3rd tama symposium (february 03, 2003, icrr, kashiwa, japan) masaki ando (department of physics,...
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3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan)
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 Event Analysis of TAMA
Burst GW analysis Non-Gaussian noise rejection TAMA DT6 data analysis
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 2
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) 3
Chirp GW signal (from compact binary inspirals )Well-predicted waveform
Matched Filtering (correlation with templates) Distinguishable from non-Gaussian noises
Continuous GW signal (from rotating neutron stars)Well-predicted waveform
Simpler waveforms (modulated sine waves)Almost stationaryNoise reduction with Long-term Integration, narrow band analysis
Burst GW signal (from Stellar core collapses)Poorly-predicted waveforms
Cannot use matched filtering to get optimal SNRLook for ‘something unusual’
Introduction (1)- Gravitational wave search -
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 4
Main output signal of a detector
Introduction (2)- Non-Gaussian noises -
= (Stationary, Gaussian noise) + (Burst GW signals)
Stable operation
Burst filters: Look for and sensitive to
Unpredicted and non-stationary waveforms
Detection efficiency is limited by non-Gaussian noises
Non-Gaussian noise rejection is indispensable
Non-Gaussian eventsNon-Gaussian events
+ (Non-Gaussian noise)
Burst GW signals Non-Gaussian noise
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 5
Non-Gaussian noise rejection
Single detectorDetector improvementData processing
(Signal behavior, auxiliary signals)
Correlation with other detectorsOther GW detectorsOther astronomical channels
(Super novae, Gamma-ray burst, etc.)
Introduction (3)- Non-Gaussian noise reduction -
Non-Gaussian noise rejection with noise behavior, …Time scale of non-Gaussian events
In this talk …
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 6
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) 7
Proposed filters for burst wave--- look for unusual signals
Power in time-frequency planeExcess 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 waveformSlope 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
Burst filters (1)- Proposed filters for burst GW -
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 8
Time- Frequency plane (spectrogram)
Excess power filterTotal power in selected time-frequency region
Burst filters (2)- Excess power filter -
2 3 4 5
–500
0
500
Am
plit
ud
e [
arb
. un
it]
Time [sec]
Burst signal
Noise + signalRaw Data (time series)
2 3 4 50
2
4
6
Tota
l p
ow
er
[arb
. u
nit
]
Time [sec]
Threshold
Total power in given T-F region
Effective if time-frequency range of the signal is known
Signal !!!
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 9
Burst wave analysis resultsEvent rate (Integrated histogram)
Burst filters (3)- Analysis results: excess power filter -
Excess power analysis
TAMA DT6 (1000hours, 2001)Simulated Gaussian noise
[sec]2.3],Hz[500 tf
10–20 10–19 10–1810–6
10–5
10–4
10–3
10–2
10–1
100
10–2
10–1
100
101
102
103
Eve
nt
Rat
e [
Rat
io]
Eve
nt
Rat
e [
even
ts/h
ou
r]
Noise level [1/Hz1/2]
Gaussian noise
Data Taking 6 total
Many non-Gaussian noises
Burst event rate of TAMA
Far from Gaussian
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 10
Main output signal of a detector
Burst filters (4)- Non-Gaussian noises -
2 3 4 50
2
4
6
Tota
l p
ow
er
[arb
. u
nit
]
Time [sec]
Threshold
Total power in given T-F region
Many Signals ???
= (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals)
Non-Gaussian eventsStable operation
Burst filters: Sensitive to short burst events
Wide frequency bandwidth Short average time
However …still have sensitivity to
Huge Non-Gaussian noises
Non-Gaussian noise rejection is indispensable
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 11
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) 12
Non-Gaussian noise rejection (1) - Target selection -
Non-Gaussian noise reductionSome assumptions are requiredSelection of analysis targets super nova explosions
0 20 40 60 80–20
–10
0
10
Am
pli
tud
e [
x10 –
20]
Time [msec]
Numerical simulation of super novaeT. Zwerger, E. Müller, Astronomy & Astrophysics, 320 (1997), 209.
