Premium
Efficient sampling for spatial uncertainty quantification in multibody system dynamics applications
Author(s) -
Schmitt Kyle P.,
Anitescu Mihai,
Negrut Dan
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2649
Subject(s) - sampling (signal processing) , computer science , multibody system , cholesky decomposition , convergence (economics) , mathematical optimization , gaussian , memory footprint , uncertainty quantification , algorithm , mathematics , filter (signal processing) , machine learning , eigenvalues and eigenvectors , physics , quantum mechanics , economics , computer vision , economic growth , operating system
We present two methods for efficiently sampling the response (trajectory space) of multibody systems operating under spatial uncertainty, when the latter is assumed to be representable with Gaussian processes. In this case, the dynamics (time evolution) of the multibody systems depends on spatially indexed uncertain parameters that span infinite‐dimensional spaces. This places a heavy computational burden on existing methodologies, an issue addressed herein with two new conditional sampling approaches. When a single instance of the uncertainty is needed in the entire domain, we use a fast Fourier transform technique. When the initial conditions are fixed and the path distribution of the dynamical system is relatively narrow, we use an incremental sampling approach that is fast and has a small memory footprint. Both methods produce the same distributions as the widely used Cholesky‐based approaches. We illustrate this convergence at a smaller computational effort and memory cost for a simple non‐linear vehicle model. Copyright © 2009 John Wiley & Sons, Ltd.