A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems

[+] Author and Article Information
J. Q. Sun

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716

J. Appl. Mech 65(4), 867-869 (Dec 01, 1998) (3 pages) doi:10.1115/1.2791924 History: Received November 11, 1997; Revised May 11, 1998; Online October 25, 2007


This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly from being linear to being strongly nonlinear. The nonuniform cell partition is shown to lead to more accurate steady-state solutions and enhance the computational efficiency of the GCM method.

Copyright © 1998 by The American Society of Mechanical Engineers
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