최적화의 최신 트렌드- 다중모델의 동시최적화 (MDO)

2011.07

한국엠에스씨소프트웨어㈜

김정원

목 차

1. 최적화란 무엇인가?

2. 최적화 기법들에 대한 비교검토

3. 다중모델에 대한 동시최적화 기법검토

4. 최적화 업무 적용에 있어서 주의할 사항들

5. 향후 최적화 기술의 발전방향

2

1. 최적화란 무엇인가?

3

Design Optimization이란?

• Design Optimization이란?

• 해석 모델의 자동 수정이다.

• (목적함수를 달성)

• (주어진 설계조건을 유지하면서…)

• 응용분야?

• o 구조설계 개선 (Sizing, Property, Shape, Topology/Topometry/Topogrphy)

• o 현실성 없는 설계로부터 현실성 있는 설계로 변환

• o 구조응답을 동일하게 구현하기 위한 모델변환

• o 시스템의 지배적인 인자 도출

• o 모델구성 평가

• o 민감도 분석

• o 기타 (설계자의 창의적인 구상 검증 등)

4

Design Optimization 개념도?

5

구조응답해석

민감도 해석

FE해석

근사 등가모델 Optimizer

Many Times

Design Cycle

Hard / Soft Convergence?

Design Optimization 의 종류?

6

• Sizing 최적화

• Property 변화

• Topometry (v2008r1부터)지원

• Shape 최적화

• GRID 위치 형상변화

• Topography (v2008r1부터)지원 (Bead Optimization)

• Topology 최적화• 불필요한 부분 제거

• v2007부터 Frequency Response지원

• v2007부터 Transient Response 지원

Other Topics?

7

• Multi-disciplinary Topology?

• Nastran SOL200의 기본제공 기능

• Composite Optimization?

• PCOMPG 지원 (v2008r1부터)

• Global Ply ID – Layer Control (v2008r1부터)

• Topology based sizing & shape Optimization?

• Topology / Topometry / Topography 지원 (v2008r1부터)

• 매우 빠른 속도로 Preliminary Design Optimization수행가능

Nonlinear Optimization?

8

• SOL400 Optimization (MD Nastran v2011 New) – 대변형 최적화

• Bi-directional SOL400_to_SOL200 internal_loop

Design Optimization Results?

9

• Response Improvement

• Input Data Update

Defining The ANALYSIS DISCIPLINES

• Executive Section

SOL 200

• Case Control Section

AcousticsInclude*

Analysis

STATICS Statics

MODES Normal Modes

BUCK Buckling

DFREQ Direct Frequency*

MFREQ Modal Frequency*

MTRAN Modal Transient*

DCEIG Direct Complex Eigenvalue Analysis*

MCEIG Modal Complex Eigenvalue Analysis*

SAERO Static Aeroelasticity

FLUTTER Flutter

10

Graphical Support

• Since Patran 2005r2:– Preprocessing of static and eigenvalue topology optimization

– Preprocessing of global minimum member size

– Smoothing, remesh and generate IGES files for 2D

– Smoothing of 3D topology designs

11

Trust Region – Adaptive Move Limits

• Move limits in SOL 200 approximate optimization can be now adjusted

in an adaptive fashion

• Merit function is a combination of objective function and maximum

violated constraint

• Trust region is ratio of the exact versus the predicted reduction of the

merit function

• Trust region is used to keep, increase, or decrease move limits

• Adjustment of move limits leads to improved quality

of the approximate model

• Should provide more robust optimization results and

faster convergence (fewer design cycles)

• Rejection of bad designs smoothes the design

optimization process

12

Trust Region – ExampleStiffened Panel

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Design Cycle

Maxim

um

Co

nstr

ain

t

MaxCon_nTr

MaxCon_Tr

13

$

PSHELL, 1, 2, 2.5

DESVAR, 1, THICK, 1., 0.1, 10.

DVPREL1, 1, PSHELL, 1, T

1, 2.0

Support of Analysis Model Value Overriding

- Design Model Value

• Example: Design plate thickness

• Leads to .f06 output

Plate thickness defined on PSHELL = 2.5

Design model value = 1. * 2.0 = 2.0

overwrites

analysis model

14

Support of Analysis Model Value Overriding

- Analysis Model Value

• Example: Design plate thickness

• Leads to in .f06

$

PSHELL, 1, 2, 2.5

DESVAR, 1, THICK, 1., 0.1, 10.

