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Register a new userStatistical early-warning indicators based on Auto-Regressive Moving-Average processes
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We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two indicators representing the total order and the total persistence of the process, linked, respectively, to the shape and to the characteristic decay time of the autocorrelation function of the process. We successfully test the method to detect transitions in a Langevin model and a 2D Ising model with nearest-neighbour interaction. We then apply the method to complex systems, namely for dynamo thresholds and financial crisis detection.
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We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $Upsilon$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von Karman swirling flow, we show that $Upsilon$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same information, using much shorter time series. We conclude that $Upsilon$ is a suitable index to reconstruct the spatial intermittency of the dissipation in both numerical and experimental turbulent fields.
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.
Acoustic Emission (AE) data from single point turning machining are analysed in this paper in order to gain a greater insight of the signal statistical properties for Tool Condition Monitoring (TCM) applications. A statistical analysis of the time series data amplitude and root mean square (RMS) value at various tool wear levels are performed, �nding that ageing features can be revealed in all cases from the observed experimental histograms. In particular, AE data amplitudes are shown to be distributed with a power-law behaviour above a cross-over value. An analytic model for the RMS values probability density function (pdf) is obtained resorting to the Jaynes maximum entropy principle (MEp); novel technique of constraining the modelling function under few fractional moments, instead of a greater amount of ordinary moments, leads to well-tailored functions for experimental histograms.
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. In this paper, we review the recent advances in this forefront and rapidly evolving field, aiming to cover topics such as compressive sensing (a novel optimization paradigm for sparse-signal reconstruction), noised-induced dynamical mapping, perturbations, reverse engineering, synchronization, inner composition alignment, global silencing, Granger Causality and alternative optimization algorithms. Often, these rely on various concepts from statistical and nonlinear physics such as phase transitions, bifurcation, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks towards the ultimate goal of controlling such systems. Despite recent progress, many challenges remain. A purpose of this Review is then to point out the specific difficulties as they arise from different contexts, so as to stimulate further efforts in this interdisciplinary field.
We propose a comprehensive framework able to address both the predictability of the first and of the second kind for high-dimensional chaotic models. For this purpose, we analyse the properties of a newly introduced multistable climate toy model constructed by coupling the Lorenz 96 model with a zero-dimensional energy balance model. First, the attractors of the system are identified with Monte Carlo Basin Bifurcation Analysis. Additionally, we are able to detect the Melancholia state separating the two attractors. Then, Neural Ordinary Differential Equations are applied in order to predict the future state of the system in both of the identified attractors.
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