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==== Project Description ====
* Introduction: Hilbert-Huang Transform (HHT)
HHT is a recently suggested empirical data transform based on adaptive bb
==== Goal ====
Line 7: Line 3:
==== 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 Auxiliary Channel Data, KAGRA Seismic/Magnetometer Data
 * Goal: Developing an improved trigger generation scheme using HHT - comparing KW triggers (and others)

==== 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

{{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.
<tablestyle="align:center">
||<bgcolor="#E0E0FF"> ||<bgcolor="#E0E0FF"><style="text-align: center;"> Fourier ||<bgcolor="#E0E0FF"> <style="text-align: center;"> Wavelet ||<bgcolor="#E0E0FF"><style="text-align: center;"> Hilbert-Huang ||
||<bgcolor="#E0E0FF"><style="text-align: center;"> Basis || <style="text-align: center;"> a priori || <style="text-align: center;"> a priori ||<style="text-align: center;"> Adaptive ||
||<bgcolor="#E0E0FF"><style="text-align: center;"> Frequency || <style="text-align: center;"> Integral transform: Global || <style="text-align: center;"> Integral transform: Regional || <style="text-align: center;"> Differentiation: Local||
||<bgcolor="#E0E0FF"><style="text-align: center;"> Presentation ||<style="text-align: center;"> Energy-Frequency || <style="text-align: center;"> Energy-Time-Frequency || <style="text-align: center;"> Energy-Time-Frequency||
||<bgcolor="#E0E0FF"> <style="text-align: center;"> Nonlinearity ||<style="text-align: center;"> No ||<style="text-align: center;"> No ||<style="text-align: center;"> Yes ||
||<bgcolor="#E0E0FF"> <style="text-align: center;"> Non-stationarity || No || Yes || Yes ||
||<bgcolor="#E0E0FF"> <style="text-align: center;"> Uncertainty || <style="text-align: center;"> Yes || <style="text-align: center;"> Yes || <style="text-align: center;"> No ||
||<bgcolor="#E0E0FF"><style="text-align: center;"> Harmonics || <style="text-align: center;"> Yes || <style="text-align: center;"> Yes || <style="text-align: center;"> No ||
</tablestyle>
Line 8: Line 29:

 * HHT-based Trigger Check with S6 LIGO Data
  * Data: L1_SUS_ITMX_OPLEV_Y / L1_LSC-DARM_ERR
  * Method: HHT operation / KW Trigger at given GPS time
  * EMD Decomposition and HSA Trigger Generation / Comparison with KW Trigger (red)
    {{attachment:S6HHT_KW.png|alt Comparison btw HHT & KW triggers of S6 aux. channel Data |width=800 height=250}}

  * Data: S6_968654557 (Big Dog Event)
  * Method: HHT operation / Big Dog time (around 8 sec in IMF3)
  * EMD Decomposition and HSA Trigger Generation (green)
    {{attachment:S6HHT_BigDog.png|alt Big Dog Trigger seen in HHT |width=800 height=250}}

 * HHT-based Trigger Check with KAGRA Data
  * Data: 20131023_SEISMIC_SEI_NS_00000-00128
  * Method: HHT operation
  * EMD Decompostion / HSA - marking in GPS time (green)
    {{attachment:20131023_seismic_SEI_NS_00000-00128_emd_0.png|alt HHT Triggers of KAGRA Seismic Data |width=850 height=250}}
  * Power Spectrum Density (Energy-Frequency Map)
    {{attachment:20131023_seismic_SEI_NS_00000-00128_psd.png|alt PSD of KAGRA Seismic Data |width=850 height=250}}

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 Auxiliary Channel Data, KAGRA Seismic/Magnetometer Data
  • Goal: Developing an improved trigger generation scheme using HHT - comparing KW triggers (and others)

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.

<tablestyle="align:center">

<style="text-align: center;"> Fourier

<style="text-align: center;"> Wavelet

<style="text-align: center;"> Hilbert-Huang

<style="text-align: center;"> Basis

<style="text-align: center;"> a priori

<style="text-align: center;"> a priori

Adaptive

<style="text-align: center;"> Frequency

<style="text-align: center;"> Integral transform: Global

<style="text-align: center;"> Integral transform: Regional

<style="text-align: center;"> Differentiation: Local

<style="text-align: center;"> Presentation

Energy-Frequency

<style="text-align: center;"> Energy-Time-Frequency

<style="text-align: center;"> Energy-Time-Frequency

<style="text-align: center;"> Nonlinearity

No

No

Yes

<style="text-align: center;"> Non-stationarity

No

Yes

Yes

<style="text-align: center;"> Uncertainty

<style="text-align: center;"> Yes

<style="text-align: center;"> Yes

<style="text-align: center;"> No

<style="text-align: center;"> Harmonics

<style="text-align: center;"> Yes

<style="text-align: center;"> Yes

<style="text-align: center;"> No

</tablestyle>

Preliminary Analysis of HHT

  • HHT-based Trigger Check with S6 LIGO Data
    • Data: L1_SUS_ITMX_OPLEV_Y / L1_LSC-DARM_ERR
    • Method: HHT operation / KW Trigger at given GPS time
    • EMD Decomposition and HSA Trigger Generation / Comparison with KW Trigger (red)

      • alt Comparison btw HHT & KW triggers of S6 aux. channel Data

    • Data: S6_968654557 (Big Dog Event)
    • Method: HHT operation / Big Dog time (around 8 sec in IMF3)
    • EMD Decomposition and HSA Trigger Generation (green)

      • alt Big Dog Trigger seen in HHT

  • HHT-based Trigger Check with KAGRA Data
    • Data: 20131023_SEISMIC_SEI_NS_00000-00128
    • Method: HHT operation
    • EMD Decompostion / HSA - marking in GPS time (green)

      • alt HHT Triggers of KAGRA Seismic Data

    • Power Spectrum Density (Energy-Frequency Map)

      • alt PSD of KAGRA Seismic Data

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)