Component Mode Synthesis

7/31/2019 Component Mode Synthesis

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June 2003 ClusterWorld

Peter Schartz, Parallel Project Manager

ClusterWorld Conference

June 2003

Full Vehicle Dynamic Analysisusing

Automated Component Modal

Synthesis


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OutlineOutline

Introduction

Background

Theory

Case Studies


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Full Vehicle Dynamic AnalysisFull Vehicle Dynamic Analysis

Noise, Vibration, and Harshness (NVH)

Roadnoise Important Items:

Acoustic level at your ear

Acceleration at your seat

Steering wheel shake

From engine idle to high RPM

Fatigue / durability

Competition


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MSC.NastranMSC.Nastran

General purpose finite element analysis program

Originated with NASA (1970s) Extensive worldwide use

Automotive

Aircraft / Spacecraft

Manufacturing


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Frequency Response AnalysisFrequency Response Analysis

Steady-state oscillatory excitation

Excitation defined explicitly in frequency domain Applied forces are known

Unknowns include displacement, velocity,

acceleration


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Two Approaches: Direct and ModalTwo Approaches: Direct and Modal

Direct:

Complex solution at each discrete frequency Physical domain

Modal:

Eigenvectors (mode shapes) instead of physical variables

Transform from physical to modal coordinates, and back

Approximation when Nmodes


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Dynamic Equation General FormDynamic Equation General Form

[ ]{ } [ ]{ } [ ]{ } { }xxxxxxxxxxPuKuBuM =++ &&&

where { }xu is the vector of grid point displacements.

{ }

= dt

duux

&is the vector of grid point velocities.

{ }

=2

2

dt

udux&&

is the vector of grid point accelerations.

x = Number of (Active) physical DOF (direct), orNumber of generalized coordinates (mode shapes)


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Industrial PracticeIndustrial Practice

If Ndof >> Nmodes, modal approach is more efficient

Computing the eigensolution becomes primarycomputational concern

Conflicting goals: analysis time vs. accuracy

Modal truncation

Accepted level of accuracy


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Industrial TrendsIndustrial Trends

Early-mid 1990s

Low frequency, structure-only Increasing model size, complexity (up to 1M DOF)

Sparse matrix methods

Vector supercomputer hardware

Mid-late 1990s

Mid frequency, structure plus fluid (acoustics)

Two and three million DOF

Cache based RISC, commodity components


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Industrial Trends (continued)Industrial Trends (continued)

Current

High frequency, structure plus fluid (acoustics)Model sizes (up to one million grid points)

Dense matrix methods

Inexpensive hardware

Future

Higher frequency

Model sizes increasing

Inexpensive network clusters


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Limitations to Modal ApproachLimitations to Modal Approach

Global eigensolution

Block-shifted Lanczos algorithm (Boeing) Vector supercomputer hardware paradigm

Large disk I/O cost

Modal density increases with frequency range

Past: Less than one million DOF, 500 modes

Overnight turnaround Present: More than one million DOF, 1000 modes

Two days or more


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Modified Modal ApproachModified Modal Approach

High level domain decomposition

Component modal reduction Global eigensolution is replaced by an approximation

MSC.Nastran Automated Component Modal Synthesis(ACMS)


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Dynamic Equation Reduction FormDynamic Equation Reduction Form

where:

a is the analysis set, to be retained: boundary points

o is the omitted set, to be eliminated: interior points

=

+

+

o

a

o

a

oooa

aoaa

o

a

oooa

aoaa

o

a

oooa

aoaa

P

P

u

u

KK

KK

u

u

BB

BB

u

u

MM

MM

&

&

&&

&&


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Component Modal SynthesisComponent Modal Synthesis

Stiffness is exact

Mass and damping reduction are approximate Independent DOF are represented by their mode shapes

Fixed boundary points used to solve for interior

Craig-Bampton method

http://analyst.gsfc.nasa.gov/FEMCI/craig_bampton

Scott Gordon, NASA Goddard


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What is ACMS?What is ACMS?

Automated Component Modal Synthesis (ACMS) combines

domain decomposition with component modal synthesis The model is divided into N domains (components)

automatically via nested dissection

Binary tree is formed Component modal reduction

Craig-Bampton (fixed boundary points)

Residual vector augmentation at each component Parallel ACMS (PACMS) is the execution of ACMS on

multiple processors in parallel


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0

25

21 2322 24

26

20191817

29 30

2827

Binary multilevel treeBinary multilevel tree


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0

25

21 2322 24

26

20191817

30

2827

Master

Slave 2

Slave 1

Slave 3

29

Static domain assignment

Binary multilevel tree - NDOM=16, DMP=4Binary multilevel tree - NDOM=16, DMP=4


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ACMS Performance AdvantageACMS Performance Advantage

