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National Aeronautics and Space Administration
Cielo: A MATLAB®-Hosted Environment forMultidisciplinary System Analysis
MathWorks Aerospace and Defense ConferenceManhattan Beach, Calif.
June 5-6, 2007
Greg Moore,Mike Chainyk, Claus Hoff,
Eric Larour, John SchiermeierJet Propulsion Laboratory, California Institute of Technology
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Outline
• Introduction: Motivation and Challenges• Cielo Overview: Objectives, Approach and Enabling Technologies• Examples• Summary
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Motivation
• Case Study: Terrestrial Planet Finder – Coronagraph– Search for, and characterize Earth-like planets in the habitable zone around
nearby stars– Distinguish planet light from starlight (1.0e-9 contrast ratios)– ~6 m class visible wavelength coronagraph operating in L2 orbit– Pre-flight, system-level hardware tests at operating conditions is impractical– Increased reliance on high-fidelity, multidisciplinary simulations.
Artist's impression of the Terrestrial Planet Finder Coronagraph (TPF-C, left) and the Terrestrial Planet Finder Interferometer (TPF- I, right).
Cutaway geometric model of deployed configuration
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Motivation• 20° Dither Maneuver Analysis: Current State of the Art
– Scenario: Stabilize, roll, collect data (>2 hrs) for speckle removal and planet detection– CAD/CAE modeling for system behavior and optical metrics using commercial tools (top
row), and MATLAB hosted procedures (bottom row)Top of PM 0.144e-3 C
-0.340 C
CAD modelAnalysis models:Thermal, mechanical, optical (common mesh)
Thermo-mechanical response:Steady-state & transient
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1x 10
−11
time (hours)
cont
rast
change in contrast vs. time
Transient WFE as Zernikes vs. Reqmts.
Transient Contrast after 20deg dither
0
0
0
0
0
0
Speckle Removal for Planet Detection
_
θ=0o roll
θ=20o roll
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• Equations of Thermal Equilibrium: (u(t) = temp)
– Time integration via generalized trapezoidal methods (Crank-Nicolson, etc.)– Nonlinear iteration via Newton-Raphson method
• Equations of Structural Dynamic Equilibrium: (u(t) = disp)
• Situation further complicated by:– Temperature-dependent materials– Radiation-material interactions– Microdynamic, and other geometric/strain/material nonlinearities
Motivation: Thermal and Structural Physics
[ ]{ } ( ) { })()(),()( tPtutuftuM =+ &&&
Conductance(Sparse)
Radiation(Dense,
unsymmetric)
Capacitance(Sparse)
Loads(Multiple subcases,Sparse or dense)
[ ]{ } [ ]{ } [ ]{ } { } { })()()()()( 4 tNtPtuRtuKtuB +=++&
Mass, Damping, Stiffness(Sparse)
Loads(Multiple subcases,
Thermal strains)
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Cielo Overview
• Goals– Enable “integrated modeling” via fundamentally-integrated thermal, structural,
and optical aberration analytic capabilities.– Overcome “Commercial Off-The-Shelf” (COTS) tool limitations– Provide a platform for continuing methods development, vertical application
development• Status
– Five year plus development effort largely by team of former MSC/NASTRAN developers
– MATLAB hosted, modular, large model implementation (> 1M structural degrees of freedom, tens of thousands of radiation exchange surfaces)
– Extensible serial and parallel components (heterogeneous computeenvironment)
– Under active development
The MATLAB environment has proven to be an effective framework, enabling implementation, deployment, and vertical application development.
