EMD performance comparison: single vs double floating points

Empirical mode decomposition (EMD) is a data-driven method used to decompose data into oscillatory components. This paper examines to what extent the defined algorithm for EMD might be susceptible to data format. Two key issues with EMD are its stability and computational speed. This paper shows that for a given signal there is no significant difference between results obtained with single (binary32) and double (binary64) floating points precision. This implies that there is no benefit in increasing floating point precision when performing EMD on devices optimised for single floating point format, such as graphical processing units (GPUs)

Bivariate Empirical Mode Decomposition

10 pages, 3 figures. Submitted to Signal Processing Letters, IEEE. Matlab/C codes and additional material are downloadable from http://perso.ens-lyon.fr/patrick.flandrinThe Empirical Mode Decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series which generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin

Integration of Human Walking Gyroscopic Data Using Empirical Mode Decomposition

The present study was aimed at evaluating the Empirical Mode Decomposition (EMD) method to estimate the 3D orientation of the lower trunk during walking using the angular velocity signals generated by a wearable inertial measurement unit (IMU) and notably flawed by drift. The IMU was mounted on the lower trunk (L4-L5) with its active axes aligned with the relevant anatomical axes. The proposed method performs an offline analysis, but has the advantage of not requiring any parameter tuning. The method was validated in two groups of 15 subjects, one during overground walking, with 180° turns, and the other during treadmill walking, both for steady-state and transient speeds, using stereophotogrammetric data. Comparative analysis of the results showed that the IMU/EMD method is able to successfully detrend the integrated angular velocities and estimate lateral bending, flexion-extension as well as axial rotations of the lower trunk during walking with RMS errors of 1 deg for straight walking and lower than 2.5 deg for walking with turns

One or two Frequencies? The empirical Mode Decomposition Answers

19 pages, 7 figures. Submitted to IEEE Trans. on Signal Proc.This paper investigates how Empirical Mode Decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviours, theoretical claims are supported by numerical experiments, and possible extensions to nonlinear oscillations are briefly outlined

On the HHT, its problems, and some solutions

Mechanical Systems and Signal Processing, Vol.22, Number 6The empirical mode decomposition (EMD) is reviewed and some questions related to its effective performance are discussed. Its interpretation in terms of AM/FM modulation is done. Solutions for its drawbacks are proposed. Numerical simulations are carried out to empirically evaluate the proposed modified EMD

Energy weighting method and its application to fault diagnosis of rolling bearing

Feature extraction of vibration signal is the key factor of machine fault diagnosis. This paper proposes a novel method of capturing shock energy based on multi-scale weight evaluation of high definition time-frequency map. Specifically, the proposed method is conducted by the following steps. First, ensemble empirical mode decomposition (EEMD) preprocessor-based Hilbert-Huang Transform (HHT) is applied to the raw signal for high definition time-frequency map acquisition. Second, an original algorithm named multi-scale binary spectrum was applied to extract impulsive energy features with different frequency characteristics. Then weights of energy can be calculated by dimensionality reduction of each binary spectrum and merged by summation after blank processing. Finally, power spectrum of compound weight of energy can reveal characteristic frequency corresponding to specific fault. In this method, the key point is enhancement of frequency spectrum using higher dimension details. The process of multi-scale binarization and weight summation were aligned and the effectiveness is verified by simulated signal processing and actual case of train bearing experiment

Energy weighting method and its application to fault diagnosis of rolling bearing

Feature extraction of vibration signal is the key factor of machine fault diagnosis. This paper proposes a novel method of capturing shock energy based on multi-scale weight evaluation of high definition time-frequency map. Specifically, the proposed method is conducted by the following steps. First, ensemble empirical mode decomposition (EEMD) preprocessor-based Hilbert-Huang Transform (HHT) is applied to the raw signal for high definition time-frequency map acquisition. Second, an original algorithm named multi-scale binary spectrum was applied to extract impulsive energy features with different frequency characteristics. Then weights of energy can be calculated by dimensionality reduction of each binary spectrum and merged by summation after blank processing. Finally, power spectrum of compound weight of energy can reveal characteristic frequency corresponding to specific fault. In this method, the key point is enhancement of frequency spectrum using higher dimension details. The process of multi-scale binarization and weight summation were aligned and the effectiveness is verified by simulated signal processing and actual case of train bearing experiment

A NOISE ESTIMATION SCHEME FOR BLIND SPECTRUM SENSING USING EMD

The scarcity of spectral resources in wireless communications, due to a fixed frequency allocation policy, is a strong limitation to the increasing demand for higher data rates. One solution is to use underutilized spectrum. Cognitive Radio (CR) technologies identify transmission opportunities in unused channels and avoid interfering with primary users. The key enabling technology is the Spectrum Sensing (SS). Different SS techniques exist, but techniques that do not require knowledge of the signals (non-coherent) are preferred. Noise estimation plays an essential role in enhancing the performance of non-coherent spectrum sensors such as energy detectors. In this thesis, we present an energy detector based on the behavior of Empirical Mode Decomposition (EMD) towards vacant channels (noise-dominant). The energy trend from the EMD processed signal is used to determine the occupancy of a given band of interest. The performance of the proposed EMD-based detector is evaluated for different noise levels and sample sizes. Further, a comparison is carried out with conventional spectrum sensing techniques to validate the efficacy of the proposed detector and the results revealed that it outperforms the other sensing methods