Some Classes of Random Fields inn-Dimensional Space, Related to Stationary Random Processes

1957 ◽  
Vol 2 (3) ◽  
pp. 273-320 ◽  
Author(s):  
A. M. Yaglom
Keyword(s):  
Random Fields ◽  
Dimensional Space ◽  
Random Processes ◽  
Stationary Random Processes

scholarly journals Analysis of Stationary Random Vibrating Systems Using Smooth Decomposition

2013 ◽  
Vol 20 (3) ◽  
pp. 493-502 ◽  
Author(s):  
Sergio Bellizzi ◽  
Rubens Sampaio
Keyword(s):  
Random Process ◽  
Covariance Matrix ◽  
Random Fields ◽  
Decomposition Method ◽  
Time Derivative ◽  
Random Processes ◽  
Stationary Random Processes ◽  
Proper Orthogonal ◽  
Free Beam ◽  
Vibrating Systems

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.

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