some applications of multicriterion strategies in mechanical …gaggle/s05/mop/... · 2005. 5....

Humboldt-Universität, Berlin, 25.5.2005

Dieter Bestle and Akin Keskin

Chair of Engineering Mechanics and Vehicle DynamicsBrandenburg University of Technology Cottbus

Some Applications of Multicriterion Strategies in Mechanical Engineering


Classification of Optimization Problems

optimization

topologyoptimization

shapeoptimization

sizing

scalaroptimization

multicriterionoptimization

scalarization

hierarchization

unconstrained constrained

)(min pp

fh

RI∈)(min p

pf

P∈

ouhRIP ppp0ph0pgp ≤≤≤=∈= ,)(,)(


What is Optimization Good For?

min

l

uP0 -∈

Ω Ω Ω

pmaximum stable speed range

0

0

0: min . . max Re( ) 0

: min . . max Re( ) 0l

lj

j

uj

j

s t

s t

λ

λ

≤ Ω ≤ Ω

Ω < Ω ≤ Ω

Ω = Ω ≤

Ω = Ω >

2 3 4, ,min max ( ) , ( ) , ( )

x tx t x t x t

γ ε∆minimum motion of inner balls

( )min Tρ ϕ

ˆ. . ( )s t s T s=

minimum time

• Designing Birthday Presents




• Solving Problems of Existing Machines

ideal contact geometry

( )

( )

max

min

r

z

ρ ψ

ρ ψ

δ

δ

0. . tans t ϕ µ≤

ideal ring shape

, ,min T

Sw

γγ +

rr r

0

0

00. . ,/r rk k

r kkrk

sS S

Gt SS

γµ−

≤=

rkS

D

H

S

S

kr

ϕ

( )ρ ψ

rδ

zδ

N

T





• System Identification

• actuator behavior

(hydraulic, pneumatic, electro-mechanical)

• dynamic behavior of passive components

• system parameters

• control behavior





• System Identification

• Virtual Prototyping

• hardware-in-the-loop optimization

• mechatronics (control design)

• multibody systems (vibrations)

• multi-disciplinary optimization

Humboldt-Universität, Berlin, 25.5.2005 ouhRIP ppp0ph0pgp ≤≤≤=∈= ,)(,)(

scalaroptimization

vectoroptimization

min f(p)p∈P

min p∈P

f1 (p)...

fn (p)

P

f1

f2

f(P)

1

2

multiple optimal compromises

f(p)

Why Multi-criterion Optimization?

a technical point of view

p1

f

single optimal solution


scalaroptimization algorithm

Reduction Principles for Vector Optimization

vector optimization problem

scalar optimization problem

…

obje

ctive

1

obje

ctive

n

constr

ain

t1

…

constr

ain

tm• scalarization

(weighted obj., distance method,

goal attainment)

• hierarchization(hierarchical opt.,

compromise method)

• combination(goal programming)


Example 1: Horizontal Platform Insulation

physical modeling

Linearization

Equivalent Mechanical Model (Q=0)

Guxy ∆−∆=∆

problem: increase of horizontal damping

( )

( )

( )212

2101

2

2

2221

1

111

01

,

ppqQV

ppqyAV

VV

pnpV

V

pnp

AppF

L

L

L

−−−=

−+−=

−=−=

−=

ɺ

ɺɺ

ɺɺɺɺ

( ) dtQqyAyqApqp

ApF

LLL ∫+∆+∆+∆+−=∆

∆=∆

αβααββα ɺɺ0011

01

( )2 1 21 2

2 2

k k kF F y k k y

d d∆ + ∆ = ∆ + + ∆ɺ ɺ


multi-measurement identification

experimentalsetup

Simulink model

2

0

1 , ,

,

T

i

F Fsim i meas i

where dtT F

meas i

ϕ

−= ∫

0,: ≥=∑ i

i

ii wwu ϕobjectives

1,:

/1

0 ≥

−= ∑ ru

rr

i

ii ϕϕ

optimization(Matlab)

measF simF



platform insulation

,ˆ

ˆmin

℘∈ f

H

p,

ˆ

ˆmin

℘∈ T

H

p

℘∈ T

f

ˆ

ˆminp

passive

active

xDQ ɺ∆=stream flow control

60 ≤≤ BVs

bar6bar4 0 ≤≤ p

[ ]TBVsp0=p

0)Re( <iλ

0.0100.012- ≤≤ D

bar6bar4 0 ≤≤ p

[ ]TDp0=p

0)Re( <iλ

bi-criterion problems

1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

0 1 2 3 50.14

0.16

0.18

0.2

0.22

0.24

0.28

1 1.5 2 2.5 3 3.5 40.14

0.16

0.18

0.2

0.22

0.24

0.28

3.26 3.27 3.280.201

0.202

0.203

passive

passive

passive

active

active

active

( )( )ii

T

iHiHf

iHH

λ

ωωπω

ω

ω

ω

Remax

1ˆ

)(max)ˆ(:2/ˆˆ

)(maxˆ

−=

==

=

objectives to be minimized



f1

f2

f(P)