Modal reduction results in fewer operations

No single large eigensolution

Disk I/O cost

Smaller order of calculations

Tens of thousands vs. millionsMore advantageous for cache based processors

Two- or Three-to-One Speedup is Typical

Parallel ACMS Increases Job Turnaround Additional speedup


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ACMS vs. Standard Modal ApproachACMS vs. Standard Modal Approach

Advantage for Problems with High Modal Density

General ACMS Performance Trend

No. of Eigenvalues

Time

Standard Modal

ACMS


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ACMS BenchmarksACMS Benchmarks

Itanium2 cluster running Linux

Two Automotive Models

Resource Utilization

CPU and Elapsed Time

Disk Space and Memory Requirements

Disk I/O Transfer Requirement

Results Comparison


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Cluster ConfigurationCluster Configuration

Node: QUAD1

HW: HP ZX1

OS: MSC.Linux

CPU: Itanium2 (2)

Mem: 12Gb

Disk: 66Gb

Node: QUAD0

HW: HP ZX1

OS: MSC.LinuxCPU Itanium2 (2)

Mem: 4Gb

Disk: 66Gb

Node: IA646

HW: Intel Tiger

OS: Redhat

CPU: Itanium2 (4)

Mem: 4Gb

Disk: 70Gb

Node: ALTIX

HW: SGI Altix

OS: Redhat

CPU: Itanium2 (4)

Mem: 8Gb

Disk: 63Gb

[Gigabit Ethernet connection][Gigabit Ethernet connection]


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Case Study 1 GM modelCase Study 1 GM model

Acoustic idle shake

312,000 grid points (1.8 million degrees of freedom) 500 modes up to 150 Hz

160 forcing frequencies up to 80 Hz

Two load cases


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Case Study 1 GM modelCase Study 1 GM model


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Case Study 1 Performance DataCase Study 1 Performance Data

Serial Performance

0

50

100

150

200

250

300

350

1-Shot ACMS-1

M

inutes

Elap

CPU

Parallel Performance

0

20

40

60

80

100

ACMS-1 ACMS-2 ACMS-4

M

inutes


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Case Study 1 Disk Space UtilizationCase Study 1 Disk Space Utilization

MaximumDisk Space - Serial

0

5

10

15

20

25

30

1-Shot ACMS-1

GB

MaximumDisk Space per Parallel Process

0

1

2

3

4

5

6

7


Gb


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Case Study 1 Disk Input/OutputCase Study 1 Disk Input/Output

Total I/O - Serial

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1-Shot ACMS-1

G

B

Max Total I/O per Parallel Process

0

200

400

600

800

1000

1200


G

B


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Case Study 2 Opel modelCase Study 2 Opel model

Acoustic analysis

1.3 million grid points (7.9 million DOF)

1000 modes up to 300 Hz

190 forcing frequencies 21 load cases


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Case Study 2 Opel model (example)Case Study 2 Opel model (example)


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Case Study 2 Opel model (example)Case Study 2 Opel model (example)


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Case Study 2 Performance DataCase Study 2 Performance Data

Serial Performance

0

20

40

60

80

100

120

140

160

1-Shot ACMS-1

H

ours

Elap

CPU

Parallel Performance

0

5

10

15

20

25


H

ours


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Case Study 2 Disk Space UtilizationCase Study 2 Disk Space Utilization

MaximumDisk Space - Serial

0

50

100

150

200

250

1-Shot ACMS-1

GB

Maximum Disk Space per Parallel Process

0

5

10

15

20

25

30


G

B


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Case Study 2 Sample ResultsCase Study 2 Sample Results

Subcase 1 Grid 1000157

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.08.0

0.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0

Frequency

Accel(t3)

1shot

acms


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Case Study 2 Sample Results (cont)Case Study 2 Sample Results (cont)

S ub case 2 Gr id 1000157

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0

Frequency

Accel

(t3)

1shot

a c m s


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Subcase 3 Grid 1000157

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0 200.0

Frequency

Accel

(t3)

1shot

acms


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Su bcas e 1 Grid 1000167

-20.0

-15.0

-10.0

-5.0

0.0

5.0

0.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0

Frequency

Accel

(t3)

1shot

acms


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S ub case 2 Gr id 1000167

-40.000

-30.000

-20.000

-10.000

0.000

10.000

20.000

30.000

40.000

50.000

60.000

0.0 25.0 50.0 75 .0 100.0 125.0 150.0 175.0 200.0

F r e q u e n c y

Accel

(t3)

1shot

a c m s


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S ub case 3 Grid 1000167

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0

Frequency

Accel(t3)

1shot

acms


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ConclusionsConclusions

ACMS technology is essential to meet current

automotive dynamic analysis needsOvernight job turnaround on inexpensive platforms

Minimum resource usage

Excellent accuracy

Parallel ACMS Useful for Increased Performance

Further adaptation required as trends continue

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Component Mode Synthesis

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