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L’analisi dei dati negli esperimenti per la rivelazione di Onde Gravitazionali

L’analisi dei dati negli esperimenti per la rivelazione di Onde Gravitazionali. L’analisi dei dati ed i problemi computazionali. I dati originali prodotti da un interferometro includono i segnali dei - canali di controllo, sensori delle sospensioni sensori ambientali

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L’analisi dei dati negli esperimenti per la rivelazione di Onde Gravitazionali

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  1. L’analisi dei dati negli esperimenti per la rivelazione di Onde Gravitazionali

  2. L’analisi dei dati ed i problemi computazionali • I dati originali prodotti da un interferometro includono i segnali dei - canali di controllo, • sensori delle sospensioni • sensori ambientali • Duplicazioni d’informazione per ridondanza 864 Gbyte/day 315 Tbytes/year Assumendo un efficiente compressione e on-line processing, i dati utili possono essere compressi di un fattore compreso tra 10 e 100 Frequenza di produzione dei dati selezionati 9 - 90 Gbyte/day (100 kbyte/s - 1Mbyte/s)

  3. Il controllo globale dell’interferometro e la curva di sensibilità Calibrazione

  4. Il caso di VIRGO • On line data processing • Interferometer control • Data acquisition • Local Readout • Frame formatting • Frame storage on-line (disks-->> data distribution) • Frame storage off-line (Tapes-->>Raw data archive) • On line Data analysis • h(t) reconstruction • Data quality • On-line filters, triggers and selection candidates

  5. Il caso di VIRGO • Frames stored on data Distribution • Debug Frames:data acquired and sent to some on line monitoring tool and/or stored on tape for diagnostic purpose. Usually, the debugging channels are not sent to the Main Frame Builder • Raw Data Frames:set of data from the multiple signals from the interferometer, the monitor channels and vetoes. They contain all the ADC channels including trend data and any log message. • Reduced Data Frames:these are frames stored on the data distribution resident on disks. They contain the reconstructed information ( h(t) ), the data quality, the Slow Monitoring Stations (including the trend data), the summary results of the data selection algorithms. • Selected Frames:they contain just the original raw data selected in time by the algorithms for the search of transient events • Trend Frames:collection of Slow monitoring Stations and data trend formatted to optimize a fast access for long stretch of data

  6. Il caso di VIRGO • RAW DATA FRAME • Data Type Number of Signals Size (kByte) Details • ADC raw data 501 signals 7608 131 monitor, 127 GC and align.,108 susp., 135 det. Bench • SMS raw data 556 signals 2 465 from towers and slow mon.,67 from detec.bench • SMS trend data 6 x 501 signals 5 For each ADC, a trend SMS, with the following signals: min, max, mean, rms, slope max, c2 Gauss fit • Frame Header 1Structure FrameH 4 General information:GPS time, frame length……… • ---------------------------------------------------------------------------------------------------------------------------------------------- • Total 7620 data compression could reduce the size of a factor 2

  7. Il caso di VIRGO • REDUCED DATA FRAME • Data Type Number of Signals Size (kByte) Details • ADC raw data 1 signal at 20 kHz (4 Bytes) 80 1 computed ITF output from det. bench, at 20 KHz • SMS raw data 556 signals (18 Sms) 2 465 from towers and slow mon.,67 from detec.bench • SMS trend data 6 x 501 signals 5 For each ADC, a trend SMS, with the following signals: min, max, mean, rms, slopemax, c2 Gauss fit • Data Quality 4 structures 4 fr AC data Moni., GC+Alig., Susp. and det. bench • Calibrated Data h(t) 4 signals at 4 kHz (4 Bytes) 80 h value resampled with or without 4 signals at 4 kHz (4 Bytes) whitening and noise removal • Frame Header 1Structure FrameH 4 General information:GPS time, frame length……… • ---------------------------------------------------------------------------------------------------------------------------------------------- • Total 175

