Time-delay Embedding Techniques Research Articles

Multivariate Graph-Based Analysis on Coefficient of Friction Signal During the Friction Process

To describe the dynamic evolutionary law and tribological behavior of the tribopair AISI 52100-AISI 1045, rotational experiments were conducted by sliding a disk against a static pin. The multidimensional phase spaces were reconstructed based on the scalar time-series by the time-delay embedding technique, and the multivariate graph-based method was used to visualize the overall picture of the phase space. The evolution of radar plots and the corresponding multivariate graph centrobaric trajectory (MGCT) is consistent with the description of “running-in, steady-state and increasing friction stages,” and can serve as effective indicators for the friction state transitions. Results show that the radar plot can inform quantitative interpretations of friction process identification. Therefore, the multivariate graph-based method is a useful approach to characterize the nonlinear dynamics of tribological behaviors.

Secure Communication Based on Hyperchaotic Chen System with Time-Delay

An experimental secure communication method based on the Chen system with time-delay is being proposed in this paper. The Chen system with time-delay is an infinite-dimensional system having more than one positive Lyapunov exponent. The message to be transmitted is encrypted using an hyperchaotic signal generated by the Chen system with time-delay and multishift cipher function. This encryption makes difficult for an eavesdropper to reconstruct the attractor by using time-delay embedding techniques, return map reconstruction, or spectral analysis, consequently, improving the security. Simulations and experiments on TI TMS320C6713 Digital Signal Processor (DSP) show improved resilience against attack and the feasibility of the proposed scheme.

Dimensionality reduction and dynamical filtering: Stimulated Brillouin scattering in optical fibers.

Stimulated Brillouin scattering (SBS) is a noise-driven nonlinear interaction between acoustical and optical waves. In optical fibers, SBS can be observed at relatively low optical powers and can severely limit signal transmission. Although SBS is initiated by high dimensional noise, it also exhibits many of the hallmarks of a complex nonlinear dynamical system. We report here a comprehensive experimental and numerical study of the fluctuations in the reflected Stokes wave produced by SBS in optical fibers. Using time series analysis, we demonstrate a reduction of dimensionality and dynamical filtering of the Stokes wave. We begin with a careful comparison of the measured average transmitted and reflected intensities from below the SBS threshold to saturation of the transmitted power. Initially the power spectra and correlation functions of the time series of the reflected wave fluctuations at the SBS threshold and above are measured and simulated. Much greater dynamical insight is provided when we study the scaling behavior of the intensity fluctuations using Hurst exponents and detrended fluctuation analysis for time scales extending over six orders of magnitude. At the highest input powers, we notice the emergence of three distinct dynamical scaling regimes: persistent, Brownian, and antipersistent. Next, we explore the Hilbert phase fluctuations of the intensity time series and amplitude-phase coupling. Finally, time-delay embedding techniques reveal a gradual reduction in dimensionality of the spatiotemporal dynamics as the laser input is increased toward saturation of the transmitted power. Through all of these techniques, we find a transition from noisier to smoother dynamics with increasing input power. We find excellent agreement between our experimental measurements and simulations.

When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone.

Discovering Time-Series Building Blocks Using the ‘Significance Engine’

This paper presents a time-series prediction framework called the “Significance Engine” which contributes to the area of time-series prediction by presenting a novel, noise resistant mechanism that combines together the techniques of Takens' Theorem and dynamic self-organising maps. It is built around the idea that time-series can be broken down into both random and non-random components and that the non-random components can be used to help predict future time-series movement. It is a highly parallel system which combines together multiple Dynamic Self-Organising Map units of the ‘Grow When Required’ type and time delay embedding techniques. It learns iteratively, so the more data the system is fed from the input distribution, the better the predictions it is able to make. After the framework has been initialised and ideally primed using historical data, it is able to recognise re-occurring patterns in highly noisy waveforms and to successfully make future predictions based on historically what occurred when these motifs were previously observed.

