthesis

Training Data

Derivatives

Approximation

• Multi Objective Genetic Algorithms for design space

exploration

• Simplex for local search

• Gradient based methods for accurate refinements

8

FRONTIER Product Properties

• ALL platforms are supported

–

Browser based technology

–

JAVA, XML, RMI, CORBA

• Capability of handling any

computing services

–

files or API (Application

Protocol Interface) …

–

from CFD to MS-EXCEL

• Optimisation Algorithms

–

Multi-Objective Genetic

Algorithm,

–

Simplex

–

Gradient based methods

–

DOE (Design of Experiments)

• Decision Support tools

–

Multi Criteria Decision

Making

–

Design Data visualization

–

Statistical tools for Design

Data Analysis (robust

design)

–

Design Data filtering

• Response Surface Models

–

Polynomial (1st, 2nd order)

–

Exponential

–

k-nearest

–

Kriging

–

Gaussian Process

–

Neural Networks

FRONTIER allows the user to extract

the maximum of information allowed

by the user-defined CPU budget

(5)

Evolutionary Algorithms

Evolutionary Algorithms,

,

some

some hystory

hystory

In USA:

1973 J.Holland first systematic

work on Genetic Algorithm

1989 Book by D.E.Goldberg

In Europe:

1969 I.Rechenberg and

H.P.Schwefel first paper on

Evolution Strategy

1992 Book by H.P. Schwefel

Since then 2 major

world-conferences are organised each

year on the unified name:

“Evolutionary Algorithm”

Now moveing to even more wider

name of “computational

intelligence”

At European level:

INGENET – Genetic Algorithms in

Engineering applications

A Framework IV Thematic Network

(1997-2001) “Evolutionary

Algorithm”

EUROGEN conferences

A simple Algorithm

d o ng g e n e r a t i o n d o ni nd i n d i v i d u a l s t r a n s l a t e b i t s i n t o v a r i a b l e s c o mp u t e o b j e c t i v e s => i n t e r f a c e t o a n al y s i s e n d d o Do s o me s t a t i s t i c s o n t h e p o p u l a t i o n i n d i v i d u a l s d o Cr e at e a n e w p o p u l at i o n : b y c r o s s o v e r : s e l e c t i n d i v i d u a l a n d r e pr oduc e b y mu t a t i o n : s e l e c t i n d i v i d u a l s a n d mut a t e e n d d o e n d do

• Select

• Modify

(6)

11

State of the art EA

SGA – simple genetic algorithm

ES µ,λ– evolution strategy

with µ individuals

λ

off-springs

Hybrid Algorithms

( Evolutinary / Gradient

opeartors )

“Self Adaptive” Algorithms

(tuning parameters are updated

during the evolution)

Self Adaptive Algorithms with

embedded meta-modelling

New development, even more

robust

Hystorical algorithms, Robust

but expencive

Efficient and Robust, latest

development

New development, efficient but

less robust

One application: 3D

wing Optimisation

Reference Airfoil:

Onera M6 wing

Mach number 0.84

Reynolds number 10e

6

(7)

13

!

Variables:

!

Coordinates of spline

control points in CATIA

!

Objectives:

!

MAX C

L

!

MIN C

D

!

MIN C

M

Computed by Star CD

Objectives and

Variables 3D case

Optimisation logic

INPUT

CA

TIA

sc

rip

t

CA

TIA

sc

rip

t

CA

TIA

sc

rip

t

St

ar

CD

St

ar

CD

St

ar

CD

OU

TP

UT

OU

TP

UT

OU

TP

UT

(8)

Optimisation Run

Optimiser: MOGA 30 x 10

Optimisation run

• Min Cd

• Constraints on:

– Cl > 0.133

– Cm < 0.0472

– Wing Volume

(9)

Results

0.0466

0.0472

Cm

0.0384

0.0436

Cd

0.133

0.133 Cl

Optimized

Onera M6

Onera M6 Onera M6 Optimized Optimized

--

12% Drag

Results

Onera M6 Onera M6

0.0466

0.0472

Cm

0.0384

0.0436

Cd

0.133

0.133 Cl

Optimized

Onera M6

Optimized Optimized

--

12% Drag

(10)

3D wing Optimisation

General Remark

• CATIAv5 – PROSTAR- STARCD – PROSTAR

design chain has been succesfully tested

• The optimisation run found significant

improvement over existing solution (Onera

M6 wing)

Courtesy

Example (1): fluid

structure interaction

GEOM_INIT

FEM_to_CFD

CFD

CFD_to_FEM

FEM

Conv?

