Applications of the synchrosqueezing transform in seismic time-frequency analysis

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. V55-V64 ◽  
Author(s):  
Roberto H. Herrera ◽  
Jiajun Han ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Seismic Signals ◽  
Time Frequency ◽  
Trade Offs ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Synchrosqueezing Transform ◽  
Instantaneous Frequencies

Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight individual components. We introduce the SST with applications for seismic signals and produced promising results on synthetic and field data examples.

scholarly journals ANALYSIS OF THE PRECIPITATION CLIMATE SIGNAL USING EMPIRICAL MODE DECOMPOSITION (EMD) OVER THE CASPIAN CATCHMENT AREA

2019 ◽  
Vol XLII-4/W18 ◽  
pp. 923-929
Author(s):  
F. Sabzehee ◽  
V. Nafisi ◽  
S. Iran Pour ◽  
B. D. Vishwakarma
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Empirical Mode Decomposition ◽  
Precipitation Time Series ◽  
Climate Signal ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Instantaneous Frequencies ◽  
Better Than

Abstract. In this paper, we employ Empirical Mode Decomposition (EMD) together with Hilbert Transform to analyze precipitation time series over the Caspian Sea catchment. Several studies have shown that EMD can extract nonlinear and non-stationary signals better than Fast Fourier Transform (FFT) and Wavelet Transform. EMD decomposes the time series into a finite number of Intrinsic Mode Functions (IMFs) in the time-frequency domain, while FFT helps us operate either in the time or the frequency domain, which fuels limitations such as the inability of nonstationary signal processing and the lack of time transparency. Although Wavelet Transform is shown to be better than FFT, it fails to detect the instantaneous frequencies and needs to have prior information about characteristics of the data. On the other hand, EMD has shown that it is almost able to determine the signal characteristics with no previous assumptions to estimate the instantaneous frequencies of the signal. In this work, EMD is applied to identify the main frequencies of precipitation time series. Thereafter, a statistical procedure is used to identify the prominent IMF of the original signal.We use the correlation coefficient, Minkowski distance and variance test to extract the relevant and prominent IMFs. The results show that IMF 1–3 are the relevant components and are related to annual and biennial variations of precipitation time series over the Caspian catchment during 2003–2016, respectively.

scholarly journals Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

2018 ◽  
Vol 376 (2126) ◽  
pp. 20170254 ◽  
Author(s):  
Jean Baptiste Tary ◽  
Roberto Henry Herrera ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Signal ◽  
American Football ◽  
Frequency Resolution ◽  
Time Varying ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Frequency Information ◽  
Synchrosqueezing Transform

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a ‘FanQuake’ signal displaying observed vibrations during an American football game, a seismic recording of the M w 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

scholarly journals NOISE CORRUPTION OF EMPIRICAL MODE DECOMPOSITION AND ITS EFFECT ON INSTANTANEOUS FREQUENCY

2010 ◽  
Vol 02 (03) ◽  
pp. 373-396 ◽  
Author(s):  
DANIEL N. KASLOVSKY ◽  
FRANÇOIS G. MEYER
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Poor Performance ◽  
Specific Mechanism ◽  
Time Frequency ◽  
Seismic Waveform ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Transition Modes ◽  
Nonstationary Data

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.

A velocity synchrosqueezing transform for fault diagnosis of planetary gearboxes under nonstationary conditions

2016 ◽  
Vol 231 (15) ◽  
pp. 2868-2884 ◽  
Author(s):  
Yunpeng Guan ◽  
Ming Liang ◽  
Dan-Sorin Necsulescu
Keyword(s):  
Fault Diagnosis ◽  
Vibration Signal ◽  
Frequency Resolution ◽  
Time Frequency ◽  
Machinery Condition Monitoring ◽  
Frequency Representation ◽  
Nonstationary Vibration ◽  
Synchrosqueezing Transform ◽  
Fine Resolution ◽  
Nonstationary Conditions

