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

Adaptive Signal Decomposition Methods for Vibration Signals of Rotating Machinery

Vibration‐based condition monitoring and fault diagnosis are becoming more common in the industry to increase machine availability and reliability. Considerable research efforts have recently been directed towards the development of adaptive signal processing methods for fault diagnosis. Two adaptive signal decomposition methods, i.e. the empirical mode decomposition (EMD) and the local mean decomposition (LMD), are widely used. This chapter is intended to summarize the recent developments mostly based on the authors’ works. It aims to provide a valuable reference for readers on the processing and analysis of vibration signals collected from rotating machinery

A Gyro Signal Characteristics Analysis Method Based on Empirical Mode Decomposition

It is difficult to analyze the nonstationary gyro signal in detail for the Allan variance (AV) analysis method. A novel approach in the time-frequency domain for gyro signal characteristics analysis is proposed based on the empirical mode decomposition and Allan variance (EMDAV). The output signal of gyro is decomposed by empirical mode decomposition (EMD) first, and then the decomposed signal is analyzed by AV algorithm. Consequently, the gyro noise characteristics are demonstrated in the time-frequency domain with a three-dimensional (3D) manner. Practical data of fiber optic gyro (FOG) and MEMS gyro are processed by the AV method and the EMDAV algorithm separately. The results indicate that the details of gyro signal characteristics in different frequency bands can be described with the help of EMDAV, and the analysis dimensions are extended compared with the common AV. The proposed EMDAV, as a complementary tool of the AV, which provides a theoretical reference for the gyro signal preprocessing, is a general approach for the analysis and evaluation of gyro performance

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD – we have considerably increased algorithm’s application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data

Ensemble Empirical Mode Decomposition: Image Data Analysis with White-noise Reflection

During the last decade, Zhaohua Wu and Norden E. Huang announced a new improvement of the original Empirical Mode Decomposition method (EMD). Ensemble Empirical Mode Decomposition and its abbreviation EEMD represents a major improvement with great versatility and robustness in noisy data filtering. EEMD consists of sifting and making an ensemble of a white noise-added signal, and treats the mean value as the final true result. This is due to the use of a finite, not infinitesimal, amplitude of white noise which forces the ensemble to exhaust all possible solutions in the sifting process. These steps collate signals of different scale in a proper intrinsic mode function (IMF) dictated by the dyadic filter bank. As EEMD is a time–space analysis method, the added white noise is averaged out with a sufficient number of trials. Here, the only persistent part that survives the averaging process is the signal component (original data), which is then treated as the true and more physically meaningful answer. The main purpose of adding white noise was to provide a uniform reference frame in the time–frequency space. The added noise collates the portion of the signal of comparable scale in a single IMF. Image data taken as time series is a non-stationary and nonlinear process to which the new proposed EEMD method can be fitted out. This paper reviews the new approach of using EEMD and demonstrates its use on the example of image data analysis, making use of some advantages of the statistical characteristics of white noise. This approach helps to deal with omnipresent noise

Turbulence Time Series Data Hole Filling using Karhunen-Loeve and ARIMA methods

Measurements of optical turbulence time series data using unattended instruments over long time intervals inevitably lead to data drop-outs or degraded signals. We present a comparison of methods using both Principal Component Analysis, which is also known as the Karhunen--Loeve decomposition, and ARIMA that seek to correct for these event-induced and mechanically-induced signal drop-outs and degradations. We report on the quality of the correction by examining the Intrinsic Mode Functions generated by Empirical Mode Decomposition. The data studied are optical turbulence parameter time series from a commercial long path length optical anemometer/scintillometer, measured over several hundred metres in outdoor environments.Comment: 8 pages, 9 figures, submitted to ICOLAD 2007, City University, London, U