The GTS1 gene product facilitates the self-organization of the energy metabolism oscillation in the continuous culture of the yeast Saccharomyces cerevisiae

To study the role of the GTS1 gene in the energy metabolism oscillation in continuous cultures of yeast from the physical aspect, time-series data of dissolved oxygen oscillations were analyzed by transforming them into power spectra and by creating two-dimensional trajectories using time delay embedding technique. We found that the wild-type cells organized themselves into a stable limit cycle oscillation and that the GTS1-deleted mutant, gts1Δ, usually showed transient oscillations whose power spectra resembled those of 1/f noise. Thus, we suggested that GTS1 plays an important role in the self-organization of the energy metabolism oscillation.

PREDICTION AND VOLATILITY OF BLACK MARKET CURRENCIES: EVIDENCE FROM RENMINBI AND RIAL EXCHANGE RATES

We perform out-of-sample prediction on both fixed and black market Chinese renminbi/US dollar, and black market rial/US dollar exchange rates by using the time-delay embedding technique and the local linear prediction method. We also predict an artificially generated chaotic time series with and without noise for the purpose of validation of the methods used in this study. In all examples tested, our prediction results significantly outperform those by the benchmark mean value predictor based on a statistic defined by Harvey et al. [11]. Another interesting result found in this paper is that one may use the embedding dimension as a measure of volatility of a financial asset.

New attempt of ultrasonic tissue characterization: decreased chaos in myocardial echo in patients with dilated cardiomyopathy

Ultrasonic radiofrequency (RF) signals returned from the myocardium may display complex behavior, including deterministic chaos, and such chaos may be a useful marker of the tissue properties that are not obtainable with myocardial integrated backscatter. Thus, RF signals were obtained from the myocardium by the transthoracic approach in seven healthy subjects and eight patients with dilated cardiomyopathy (DCM). They were analyzed by a time-delay embedding technique to construct a continuous 3-D trajectory. The attractor formed a thick ring-like structure consisting of a relatively empty, roughly circular, core region in all healthy subjects. In DCM patients, the ring-like structure is thinned with a distinct empty circular core region. When the relation between embedding dimension and averaged correlation dimension was compared, the correlation dimension reached a plateau at the value of 3.5 in healthy subjects, and at the value of 2.6 in DCM patients. In conclusion, chaotic behavior is prevalent in the RF signals for the healthy myocardium, and a decrease in such chaos may be indicative of the damaged myocardium in DCM patients. (E-mail:masuyama@medone.med.osaka-u.ac.jp)

Nonlinear deterministic forecasting of daily dollar exchange rates

We perform out-of-sample predictions on several dollar exchange rate returns by using time-delay embedding techniques and a local linear predictor. We compared our predictions with those by a mean value predictor. Some of our predictions of the exchange rate returns outperform the predictions of the same series by the mean value predictor. However, these improvements were not statistically significant. Another interesting result in this paper which was obtained by using a recently developed technique of nonlinear dynamics is that all exchange rate return series we tested have a very high embedding dimension. Additionally, evidence indicates that these series are likely generated by high dimensional systems with measurement noise or by high dimensional nonlinear stochastic systems, that is, nonlinear deterministic systems with dynamic noise.

Could nonlinear dynamics contribute to intra-day risk management?

We use techniques drawn from the field of nonlinear dynamics, often popularly referred to as chaos theory, to study high frequency (tick by tick) time series of foreign exchange and interest rates. The existence of strange attractors is extensively investigated by applying the nearest-neighbours algorithm for the computation of fractal dimensions to the signals reconstructed with the time-delay embedding technique. Furthermore, the state space reconstruction allows us to test whether, in the course of a business day, forecasts based on this technique could improve the timing of hedge trades, in the foreign exchange and interest rate markets. We find that this approach does not reduce hedging costs. This casts strong doubts on the ability of nonlinear dynamics to be of any practical use in financial risk management.