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Mathematical Problems in Engineering
Volume 2012, Article ID 574291, 20 pages
Research Article

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

Received 11 August 2011; Revised 6 January 2012; Accepted 26 January 2012

Academic Editor: Mohammad Younis

Copyright © 2012 S. L. Han and Takeshi Kinoshita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC). The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.