78 gravitational waveforms Various waveforms Do not cover all conditions
Not suitable for templates
Common characteristics Pulse-like waveform
Large power in short time
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 13
Non-Gaussian noise rejection (2) - Concept -
Non-Gaussian noise reductionDistinguish 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 outputAveraged noise power2nd-order moment of noise power
Estimate parameter : ‘GW likelihood’
Reduce non-Gaussian noises without rejecting GW signals
jPC 1
2
2
12
2
2
j
j
P
PC
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 14
0 10 20 30
100
101
102
c 1
(N
ois
e p
ow
er)
c2 (Gaussianity)
Stable, no signal
Short spikes
Long burst noises
Non-Gaussian noise rejection (3) - Noise evaluation with C1-C2 correlation -
Detector output model
Correlation plot: C1 and C2
Stable operation
Short pulse
Degradation of noise level many burst noises
0,1 21 CC
large,small 21 CC
small,large 21 CC
Time scale ofGW signal, noise
Short
Long
= (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals)
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 15
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
Monte-Carlo simulationConsistent with theoretical predictionEstimate False Dismissal Rate
set thresholds
Theoretical curve
C2
C1
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 16
Non-Gaussian noise rejection (5)- Data processing -
Data Processing1. Calculate Spectrogram by FFT2. Extract a certain time-frequency region
to be evaluated3. Evaluate GW likelihood at each frequency
(Threshold Dth )
4. Reject given time region if it has large ‘non-GW like’ ratio
(Threshold Rth)
5. Calculate total power for given T-F region
‘Filter’ outputs for each time chunk
Total power in selected time-frequency region
‘Stable time’ or detector ‘Dead time’
Raw data
Spectrogram
Evaluation
Rejection, Total power
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 17
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) 18
TAMA300 data evaluation (1)- Data Taking 6 -
Data Taking 6 (August 1- September 20, 2001, 50 days)
Over 1000 hours’ observation data
Thu SunTueMon Fri SatWedAug. 01 03
08
Operated (over 10min) High–speed data taking
Time in JST
15
22
29
05
12
191817
10
03
27
13
06 07
14
2120
28
04
11 13
06
30
23
16
09
02
10
17
24
31
07
14 15
08
Sep. 01
25
18
11
04 05
12
19
26
02
09
16
20
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 19
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)
No
ise
leve
l [
/Hz1/
2 ]
Time [hour]
Typical noise level (6min. Avg.)
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 20
TAMA300 data evaluation (3) - Selection of parameters -
Selection of time window, frequency bandTime window: smaller larger S/N
… Lower frequency resolution (Easily affected by AC line etc.)
Frequency band: wider larger S/N… Use frequency band
with larger noise level
Determination of thresholds2 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
[Hz] 500
[sec], 2.3
f
t
ppm) 1(F.D.
0.6
,2
th
th
R
D
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 21
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]
103
10–20
10–19
10–18
No
ise
leve
l [1/
Hz1/
2]
Frequency [Hz]200 500 2x103
Typical noise level
Selected frequencies
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 22
TAMA300 data evaluation (5)- time-series data -
Data Taking 6 time-series dataConfirm reduction of non-Gaussian noises (in daytime)
Rejected data : 10.7% (False dismissal rate < 1ppm)
No
ise
leve
l [
/Hz1/
2 ]
Time [hour]
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 23
10–20 10–19 10–1810–6
10–5
10–4
10–3
10–2
10–1
100
10–2
10–1
100
101
102
103
Eve
nt
Rat
e [
Rat
io]
Eve
nt
Rat
e [
even
ts/h
ou
r]
Noise level [1/Hz1/2]
Gaussian noise
Data Taking 6 total
After noise rejection
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 : 1/1000
Effective Noise reduction
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 24
10–20 10–19 10–1810–6
10–5
10–4
10–3
10–2
10–1
100
10–2
10–1
100
101
102
103
Eve
nt
Rat
e [
Rat
io]
Eve
nt
Rat
e [
even
ts/h
ou
r]
Noise level [1/Hz1/2
]
Gaussian noise
Data Taking 6 total
After noise rejection
TAMA300 data evaluation (7)- event rate -
Event rate for burst GWhrms: 3x10-17 (10msec spike) 10-2 events/hour30 times better in stable hours
Cont. stable 12 hours
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 25
Summary
Non-Gaussian noise evaluationDistinguish 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
Non-Gaussian noise reduction with TAMA dataData quality evaluationReduce 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) 26
Current and Future Tasks
Non-Gaussian noise rejection with main signalSelection of analysis parameters
(Data length, Frequency band, Thresholds)Other statistics
Rejection effortsSingle detector
Detector improvementData processing (Signal behavior, auxiliary signals)
Correlation with other detectorsOther GW detectorsOther astronomical channels
(Super novae, Gamma-ray burst, etc.)