*jf

*if

* *: i j = F f f

Fββββ

nFβ t+

n

single EP-solution

)(pfnFβ =+ t

ttP

min,∈p

. .s t

.const=β

)(pfnFβ =+ t

ttP

min,, βp∈

. .s t

1,0 =∑≥ ii ββ

knee search

Normal Boundary Intersection Approach

related to I. Das and J.E. Dennis

recursive knee search


2) lower and upper recursion limits

Recursive Knee Search

individual minima

• initial design

initial design

knee search

global optimality

localoptimality

stoppingcriteria

trade-off curve

2/λλ =

fulfilled

fulfilled

recursionloop

• stopping criteria

• bounds on knee search

( ) ( )(0)i j i1 1,1randλ ε∗ ∗ ∗= + + − − p p p p

( )1

0,1 , 0, min 1, 1λ ελ

∈ ∈ −

. . 0.2, 0.5e g ε λ= =

| | , . . 0.1t t e g t≤ =1)

1)

2) min max[ , ], . . [0.4,0.6]e gβ β β β∈ ∈

,]1,1[−∈t

• local optimality

1) solution feasible2) local EP-optimality3) limits on No. of non-successful restarts

Matlab applet


VIT-project (Virtual Turbomachinery, LuFo III)

Improvement of current Rolls-Royce compressor design process

by tool integration and optimization

step 1: tool by tool analysis of current compressor design process

step 2: automation and integration of single analysis tools into an optimization environment

step 3: partial automation of multidisciplinary design process

Tool8

Tool7

Tool5

Tool1

Tool2

Tool3

Tool4Tool6

iSight

the future: automation of whole multidisciplinary design process

Example 2: Compressor Design Process


Aerodynamics (Keskin)

cw

u

MeanlinePrediction

Throughflow 2D Blading 3D Blading

Design 2D-Thermal

Design and Stress (Otto)

High Cycle and Low CycleFatigue


MeanlinePrediction

annulus parameterization

0 5 10 15 20 25 304

6

8

10

12Annulus Line

• classical

point-wise definition

• Reduced parameter

definition

(Bézier-splines

with 4 control points)

0 10 20 305

6

7

8

9Mid-Height Line

0 10 20 300

2

4

6Thickness Line

2 2 3 3 2 2 3 3, , , , , , ,

T

x y x y x y x ydesign parameters b b b b t t t t = p

Matlab applet


polyc,max η p

6.0 max ≤iiΨ

1.1max ', ≤RiI

iM

8.0max , ≤SiI

iM

55.0max ≤Ri

iDF

55.0max ≤Si

iDF

58.0max ≥Ri

iDH

58.0max ≥Si

iDH 92.0 max , ≤ih

iC

27.0, ≤S

NE sM

s,N, i …1∈

SM maxp

25SM %≥

MeanlinePrediction

criteria

constraints


87.5 88 88.5 89 89.5 90 90.5

Pareto Opitimal Solutions for Meanline Annulus Modification

Datum, Human Designer

iSight, MIGA, 4CP

Pareto Optimal Design

Results for Bézier-splines with 4 control points

E3E

human design

MeanlinePrediction

Polytropic Efficiency, ηηηηpoly

[%]

Su

rge

Ma

rgin

, S

M [

%]


0 10 20 305

6

7

8

9Mid-Height Line

0 10 20 300

2

4

6Thickness Line

0 5 10 15 20 25 304

6

8

10

12Annulus Line

4 control points allow

1 turning point, only !E3E has two

turning points

explanation for sub-optimal solution 1. parameterization too restrictive

5 control points

MeanlinePrediction


polyc,max η p

6.0 max ≤iiΨ

1.1max ', ≤RiI

iM

8.0max , ≤SiI

iM

55.0max ≤Ri

iDF

55.0max ≤Si

iDF

58.0max ≥Ri

iDH

58.0max ≥Si


iC

27.0, ≤S

NE sM

s,N, i …1∈

SM maxp

25SM %≥

criteria

constraints

explanation for sub-optimal solution 2. constraints too restrictive

MeanlinePrediction

0.93

0.285




iSight, MIGA, 4CP

iSight, MIGA, 5CP


Matlab applet

MeanlinePrediction

E3E

human designPolytropic Efficiency, ηηηηpoly

[%]

Su

rge

Ma

rgin

, S

M [

%]


E3E

max. efficiency

E3E

max. surge margin

MeanlinePrediction




iSight, MIGA, 5CP

iSight, NLPQL, 5CP


MeanlinePrediction

E3E

human designPolytropic Efficiency, ηηηηpoly

[%]

