UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: Feb. 26, 2001

Title:
A Functional Analytic Approach to the Propagation and Management of Uncertainty
in Model-Based Predictions.

Speaker:
       Roger Ghanem
       The Johns Hopkins University, Baltimore, MD


Abstract:
The performance of a system can be meaningfully defined as a measure of
the closeness between the observed and the predicted state of the system. 
Understanding the uncertainty underlying this difference, identifying
its controlling factors, and quantifying the propagation of these factors
through the mathematical model adopted for the system can lead to
the design of systems with improved performance. 

With recent advances in sensing and computational technologies,
the possibility arises for probing nature at a previously
unimagined scale, as well as for predicting its evolution with
increasingly complex mathematical models.  The significant recent increase
in both quality and quantity of experimental observations provides
a very fertile ground for the development of various models of data
that can be integrated into mechanistic-based models.  In particular,
probabilistic-based models of data are very appealing in view of the rich
mathematical toolbox available for their manipulation.

This talk will present a framework for the propagation of 
probabilistically-modeled data through mechanistic models of
natural and engineered systems.  The framework is based on identifying
random variables and processes with their projections on 
the Polynomial Chaos, a basis in a suitable Hilbert space of second order
random variables.  The problem is thus restated in the context 
of deterministic approximation theory.  A Galerkin projection procedure
is utilized to compute an optimal representation of the response of
the system as a function of the uncertainties in its data.  The format
of the solution is particularly well-suited to the analysis of
complex systems with interacting subsystems.  Post-processing
procedures suitable for resource allocation, performance-based design
and reliability analysis will also be presented.  The framework will be
demonstrated by its application to problems in structural and 
soil dynamics and flow in porous media.