Computational Methods for Optimal Design and Control: Proceedings of the AFOSR Workshop on Optimal Design and Control Arlington, Virginia 30 September–3 October, 1997

466 Pages·1998·15.24 MB·English

by  Paul Andersson

Progress in Systems and Control Theory
Volume 24
Series Editor
Christopher 1. Bymes, Washington University
Computational Methods
for Optimal Design and Control
Proceedings of the AFOSR Workshop
on Optimal Design and Control
Arlington, Virginia
30 September-3 October, 1997
Jeff Borggaard, John Bums,
Eugene Cliff, and Scott Schreck
Editors
Springer Science+Business Media, LLC
Jeff Borggaard JohnBums
Ctr. for Optimal Design arul Control Ctr. for Optimal Design arul Control
Sibley School of Mechanica1 Interdisciplinary Ctr. for
arul Aerospace Engineering Applied Mathematics
Cornell University Virginia Tech
Ithaca, NY 14853 Blacksburg, VA 24061
Eugene Cliff Scott Schreck
Ctr. for Optimal Design and Control Directorate of Mathematics
Interdisciplinary Ctr. for arul Geosciences
Applied Mathematlcs Air Force Oftice of Scientific Research
Virginia Tech Bolling Air Force Base
Blacksburg, VA 24061 Washington, DC 20332
Library of Congress Cataloging-in-Publication Data
Computationa1 methods for optimal design and control / Jeff Borggaard
... [et al.].
p. cm.
lncludes bibliographical references and index.
ISBN 978-1-4612-7279-3 ISBN 978-1-4612-1780-0 (eBook)
DOI 10.1007/978-1-4612-1780-0
paper)
1. Automatic control-Mathematical mode1s--Congresses.
2. Mathematical optimization-Congresses. 1. Borggaard, Jeffrey.
1964-
TJ212.C57 1998
629.8--dc21 98-16280
m
Printed on acid-free paper ®
© 1998 Springer Science+Business Media New YorkH(l2l
Originally published by Birkhăuser Boston in 1998
Softcover reprint of the hardcover 1s t edition 1998
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ISBN 978-1-4612-7279-3
Typeset by the Editors in HlJrEX.
987 6 5 4 3 2 1
CONTENTS
Preface. . . vii
Contributors ix
Optimal Disturbances in Boundary Layers
P. Andersson, M. Berggren and D. Henningson . . . . . . . . . . . 1
MDO -A Mathematical View Point
E. Arian . ........ . . . 27
Optimization Using Surrogate Objectives on a Helicopter Test Example
A. Booker, J. Dennis Jr., P. Frank, D. Serafini and V. Torczon.. .. 49
Observations in Adaptive Refinement Strategies for Optimal Design
1. Borggaard and D. Pelletier . . . . . . . . . . . . . . . . . 59
The Simplex Gradient and Noisy Optimization Problems
D. Bortz and C. Kelley . . . . . . . . . . . . ...... 77
Adjoint-Based Methods in Aerodynamic Design Optimization
E. Cliff, M. Heinkenschloss and A. Shenoy . . . . . . . . . . . . 91
Semi-Automatic Differentiation
T. Coleman, F. Santosa and A. Verma .... 113
Robust Reduced-Order Controller of Transitional Boundary Layers
L. Cortelezzi and 1. Speyer . . . . . . . . . . . . . . . . . . 127
Modem Optimization Methods for Structural Optimization under
Flutter Constraints
M. Fahl and E. Sachs .................... 137
On Shape Optimization and Related Issues
R. Glowinski and J. He . . . .. ............. 151
Using Sensitivities for Flow Analysis
A. Godfrey ........ . . . . . 181
Sensitivities in Computational Methods for Optimal Flow Control
M. Gunzburger . . . . . . . . . . . . . . . . . . . . . . . 197
vi
Fictitious Domain Approaches in Shape Optimization
J. Haslinger . . . . . . . . . . . . . . . . ...... 237
Process Modeling and Optimization: Issues and Challenges
J.-F. Hetu, F. ninca and D. Pelletier . . . . . . . . . . . . . . . 249
Automatic Differentiation and Navier-Stokes Computations
P. Hovland, B. Mohammacli and C. Bischof. . . . " .... 265
Numerical Computation of Sensitivities and the Adjoint Approach
R. Lewis .....•.•............ .... 285
Sensor!A ctuator Placement via Optimal Distributed Control of
Exterior Stokes Flow
J. Lontari6. . . . . . . . . • . . . . . . • . . . . . . 303
Fast Bounds for Outputs of Partial Differential Equations
M. Paraschivoiu, J. Peraire, Y. Maday and A. Patera . . .. 323
A Comparison of Local and Global Projections in Design Sensitivity
Computations
L. Stanley and D. Stewart . . . . . . . . . . . . . . . . . . . 361
Gradients, Curvature, and Visual Tracking
A. Thnnenbaum and A. Yezzi, Jr. . . . ...... 375
Adjoint Methods for Inverse Free Convection Problems with
Application to Solidification Processes
N. Zabaras. . . . . . . . . . . . . . . • . . . . . . 391
Shape Differential Equation with a Non Smooth Field
J.-P. ZoMsio . . • . • • • . . . . . . . . . . . . . . • . . 427
PREFACE
This volume contains the proceedings of the Second International Workshop on
Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo
ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The
proceedings of that meeting also appeared in the Birkhauser series on Progress in
Systems and Control Theory and may be obtained through Birkhauser.
