Identification of Nonlinearities in Mechanical Systems Using Recurrence Plots

Abstract

The identification of nonlinear vibrations in mechanical systems is an unsolved problem. The structure of the measured data and waveforms have been studied for many years, and different techniques have been applied. Nevertheless, there is no single technique for identifying the nonlinear parameters. Parameter identification can be conducted either with a parametric approach or with a non-parametric approach. Among parametric approaches many researchers have work with the Hilbert transform, continuous and discrete wavelet transform, nonlinear modal analysis, phase space. Meanwhile, nonparametric procedures include fractal analysis, Hurt factor, and approximate entropy. In this paper, the recurrence plots are applied for the identification of nonlinear parameters. Recurrence plots are constructed from the phase space. To calibrate the method, the recurrence plots were obtained from two theoretical models, a Van der Pol pendulum, and a Duffing mass-lump model. Then, the recurrence plots were constructed from a mechanical gearbox. Recurrence plots are an alternative solution for the identification of nonlinearities in mechanical systems.