Experimental assessment of polynomial nonlinear state-space and nonlinear-mode models for near-resonant vibrations

TL;DR

This paper compares two nonlinear system identification methods—nonlinear-mode models and polynomial nonlinear state-space models—applied to experimental beams, evaluating their accuracy in predicting near-resonant vibrations under various excitations.

Contribution

It provides an experimental comparison of nonlinear-mode and polynomial state-space models for near-resonant vibrations, highlighting their respective strengths and limitations.

Findings

Nonlinear-mode models excel at resonance peaks and near-resonance accuracy.

State-space models offer broader dynamic range but are input-dependent.

Polynomial basis functions limit the accuracy of state-space models for real nonlinearities.

Abstract

In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a phase-locked loop controller is implemented to acquire periodic oscillations near resonance and construct a nonlinear-mode model. This model is based on amplitude-dependent modal properties, i.e. does not require nonlinear basis functions. The second methodology exploits uncontrolled experiments with broadband random inputs to build polynomial nonlinear state-space models using advanced system identification tools. The methods are applied to two experimental test rigs, a magnetic cantilever beam and a free-free beam with a lap joint. The respective models of both methods and both specimens are then challenged to predict dynamic, near-resonant behavior observed under different sine and sine-sweep excitations. The vibration prediction of the nonlinear-mode and state-space models clearly highlight the capabilities and limitations of the models. The nonlinear-mode model, by design, yields a perfect match at resonance peaks and high accuracy in close vicinity. However, it is limited to well-spaced modes and sinusoidal excitation. The state-space model covers a wider dynamic range, including transient excitations. However, the real-life nonlinearities considered in this study can only be approximated by polynomial basis functions. Consequently, the identified state-space models are found to be highly input-dependent, in particular for sinusoidal excitations where they are found to lead to a low predictive capability.