  8. Diagramma di flusso dell’analisi dati

  9. The expected signal h is a short pulse ( a few ms). Bursts The expected value on Earth, if 1% of Mo is converted into g.w. in the GC, is of the order of 10-18

  10. Supernovae • Impulsive events, GW emitted only in non-spherical collapse • Big uncertainties in the simulation codes: waveform “unpredictable” (templates unreliable) • Coincidence detection necessary • Amplitude: • h~10-21 30 kpc/r axisymmetric collapse • h~10-21 10 Mpc/r non-axisymmetric collapse • Rate: a tens/year in the VIRGO cluster [Zwerger-Müller, www.mpa-garching.mpg.de/ ~ewald/GRAV/grav.html

  11. Algoritmi per la rivelazione di burst • Nessuna conoscenza a priori della forma del segnale • Nel caso degli interferometri che hanno una banda di rivelazione estesa (da pochi Hz a pochi kHz), non è possibile schematizzare il segnale come una semplice δ-function. • Tutti i filtri proposti sono inesorabilmente sub-ottimali, nel senso che sono più o meno lontani dalle prestazioni del Filtro Lineare Ottimo ( vedi trapsaprenza successiva). • Alcuni filtri applicati sui dati “sbiancati”: • Valore di conteggio nell’intervallo di tempo elementare: il filtro seleziona select tutti gli intervalli elemntari che hanno un segnale al di sopra di una data soglia ( il piu’ semplice ) • Filtro a Norma: il massimo della funzione di autocorrelazione dell’uscita: • Peak Correlation: P(N,k) = Σ x(i+k) f([i-N/2]t) dove f(t) =exp (-t2 /2 τ2) definita in [-3 τ,3τ]

  12. Il filtro lineare ottimo L’uscita del rivelatore è o(t) , sommma del segnale h(t)e e del rumore n(t): o(t)=h(t)+n(t) Il filtro adattato è una tecnica lineare di “ patter-matching “ che permette di esaltare il rapporto Segnale su Rumore (SNR). Per applicare questa tecnica noi dobbiamo porre in ingresso le seguenti informazioni: 1) Ipotesi sulla forma del segnale d’ingresso o della sua trasformata di Fourier H(f) 2) Le proprietà spettrali del rumore S(f) L’uscita del filtro c(t)è

  13. Filtro Adattato • Nelle telecomunicazioni un filtro adattato o filtro ottimo (è ottenuto correlando un segnale conosciuto con un segnale incognito per rivelare la presenza di un marcatore all'interno del segnale incognito. • Ciò è equivalente ad effettuare l'operazione di convoluzione tra il segnale incognito ed una versione tempo-invertita del segnale noto. • Il filtro adattato è il filtro lineare ottimo per la massimizzazione del Rapporto segnale/rumore (SNR) in presenza di rumore stocastico additivo. • I filtri adattati sono comunemente usati in ambito radar, in cui un segnale conosciuto viene trasmesso, ed il segnale riflesso è esaminato per la ricerca di elementi comuni con il segnale trasmesso. Altre applicazioni del filtro adattato si ritrovano nell'elaborazione digitale delle immagini, ad esempio per incrementare il rapporto SNR in fotografie a raggi X.

  14. Derivazione del Filtro adattato

  15. Caso Generale

  16. Burst Searches: an example of algorithm:Excess Power Statistic (W. Anderson et al.) • The algorithm [1]: • Pick a start time ts, a time duration dt (containing N data samples), and a frequency band [fs; fs + df]. • Fast Fourier transform (FFT) the block of (time domain) detector data for the chosen duration and start time. • Sum the power in the frequency band [fs; fs + df]. • Calculate the probability of having obtained the summed power from Gaussian noise alone using a c2 distribution with 2 dt df degrees of freedom. • If the probability is significantly small for noise alone, record a detection. • Repeat the process for all desired choices of start times ts, durations dt, starting frequencies fs and bandwidths df. [1] A power filter for the detection of burst sources of gravitational radiation in interferometric detectors. Authors: Warren G. Anderson, Patrick R. Brady, Jolien D. E. Creighton, Eanna E. Flanagan. gr-qc/0001044

