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Burst Event Analysis of TAMA

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### Burst Event Analysis of TAMA

78 gravitational waveforms Non-Gaussian noise rejection (1) - Target selection -

Masaki Ando

(Department of physics, University of Tokyo)

K. Arai, R. Takahashi, D. Tatsumi, P. Beyersdorf, S. Kawamura,

S. Miyoki, N. Mio, S. Moriwaki, K. Numata,N. Kanda, Y. Aso,

M.-K. Fujimoto, K. Tsubono, K. Kuroda,

and the TAMA collaboration

- Burst GW analysis
- Non-Gaussian noise rejection
- TAMA DT6 data analysis

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Contents

- Introduction
- Burst GW analysis

- Burst filters
- Excess filter and non-Gaussian noises

- Rejection of non-Gaussian noises
- Concept, implementation

- Data analysis with TAMA300 data
- TAMA data
- Noise reduction, burst event rate

- Summary

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Introduction (1)- Gravitational wave search -

- Chirp GW signal(from compact binary inspirals )
- Well-predicted waveform
Matched Filtering (correlation with templates)

Distinguishable from non-Gaussian noises

- Well-predicted waveform
- Continuous GW signal(from rotating neutron stars)
- Well-predicted waveform
Simpler waveforms (modulated sine waves)

Almost stationary

Noise reduction with

Long-term Integration, narrow band analysis

- Well-predicted waveform
- Burst GW signal(from Stellar core collapses)
- Poorly-predicted waveforms
Cannot use matched filtering to get optimal SNR

Look for ‘something unusual’

- Poorly-predicted waveforms

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

+ (Non-Gaussian noise)

Non-Gaussian events

- Burst GW signals
- Non-Gaussian noise

Detection efficiency is limited

by non-Gaussian noises

Non-Gaussian noise rejectionis indispensable

Introduction (2)- Non-Gaussian noises -- Main output signal of a detector

= (Stationary, Gaussian noise) + (Burst GW signals)

Stable operation

Non-Gaussian events

Burst filters:

Look for and sensitive to

Unpredicted and non-stationary waveforms

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection with noise behavior, …

Time scale of non-Gaussian events

Introduction (3)- Non-Gaussian noise reduction -- Non-Gaussian noise rejection
- Single detector
- Detector improvement
- Data processing
(Signal behavior, auxiliary signals)

- Correlation with other detectors
- Other GW detectors
- Other astronomical channels
(Super novae, Gamma-ray burst, etc.)

- Single detector

In this talk …

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Contents

- Introduction
- Burst GW analysis

- Burst filters
- Excess filter and non-Gaussian noises

- Rejection of non-Gaussian noises
- Concept, implementation

- Data analysis with TAMA300 data
- TAMA data,
- Noise reduction, burst event rate

- Summary

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Burst filters (1)- Proposed filters for burst GW -

- Proposed filters for burst wave
--- look for unusual signals

- Power in time-frequency plane
- Excess power: Phys. Rev. D 63, 042003 (2001)
- Clusters of high-power pixels in the time-frequency plane
: Phys. Rev. D 61, 122002 (2000)

- Correlation with typical waveform
- Slope detector: Phys. Rev. D 63, 042002 (2001)
- Correlation with single pulse: Phys. Rev. D 59, 082002 (1999)
Evaluate with certain statistics

set thresholds record large events

- Power in time-frequency plane

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Time- Frequency plane

(spectrogram)

Total power in given T-F region

Signal !!!

Effective if

time-frequency range of the signal

is known

Burst filters (2)- Excess power filter -- Excess power filter
- Total power in selected time-frequency region

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Many non-Gaussian noises

Burst filters (3)- Analysis results: excess power filter -- Burst wave analysis results
- Event rate (Integrated histogram)

Excess power analysis

- TAMA DT6
(1000hours, 2001)

- Simulated Gaussian noise

Burst event rate of TAMA

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

However …

still have sensitivity to

Huge Non-Gaussian noises

Non-Gaussian noise rejection

is indispensable

Burst filters (4)- Non-Gaussian noises -- Main output signal of a detector

= (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals)

Stable operation

Non-Gaussian events

Burst filters:

Sensitive to short burst events

- Wide frequency bandwidth
- Short average time

Total power in given T-F region

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Contents

- Introduction
- Burst GW analysis

- Burst filters
- Excess filter and non-Gaussian noises

- Rejection of non-Gaussian noises
- Concept, implementation

- Data analysis with TAMA300 data
- TAMA data,
- Noise reduction, burst event rate

- Summary

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

- Numerical simulation of super novae
- T. Zwerger, E. Müller, Astronomy & Astrophysics, 320 (1997), 209.

