Burst Event Analysis of TAMA Burst GW analysis
Burst Event Analysis of TAMA Burst GW analysis Non-Gaussian noise rejection TAMA DT 6 data analysis 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 3 rd 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 TAMA 300 data TAMA data Noise reduction, burst event rate Summary 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 2
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 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 Burst GW signal (from Stellar core collapses) Poorly-predicted waveforms Cannot use matched filtering to get optimal SNR Look for ‘something unusual’ 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 3
Introduction (2) - Non-Gaussian noises - Main output signal of a detector = (Stationary, Gaussian noise) + (Burst GW signals) + (Non-Gaussian noise) Stable operation Non-Gaussian events Burst filters: Look for and sensitive to Unpredicted and non-stationary waveforms Burst GW signals Non-Gaussian noise Detection efficiency is limited by non-Gaussian noises Non-Gaussian noise rejection is indispensable 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 4
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. ) In this talk … Non-Gaussian noise rejection with noise behavior, … Time scale of non-Gaussian events 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 5
Contents Introduction Burst GW analysis Burst filters Excess filter and non-Gaussian noises Rejection of non-Gaussian noises Concept, implementation Data analysis with TAMA 300 data TAMA data, Noise reduction, burst event rate Summary 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 6
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 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 7
Burst filters (2) - Excess power filter Total power in selected time-frequency region Raw Data (time series) Time- Frequency plane (spectrogram) Total power in given T-F region Signal !!! Effective if time-frequency range of the signal is known 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 8
Burst filters (3) - Analysis results: excess power filter - Burst wave analysis results Event rate (Integrated histogram) Excess power analysis Burst event rate of TAMA DT 6 (1000 hours, 2001) Simulated Gaussian noise Far from Gaussian Many non-Gaussian noises 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 9
Burst filters (4) - Non-Gaussian noises - Main output signal of a detector = (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals) Stable operation Many Signals ? ? ? Non-Gaussian events Burst filters: Sensitive to short burst events Wide frequency bandwidth Short average time However … still have sensitivity to Huge Non-Gaussian noises Total power in given T-F region Non-Gaussian noise rejection is indispensable 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 10
Contents Introduction Burst GW analysis Burst filters Excess filter and non-Gaussian noises Rejection of non-Gaussian noises Concept, implementation Data analysis with TAMA 300 data TAMA data, Noise reduction, burst event rate Summary 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 11
Non-Gaussian noise rejection (1) - Target selection - Non-Gaussian noise reduction Some assumptions are required Selection of analysis targets super nova explosions Numerical simulation of super novae T. 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 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 12
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 2 nd-order moment of noise power Estimate parameter : ‘GW likelihood’ Reduce non-Gaussian noises without rejecting GW signals 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 13
Non-Gaussian noise rejection (3) - Noise evaluation with C 1 -C 2 correlation - Detector output model = (Stationary, Gaussian noise) + (Non-Gaussian noise) + (Burst GW signals) Correlation plot: C 1 and C 2 Time scale of GW signal, noise Stable operation Short pulse Long Degradation of noise level many burst noises 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) Short 14
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 Theoretical curve C 1 Reduce non-Gaussian noise Without rejecting GW signals C 2 Monte-Carlo simulation Consistent with theoretical prediction Estimate False Dismissal Rate set thresholds 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 15
Non-Gaussian noise rejection (5) - Data processing - Data Processing 1. Calculate Spectrogram by FFT Raw data 2. Extract a certain time-frequency region to be evaluated 3. 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 Spectrogram Evaluation ‘Filter’ outputs for each time chunk Total power in selected time-frequency region ‘Stable time’ or detector ‘Dead time’ Rejection, Total power 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 16
Contents Introduction Burst GW analysis Burst filters Excess filter and non-Gaussian noises Rejection of non-Gaussian noises Concept, implementation Data analysis with TAMA 300 data TAMA data Noise reduction, burst event rate Summary 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 17
