Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Abstract

Abstract Time series analysis of real-world measurements is fundamental in natural sciences and engineering, and machine learning has been recently of great assistance especially for classification of signals and their understanding. Yet, the underlying system’s nonlinear response behaviour is often neglected. Recurrence Plot (RP) based Fourier-spectra constructed through τ-Recurrence Rate (RR τ ) have shown the potential to reveal nonlinear traits otherwise hidden from conventional data processing. We report a so far disregarded eligibility for signal classification of nonlinear time series by training RESnet-50 on spectrogram images, which allows recurrence-spectra to outcompete conventional Fourier analysis. To exemplify its functioning, we employ a simple nonlinear physical flow of a continuous stirred tank reactor, able to exhibit exothermic, first order, irreversible, cubic autocatalytic chemical reactions, and a plethora of fast-slow dynamics. For dynamics with noise being ten times stronger than the signal, the classification accuracy was up to ≈ 75% compared to ≈ 17% for the periodogram. We show that an increase in entropy only detected by the RR τ allows differentiation. This shows that RP power spectra, combined with off-the-shelf machine learning techniques, have the potential to significantly improve the detection of nonlinear and noise contaminated signals.