- Various waveforms
- Do not cover all conditions
Not suitable for templates

- Non-Gaussian noise reduction
- Some assumptions are required
- Selection of analysis targets super nova explosions

- Common characteristics
- Pulse-like waveform
- Large power in short time

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection (2) - Concept -

- Non-Gaussian noise reduction
Distinguish GW signal from non-Gaussian noises

with time-scale of the ‘unusual signals’

GW from gravitational core collapse < 100 msec,

Noise caused by IFO instability > a few sec

- 2 statistics in detector output
- Averaged noise power
- 2nd-order moment of noise power
Estimate parameter : ‘GW likelihood’

Reduce non-Gaussian noises

without rejecting GW signals

- 2 statistics in detector output

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

GW signal, noise

Long

Short

Non-Gaussian noise rejection (3) - Noise evaluation with C1-C2correlation -- Detector output model
- Correlation plot:
C1 and C2

- Stable operation
- Short pulse
- Degradation of noise level
many burst noises

= (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals)

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection (4) - Theoretical curve in correlation plot -

- Data model
Gaussian noise + GW signals

Theoretical curve in correlation plot

(Consistent with simulation results)

- Distance (D) to the curve
--- Likelihood to be GW signal

Reduce non-Gaussian noise

Without rejecting GW signals

- Distance (D) to the curve
- Monte-Carlo simulation
- Consistent with theoretical prediction
- Estimate False Dismissal Rate
set thresholds

Theoretical curve

C1

C2

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Evaluation

Rejection, Total power

Non-Gaussian noise rejection (5)- Data processing -- Data Processing
- Calculate Spectrogram by FFT
- Extract a certain time-frequency region
to be evaluated

- Evaluate GW likelihood at each frequency
(Threshold Dth )

- Reject given time region
if it has large ‘non-GW like’ ratio

(Threshold Rth)

- Calculate total power for given T-F region

- ‘Filter’ outputsfor each time chunk
- Total power
in selected time-frequency region

- ‘Stable time’ or detector ‘Dead time’

- Total power

Raw data

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Contents

- Introduction
- Burst GW analysis

- Burst filters
- Excess filter and non-Gaussian noises

- Rejection of non-Gaussian noises
- Concept, implementation

- Data analysis with TAMA300 data
- TAMA data
- Noise reduction, burst event rate

- Summary

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (1)- Data Taking 6 -

- Data Taking 6 (August 1- September 20, 2001, 50 days)

Over 1000 hours’ observation data

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (2)- Time-series data -

- Data Taking 6 time-series data
(Average time: 3.2sec, Bandwidth : 500Hz)

Large non-Gaussian noises(mainly in daytime)

Noise level [ /Hz1/2]

Typical noise level (6min. Avg.)

Time [hour]

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (3) - Selection of parameters - Determination of thresholds

- Selection of time window, frequency band
- Time window: smaller larger S/N
- … Lower frequency resolution
(Easily affected by AC line etc.)

- … Lower frequency resolution

- Time window: smaller larger S/N
- Frequency band: wider larger S/N
- … Use frequency band
with larger noise level

- … Use frequency band

- 2 thresholds:
- Distance to theoretical curve: Dth ,
- Ratio of non-Gaussian frequency band: Rth

- Rejection efficiency:
Depends on characteristics of non-Gaussian noise

- Should be optimized depending on noise behavior

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (4) - Typical noise level of TAMA300 -

- Typical noise level of TAMA300 during DT6
About 7x10-21 /Hz1/2

- Selection of frequency bands for analysis Δf=500 [Hz]

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (5)- time-series data -

- Data Taking 6 time-series data
Confirm reduction of non-Gaussian noises(in daytime)

Rejected data : 10.7%

(False dismissal rate < 1ppm)

Noise level [ /Hz1/2]

Time [hour]

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Noise reduction

Reduction : 1/1000

TAMA300 data evaluation (6)- event rate -- Event rate (Integrated histogram)
- Reduction ratio (total : 10.7%)
- Small events < 1.1 x10-20 /Hz1/2 : 1.7%
- Large events > 1.7x10-20 /Hz1/2 : 86.3%

- Reduction ratio (total : 10.7%)

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation (7)- event rate -

- Event rate for burst GW
- hrms: 3x10-17 (10msec spike) 10-2 events/hour
- 30 times better in stable hours

Cont. stable 12 hours

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Summary

- Non-Gaussian noise evaluation
- Distinguish GW signal from non-Gaussian noises
with time scale of the ‘unusual signal’

- Reduce non-Gaussian noises
without rejection GW signals

- Better upper limits, detection efficiency

- Reduce non-Gaussian noises

- Distinguish GW signal from non-Gaussian noises
- Non-Gaussian noise reduction with TAMA data
- Data quality evaluation
- Reduce non-Gaussian noise: 1/1000
- Upper limit for burst GW signal hrms～3x10-17
10-2 events/hour (10msec pulse, non-optimized)

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Current and Future Tasks Rejection efforts Real-time analysis

- Non-Gaussian noise rejection with main signal
- Selection of analysis parameters
(Data length, Frequency band, Thresholds)

- Other statistics

- Selection of analysis parameters

- Single detector
- Detector improvement
- Data processing (Signal behavior, auxiliary signals)

- Correlation with other detectors
- Other GW detectors
- Other astronomical channels
(Super novae, Gamma-ray burst, etc.)

