Numerical Assessment of Polynomial Nonlinear State-Space and Nonlinear-Mode Models for Near-Resonant Vibrations

Abstract

In the present article, we follow up our recent work on the experimental assessment of two data-driven nonlinear system identification methodologies. The first methodology constructs a single nonlinear-mode model from periodic vibration data obtained under phase-controlled harmonic excitation. The second methodology constructs a state-space model with polynomial nonlinear terms from vibration data obtained under uncontrolled broadband random excitation. The conclusions drawn from our previous work (experimental) were limited by uncertainties inherent to the specimen, instrumentation, and signal processing. To avoid these uncertainties in the present work, we pursued a completely numerical approach based on synthetic measurement data obtained from simulated experiments. Three benchmarks are considered, which feature geometric, unilateral contact, and dry friction nonlinearity, respectively. As in our previous work, we assessed the prediction accuracy of the identified models with a focus on the regime near a particular resonance. This way, we confirmed our findings on the strengths and weaknesses of the two methodologies and derive several new findings: First, the state-space method struggles even for polynomial nonlinearities if the training data is chaotic. Second, the polynomial state-space models can reach high accuracy only in a rather limited range of vibration levels for systems with non-polynomial nonlinearities. Such cases demonstrate the sensitivity to training data inherent in the method, as model errors are inevitable here. Third, although the excitation does not perfectly isolate the nonlinear mode (exciter-structure interaction, uncontrolled higher harmonics, local instead of distributed excitation), the modal properties are identified with high accuracy.

Nonlinear modal testing of damped structures: Velocity feedback vs. phase resonance

“…1). In comparison, phase resonance testing is not affected by the exciter's phase lag as long as the phase between measured excitation force and response is controlled (see [22,26] for similar simulated experiments using a PLL controller).…”

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

“…Mangan et al [19] have introduced model selection via sparse regression algorithms for linear-in-parameters problems. The polynomial nonlinear statespace (PNLSS) method [20,21] has also been used to select nonlinear models based on high order polynomials. However, different applications, such as the nonlinear identification of aero-engine structure [22], showed that the number of parameters included in the selected model by PNLSS is high and might not be parsimonious.…”