Abstract: J. Kumar, O. Sedehi, B. Halkon, S. Oberst (in press)

In signal analysis, information content reflects the extent to which uncertainty is reduced and decision-making confidence is improved. Nevertheless, measuring information content from noisy time series with mathematical modelling remains challenging. In nonlinear time-series analysis, recurrence plots and their quantification analysis are increasingly used to study vibro-acoustic and oscillatory systems. Joint recurrence quantification analysis (JRQA) allows the computation of features based on the dynamics of multiple, potentially physically distinct, phase spaces. Here, a two-coupled model of analytical saline oscillators is used, which offers controllable coupling parameters and rich synchronisation behaviour. However, JRQA has not been used to analyse coupling direction and phase synchronisation in analytical saline oscillator models, nor has diagonal-wise joint recurrence-based power spectral entropy been explored for measuring common information content in signals. Our results show that the joint recurrence rate increases with the coupling strength parameter and synchronisation level, while the power spectral entropy, as a measure of information content, decreases in the noise-free case. Further, by progressively decreasing the signal-to-noise ratio from 20 dB to -20 dB through the addition of Gaussian white noise, the information content is increased. Our findings demonstrate that joint recurrence-based power spectral entropy can provide an effective measure of common information embedded in time-series data. By quantifying the shared recurrent dynamics between signals, joint recurrence quantification analysis may be useful for multi-sensor signal analysis, particularly when the objective is to identify weak dynamical signatures that are not clearly observable in individual sensors. This approach could improve decision-making confidence in the future by enabling the detection of micro-vibrations buried in noise using low-cost, off-the-shelf sensors.

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Investigating the information content of multiple signals using joint recurrence quantification