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