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Shock and Vibration
Volume 12, Issue 5, Pages 317-331

Use of Response Surface Metamodels for Identification of Stiffness and Damping Coefficients in a Simple Dynamic System

A.C. Rutherford,1 D.J. Inman,2 G. Park,1 and F.M. Hemez1

1Los Alamos National Laboratory, ESA-WR, M/S P946 Los Alamos, NM 87544, USA
2Center for Intelligent Materials Systems and Structures, Mechanical Engineering Department, Virginia Polytechnic Institute and State University, M/C 0261 Blacksburg, VA 24061, USA

Received 27 August 2003; Revised 9 December 2004

Copyright © 2005 Hindawi Publishing Corporation. 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.


Metamodels have been used with success in many areas of engineering for decades but only recently in the field of structural dynamics. A metamodel is a fast running surrogate that is typically used to aid an analyst or test engineer in the fast and efficient exploration of the design space. Response surface metamodels are used in this work to perform parameter identification of a simple five degree of freedom system, motivated by their low training requirements and ease of use. In structural dynamics applications, response surface metamodels have been utilized in a forward sense, for activities such as sensitivity analysis or uncertainty quantification. In this study a polynomial response surface model is developed, relating system parameters to measurable output features. Once this relationship is established, the response surface is used in an inverse sense to identify system parameters from measured output features.

A design of experiments is utilized to choose points, representing a fraction of the full design space of interest, for fitting the response surface metamodel. Two parameters commonly used to characterize damage in a structural system, stiffness and damping, are identified. First changes are identified and located with success in a linear 5DOF system. Then parameter identification is attempted with a nonlinear 5DOF system and limited success is achieved. This work will demonstrate that use of response surface metamodels in an inverse sense shows promise for use in system parameter identification for both linear and weakly nonlinear systems and that the method has potential for use in damage identification applications.