  17. chirp Coalescing Binaries • Compact stars (NS/NS, NS/BH, BH/BH) • Inspiral signal accurately predictable • Newtonian dynamics • Post-Newtonian corrections (3PN, (v/c)11/2) [L.Blanchet et al., CQG 13, 1996] • Detection rate (predicted event rate VIRGO sensitivity) • <1/yr for NS/NS • 2-3/yr for BH/BH • The classic search method is based on the Matched filter. • Signal hypothesis (a chirp dependent on some physical parameters). FFT+ zero padding. • Spectral Noise estimation from the data. FFT • Correlation between them in the frequency domain (scalar product) • Anti FFT

  18. The optimum linear filter • Signal known, optimal filtering possible • Produce a set of templates with different mass and orbit parameters: hn(m1,m2,…) • Correlate templates and ITF output ITF output = noise+signal Correlation of ITF out and template Filtered variable Computational cost to perform transform (FFT): 5 N log2 [N] ﾐ1000 s of 16384 Sample/s data: 2x109 floating point operations (FLOP) ﾐTo keep up with data: 2 MFLOP/s (MFLOPS) ﾐPerform 20,000 at same time: 40 GFLOPS -> clusters of CPUs ﾐ90+% of CPU time involved in f<->t transformations

  19. E.Cuoco

  20. How Far Can They See? • The detector sensitivity can be measured by the distance to an ideally oriented NS/NS coalescing binary system that would produce a SNR=5 (r5NS/NS) • VIRGO SNR for coalescing BH @100 Mpc

  21. Standard candles: distance and redshift of the source can be found out of the waveform of a NS/NS [Schutz, Nature, 1986] • Test for GR: accurate measurements of inspiral waveform can test gravity in the strong field regime [Damour, Esposito-Farese, gr-qc/9803031] • Nuclear physics: before coalescence waveform sensitive to the equation of state [Cutler et al., PRL, 70, 1993]

  22. The search of continuous signals • The search method is based on a hierarchical method. • Filling a Short FFT data base ( the data are dived in different band of frequencies) • Construction of Time Frequency maps • Hough Transform • Candidate Selection • Coherent search in the selected frequency ranges (Zooming, Doppler correction , FFT…..) • New iteration • The search is applied on the reduced data transferred in Rome and stored in the SFFT data base

  23. Continuous signals Signals from rotating neutron stars, stars in binary systems

  24. Rotating Neutron Stars • Non-axisymmetric rotating NS emit periodic GW at f=2 fspin • SNR can be increased by integrating the signal for long time (months) • Doppler correction of Earth motion ( Df / f ~ 10-4 ) must be taken into account • 109 NS in the galaxy, ~800 known; the blind search requires high computing power and smart algorithms ased on a hierarchical search strategy (Hough transform)

  25. How to solve the problem of the limited computational power. The search divided in steps and in the first step we don’t use the phase information.An example of incoherent step followed by a coherent one (Complex FFT) • create Data Base of short FFT and then derive the periodograms. • Create a time-frequency map of the peaks above a threshold • For each spin-down parameters point and each • frequency value, create a sky map (“Hough map”); to • create a H map, sum an annulus of “1” for each peak; • an histogram is then created, that must have a • prominent peak at the “source”

  26. Time-frequency peak map

  27. Hough map – single annulus

  28. Hough map – source reconstruction

  29. Requirements • SFFT data base 525 Gbyte /year • Time-Frequency data quality 20 GByte/year • Partial Hough Transform Output 40 Tbyte/year • Candidate Source data base 20 GByte/year • Scheduled tests • Search limited to the frequency interval 10 Hz - 1.25 kHz. The computation will cover few weeks of data taken by the CITF. • Method applied to the dataof resonant antennas: data taken in a small bandwidth of 2 Hz around the two peaks in the 900 Hz region • 8000 SI95 and 10 Tbyte of storage disk.

