component mode synthesis
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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
ACMS-1 ACMS-2 ACMS-4
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
ACMS-1 ACMS-2 ACMS-4
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
ACMS-1 ACMS-2 ACMS-4
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
ACMS-1 ACMS-2 ACMS-4
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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Case Study 2 Sample Results (cont)Case Study 2 Sample Results (cont)
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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Case Study 2 Sample Results (cont)Case Study 2 Sample Results (cont)
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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Case Study 2 Sample Results (cont)Case Study 2 Sample Results (cont)
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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Case Study 2 Sample Results (cont)Case Study 2 Sample Results (cont)
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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