Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 175036, 25 pages
Research Article

Investigation of a Stochastic Inverse Method to Estimate an External Force: Applications to a Wave-Structure Interaction

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

Received 24 February 2012; Revised 9 April 2012; Accepted 25 April 2012

Academic Editor: Moran Wang

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 determination of an external force is a very important task for the purpose of control, monitoring, and analysis of damages on structural system. This paper studies a stochastic inverse method that can be used for determining external forces acting on a nonlinear vibrating system. For the purpose of estimation, a stochastic inverse function is formulated to link an unknown external force to an observable quantity. The external force is then estimated from measurements of dynamic responses through the formulated stochastic inverse model. The applicability of the proposed method was verified with numerical examples and laboratory tests concerning the wave-structure interaction problem. The results showed that the proposed method is reliable to estimate the external force acting on a nonlinear system.