These workshops were sponsored by the Air Force Office of Scientific Re
search through the Center for Optimal Design and Control (CODAC) at Vrrginia
Tech. The meetings provided a forum for the exchange of new ideas and were
designed to bring together diverse viewpoints and to highlight new applications.
The primary goal of the workshops was to assess the current status of research and
to analyze future directions in optimization based design and control. The present
volume contains the technical papers presented at the Second Workshop. More
than 65 participants from 6 countries attended the meeting and contributed to its
success.
It has long been recognized that many modern optimal design problems are
best viewed as variational and optimal control problems. Indeed, the famous
problem of determining the body of revolution that produces a minimum drag
nose shape in hypersonic How was first proposed by Newton in 1686. Optimal
control approaches to design can provide theoretical and computational insight
into these problems. This volume contains a number of papers which deal with
computational aspects of optimal control.
The workshop was a gathering of engineers and mathematicians actively in
volved in innovative research in control and optimization, with an emphasis placed
on optimal design problems governed by partial differential equations. Many dif
ficulties arise when trying to implement apprOximation techniques for these prob
lems. These difficulties range from computational issues, such as the accuracy,
ease and efficiency of state/function and gradient calculations, to concerns about
integrating calculations from several subdisciplines. For example, contributions
concerning gradient calculations can be loosely broken into three categories: (i)
Automatic Differentiation, (ii) Adjoint Methods and (iii) Sensitivity Equations
Methods.
In many cases, a detailed solution of the full physics-based state equations
(partial differential equations or large systems of ordinary differential equations)
is expensive. However, reduced order models with varying levels of validity can
often be used to develop optimal design strategies. Several articles describe tech
niques for managing models in optimization algorithms. Model management is
also considered for the case where different disciplines must be integrated. Model
uncertainty caused by coarse approximations of partial differential equations or
by obtaining function evaluations through experiment can introduce unacceptable
noise in the design objective function. Convergence of optimization algorithms
for problems with model uncertainty is discussed by various contributors.
viii
Many important optimal design applications can be formulated as shape opti
mization problems. Shape optimization leads to additional difficulties and often
requires the development of special techniques to address complex theoretical and
computational issues. These difficulties range from theoretical considerations in
volving the development of proper mathematical framework for the discussion
of shape derivatives, to computational methods for efficient calculation, or elim
ination of mesh gradients. Sensitivity equation methods and fictitious domain
approaches to these problems are found in various articles on shape optimization.
The diverse background and experience of the participants, ranging from ac
ademia, to industry,to government laboratories, lead to a variety of techniques
to address these difficulties. Overall, it is clear that there has been significant
progress in the development of new computational and mathematical tools for op
timal design and control. Moreover, these tools are being applied to very complex
systems and have important applications to aerodynamic design, tluid tlows, ma
terials processing, inverse design and feedback control. On the other hand, there
are many theoretical and practical issues that have not been resolved, and when
resolved, could lead to revolutionary advances in design and control methodol
ogy. During the workshop the participants submitted position papers that identi
fied these issues and suggested future research directions to address these difficult
problems. The conclusions based on these suggestions will appear in a follow-up
volume.
