Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Lagrangian single particle turbulent statistics through the Hilbert-Huang Transform

The Hilbert-Huang transform is applied to analyze single particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions, C_{i}(t), and of their instantaneous frequency, \omega_{i}(t). On the basis of this decomposition we define the \omega-conditioned statistical moments of the C_{i} modes, named q-order Hilbert Spectra (HS). We show that such new quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (Structure Functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present a clear empirical evidence that the energy-like quantity, i.e. the second-order HS, displays a linear scaling in time in the inertial range, as expected from dimensional analysis and never observed before. We also measure high order moment scaling exponents in a direct way, without resorting the Extended Self Similarity (ESS) procedure. This leads to a new estimate of the Lagrangian structure functions exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed in [Biferale et al., Phys. Rev. Lett. vol. 93, 064502 (2004)].Comment: 5 pages, 5 figure

On the behavior of EMD and MEMD in presence of symmetric alpha-stable noise

EmpiricalMode Decomposition (EMD) and its extended versions such as Multivariate EMD (MEMD) are data-driven techniques that represent nonlinear and non-stationary data as a sum of a finite zero-mean AM-FM components referred to as Intrinsic Mode Functions (IMFs). The aim of this work is to analyze the behavior of EMD and MEMD in stochastic situations involving non-Gaussian noise, more precisely, we examine the case of Symmetric Alpha-Stable noise. We report numerical experiments supporting the claim that both EMD and MEMD act, essentially, as filter banks on each channel of the input signal in the case of Symmetric Alpha Stable noise. Reported results show that, unlike EMD, MEMD has the ability to align common frequency modes across multiple channels in same index IMFs. Further, simulations show that, contrary to EMD, for MEMD the stability property is well satisfied for the modes of lower indices and this result is exploited for the estimation of the stability index of the Symmetric Alpha Stable input signal

EEMD-based windturbinebearingfailuredetectionusing the generatorstatorcurrenthomopolarcomponent

International audienceFailure detection has always been a demanding task in the electrical machines community; it has become more challenging in wind energy conversion systems because sustainability and viability of wind farms are highly dependent on the reduction of the operational and maintenance costs. Indeed the most efficient way of reducing these costs would be to continuously monitor the condition of these systems. This allows for early detection of the generator health degeneration, facilitating a proactive response, minimizing downtime, and maximizing productivity. This paper provides then an assessment of a failure detection techniques based on the homopolar component of the generator stator current and attempts to highlight the use of the ensemble empirical mode decomposition as a tool for failure detection in wind turbine generators for stationary and non stationary cases

Relationship between Remittances and Macroeconomic Variables in Times of Political and Social Upheaval: Evidence from Tunisia's Arab Spring

If Tunisia was hailed as a success story with its high rankings on economic, educational, and other indicators compared to other Arab countries, the 2011 popular uprisings demonstrate the need for political reforms but also major economic reforms. The Arab spring highlights the fragility of its main economic pillars including the tourism and the foreign direct investment. In such turbulent times, the paper examines the economic impact of migrant' remittances, expected to have a countercyclical behavior. Our results reveal that prior to the Arab Spring, the impacts of remittances on growth and consumption seem negative and positive respectively, while they varyingly influence local investment. These three relationships held in the short-run. By considering the period surrounding the 2011 uprisings, the investment effect of remittances becomes negative and weak in the short-and medium-run, whereas positive and strong remittances' impacts on growth and consumption are found in the long term.Comment: ERF 23rd Annual Conference , Mar 2017, Amman, Jorda

A Comparative Analysis of Signal Decomposition Techniques for Structural Health Monitoring on an Experimental Benchmark

Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals

Empirical mode decomposition of wind speed signals

Empirical Mode Decomposition (EMD) is a powerful signal processing technique with diverse applications, particularly in the analysis of non-stationary data. In this study, we assess the capabilities of EMD for wind data analysis, aiming to uncover its effectiveness in capturing intricate temporal patterns and decomposing data into Intrinsic Mode Functions (IMFs) to identify crucial frequency components. Various methods of sifting have been studied as the IMFs and therefore results may vary according to the type. It has been concluded that the Ensemble Empirical Mode Decomposition (EEMD) is the most suitable method for these data. A comparison with Fourier analysis is also conducted to elucidate the strengths and limitations of each method. Furthermore, this investigation examines the Average Diurnal Variation (ADV) and Average Seasonal Variation (ASV) patterns within the wind data. It is found that these patters have a physical significance and interpretation of the IMFs and that it is easier to use EMD than Fourier for wind signals

Linear Versus Nonlinear Methods for Detecting Magnetospheric and Ionospheric Current Systems Patterns

Abstract There is a growing interest in the development of models and methods of analysis aimed to recognize in the geomagnetic field signals the different contributions coming from the various sources both internal and external to the Earth. Many models describing the geomagnetic field of internal and external origin have been developed. Here, we investigate the possibility to recognize in the magnetic field of external origin the different contributions coming from external sources. We consider the measurements of the vertical component of the geomagnetic field recorded by the European Space Agency (ESA) Swarm A and B satellites at low and mid latitudes during a geomagnetically quiet period. We apply two different methods of analysis: a linear method, that is, the empirical orthogonal function (EOF), and a nonlinear one, that is, the multivariate empirical mode decomposition (MEMD). Due to the high nonlinear behavior of the different external contributions to the magnetic signal the MEMD seems to recognize better than EOF the main intrinsic modes capable of describing the different magnetic spatial structures embedded in the analyzed signal. By applying the MEMD only five modes and a residue are necessary to recognize the different contributions coming from the external sources in the magnetic signal against the 26 modes that are necessary in the case of the EOF. This study is an example of the potential of the MEMD to give new insights into the analysis of the geomagnetic field of external origin and to separate the ionospheric signal from the magnetospheric one in a simple and rapid way