Subspace-Based Identification of a Distributed Nonlinearity in Time and Frequency Domains

Abstract

Nonlinear system identification has become of great interest during the last decades. However, a common and shared framework is not present yet, and the identification may be challenging, especially when real engineering structures are considered with strong nonlinearities. Subspace methods have proved to be effective when dealing with local nonlinearities, both in time domain (TNSI method) and in frequency domain (FNSI method). This study reports an improvement for both methods, as a first attempt to account for distributed nonlinearities, which is still an open question in the research community. A numerical beam under moderately large oscillations that exhibits geometric nonlinearity is considered. The object of the identification process is to exploit its behavior through the correct identification of the parameters that define the nonlinearity. Results show a high level of confidence between the two methods, and suggest that a more complete analysis of distributed nonlinear phenomena can be conducted based on these approaches.

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

“…This class of methods include the nonlinear subspace identification (NSI) technique [21,22] and the polynomial nonlinear state-space approach (PNLSS) [23]. The former in particular is based on the feedback interpretation of the nonlinearity [24,25] combined with the classical subspace identification framework, and it has been adopted to identify both localized and distributed nonlinearities [26][27][28], and bistable systems [29][30][31]. In order to adopt the NSI technique, the following prior information must be known/assumed: (1) the functional form of the nonlinearities of the system, in the following called ''nonlinear basis functions''; (2) the location of the nonlinearities (in the case of localized nonlinear behavior).…”

Free‐Decay Nonlinear System Identification via Mass‐Change Scheme

“…e measured data are then processed using the subspace formulation, derived from the linear system identification theory [11,12] and adapted to the nonlinear case. NSI has proved to be very efficient in several occasions, with both localized and distributed nonlinearities [13,14].…”

An Excursion in the Dynamics of Flexible Beams: From Modal Analysis to Nonlinear Modes

“…Major efforts have been made in the computation of nonlinear normal modes (NNM) of high-dimensional systems [64,65], of non-conservative system [66,67,68,46,69] and in the application of nonlinear normal modes for model reductions [70,71]. The experimental identification of NNM is also under development, where the traditional experimental modal analysis is being adjusted to nonlinear systems [57,72,73,74,75,76]. Review articles covering the latest developments in the computation and identification of NNM can be found in [13,77,78,79].…”