Discrepancies frequently occur between a physical system\'s responses and predictions obtained from mathematical models.
Ryon Chair in Engineering in the Department of Mechanical Engineering and Materials Science at Rice University..
B.
Spanos is the L.
Pol D.
Ghanem is a Professor at University of Southern California\'s Department of Aerospace and Mechanical Engineering in Los Angeles.
About the Author: Roger G.
In this context, the solution process is approximated by its projection onto a Finite subspace spanned by these polynomials.
Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a Spectral representation is identified in terms of polynomial chaos.
Implementing the concept of generalized inverse leads to an explicit expression for the response process as a multivariate polynomial functional of a set of uncorrelated random variables.
Various Spectral approximations for the Stochastic response of the system are obtained.
Relying on the Spectral properties of the covariance function, the Karhunen-Loeve expansion is employed to represent these processes in terms of a countable set of uncorrected random variables, casting the problem in a Finite dimensional setting.
Random system parameters are modeled as second-order Stochastic processes, defined by their mean and covariance functions.
This text analyzes a class of discrete mathematical models of engineering systems, identifying key issues and reviewing relevant theoretical concepts, with particular attention to a Spectral approach.
The Spectral Stochastic Finite Element Method (SSFEM) has proven successful at forecasting a variety of uncertainties in calculating system responses.
Discrepancies frequently occur between a physical system\'s responses and predictions obtained from mathematical models
