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Shock and Vibration
Volume 15 (2008), Issue 3-4, Pages 345-354

Subspace-Based Identification of Nonlinear Structures

S. Marchesiello and L. Garibaldi

Dipartimento di Meccanica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received 29 April 2007; Revised 29 April 2007

Copyright © 2008 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.


Conventional linear estimators give results contaminated in presence of nonlinearities and the extraction of underlying linear system properties is thus difficult. To overcome this problem, the implementation of a recently developed method, called Nonlinear Subspace Identification (NSI), is considered in this paper, by using the perspective of nonlinearities as unmeasured internal feedback forces. Although its formulation is very simple, particular care has to be taken to reduce the ill-conditioning of the problem, in order to find numerically stable solutions. To this purpose, the robustness and the high numerical performances of the subspace algorithms are successfully exploited, as shown by the implementation of the proposed method on simulated multi-degree-of-freedom systems with typical nonlinear characteristics as well as on an experimental case. These examples demonstrate that the application of subspace algorithms to nonlinear system identification gives better conditioning and computational efficiency with respect to the most recent nonlinear techniques. Moreover, the capability of the NSI method of simultaneously dealing with several nonlinear terms, with a light computational effort, may be also exploited in those situations where no a priori knowledge of the location and the type of nonlinearities is given, being this method well capable of detecting the contribution of the dominant nonlinearities.

On the basis of the results discussed in this paper, and compared with those of other well-assessed nonlinear techniques, the proposed method appears having the chances to become a robust procedure to be widely exploited in many industrial fields, being its capability of separating linear and nonlinear contribution terms widely requested in mechanical and civil engineering field.