Su

rge

Ma

rgin

, S

M [

%]




iSight, MIGA, 5CP

iSight, NLPQL, 5CP


SM increase 17.3%

ηp increase 0.17%

MeanlinePrediction

E3E

human design Polytropic Efficiency, ηηηηpoly

[%]

Su

rge

Ma

rgin

, S

M [

%]


pressure ratio

1 2 3 4 5 6 7 8 91

1.2

1.4

1.6

1.8Parametric Stage Pressure Ratio Distribution

1 2 3 4 5 6 7 8 91

1.2

1.4

1.6

1.8Applied Stage Pressure Ratio Distribution

2 2 3 3 4 4 2 2 3 3 4 4, , , , , , , , , , , ,x y x y x y x y x y x yb b b b b b t t t t t t= p

1 2 2 3 3 4 4 5, , , , , , ,

T

y x y x y x y yp p p p p p p p

MeanlinePrediction

Annulus Line & Pressure Ratio Optimization


polyc, max ηp

6.0 max ≤iiΨ

1.1max ', ≤RiI

iM

8.0max , ≤SiI

iM

55.0max ≤Ri

iDF

55.0max ≤Si

iDF

58.0max ≥Ri

iDH

58.0max ≥Si


iC

285.0,

≤SNE s

M

M max Sp

s,N, i …1∈

1 0 2 0jy. p .≤ ≤

51 ,, j …∈

c max Πp

criteria

constraints

MeanlinePrediction

25SM %≥

ignored



21.5886

22.0712

22.5538

23.0363

23.5189

24.0015

24.4841

24.9667

25.4492

25.9318

26.4144

26.897

Πi

*

MeanlinePrediction

E3E

human design


Polytropic Efficiency, ηηηηpoly

[%]

Su

rge

Ma

rgin

, S

M [

%]


MeanlinePrediction



Comparison: some numbers

18.2h839

(~8%)

10637

(~99%)10768

NLPQL 5CP

(Annulus)

94.1h

30.5h

19.3h

total

time

11909

(~28%)

42854

(~79%)54000

MIGA 5CP

(Annulus+PR)

5559

(~40%)

13743

(~86%)16000

MIGA 5CP

(Annulus)

4174

(~58%)

7166

(~90%)8000

MIGA 4CP

(Annulus)

feasibleconvergedfunction

evals

17min24

(~16%)

151

(100%)151

NLPQL 5CP

(Annulus)

best efficiency

MeanlinePrediction


Off-Design

Process Overview

Throughflow


-0.59293051

0.964143808

0.03 K

0.023 %

0.19 %

~2.1min

3.6 h

98

iSight

(Case1)

1.01857design parameter χ

0.83 KT criterion (∆T ≤ 1K)

-0.59design parameter ∆D

0.53 %η criterion (∆η/η ≤ 1%)

0.22 %Π criterion (∆Π/Π ≤ 1%)

~21mintime for one iteration

8 hoverall opt. time

No. iterations (feasible) 23

human

eng.

D,min

Tχ

η η

∆

∆ ∆Π Π ∆

multi criteriaproblem

nonlinearprogrammingproblem

Dmin u

χ∆ ,where ( )

2 22

100 100u Tη

η

∆ ∆Π = ⋅ + ⋅ + ∆

Π

best fastest

-0.5

1.0

1.2 K

0.544 %

0.063 %

~2.1min

1.6 h

46

iSight

(Case2)

0.95351

0.98 K

-0.62655

0.162 %

0.032 %

~2.1min

0.76 h

22

iSight

(Case3)

Throughflow

eng.


20

20

20

20

20

20

20

20

20

20

40

40

40

40

40

40

40

40 40

40

40

40

40

40

60

60

60

60

60

60

60

60 60

60

60

60

60

80

80

80

80

80

80

80

80

80

80

80

80

80

100

100

100

100

100

100

100

100

100

100

100

120

120

120

120

120

120

120

120

120

120

140

140

140

140

140

140

140

140

160

160

160

160

160

160

160

180

180

180

180

180

180

200

200200

200

200

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0A

dditio

nalD

evia

tion

[deg]

∆D

0.6 0.8 1.0 1.2 1.4

0.6 0.8 1.0 1.2 1.4

Pressure Loss Coefficient Factor [-]χ

0

20

40

60

80

100

120

140

160

180

200

ConvergedSolution

EngineeriSight

iSight

Throughflow


Conclusions

• by nature, technical design problems are multi-criterion optimization problems

• multi-criterion optimization cuts down costs by releasing human design engineer from time-consuming parameter studies without taking him off the decision process

• multi-criterion optimization is a valuable tool for a variety of practical applications as

- optimal system design (active and passive)- identification- search for admissible solutions (stability)

• multi-criterion optimization finds better results than human designer

• integrated system design allows heterogeneous analysis tools on heterogeneous platforms

some applications of multicriterion strategies in mechanical …gaggle/s05/mop/... · 2005. 5....

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