OUTPUT

Design of a composite

wing

CFD Code STAR-CD

Structural code MARC

(11)

!

MIN mass

!

MIN deformation

!

MAX Lift

!

MIN Drag

!

MAX Lift/Drag ratio

Profile NACA4412

C/L = 10

L

C

Example (1): fluid

-

structure

interaction

Objectives

Coupling StarCD & MARC

!

Parabolic variation of

thickness (3 variables)

!

Relative thickness of

layers (2 variables)

!

Fibers orientation (3

variables)

!

Materials:

!

VICOTEX

1454/48%/G1051

(epoxy+carbon

bi-directional)

!

NCHM 1748/38%/M46J

(epoxi+carbonio

uni-directional)

Example (1): fluid

-

structure

interaction

(12)

23

ALE

(Arbitrary Lagragian Eulerian)

DMM

(Dinamic Mesh Methods)

Hard coupled

Closely-coupled*

loosely-coupled

Soft coupled

Tipo di accoppiamento

• Pressure values are passed

to the structural code

• Displacements are passed to

the CFD code

• Interpolation is needed

Example (1): fluid

-

structure

interaction

Coupling StarCD & MARC

INPUT

MARC Script

St

a

rC

D

St

a

rC

D

St

a

rC

D

CFD-FEM

CFD

-

FEM

Pr

o

s

ta

r

Pr

o

s

ta

r

Pr

o

s

ta

r

FE

M

-C

FD

FE

M

FE

M

--

CF

D

CF

D

OUTPUT

C

O

N

V

.?

C

O

N

V

.?

C

O

N

V

.?

Example (1): fluid

-

structure

interaction

(13)

25

Prot.1 Prot.2 Prot.4 Rigid

Var.1 45.0 10.0 18.8 Var.2 43.7 27.6 18.9 Var.3 90.0 -74.4 -44.6 Var.4 44.3 72.9 -44.6 Var.5 87.4 -58.8 -44.6 Var.6 0.0012 0.0025 0.0016 Var.7 0.0006 0.0008 0.0011 Var.8 0.0005 0.0004 0.0007 Mass 0.226 0.356 0.341 Lift 0.03048 0.03196 0.02632 0.03132 Drag 0.00351 0.00376 0.00302 0.00358 Def. 15.51 24.79 151.91 Eff. 8.71 8.50 8.81 8.77

Best performances are obtained

using the deformable structure !

Example (1): fluid

-

structure

interaction Computed conf.

Coupling StarCD & MARC

Prot.4

- MAX efficiency

• root increased load

• tip decreased load

Example (1): fluid

-

structure

interaction

(14)

27

Prot. 2

MAX lift, low efficiency

• root increased Load

• tip increased Load

Example (1): fluid

-

structure

interaction

Coupling StarCD & MARC

28

Design problem

• An existing gas-turbine axial wheel must be

improved, therefore:

–

the static pressure ratio is given

–

hub and shroud shape are given

–

inlet is given, exit angle should match the stator

–

the efficiency should be possibly improved

–

the number of blades possibly reduced

–

the mass of the blade (centrifugal forces) be reduced

(15)

29

Simulation set

Simulation set-

-up

up

•

• Problem simplification:

Problem simplification:

–

– GEOMETRY: no tip clearanceGEOMETRY: no tip clearance

–

– PHYSICS: steady state analysisPHYSICS: steady state analysis

– MESH: 95200 nodes with NI=70 (inlet to outlet) NJ=40 (periodicity) NK=34 (hub to shroud)

