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==== Project Description ==== ==== Project Description and Goal ====
 * Member: John J. Oh, Sang Hoon Oh, Edwin J. Son (NIMS), Young-Min Kim (Pusan National Univ.), Kazuhiro Hayama (Osaka Univ.)
 * Used Data: S6 AuxChannel Data / KAGRA Seismic/Magnetometer Data
 * ...
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 * Introduction: Hilbert-Huang Transform (HHT) ==== Introduction: Hilbert-Huang Transform (HHT) ====
{{attachment:emds.png||align="left"}}
    HHT is a recently suggested empirical data transform based on adaptive bases. So it is very useful for analyzing non-linear and/or non-stationary data. The HHT consists of two main parts: 1) empirical mode decomposition (EMD) 2) Hilbert spectral analysis (HSA). The EMD can decompose the original data into some appropriate data sets that contributes to some frequency bands. Basically the EMD is described by a sifting processes with {{https://upload.wikimedia.org/math/e/e/4/ee4471f673afaddfc791f692cf250f6b.png}}, which shows that the EMD performs the subtraction between the original data (or the previously generated data) and its average of envelopes, repeatedly, called '''''intrinsic mode functions (IMF)''''', expressed by {{https://upload.wikimedia.org/math/7/e/c/7ec2bae54bcdd79fab725ef8d6c5314c.png}} and {{https://upload.wikimedia.org/math/6/5/3/65349fc2c693c1b809562b59f4b5e172.png}}. And the normalized squared difference (NSD) between two successive sifting operations is defined as
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{{attachment:emd2.png||align="left"}}
HHT is a recently suggested empirical data transform based on adaptive bases. So it is very useful for analyzing non-linear and/or non-stationary data. The HHT consists of two main parts: 1) empirical mode decomposition (EMD) 2) Hilbert transform. The EMD can decompose
the original data into some appropriate data sets that contributes to some frequency bands. Basically the EMD is described by a sifting processes with {{https://upload.wikimedia.org/math/e/e/4/ee4471f673afaddfc791f692cf250f6b.png}}, which shows that the EMD performs the subtraction between the original data (or the previously generated data) and its average of envelopes, repeatedly, called '''''intrinsic mode functions (IMF)''''', expressed by {{https://upload.wikimedia.org/math/7/e/c/7ec2bae54bcdd79fab725ef8d6c5314c.png}} and {{https://upload.wikimedia.org/math/6/5/3/65349fc2c693c1b809562b59f4b5e172.png}}. The Hilbert transform of the ''EMDed data'' consists of the amplitude and phase parts and we see that the original data can be expressed by the summation of the whole IMFs, which is
{{https://upload.wikimedia.org/math/6/f/d/6fdad0aefbac705612d1e8541fcd9eef.png}}.
{{https://upload.wikimedia.org/math/1/8/a/18aba9375519cd1b75a761363eea55b7.png}},
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Comparing to the (Fast) Fourier Transform (FFT), {{https://upload.wikimedia.org/math/2/7/7/277cc4bee5968c6ca2d4c78747d18689.png}}, we easily see that the HHT deals with the time-variant amplitude and phase data with adaptive bases. which should be small. The stoppage criterion of this process is determined by comparing between the NSD and the predetermined value - if NSD is smaller than a predetermined value, the process is stopped.
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   The Hilbert transform of the ''EMDed data'' consists of the amplitude and phase parts and we see that the original data can be expressed by the summation of the whole IMFs, which is {{https://upload.wikimedia.org/math/6/f/d/6fdad0aefbac705612d1e8541fcd9eef.png}}.
    Comparing to the (Fast) Fourier Transform (FFT), {{https://upload.wikimedia.org/math/2/7/7/277cc4bee5968c6ca2d4c78747d18689.png}}, we easily see that the HHT deals with the time-variant amplitude and phase data with adaptive bases. We compare the HHT to other two different transforms in the following table.
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==== Goal ====

HHT based Instrumental Glitch Trigger Generation

Project Description and Goal

  • Member: John J. Oh, Sang Hoon Oh, Edwin J. Son (NIMS), Young-Min Kim (Pusan National Univ.), Kazuhiro Hayama (Osaka Univ.)
  • Used Data: S6 AuxChannel Data / KAGRA Seismic/Magnetometer Data

  • ...

Introduction: Hilbert-Huang Transform (HHT)

emds.png

  • HHT is a recently suggested empirical data transform based on adaptive bases. So it is very useful for analyzing non-linear and/or non-stationary data. The HHT consists of two main parts: 1) empirical mode decomposition (EMD) 2) Hilbert spectral analysis (HSA). The EMD can decompose the original data into some appropriate data sets that contributes to some frequency bands. Basically the EMD is described by a sifting processes with https://upload.wikimedia.org/math/e/e/4/ee4471f673afaddfc791f692cf250f6b.png, which shows that the EMD performs the subtraction between the original data (or the previously generated data) and its average of envelopes, repeatedly, called intrinsic mode functions (IMF), expressed by https://upload.wikimedia.org/math/7/e/c/7ec2bae54bcdd79fab725ef8d6c5314c.png and https://upload.wikimedia.org/math/6/5/3/65349fc2c693c1b809562b59f4b5e172.png. And the normalized squared difference (NSD) between two successive sifting operations is defined as

https://upload.wikimedia.org/math/1/8/a/18aba9375519cd1b75a761363eea55b7.png,

which should be small. The stoppage criterion of this process is determined by comparing between the NSD and the predetermined value - if NSD is smaller than a predetermined value, the process is stopped.

  • The Hilbert transform of the EMDed data consists of the amplitude and phase parts and we see that the original data can be expressed by the summation of the whole IMFs, which is https://upload.wikimedia.org/math/6/f/d/6fdad0aefbac705612d1e8541fcd9eef.png.

    • Comparing to the (Fast) Fourier Transform (FFT), https://upload.wikimedia.org/math/2/7/7/277cc4bee5968c6ca2d4c78747d18689.png, we easily see that the HHT deals with the time-variant amplitude and phase data with adaptive bases. We compare the HHT to other two different transforms in the following table.

Fourier

Wavelet

Hilbert-Huang

Basis

a priori

a priori

Adaptive

Frequency

Integral transform: Global

Integral transform: Regional

Differentiation: Local

Presentation

Energy-Frequency

Energy-Time-Frequency

Energy-Time-Frequency

Nonlinearity

No

No

Yes

Non-stationarity

No

Yes

Yes

Uncertainty

Yes

Yes

No

Harmonics

Yes

Yes

No

Preliminary Analysis of HHT

Trigger Generation Method

Simulation Results

Comparison to Klein-Welle and Other Methods

HHT based Instrumental Glitch Trigger Generation (last edited 2014-01-09 12:58:08 by johnoh)