  30. Computational power and storage hierarchically distributed in the Virgo INFN sections and laboratories of the collaboration and structured in the classes of computer centers • Tier 0 Virgo- Cascina; • Tier 1 Lyon – IN2P3, Bologna - CNAF/INFN • Tiers 2: Roma 1 and Napoli; Use of GRID technology

  31. Stochastic Background Cosmological origin: it is the result of processes that happened immediately after the Big-Bang. If measured, it will allow to discriminate various cosmological models Astrophysical origin: it is the result of more recent event (redshift z order of 2-5). It is due to unresolved processes of gravitational collapses. It will provide information on star formation rates, supernova rates, black holes......

  32. Relic Stochastic Background • Imprinting of the early expansion of the universe • Need two correlated ITFs • Standard inflation produces a background too low • Hope from string models [Buonanno et al., PRD (1997)]

  33. V. Ferrari, S. Matarrese, R. Scheinder: Mont. Not.R. Astron. Soc. 303, (1999) 247 & 258 String cosmology

  34. Stochastic GW Background Detection • Cross-correlate the output of two (independent) detectors with a suitable filter kernel: • Requires: (i) Two detectors must have overlapping frequency response functions i.e., (ii) Detectors sensitive to same polarization state (+, x) of radiation field, hGW. (iii) Baseline separation must be suitably “short”:

  35. Stochastic Background Correlation • Ideally, the stochastic background correlation increases with integration time as: • Assumes no additional sources of correlated noise • cannot discriminate with a single measurement • Mutual orientation dependence of GW background signal may be exploited to discriminate among possible correlated sources • References: • P.F. Michelson, Mon. Not. Roy. Astron. Soc. 227, 933 (1987). • N. Christensen, Phys. Rev. D46, 5250 (1992) • E. Flanagan, Phys. Rev. D48, 2389 (1993), astro-ph9305029 • B. Allen and J. Romano, Phys. Rev. D59, 102001 (1999), gr-qc9710117 • M. Maggiore, Trieste, June 2000: Gravitational Waves: A Challenge to Theoretical Astrophysics, gr-qc-0008027 • L.S. Finn and A. Lazzarini, Phys. Rev. D, 15 (2001)

  36. Optimal filtering in the presence of background correlation hi=GW signal in detector i ni= noise in detector i <=Template for this problem WGW(f) = 1/r0 drGW/d(ln[f]) g(f, W1, W2) = geometric overlap reduction factor depends on antenna orientations

  37. Optimal filter for this problem Optimal filtering in the presence of background correlation Choose two orientations of one detector { W1, W1’ }, for which g(f, W1, W2) = - g(f, W1’, W2), denote C+, C- values of integrated correlation in these two orientations: max

  38. Detection Confidence • Detection computation: • Coincidence with other GW detectors • Coincidence with non-GW detectors (optical, g, X, n) • Matched filtering for known signals • Correlations for stochastic background • Environmental monitoring on site • ‘fast’ monitoring of seismic, acoustic, e.m. noise • ‘slow’ monitoring of tilts, temperature, weather

  39. Rejection of statistically uncorrelated random events Coincidence window duration determined by baselines, always less than 2*13000km/(300000km/s) = 0.086s For l = 1/min ,N=3 and TLIGO =0.02s: rate reduction is 10-7 For l = 1/min, N=4 and T12=T23= TLIGO =0.02s and T34=Tmax=0.086s: rate reduction is 1.6 x 10-10 Coincidence windows among detectors

  40. Rejection of statistically uncorrelated random events Two Sites - Three Interferometers Single Interferometer - limited by non-gaussian noise ~70/hr Hanford -- 2x coincidence requirement (x1000 reduction) ~1/day Hanford + Livingston -- 3x coincidence (another x5000 reduction) <0.1/yr LLO 4 km LHO 4 km + 2 km GOAL False alarm events per decade All LIGO Interferometers LIGO + VIRGO + GEO LIGO + VIRGO Background events per hour per interferometer Coincidence windows among detectors

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