THE UNIQUENESS OF THE INSTANTANEOUS FREQUENCY BASED ON INTRINSIC MODE FUNCTION

2013 ◽  
Vol 05 (03) ◽  
pp. 1350011 ◽  
Author(s):  
NORDEN E. HUANG ◽  
VINCENT YOUNG ◽  
MENTZUNG LO ◽  
YUNG HUNG WANG ◽  
C. K. PENG ◽  
...  
Keyword(s):  
Instantaneous Frequency ◽  
Phase Function ◽  
Intrinsic Mode Function ◽  
Constructive Method ◽  
Instantaneous Amplitude ◽  
Amplitude Function ◽  
Physical Sense ◽  
Mode Function

It has been claimed that any expression of a(t) cos θ(t) with a(t) as the instantaneous amplitude and cos θ(t) as the carrier varying along with the phase θ(t) could not be uniquely defined. However, based on the fact that a(t) cos θ(t) with all its variational forms have the same numerical value at any given time, we propose the existence of a unique true intrinsic amplitude function ai(t) and phase function θi(t) that ai(t) cos θi(t) satisfying the envelope–carrier relationship is the only expression making physical sense. A constructive method is also presented to find such amplitude-phase pair uniquely from any Intrinsic Mode Function (IMF). As a result, we can treat any IMF in the form of ai(t) cos θi(t) as the unique defined amplitude-phase pair, from which the instantaneous frequency (IF) can also be determined.

Theory of 2-D complex seismic trace analysis

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 264-272 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Trace Analysis ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Instantaneous Amplitude ◽  
Dip Angle

The ideas of 1-D complex seismic trace analysis extend readily to two dimensions. Two‐dimensional instantaneous amplitude and phase are scalars, and 2-D instantaneous frequency and bandwidth are vectors perpendicular to local wavefronts, each defined by a magnitude and a dip angle. The two independent measures of instantaneous dip correspond to instantaneous apparent phase velocity and group velocity. Instantaneous phase dips are aliased for steep reflection dips following the same rule that governs the aliasing of 2-D sinusoids in f-k space. Two‐dimensional frequency and bandwidth are appropriate for migrated data, whereas 1-D frequency and bandwidth are appropriate for unmigrated data. The 2-D Hilbert transform and 2-D complex trace attributes can be efficiently computed with little more effort than their 1-D counterparts. In three dimensions, amplitude and phase remain scalars, but frequency and bandwidth are 3-D vectors with magnitude, dip angle, and azimuth.

scholarly journals Fault Diagnosis of Rolling Bearing Based on Multiscale Intrinsic Mode Function Permutation Entropy and a Stacked Sparse Denoising Autoencoder

2019 ◽  
Vol 9 (13) ◽  
pp. 2743 ◽  
Author(s):  
Dai ◽  
Tang ◽  
Shao ◽  
Huang ◽  
Wang
Keyword(s):  
Fault Diagnosis ◽  
Rolling Bearing ◽  
Ensemble Empirical Mode Decomposition ◽  
Health Condition ◽  
Intrinsic Mode Function ◽  
Permutation Entropy ◽  
Diagnostic Model ◽  
Denoising Autoencoder ◽  
Essential Information ◽  
Mode Function

Effective intelligent fault diagnosis of bearings is important for improving safety and reliability of machine. Benefiting from the training advantages, deep learning method can automatically and adaptively learn more abstract and high-level features without much priori knowledge. To realize representative features mining and automatic recognition of bearing health condition, a diagnostic model of stacked sparse denoising autoencoder (SSDAE) which combines sparse autoencoder (SAE) and denoising autoencoder (DAE) is proposed in this paper. The sparse criterion in SAE, corrupting operation in DAE and reasonable designing of the stack order of autoencoders help to mine essential information of the input and improve fault pattern classification robustness. In order to provide better input features for the constructed network, the raw non-stationary and nonlinear vibration signals are processed with ensemble empirical mode decomposition (EEMD) and multiscale permutation entropy (MPE). MPE features which are extracted based on both the selected characteristic frequency-related intrinsic mode function components (IMFs) and the raw signal, are used as low-level feature for the input of the proposed diagnostic model for health condition recognition and classification. Two experiments based on the Case Western Reserve University (CWRU) dataset and the measurement dataset from laboratory were conducted, and results demonstrate the effectiveness of the proposed method and highlight its excellent performance relative to existing methods.

Sign in / Sign up

Export Citation Format

Share Document