Compact Probabilistic Representation of Random Processes

[+] Author and Article Information
S. F. Masri, R. K. Miller

Civil Engineering Department, University of Southern California, Los Angeles, Calif. 90007

J. Appl. Mech 49(4), 871-876 (Dec 01, 1982) (6 pages) doi:10.1115/1.3162630 History: Received October 01, 1981; Revised March 01, 1982; Online July 21, 2009


A method is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that results in simplified, analytical, random-vibration transmission studies. The method uses two-dimensional orthogonal functions to represent the covariance kernel of the underlying random process. Such a representation leads to a relatively simple analytical expression for the covariance kernel of the linear system response which consists of two independent groups of terms: one reflecting the input characteristics, and the other accounting for the transmission properties of the excited dynamic system. The utility of the method is demonstrated by application to a covariance kernel widely used in random-vibration studies.

Copyright © 1982 by ASME
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