Real-time analysisWill be implemented soon…
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 27
Non-Gaussian noise rejection - Advantages -
AdvantagesSimply calculated parameters
Averaged power, 2nd order moment
Robust for change(signal amplitude, waveform, noise level drift)
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 28
TAMA300 data evaluation - Estimation of averaged noise level -
Estimation of averaged (typical) noise levelCritical for non-Gaussian noise rejection
Calculated for each frequency bandUse latest stable data
Noise level < typical x
Gaussianity < 0.1 Average for 6 min.
2
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TAMA data analysis- Data distribution and analysis -
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 30
Non-Gaussian noise rejection- Hardware and software -
Computer for analysisBeowolf PC cluster
Athlon MP2000+ 20CPU, 10 nodeStorage : 1TByte RAID
60GByte local HDDs/each nodeMemory : 2GByteConnection : Gigabit ethanet
SoftwareOS : Red Hat Linux 7.2Job management : OpenPBS
(Portable Batch-queuing System)for parallel processing : MPICompiler : PGI C/C++ Workstation Software : Matlab, Matlab compiler
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 31
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 CPUMinimum load for networkEasy programming, optimization
Benchmark test
Degradation with many CPUsData-readout time from HDDLimited memory bus
in each node
(max)35
)CPU 1(5.4
)(
)(
AnalysisforTime
TimeTakingData
0 2 4 6 8 10 12 14 16 180
10
20
30
40
50
60
0
1
2
3
4
5
6
number of CPUs
Tota
l sp
ee
d
(data time/calc. time)
Sin
gle
CP
U s
pe
ed
Data analysis speed
Linea
r per
form
ance
Single CPU
Total
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 32
10–20 10–19 10–18100
101
102
103
104
105
Co
un
t
Strain PSD [1/Hz 1/2]
DT6 total (1060 hours)
After noise reduction(89.3%, 946 hours)
TAMA300 data evaluation - histogram -
Histogram of noise levelReduction of non-Gaussian noises
Reduction: about 1/10
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 33
TAMA300 data evaluation - Threshold selection -
Event number for threshold Rth
0 0.2 0.4 0.6 0.8 110
0
101
102
103
104
105
Eve
nt
nu
mb
er
Rth
< 1.1x10–20
Data Taking 6 total
> 1.1x10–20
> 1.7x10–20
> 3x10–20> 1x10–21
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 34
Non-Gaussian noise evaluation - Evaluation parameters -
Statistics in detector outputAveraged power (normalized by a typical noise power)
stationarity of data
Higher moment of noise power Gaussianity of data
Stationary and Gaussian noises Pj : exponential distribution
jPC 1
2
2
12
2
2
j
j
P
PC
0,1 21 CC
log
10(C
ou
nt)
Noise Power
C2 =0 : Gaussian
C2 <0
C2 >0
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 35
0 10 20 30
100
101
102
103
D
( C2 theory ,C1 theory )
( C2 ,C1 )
C2
C1
=0 =1
=10
=100
Non-Gaussian noise evaluation - Distance from theoretical curve -
Theoretical calculationDetector 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
Distance from the curve (deviation)
Search α for minimum D
2
1221
2theory221theory22theory1112
2theory112
2 21
SSSM
CCSCCCCSCCSM
D
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 36
Burst wave analysis - proposed filters -
Excess powerExcess 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)
Slope detectorEfficient 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)
Clusters of high-power pixels in the time-frequency planeRobust test for detecting nonstationarity in data from gravitational wave detectors
Soumya D. Mohanty (Pennsylvania State University),Phys. Rev. D 61, 122002 (2000)
Correlation with single pulseDetection of gravitational wave bursts by interferometric detectors
Nicolas Arnaud, Fabien Cavalier, Michel Davier, and Patrice Hello (LAL, Orsay), Phys. Rev. D 59, 082002 (1999)
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 37
Excess powerSet :
start time , interval (contain N data points),and frequency band
FFT of these data pointsSum up power for determined frequency bandEstimate probability for the resultant power
Assumption : distribution with degree of freedomnormalized data (unity standard deviation)
Record ‘event’ if probability is significantRepeat with other , ,
Burst wave analysis - Excess power -
3rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 38
Burst wave analysis - Slope Detector, TF Cluster -
Slope DetectorLinear fitting for N data points (y=at+b)Evaluate with a and b
TF ClusterCalculate spectrogramSet a threshold for noise powerIdentify clusters in time-frequency planeCalculate total power of clusters,
and compare with a threshold