TAMA 300 data evaluation (1) - Data Taking 6 (August 1 - September 20, 2001, 50 days) Over 1000 hours’ observation data 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 18
TAMA 300 data evaluation (2) - Time-series data - Data Taking 6 time-series data (Average time: 3. 2 sec, Bandwidth : 500 Hz) Noise level [ /Hz 1/2] Large non-Gaussian noises (mainly in daytime) Typical noise level (6 min. Avg. ) Time [hour] 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 19
TAMA 300 data evaluation (3) - Selection of parameters - Selection of time window, frequency band Time 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 thresholds 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 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 20
TAMA 300 data evaluation (4) - Typical noise level of TAMA 300 during DT 6 About 7 x 10 -21 /Hz 1/2 Selection of frequency bands for analysis Δf=500 [Hz] 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 21
TAMA 300 data evaluation (5) - time-series data - Data Taking 6 time-series data Noise level [ /Hz 1/2] Confirm reduction of non-Gaussian noises (in daytime) Rejected data : 10. 7% (False dismissal rate < 1 ppm) Time [hour] 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 22
TAMA 300 data evaluation (6) - event rate - Event rate (Integrated histogram) Reduction ratio (total : 10. 7%) Small events < 1. 1 x 10 -20 /Hz 1/2 : 1. 7% Large events > 1. 7 x 10 -20 /Hz 1/2 : 86. 3% Effective Noise reduction Reduction : 1/1000 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 23
TAMA 300 data evaluation (7) - event rate - Event rate for burst GW hrms: 3 x 10 -17 (10 msec spike) 10 -2 events/hour 30 times better in stable hours Cont. stable 12 hours 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 24
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 Non-Gaussian noise reduction with TAMA data Data quality evaluation Reduce non-Gaussian noise: 1/1000 Upper limit for burst GW signal hrms~ 3 x 10 -17 10 -2 events/hour (10 msec pulse, non-optimized) 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 25
Current and Future Tasks Non-Gaussian noise rejection with main signal Selection of analysis parameters (Data length, Frequency band, Thresholds) Other statistics Rejection efforts 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. ) Real-time analysis Will be implemented soon… 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 26
Non-Gaussian noise rejection - Advantages Simply calculated parameters Averaged power, 2 nd order moment Robust for change (signal amplitude, waveform, noise level drift) 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 27
TAMA 300 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. 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 28
TAMA data analysis - Data distribution and analysis - 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 29
Non-Gaussian noise rejection - Hardware and software - Computer for analysis Beowolf PC cluster Athlon MP 2000+ 20 CPU, 10 node Storage : 1 TByte RAID 60 GByte local HDDs/each node Memory : 2 GByte Connection : Gigabit ethanet Software OS : Red Hat Linux 7. 2 Job management : Open. PBS (Portable Batch-queuing System) for parallel processing : MPI Compiler : PGI C/C++ Workstation Software : Matlab, Matlab compiler 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 30
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 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 31
TAMA 300 data evaluation - histogram - Histogram of noise level Reduction of non-Gaussian noises Reduction: about 1/10 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 32
TAMA 300 data evaluation - Threshold selection - Event number for threshold Rth 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 33
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 Stationary and Gaussian noises Pj : exponential distribution 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 34
Non-Gaussian noise evaluation - Distance from theoretical curve - Theoretical calculation Detector output Gaussian noise + Non-Gaussian noise C 1, C 2, variance (S 1, S 2), covariance (S 12) function of signal amplitude (α) C 1, C 2 with certain amplitude (α) 2 -D Gaussian distribution Distance from the curve (deviation) Search α for minimum D 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 35
Burst wave analysis - proposed filters 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) 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) 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) 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) 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 36
Burst wave analysis - 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) Record ‘event’ if probability is significant Repeat with other , , 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 37
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 3 rd TAMA Symposium (February 03, 2003, ICRR, Kashiwa, Japan) 38
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