Will be implemented soon…

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection - Advantages -

- Advantages
- Simply calculated parameters
- Averaged power, 2nd order moment

- Robust for change
(signal amplitude, waveform, noise level drift)

- Simply calculated parameters

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation - Estimation of averaged noise level -

- Estimation of averaged (typical) noise level
- Critical for non-Gaussian noise rejection
- Calculated for each frequency band
- Use latest stable data
Noise level < typical x

Gaussianity < 0.1

- Average for 6 min.

- Use latest stable data

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA data analysis- Data distribution and analysis -

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection- Hardware and software -

- Computer for analysis
- Beowolf PC cluster
- Athlon MP2000+ 20CPU, 10 node
- Storage : 1TByte RAID
60GByte local HDDs/each node

- Memory : 2GByte
- Connection : Gigabit ethanet

- Software
- OS : Red Hat Linux 7.2
- Job management : OpenPBS
(Portable Batch-queuing System)

- for parallel processing : MPI
- Compiler : PGI C/C++ Workstation
- Software : Matlab, Matlab compiler

- Beowolf PC cluster

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise rejection- Computation time -

- Analysis time: 90% is for spectrogram calculation
- 1 file (about 1 mon. data)
2560 FFT calculations (N FFT = 212 )

- Distributed calculation with several CPUs (not a parallel computation)
- Assign data files to each CPU
- Minimum load for network
- Easy programming, optimization

- Benchmark test
- Degradation with many CPUs
- Data-readout time from HDD
- Limited memory bus
in each node

- Degradation with many CPUs

- Distributed calculation with several CPUs (not a parallel computation)

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation - histogram -

- Histogram of noise level
Reduction of non-Gaussian noises

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

TAMA300 data evaluation - Threshold selection -

- Event number for threshold Rth

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise evaluation - Evaluation parameters -

- Statistics in detector output
- Averaged power (normalized by a typical noise power)
stationarity of data

- Higher moment of noise power
Gaussianity of data

- Averaged power (normalized by a typical noise power)
- Stationary and Gaussian noises
Pj : exponential distribution

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Non-Gaussian noise evaluation - Distance from theoretical curve - Distance from the curve (deviation) Search α for minimum D

- Theoretical calculation
- Detector output
Gaussian noise + Non-Gaussian noise

C1,C2, variance (S1,S2), covariance (S12)

function of signal amplitude (α)

C1, C2with certain amplitude (α)

2-D Gaussian distribution

- Detector output

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Burst wave analysis - proposed filters -

- Excess power
- Excess power statistic for detection of burst sources of gravitational radiation
Warren G. Anderson, Patrick R. Brady, Jolien D. E. Creighton, and Éanna É. Flanagan

(University of Texas, University of Wisconsin-Milwaukee etc),

Phys. Rev. D 63, 042003 (2001)

- Excess power statistic for detection of burst sources of gravitational radiation
- Slope detector
- Efficient filter for detecting gravitational wave bursts in interferometric detectors
Thierry Pradier, Nicolas Arnaud, Marie-Anne Bizouard, Fabien Cavalier,

Michel Davier, and Patrice Hello (LAL, Orsay),

Phys. Rev. D 63, 042002 (2001)

- Efficient filter for detecting gravitational wave bursts in interferometric detectors
- Clusters of high-power pixels in the time-frequency plane
- Robust test for detecting nonstationarity in data from gravitational wave detectors
Soumya D. Mohanty (Pennsylvania State University),

Phys. Rev. D 61, 122002 (2000)

- Robust test for detecting nonstationarity in data from gravitational wave detectors
- Correlation with single pulse
- Detection of gravitational wave bursts by interferometric detectors
Nicolas Arnaud, Fabien Cavalier, Michel Davier, and Patrice Hello (LAL, Orsay),

Phys. Rev. D 59, 082002 (1999)

- Detection of gravitational wave bursts by interferometric detectors

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Burst wave analysis - Excess power -

- Excess power
- Set :
start time , interval (contain N data points),

and frequency band

- FFT of these data points
- Sum up power for determined frequency band
- Estimate probability for the resultant power
- Assumption :
- distribution with degree of freedom
- normalized data (unity standard deviation)

- Assumption :
- Record ‘event’ if probability is significant
- Repeat with other , ,

- Set :

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

Burst wave analysis - Slope Detector, TF Cluster -

- Slope Detector
- Linear fitting for N data points (y=at+b)
- Evaluate with a and b

- TF Cluster
- Calculate spectrogram
- Set a threshold for noise power
- Identify clusters in time-frequency plane
- Calculate total power of clusters,
and compare with a threshold

3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)

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