Independent component analysis for uncertainty representation of stochastic systems
The predictive accuracy of stochastic systems depends on the calibration accuracy of its uncertain parameters modelled as random process. The probabilistic representation of these uncertain parameters can be achieved by Karhunen-Loeve Expansion (KLE) in which a random process is approximated by a set of decorrelated (statistically orthogonal) random variables. For a non-Gaussian process, although the set of random variables resulting from KLE expansion are pair-wise decorrelated, they are not generally independent. The lack of independence among these random quantities demands computationally intensive joint statistical characterisations (e.g. estimation of a joint probability distribution function). This paper explores the possibility of an alternative representation of a non-Gaussian stochastic process by a set of independent (or as independent as possible) random variables using Independent Component Analysis (ICA). The approach approximates a non-Gaussian random process by a set of random variables satisfying higher order decorrelation properties. The mathematical framework is elucidated from the context of its application to stochastic partial differential equations in mechanics. Copyright
|49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference|
|Organisation||Department of Civil and Environmental Engineering|
Khalil, M. (Mohammad), & Sarkar, A. (2008). Independent component analysis for uncertainty representation of stochastic systems. Presented at the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.