Skip to main content
padlock icon - secure page this page is secure

Uncertainty Quantification for Systems with Random Initial Conditions Using Wiener–Hermite Expansions

Buy Article:

$59.00 + tax (Refund Policy)

A number of engineering problems, including laminar-turbulent transition in convectively unstable flows, require predicting the evolution of a nonlinear dynamical system under uncertain initial conditions. The method of Wiener–Hermite expansion is an attractive alternative to modeling methods, which solve for the joint probability density function of the stochastic amplitudes. These problems include the “curse of dimensionality” and closure problems. In this paper, we apply truncated Wiener–Hermite expansions with both fixed and time-varying bases to a model stochastic system with three degrees of freedom. The model problem represents the combined effects of quadratic nonlinearity and stochastic initial conditions in a generic setting and occurs in related forms in both classical dynamics, turbulence theory, and the nonlinear theory of hydrodynamic stability. In this problem, the truncated Wiener–Hermite expansions give a good account of short-time behavior, but not of the long-time relaxation characteristic of this system. It is concluded that successful application of truncated Wiener–Hermite expansions may require special adaptations for each physical problem.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Affiliations: NASA Langley Research Center

Publication date: February 1, 2005

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more