Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

Abstract

The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, firstgeneration framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.individually on each degree-of-freedom response amplitude and that existing coupling effects are negligible. For these reasons, nonlinear system identification has not reached yet the same level of maturity as linear system identification, which is routinely applied to engineering structures [7], in particular to aircraft structures [8].The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 [9] constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. The FNSI method is a nonlinear generalisation of the well known subspace identification algorithms [10,11], which are widely used for linear system identification [12,13]. The FNSI method derives models of mechanical systems possessing localised nonlinearities directly from measured data and without resorting to a preexisting numerical model, e.g. a finite element model [11]. The method pursues the twofold objective of identifying the underlying linear system, on one side, and, on the other, the lumped nonlinearities. FNSI is applicable to multiple-input, multiple-output structures with high nonproportional damping and high modal density, and makes no assumption as to the importance of nonlinearity in the measured dynamics [9]. The key to the method is the interpretation of nonlinear forces as feedback forces applied to the underlying linear structure, which allows high-dimensional inverse problems and strongly nonlinear regimes of motion to be tackled. The effects of lumped nonlinear inputs in the system are represented by using a linear-in-the-paramete...

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

“…In particular, the stabilization of modal masses is included as described in [35,36] along with natural frequencies, damping ratios and mode shapes. More recent developments of NSI use modal decomposition to have a better estimation of the coefficients of the nonlinearities and to remove possible spurious poles from the identified model [35][36][37].…”

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

“…This should be considered as a first attempt to identify distributed nonlinearities, which is still an open point in the research community. Two methods are used, both based on subspace identification [5]: TNSI (Time Nonlinear Subspace Identification) [1,6] and FNSI (Frequency Nonlinear Subspace Identification) [7][8]. The main difference between TNSI and FNSI is the domain in which they work, which is time for the first and frequency for the second.…”