Finally, we would like to acknowledge the efforts of the Organizing Commit
tee, the graduate students at Virginia Tech and the staff at ICAM. In particular,
special thanks goes to Dr. Bernard Grossman, Melissa Chase and Sydney Crow
der for their help in putting together the interesting and informative workshop
that led to these proceedings. We also gratefully acknowledge the support of the
Air Force Office of Scientific Research for funding the workshop under AFOSR
grants F49620-97-1-0264 and F49620-96-1-0329.
Jeff Borggaard, John Burns,
Eugene Cliff and Scott Schreck
Blacksburg
December 1997
CONTRIBUTORS
Paul Andersson - FFA, the Aeronautical Research Institute Sweden, Computa
tional Aerodynamics Department, P.O Box 11021, S-161 11 Bromma, Swe
den.
Eyal Arian - Institute for Computer Applications in Science and Engineering,
Mail Stop 403, NASA Langley Research Center, Hampton, VA 23681.
Martin Berggren - FFA, the Aeronautical Research Institute Sweden, Computa
tional Aerodynamics Department, P.O Box 11021, S-161 11 Bromma, Swe
den.
Christian Bischof - Mathematics and Computer Science Division, Argonne Na
tional Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439-4844.
Andrew Booker - Mathematics & Engineering Analysis, Boeing Information Sup
port Services.
Jeff Borggaard - Sibley School of Mechanical and Aerospace Engineering, Up
son Hall, Cornell University, Ithaca, NY 14853.
David Bortz - North Carolina State University, Department of Mathematics, Cen
ter for Research in Scientific Computation, Box 8205, Raleigh, NC 27695-
8205.
Eugene Diff - Center for Optimal Design and Control, Interdisciplinary Center
for Applied Mathematics, VIrginia Tech, West Campus Drive, Blacksburg,
VA 24061-0531.
Thomas Coleman - Computer Science Department and Center for Applied Math
ematics, Cornell University, Ithaca, NY 14850.
Luca Cortelezzi - Department of Mechanical and Aerospace Engineering and
Department of Mathematics, University of California, Los Angeles, CA
90095.
John Dennis, Jt. - Department of Computational and Applied Mathematics, Cen
ter for Research on Parallel Computation, Rice University, Houston, TX.
M. Fahl - FB IV -Mathematik, Universitlit Trier, 54286 Trier, Germany.
Paul Frank - Mathematics & Engineering Analysis Boeing Information Support
Services.
x
Roland Glowinslci - University of Houston, Department of Mathematics, Hous
ton, TX 77204-3476.
Andrew Godfrey - Aerosoft, Inc., 1872 Pratt Drive, Ste. 1275, Blacksburg, VA
24060.
Max Gunzburger - Department of Mathematics, Iowa State University, Ames, IA
50011-2064.
Jaroslav Haslinger - Charles University, Prague.
liwen He - University of Houston, Department of Mathematics, Houston, TX
77204-3476.
Matthias Heinkenschloss - Department of Computational and Applied Mathe
matics, Rice University, Houston, TX.
Dan Henningson - FFA, the Aeronautical Research Institute Sweden, Compu
tational Aerodynamics Department, P.O Box 11021, S-161 11 Bromma,
Sweden.
lean-Franr;ois H~tu - Industrial Materials Institute, National Research Council
Canada, 75, de Mortagne, Boucherville, QC, Canada J4B 6Y4 .
Paul Hovland - Mathematics and Computer Science Division, Argonne National
Laboratory, 9700 S. Cass Avenue, Argonne, II.. 60439-4844.
Florin Dinca - Industrial Materials Institute, National Research Council Canada,
75, de Mortagne, Boucherville, QC, CanadaJ4B 6Y4.
C. Tim Kelley - North Carolina State University, Department of Mathematics,
Center for Research in Scientific Computation, Box 8205, Raleigh, NC
27695-8205.
Robert Michael Lewis - Institute for Computer Applications in Science and En
gineering, Mail Stop 403, NASA Langley Research Center, Hampton, VA
23681-0001.
losip Lonearic - Institute for Computer Applications in Science and Engineer
ing, Mail Stop 403, NASA Langley Research Center, Hampton, VA 23681-
0001.
Yvon Maday - Laboratoire d' Analyse Nummque, Universilt Pierre and Marie
Curie (Paris VI).
Bijan Mohammadi - University ofMontpellier II and INRIA, Math. Dept, CC51,
34095 Montpellier Cedex 5, France.