DVPREL1, 1, PSHELL, 1, T

1, PVAL

Design value is taken from the 4th entry

of PSHELL

15

SOL200 AESO Creation run

Sample input for an AESO creation run (aeso1.dat)

assign a file name to the assembly run

activate the AESO creation run

DRATIO (optional)

1

1

2 3

2

3

16

SOL200 AESO Assembly Run

Sample of the Assembly File (aeso1_2dat)

17

Dynamic road response optimization of a car

Model Statistics

Random inputs applied on left and right suspension, including cross-correlation

Examples 1 – SOL200 Optimization

Grids 23K

Total DOFs 137K

DOFs in Residual 7K

Elements 37K

Subcases 2

Frequencies 61

Response points 3-4.00E-03

0.00E+00

4.00E-03

8.00E-03

1.20E-02

1.60E-02

4 6 8 10 12 14

FrequencyIn

pu

t S

pectr

a

LEFT SUSP

RIGHT SUSP

REAL L/R

IMAG L/R

Input Power Spectra

18

Design Tasks

Design Variables : spring constant of 9 elastic elements to model

engine mount

Responses : PSD of accelerations at driver’s seat, passenger’s seat

and steering column

Case A: minimize the sum of RMS acceleration at Driver’s seat and

passenger’s seat while limiting the PSD response at steering

column

Case B: minimize the RMS acceleration at Driver’s seat and

maintain frequency dependent limits on driver’s seat

Examples 1 – SOL200 Optimization

19

Examples 1 – Case A : Objective Function– Case B : Design Objective

Sum of RMS

- reduced from 0.154 to 0.130

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

4 6 8 10 12 14

Frequency (Hz)

Su

mm

ed

Ac

ce

lera

tio

ns

SUM Init

Sum final

20

RMS

- reduced from 0.071 to 0.058

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

4 6 8 10 12 14

Frequency (Hz)

Passen

ger A

cceleratio

n

2033 Init

2033 Final

Dynamic Optimization of A car body

Analysis model statistics

207098 grid points

1.24 million DOFs

209079 elements

Design task statistics

Design variables: vary the height and width of some

box cross sections of 183 beam elements

Objective: minimize the structural weight

Constraints: maintaining 1st, 2nd and 3rd modes above given limits.

Examples 2 - SOL200 AESO

Image vehicle model

21

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8 9Design Cycle

Clo

ck

Tim

e (

Min

ute

) Total Time (Single Run)

Total Time (AESO)

Examples 2 - AESO Results and Performance

The final objective by AESO matches that of a single shot

run within a relative error of 1%.

Speed up is 4+ fold

22

2. 최적화 기법들에 대한 비교검토

23

Size / Shape Optimization

24

• Sizing 최적화

• Property 변화

• Topometry (v2008r1부터)지원

• Shape 최적화

• GRID 위치 형상변화

• Topography (v2008r1부터)지원 (Bead Optimization)

Topology Optimization

• 새로운 최적화 기법의 효시

• Topology / Topometry / Topography 방법의 기본 알고리즘

• 빠른 시간내에 해석결과를 도출

• 초기 개념 설계에 최적

25

Example: MBB Beam Baseline (Cont.)

$ BASELIN Toppology Optimization / XMY

SOL 200 $ OPTIMIZATION

$ Direct Text Input for Executive Control

CEND

TITLE = MBB BEAM Baseline

ECHO = NONE

$ Direct Text Input for Global Case Control Data

DESGLB = 1

SUBCASE 1

DESOBJ = 1

$ Subcase name : Default

SUBTITLE=Default

SPC = 2

LOAD = 2

ANALYSIS = STATICS

BEGIN BULK

PARAM POST 0

PARAM AUTOSPC YES

PARAM,NOCOMPS,-1

PARAM PRTMAXIM YES

$

DCONSTR 1 2 .5

TOPVAR, 1 , Tshel, Pshell, .5, , , , 1

DRESP1 2 FRMASS FRMASS

DRESP1 1 COMPL COMP

DOPTPRM, DESMAX, 100

INCLUDE 'model.dat'

ENDDATA

Optimization without restriction

26

Example: MBB Beam Baseline (Cont.)

