Abstract: A modified Karhunen-Loève Decomposition/Proper Orthogonal
Decomposition method, named Smooth Decomposition (SD) (also named smooth
Karhunen-Loève decomposition), was recently introduced to analyze
stationary random signal. It is based on a generalized eigenproblem defined
from the covariance matrix of the random process and the covariance matrix of
the associated time-derivative random process. The SD appears to be an
interesting tool in terms of modal analysis. In this paper, the SD will be
described in case of stationary random processes and extended also to
stationary random fields. The main properties will be discussed and illustrated
on a randomly excited clamped-free beam.
Keywords: Karhunen-Loève decomposition, random vibration, random fields, modal analysis
