HHT based Instrumental Glitch Trigger Generation
Project Description and Goal
 Member: John J. Oh, Sang Hoon Oh, Edwin J. Son (NIMS), YoungMin 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: HilbertHuang Transform (HHT)
HHT is a recently suggested empirical data transform based on adaptive bases. So it is very useful for analyzing nonlinear and/or nonstationary 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 , 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 and . And the normalized squared difference (NSD) between two successive sifting operations is defined as
,
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 .
Comparing to the (Fast) Fourier Transform (FFT), , we easily see that the HHT deals with the timevariant amplitude and phase data with adaptive bases. We compare the HHT to other two different transforms in the following table.

Fourier 
Wavelet 
HilbertHuang 
Basis 
a priori 
a priori 
Adaptive 
Frequency 
Integral transform: Global 
Integral transform: Regional 
Differentiation: Local 
Presentation 
EnergyFrequency 
EnergyTimeFrequency 
EnergyTimeFrequency 
Nonlinearity 
No 
No 
Yes 
Nonstationarity 
No 
Yes 
Yes 
Uncertainty 
Yes 
Yes 
No 
Harmonics 
Yes 
Yes 
No 
Trigger Generation Method
 Trigger Generation Criterion (Should be tuned later)
Ref.) Li MingAi, Yang LinBao, and Yang JinFu, Commun. Info. Sci. Mag. Eng., Vol.1, No.2, PP.16 (2011)
 When amplitude exceeds the threshold:
 then a trigger candidate is reported, where
.
Preliminary Analysis of HHT
Here, we show some preliminary results done so far using HHT with S6 LIGO data and KAGRA data. First we ran HHT code written in python  mainly consists of EMD and HSA parts with auxiliary channel data in LIGO S6, for example, L1_SUS_ITMX_OPLEV_Y and L1_LSC_DARM_ERR. We ran the code for so many data sets but here some of them are presented to explain our motivation.
HHTbased Trigger Check with S6 LIGO Data
 Data: L1_SUS_ITMX_OPLEV_Y / L1_LSCDARM_ERR
 Method: HHT operation / KW Trigger at given GPS time
 EMD Decomposition and HSA Trigger Generation / Comparison with KW Trigger (red)
 The first thing is to compare the result done by HHT with the KW trigger as confirmed as an instrumental glitch (red in the figure).
 For the KW trigger at a given GPS time, HHT can find the same trigger.
 In IMF1 figure (Aux), HHT can also find very small glitchlike peaks (at 0.8, 1.8, and 2.7 GPS time)
 In IMF5 figure (DARM), HHT finds the same glitch found in the KW transform at around 3.0 as well as so many glitch candidates before and after the red event time.
 Data: S6_968654557 (Big Dog Event)
 Method: HHT operation / Big Dog time (around 8 sec in IMF3)
 EMD Decomposition and HSA Trigger Generation (green)
 To find the characteristic of HHT, we ran the code for the famous Big Dog Event (h of t data: obtained in the LIGO website).
 The Big Dog Event lasts around 5 seconds in different frequency bands (starts from 30Hz to 100Hz)
 In IMF3, the strongest peak at right before 8 second can be detected while other small trigger candidates can be found by our trigger generation scheme.
 In IMF6, there are one trigger candidate at around 7 sec.
 In conclusion, all these candidates could be GW signal or instrumental glitches. However the conclusion is that we can find some abnormal features of data in individually decomposed modes generated by HHT.
HHTbased Trigger Check with KAGRA Data
 Data: 20131023_SEISMIC_SEI_NS_0000000128
 Method: HHT operation
 EMD Decompostion / HSA  marking in GPS time (green)
 We just show a sampled analysis of SEISMIC channel data analysis of KAGRA.
 As shown in S6 Data, the trigger generation pipeline can detect triggers in each mode (IMF).
 Power Spectrum Density (EnergyFrequency Map)
 PSD figure gives us an interesting feature of HHT (EnergyFrequency Map).
 This figure shows that HHT can efficiently decompose the original data (blue) in an appropriate way with effective frequency bands.
 For example, in the second figure below, suppose we have 10 IMFs and one residual, the IMF1 is nicely matched in 250~500 Hz, the IMF2 in 150~250Hz, the IMF3 in 80~100Hz, and so on.
 So each IMF represent the dominant original noise in a certain frequency band.
Action Items
 Generate KW triggers for KAGRA Data
 Trigger candidate scattered plots, comparing two triggers.
 Count overlapped triggers and unoverlapped triggers  making statistics.
 ...
Simulation Results