MURI announcement (abridged)

MULTIDISCIPLINARY RESEARCH PROGRAM OF THE UNIVERSITY RESEARCH INITIATIVE
FISCAL YEAR 1996


FY96 MURI Topic:  MATHEMATICAL INFRASTRUCTURE FOR ROBUST VIRTUAL 
ENGINEERING

Background:  One of the most generic trends in technology is the increasing
reliance on simulation for the design and analysis of complex systems and for
the training of personnel.  Large networks of computers with shared data bases
and high-speed communication are used in everything from the design and
manufacture of vehicles, such as the B-2 and the Boeing 777, to full
battlefield simulations.  The advantages and power of this approach are
well-known and there is a broad commitment throughout the engineering community
and DOD to what we might call "virtual engineering."  Because of the critical
role it will play in future military decision processes it is important that
this technology be as robust and reliable as possible.

What is not widely appreciated are some of the mathematical questions that will
become increasingly central to expanding the success of this technology.
Underlying virtual design technology is the construction of complex
mathematical models which are intended to accurately represent physical
systems.  Such models typically take the form of large, complex, coupled
systems of nonlinear differential or difference equations.  Unfortunately, no
matter how sophisticated our models, there is always some difference between
the model and the real world.  For example, in a model of an aircraft, there is
uncertainty in modeling the mass distribution, the aerodynamic forces generated
by the fluid flow past the vehicle, the flexibility of the materials, the
thrust of the engine, the characteristics of the atmosphere, and so on.  Such
uncertainties at the vehicle level can  be thought of as arising from
uncertainties in subsystem models (or component models), and in turn lead to
uncertainties in simulations involving multiple components.  It is essential
that realistic systems models explicitly account for such uncertainties, by
using sets of models rather than a single idealized model.

Model uncertainty leads to unpredictability, which mirrors the unpredictability
of real systems.  This has two important aspects. One is that differential
equations can exhibit extreme sensitivity to variations in model assumptions,
parameters, and initial conditions.  This has been studied extensively in the
area of robust control and also in dynamical systems in the context of
deterministic chaos.  The second is the combinatorial complexity of evaluating
all the model combinations that arise from possible variations in assumptions,
parameters, and initial conditions in all the subsystems, which makes a brute
force enumeration prohibitively expensive.  These are some of the fundamental
limitations on the predictability of models, and will not be eliminated by any
advances in computational power.  Thus in developing robust and reliable
modeling and simulation software it is important to keep in mind there are
certain "hard" limits on the predictability of some simulations; it is,
nonetheless, extremely important to understand and quantify the limits on the
predictability of full system simulations in terms of the uncertainties in its
component models.  Current modeling and simulation enterprises do not have good
strategies for dealing with these uncertainties, or for understanding how they
propagate through the system model, and ultimately affect the decision making
process they were intended to serve.  Focused basic research in this problem
area can be expected to have an extremely important impact on how DOD uses
modeling and simulation capabilities to make critical decisions.

Objective:  The purpose of this research is to develop a highly structured
mathematical approach to the modeling, identification, and explicit
quantification of uncertainties of complex nonlinear systems of interest to
DOD, and to produce radically new robust and reliable modeling and simulation
tools which will make it possible to understand and quantify the system
sensitivities to uncertainties which could limit the model's predictive
capabilities.  It is expected that this research will culminate in a modular,
reusable, integrated software infrastructure, which is portable across a range
of machines from workstations, networks of workstations, to massively parallel
machines, and that it will provide an unprecedented capability for integrating
heterogeneous components consisting of hierarchies of subsystem models and
their uncertainties into a robust and reliable model for the full system.  An
open software kernel should be developed and maintained so that new research
advances can be quickly incorporated, tested, and deployed.  This new robust
virtual engineering environment will facilitate the careful exploration of the
natural connections among modeling, data, and design, as well as provide
revolutionary new design, analysis, and virtual experimentation capabilities.
The fields of robust control and dynamical systems have been dealing with
exactly these issues with enormous success, but separately and in more limited
and constrained contexts.  Fortunately, it appears that some of these
techniques, when properly blended are potentially applicable to many of the
broader problems of virtual engineering.  Proposals responding to this topic
must have a targeted application testbed.  Testbeds of interest in this
initiative include but are not limited to the following:  the modeling,
simulation, design and analysis issues in complex air combat scenarios, and in
new aircraft configurations based on aerodynamic, aeroelastic, electromagnetic,
and maintenance requirements.

This initiative is not intended to advance the state-of-the-art in numerical
methods for the component models.  It is expected that proposers will capture
and effectively use existing software.

Research Concentration Areas:

Computer Science:  Computer science topics include the development of an
appropriate modeling and simulation visual programming language; a suitable
software architecture and software engineering environment; techniques for
model-based graphical rendering of dynamical scenes using appropriate kinematic
constraints and model aggregation strategies; appropriate data abstractions;
and hardware-in-the-loop simulation capabilities.  Exploit existing
capabilities where possible (object oriented languages, virtual reality, CAD,
etc.).  Develop suitable approximate algorithms for breaking the computational
complexity barrier in a variety of NP-hard problems which arise in robust
virtual engineering.

Physics , Dynamical Systems Theory, and Computational Mathematics:  Full system
modeling and exploitation of modern nonlinear analysis capabilities.  This
includes the modeling of all physical subsystems (component models) as well as
interfaces and interconnections.  Also model (where necessary) sensors or
actuator dynamics, communications links, and signal processing activities.  For
each component build appropriate hierarchies of models of increasing fidelity
with estimates of model uncertainty.  Exploit new work on efficient and
reliable, statistically based computational surrogates where appropriate.

Robust Control:  Exploit past successes in robust control systems theory where
possible.  Develop suitable new strategies for modeling, identification, and
explicit quantification of uncertainties based on these successes.  Devise new
techniques for understanding and quantifying the sensitivities of the model to
the uncertainties in its components.

Probability and Statistics:  Assist in the development of sound methodologies
for identification and quantification of uncertainties as well as in the
development of sound, statistically based, simplified computational surrogates
for component modeling.  Develop suitable Monte Carlo methods and statistical
analysis techniques for use in data analysis and virtual experiments.

Impact:  Success in this work on the mathematical infrastructure for robust
virtual engineering would be a major step in realizing the full potential of
the modeling and simulation enterprise.  The chief impact of this research will
be in reducing the design cycle for new or modified weapons systems while at
the same time improving their affordability, maintainability, and performance.

Point-of-contact:  Dr. Marc Jacobs, AFOSR/NM, (202) 767-5027