Time–frequency analysis is widely used in the field of machinery condition monitoring and fault diagnosis under nonstationary conditions. Among the time–frequency methods synchrosqueezing transform outperforms others in providing fine-resolution time–frequency representation. However, it suffers from time–frequency smear when analysing nonstationary signals. To address this issue, this paper proposes a new synchrosqueezing-transform-based method which works by (1) mapping the raw nonstationary vibration signal into a corresponding stationary angle domain signal to meet the stationarity requirement of the synchrosqueezing transform, (2) performing the synchrosqueezing transform of the corresponding signal and (3) restoring the time–frequency representation of the raw signal from the synchrosqueezing transform result of the corresponding signal. As the synchrosqueezing transform is applied to the stationary corresponding signal, the time–frequency smear is eliminated in the synchrosqueezing transform result of the corresponding signal and the final signal time–frequency representation. As such the proposed method can generate a smear-free time–frequency representation with fine time–frequency resolution and thus provide more reliable diagnosis decisions. A fast implementation algorithm is also developed to simplify the implementation of the proposed method. The effectiveness of the proposed method is validated using both simulated and experimental vibration signals of planetary gearboxes.

Empirical mode decomposition for seismic time-frequency analysis

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. O9-O19 ◽  
Author(s):  
Jiajun Han ◽  
Mirko van der Baan
Keyword(s):  
Empirical Mode Decomposition ◽  
Frequency Analysis ◽  
Real Data ◽  
Seismic Signal ◽  
Ensemble Empirical Mode Decomposition ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Instantaneous Frequencies ◽  
Short Time

Time-frequency analysis plays a significant role in seismic data processing and interpretation. Complete ensemble empirical mode decomposition decomposes a seismic signal into a sum of oscillatory components, with guaranteed positive and smoothly varying instantaneous frequencies. Analysis on synthetic and real data demonstrates that this method promises higher spectral-spatial resolution than the short-time Fourier transform or wavelet transform. Application on field data thus offers the potential of highlighting subtle geologic structures that might otherwise escape unnoticed.

Transform Operator Pair Assisted Hilbert–Huang Transform for Signals With Instantaneous Frequency Intersections

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Yuxin Sun ◽  
Chungang Zhuang ◽  
Zhenhua Xiong
Keyword(s):  
A Priori ◽  
Low Frequency ◽  
Ensemble Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Start Up ◽  
Instantaneous Frequencies

Due to low frequency resolution for closely spaced spectral components, i.e., the instantaneous frequencies (IFs) lie within an octave or even have intersections, the Hilbert–Huang transform (HHT) fails to separate such signals and consequently generates inaccurate time–frequency distribution (TFD). In this paper, a transform operator pair assisted HHT is proposed to improve the capability of the HHT to separate signals, especially those with IF intersections. The two operators of a pair are constructed to remove the chosen component that is clearly observed in the TFD of the signal, and then recover it from intrinsic mode functions (IMFs). With this approach, the components can be clearly separated and the intersections can also be identified in the TFD. Since a priori knowledge of the transform operator is usually not available in real applications, an iterative algorithm is presented to obtain a global transform operator. The effectiveness of the proposed algorithm is demonstrated by analysis of numerical signals and a real signal collected from a cracked rotor–bearing system during the start-up process. Moreover, the proposed approach is shown to be superior to the normalized Hilbert transform (NHT) as well as the ensemble empirical mode decomposition (EEMD).

Research on Fault Diagnosis Method Based on Empirical Mode Decomposition & Time-Frequency Reassignment

2012 ◽  
Vol 433-440 ◽  
pp. 6256-6261
Author(s):  
Zhi Hua Hao ◽  
Zhuang Ma ◽  
Hao Miao Zhou
Keyword(s):  
Empirical Mode Decomposition ◽  
Simulation Analysis ◽  
Intrinsic Mode Function ◽  
Time Frequency ◽  
Mode Function ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Cross Terms ◽  
Decomposition Time ◽  
The Cross

The reassignment method is a technique for sharpening a time-frequency representation by mapping the data to time-frequency coordinates that are nearer to the true region of support of the analyzed signal. The reassignment method has been proved to produce a better localization of the signal components and improve the readability of the time-frequency representation by concentrating its energy at a center of gravity. But there are still few cross-terms. Then, the empirical mode decomposition is introduced to the reassignment method to suppress the interference of the cross-term encountered in processing the multi-component signals. The multi-component signal can be decomposed into a finite number intrinsic mode function by using EMD. Then, the reassignment method can be calculated for each of the intrinsic mode function. Simulation analysis is presented to show that this method can improve the localization of time-frequency representation and reduce the cross terms. The vibration signals measured from diesel engine in the stage of deflagrate were analyzed with the reassignment method. Experimental results indicate that this method has good potential in mechanical fault feature extraction.

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