Desmax

default

27

Example: MBB Beam - Minimum Member Size

$ Toppology Optimization with Minimum Size Control Example 1/ XMY

SOL 200 $ OPTIMIZATION

CEND

TITLE = MBB BEAM Minimum Member Size (global)

ECHO = NONE

$ Direct Text Input for Global Case Control Data

DESGLB = 1

SUBCASE 1

DESOBJ = 1

$ Subcase name : Default

SUBTITLE=Default

SPC = 2

LOAD = 2

ANALYSIS = STATICS

BEGIN BULK

PARAM POST 0

PARAM AUTOSPC YES

PARAM,NOCOMPS,-1

PARAM PRTMAXIM YES

$

DOPTPRM, TDMIN, 0.5, DESMAX, 100

DCONSTR 1 2 .5

TOPVAR, 1 , Tshel, Pshell, .5, , , , 1

DRESP1 2 FRMASS FRMASS

DRESP1 1 COMPL COMP

INCLUDE 'model.dat'

ENDDATA

first option: global minimum thickness

(applies to complete design region)

28

Example: MBB Beam

$ Toppology Opt with Minimum Size Control and symmetry

SOL 200 $ OPTIMIZATION

CEND

TITLE = MBB BEAM Minimum Member Size + Symmetry

ECHO = NONE

$ Direct Text Input for Global Case Control Data

DESOBJ = 1

DESGLB = 1

SUBCASE 1

$ Subcase name : Default

SUBTITLE=Default

SPC = 2

LOAD = 2

ANALYSIS = STATICS

BEGIN BULK

PARAM POST 0

PARAM AUTOSPC YES

PARAM,NOCOMPS,-1

PARAM PRTMAXIM YES

$

CORD1R 1 10001 10002 10003

GRID 10001 3. 1. 0.0

GRID 10002 3. 1. 1.0

GRID 10003 4. 1. 0.0

DCONSTR 1 2 .5

TOPVAR, 1 , Tshel, Pshell, .5, , , , 1

, SYM , 1 YZ, ZX

, TDMIN, 0.15

DRESP1 2 FRMASS FRMASS

DRESP1 1 COMPL COMP

DOPTPRM, DESMAX, 100

INCLUDE 'model.dat'

ENDDATA

minimum member size + double symmetry

30 design cycles

100 design cycles

29

One die+ YZ

Symmetry

Two dies + YZ

Symmetry

Torsion Beam – Other Options

30

Example: Engine Mount (cont.)casting constraints in x and y direction

14 loadcases

Without restriction With restriction

31

Topometry Optimization

• 설계 영역에 속해 있는 요소들의 대한 요소 특성 값들을 주어진 조건에 맞도록 변경.

사용자는 요소 특성 (두께 등.)과 재료 물성(E, GE 등)을 설계

• Topometry는 전통적인 전응력설계(Fully Stressed Design, FSD)로 쉽게 확장 가능

• 재료의 가감에 대한 아이디어를 제공 (topology는 제거만 가능)

• Topology의 결과는 0-1로 표현 되지만 topometry는 연속 변수로 표현 가능

• 요소 사이즈 결정에 대한 아이디어 제공

• Test-Analysis Correlation

• Non-volume 요소의 최적 위치에 대한 아이디어

• PDAMP, PELAS, PMASS, PBUSH, PVISC, PGAP, NSM, NSM1, NSML,

PACBAR, PFAST

32

Example 2 – Topometry

• Element results in jobname.des

• Use Patran/Results to display

TOMVAR, 1 , PSHELL, 10, T , 2.0, 1.0, 3.0

TOMVAR, 2 , PSHELL, 39150, T , 2.4, 1.2, 3.6

33

Topography Optimization

• Reinforcement bead 패턴을 주어진 bead 치수 한계(bead의 최소 넓이, 최대 높이, draw angle등) 내에서 제한 조건을 만족하는 최적 모델을 제공하는 형상 최적화 기능의 일종

• Shape Optimization의 일종

• Sheet metal part에 유용

• 기존 Optimization 파일에 BEADVAR 명령 추가

34

• Topography Optimization Features

– Bead minimum width (MW). This parameter controls the width of the beads.

– Maximum bead height (MH). This parameter sets the maximum height

– Draw angle in degrees (ANG)

– Buffer zone between designed and non-designable parts

MW

MHANG

Non-design elementsNon-design elements

Design elementsno buffer zone

Buffer zone

Topography Optimization

35

Example 1 – Topography

• A square fixed at all boundary

• Objective Maximize 1st Frequency

– Minimum width = 10.0

– Maximum height = 20.0

– Draw angle = 70.0

– Grids associated BC is fixed

• Initial design

– 1st Frequency = 0.568HZ

• Output quantities

– Design history in *.f06

– Updated grid location *.pchSOL200 1st Freq. =4.78 Hz

36

Example 2 – Topography

• Minimize Sum of Compliance over four load cases

(i.e., maximize stiffness) = 2.06E+3 at initial

– CQAD4 13817

– GRID 14095

– PSHELL 2

– Minimum width = 50.0

– Maximum height = 10.0

– Draw angle = 70.0

– Grids associated BC is fixed

• Output quantities

– Design history in *.f06

– Updated grid location *.pch

37

Example 3 – Topography (from Auto Customer)

