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Proceedings of the 9h AIAA/ISSMO Symposium on Multi-disciplinary Analysis and Optimization,
September 4-6, 2002, Grand Hyatt, Atlanta, GA. Paper number AIAA-2002-5420.
INFORMATION-GAP ROBUSTNESS FOR THE TEST-ANALYSIS
CORRELATION OF A NONLINEAR TRANSIENT SIMULATION
Frangois M. Hemez'
Engineering Sciences and Applications, ESA-WR
Los Alamos National Laboratory
Mail Stop P946, Los Alamos, New Mexico, U.S.A.
Yakov Ben-Haimt
Faculty of Mechanical Engineering
Technion-Israel Institute of Technology
Haifa 32000, Israel
Scott Cogant
Laboratoire de Mtcanique Appliqute Raymond Chalat
University de Franche-Comte
24, rue de l'Epitaphe, 25030 Besangon, France
ABSTRACT
An alternative to the theory of probability is applied to the problem of assessing the robustness of test-analysis
correlation to parametric sources of uncertainty. The analysis technique is based on the theory of information-gap,
which models the clustering of uncertain events in families of nested sets instead of assuming a probability structure.
The system investigated is the propagation of a transient impact through a layer of hyper-elastic material. The two
sources of non-linearity are the softening of the constitutive law implemented to model the hyper-elastic material
and contact dynamics at the interface between metallic and crushable materials. The robustness of test-analysis
correlation to sources of parametric variability is first studied to identify the parameters of the model that
significantly influence the agreement between measurements and predictions. Calibration under non-probabilistic
uncertainty is then illustrated. Finally, two information-gap models of uncertainty are embedded to represent
uncertainty not only in the knowledge of the model's parameters but also in the form of the model itself. Although
computationally expensive, it is demonstrated that the information-gap reasoning can greatly enhance our
understanding of a moderately complex system when the theory of probability cannot be applied due to insufficient
information.
I. INTRODUCTION
One central difficulty in identifying the form of a
numerical model and calibrating the values of its
parameters is that the identification and calibration
results can be ambiguous. Alternative combinations of
model forms and parameter values can yield
essentially equally good reproduction of test data. This
ambiguity is sometimes analyzed in terms of
analytical or numerical ill-conditioning or instability.
This ambiguity is further exacerbated by the fact that
not only decision variables are involved, but numerous
other unknown or uncertain variables fluctuate beyond
the control of the experimenter, and sometimes even
without the experimenter's awareness of their presence
or relevance. In short, ambiguity can occur whenever
"variables"-meaning input parameters, models or
conceptual forms-can interact to reproduce the data
in more than one way.
Uncertainty plays a central role in calibration and
ambiguity of identification. Clearly, conceptual
ambiguity and numerical ambiguity are the result of
imprecision or lack of information, both of which also
result from uncertainty. Epistemic uncertainty occurs
Technical staff member, "Validation Methods" team, hemez@lanl.gov, AIAA member.
t Professor, Yitzhak Moda'i Chair in Technology and Economics, yakov@techunix.technion.ac.il.
* Research Associate, French National Center of Scientific Research, scott.cogan@univ-fcomte.fr.
Copyright 2002 by F.M. Hemez (Los Alamos National Laboratory), Y. Ben-Haim (Technion Israel Institute of
Technology) and S. Cogan (Universit6 de Franche-Comtd). Published by the American Institute of Aeronautics and
Astronautics, Inc., with permission.
1
Accepted for unlimited, public release on June 11, 2002.
American Institute of Aeronautics and Astronautics.
LA-UR-02-3538. Unclassified.
