Abstract: 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.
Keywords: Nonlinear identification, subspace methods, time domain