• Maximize 1st Frequency

– Design the base only

– Minimum width = 10.0

– Maximum height = 20.0

– Draw angle = 70.0

– Grids associated RBE2 is fixed

– Use Case Control Set and

BEADVAR “NGSET” to

fix grids

– 1st Freq = 582 HZ SOL200 Result 654 Hz

38

3. 다중모델에 대한 동시최적화 기법검토

39

MultiOpt (MD Nastran - interenal-loop)

40

Example - MultiOpt

• 108 Design Variable

- Static Model

- NVH Model

41

Nonlinear Expansion

(MD Nastran DRESP3 Entry - external-loop)

42

External Multi-Model Process

(MD Nastran + Model Center)

43

4. 최적화 업무 적용에 있어서 주의할 사항들

44

Design Optimization 업무에서 주의할 사항들…

45

• 응용분야?

• o 구조설계 개선 (Sizing, Property, Shape, Topology/Topometry/Topogrphy)

• o 현실성 없는 설계로부터 현실성 있는 설계로 변환

• o 구조응답을 동일하게 구현하기 위한 모델변환

• o 시스템의 지배적인 인자 도출

• o 모델구성 평가

• o 민감도 분석

• o 기타 (설계자의 창의적인 구상 검증 등)

최적화는 Peak만을 줄여준다.

부가된 제한조건만을 만족시킨다.

답은 여러 가지가 있을 수 있으며, 결과가 최선이 아닐 수 있다.

최적화를 강하게 하면 할수록 강건성은 계속 저하한다.

경험이 있는 엔지니어의 판단이

특히 더 중요하다.

5. 향후 최적화 기술의 발전방향

46

해석 개념의 발전방향 변화 트렌드

구조응답해석

(현상 규명)

47

응답최적화

(생산비용 최소화)

응답 강건성 검증

(A/S 비용의 최소화)

SOL103.

SOL111.

.

.

SOL200ANAL=Modes.

SOL200ANAL=MFREQ.

SOL200,SOL400Stochastic.

.

.

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8 9Design Cycle

Clo

ck

Tim

e (

Min

ute

) Total Time (Single Run)

Total Time (AESO)

Enhancement of AESO

Further Enhancement of AESO

(Automatic External Superelement Optimization)

Speed up !!!

48

Enhancement of ACMS

• Example 1 (with K4 damping)– SOL 111

– DOF: 7,300,000

– Elements: 900,000

– 3600 modes up to 800Hz

– Forcing frequencies: 320

• Example 2 (with K4 damping)– SOL 111

– DOF: 8,500,000

– Elements: ~1 million

– 7197 modes up to 800Hz

– Forcing frequencies: 700

49

13.15

5.98

3.08

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00 Elapsed Time (Hrs)

47.28

9.74 4.39

0.00

10.00

20.00

30.00

40.00

50.00

Elapsed Time (Hrs)

2010 20112011 SMP=2

DMP=22010 2011

2011 SMP=2

DMP=2

Further Enhancement of ACMS

(Automatic Component Modal Synthesis)

Speed up !!!

OpenMDOTM External Optimizer Service

• Complements MSC’s optimization

capabilities

• User defined SCA service

introduced to access external

optimizers

• Benefits

– Flexibility to use third party or

internally developed optimizers

– Researchers to assess the ability

of their algorithms vs. COTS

implementations

50

Improved

Design

Ride &

Handling, E

xplicit

RSM

DOE

Linear Multi-Model Optimization

Nonlinear Multi-Model Optimization

Multi-Model / Multi-Disciplinary Optimization

MMO Auto Applications:

Analyze Systems with Common Parts

• 4 doors/2 doors Versions of a Car

• V6/V8 Cylinder Engine Configurations

• Sports/Standard Suspensions

MDO Auto Applications:

Analyze Systems with Multiple

Disciplines

• Brakes: Squeal (Acoustics), Wear

(Thermo-Mechanical)

• Engines: Whine (NVH), Durability

(Thermo-Mechanical)

• Full Vehicle: Durability, NVH, Ride &

Handling, Crash

51

감사합니다.

52