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Cielo Overview• Solution Approach:
– Common finite element model representation• Single model with multidisciplinary attributes• Data-driven via augmented NASTRAN file formats
– MATLAB hosting• Open, extensible, scalable architecture enabled by rich MATLAB environment• mexFunction modules for specific, cpu-intensive phases• Solution control, postprocessing in MATLAB• Toolbox deployment
“STOP” Analysis: “Go” Analysis:
Geometry
Meshing
Cielo
Optical Metrics
Optical Metrics
Geometry
Meshing
Mapping; T(t)
Structural Analysis
Optical Aberrations
Thermal SolverView factors
Exchange factors
Radiation matrix
Loads generation
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Thermal Solution Implementation• Solution Procedures:
– High-level MATLAB scripts for solution control, functional module calls– Conceptually similar to NASTRAN’s DMAP sequences– Natural interface to extended functionality (e.g. In-house codes, Simulink, …)
= Module (mexFunction) = MATLAB script, utility
Data input,initialization State Time step Orbit
positioning
View factorsRadiation matrixLoads
Coefficient matrix Residual Matrix
decomposition Convergence
nn
y
Next State
Exchange factorsElementsElements
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Solnx
GUIx
DataxDatax
ModxModx
Customuser components
HostLayer(MATLAB API)
Object-based Data LayerObject-based Data Layer
GUI/results postprocessing
Solution sequences
Inputdata file
CADModeling
tools
CADModeling
tools
ViewView OpticsOpticsOrbitOrbit …Computationalmodules (serialor parallel)
Data API
MATLAB
Optional MATLAB
input
Cielo Architecture
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Parallel Architecture
Remote ServerLocal Client
TCP/IP
Cielo Modulewrappers
(mexFunction)
Connection Manager
Compute Manager
Cielo ModuleCores
Parallel ComputingLibraries
TCP/IP
MPI Ring
MATLAB ProcessMATLAB Process
Client/Server Architecture:• Enables calls to “parallelized” Cielomodules• TCP/IP-based communications• Remote Server operations driven by local MATLAB process• Extended Parallel Compute Library interface (PETSc, Plapack, etc.)
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Distributed Computing Example
• TPF-C Alternative Sunshade concept:– Study heat dissipation effects from “open” sunshade (packaging, deployment concerns)– Multi-layer sunshield treated as diffusely exchanging surfaces (first approximation)– Investigate steady-state and short- and long-term transient solutions
• Computationally:– Numerical conditioning, adaptive time-stepping, numerical stability for low-capacitance
systems (and other extreme cases, as in high-capacitance tests shown here)
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Distributed Computing Example
• MATLAB hosted implementation allows:– Client process interaction with local, and remote
modules– Remote “embarrassingly parallel” computations,
with results sets returned to the client workspace– Data postprocessing, user-level interaction
within consistent, familiar MATLAB environment
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Thermal/Optical Distortion Example
• Space Interferometry Mission (SIM)– Precisely measure angles between stellar
objects for astrometric and planet detection purposes
– 10 meter rigid baseline interferometer– Flight Environment
• Earth-trailing solar orbit• Benign radiation environment
• Thermal distortion analysis of Relay Optic #2B– Key optical element in science compressor unit– Transient thermal distortion analysis,
corresponding surface aberrations and optical metrics
– Geometry modeling, thermal and structural meshing in UG NX
– UG NX TMG Thermal Analysis, temperature mapping to UG NX mesh (though thermal analysis could have been done Cielo)
– Distortion analysis, optical aberrations in Cielo– Hosting, and optical response postprocessing in
MATLAB
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Thermal/Optical Distortion Example
Thermal Solutions (UG NX TMG)• 5 steady-state cases• 2 transient (655 total time steps, ~21 hrs of transient phenomena)• Temperature mapping in I-deas
Thermal Distortion (Cielo)• Normal modes model verification• Transient distortions in single runs (414 time steps in TC11, 241 in TC12)
Optical Aberrations (Cielo)• Optical element definition as part of structural model• Aberrations/interferogram file generation in Cielo• Visualization, optical metrics, data postprocessing in MATLAB
“External” Analysis Phase MATLAB hosted Analyses
TC11 without Rigid-Body Motion
-8.00E-07
-6.00E-07
-4.00E-07
-2.00E-07
0.00E+00
2.00E-07
4.00E-07
6.00E-07
8.00E-07
1.00E-06
0 10000 20000 30000 40000 50000 60000 70000 80000
time (sec)
surf
ace
aber
ratio
n (m
m)
max2min2pv2rms2
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Summary
Cielo effectively implements thermal, structural, and optical aberration analyses in an open, extensible manner.
“Integrated modeling” can be a natural conclusion if the analytical capabilities are themselves fundamentally integrated.
MATLAB provides a rational environment for complex solution procedure development and deployment.
Current, future work in areas of:• Specular exchange, transmissive, specular effects• Nonlinear characterizations• Design sensitivity and optimization• Vertical application development, Simulink integration