– BC: periodic, moving walls, inlet: pressure, turbulence, temperature and velocity distribution;

• CPU for one analysis:

4 hours on one processor

PENTIUM III 550Mhz,

128Mbyte

Optimisation set

Optimisation set-

-up

up

•

• General Requirements:

General Requirements:

–

the geometric input

parameters must not yield

excessive distortion

–

all simulations have to run to

the same convergence level

–

radial stacking has to be fixed

–

expansion ratio has to be

fixed

•

• Constraints:

Constraints:

–

new efficiency

>

old efficiency

–

mean

mean exit angle

<

original blade

+1°

–

mean

mean exit angle

>

original blade

-

1°

–

max

max exit angle

<

original blade

+5°

–

min

min exit angle

>

original blade

-

5°

•

• Variables:

Variables:

–

# of blades (1 parameter)

–

profile thickness (%of

increment, 1 parameter)

–

tapering (linear, 1

parameter)

–

angles of 5 profiles from hub

to shroud (5 parameters)

–

profile shape at 90% radius

(4 parameters)

•

• Objectives:

Objectives:

–

minimise

the

number of

blades

–

minimise

the

taper ratio

hub

to shroud

–

maximise

profile

thickness

–

(16)

Geometry

parameterisation

• angles of 5 profiles

from hub to shroud (5

parameters)

• tapering (linear, 1

parameter)

+

=

• profile thickness (% of

increment, 1

parameter)

+

=

• profile shape at 90%

radius (4 parameters)

Design Logic

Input

variables

output

variables

Input

files

output

files

applications

transfer files

logic

controls

objectives $

constraints 0o0

(17)

Optimisation strategy

•

• Initial screening

Initial screening

–

MOGA 36 x 10 (320 simulations considering

repeated analysis

repeated analysis)

)

–

4 objectives

–

analysis of results

–

4.4 days

•

• First refinement

First refinement

–

MOGA 30 x 10 (184 simulations)

–

2 Objectives

–

analysis of results

–

2.5 days

•

• Final Optimisation

Final Optimisation

–

Single objective, 30 x 10 (168 simulations)

–

One optimal geometry found

–

2.3 days

12 processors Linux

cluster

running 12 TASCFlow

simulations concurrently

handled by FRONTIER

Initial screening

The first optimisation run shows:

–

from 84 to 90 blades efficiency

improvements are possible

–

profile thickness can be increased

–

tapering can be introduced

Original blade eff.

E

ff

.

T

h

ic

.

#Bla.

T

a

p

.

(18)

35

First run Pareto

solutions

• 2 parameters and

objectives can now

be fixed:

–

84 Blades

–

6% Tapering

E

ff

.

T

h

ic

.

#Bla.

T

a

p

.

36 University of Trieste Dipartimento di Energetica Original blade

Eff.

T

h

ic

.

Eff.

T

h

ic

.

Refinement with 2

Objectives

• 4 solutions are not dominated

84 blades, 6% Tapering, 25%

thicker, efficiency 0.927

(19)

37

Final

Optimisation

• 84 Blades, 6% Tapering, 12.5% Increased Thickness

(both side, suction and pressure side, total 25%)

• Efficiency 0.928

Optimisation final

results

Parameter

Original

Blade

Optimized

blade

# blades

90

84 Taper

100%

94%

Thickness

100%

125%

Efficiency

92.00%

92.80%

Expansion ratio

2.11

2.10 Outflow angle

59.87 59.0131

Reaction rate

0.3579

0.4102

(20)

Results

Original

Optimised

Conclusion

• Evolutionary Algorithms are one component of the design

optimisation process

• Recently developed algorithms are robust and efficient

• But…

• … the design otimisation process, whatever is the algorithm, is

not

a

push-button-get-result

process but is a

knowledge

acquisition, knowledge exploitation, decision-making

process that, to be effective must have all the following

ingredients:

–

Parametric models

–

Mathematical algorithms

–

Flexible IT infrastructure