Soma Mukherjee LSC, Hanford, Aug.19 '04 Generation of realistic data segments: production and application. Soma Mukherjee Centre for Gravitational Wave.

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Presentation transcript:

Soma Mukherjee LSC, Hanford, Aug.19 '04 Generation of realistic data segments: production and application. Soma Mukherjee Centre for Gravitational Wave Astronomy D ept. of Physics and Astronomy University of Texas Brownsville LIGO G Z

Soma Mukherjee LSC, Hanford, Aug.19 '04 Motivation An effort to simulate segments of detector noise such that it shares same statistical characteristics as the data itself, i.e. it shows same kind of non-stationarity as present in the data. We can not predict the nature of non–stationarity at a prior time, but we can characterize the variation to construct simulated data. Astrophysical searches estimate efficiency and tune parameters of search algorithms from playground data. Data is non-stationary. E.g. a 60 s stretch of data may not have same value of variance as another 60 s at a later time. Thus any comparison or any estimation work carried out with sampled real data will have bias introduced in it. Certain search algorithms require comparison of different data segments. These are different quantities when data is non-stationary.

Soma Mukherjee LSC, Hanford, Aug.19 '04 Outline : Description of the model. Results. Existing modeled data. Examples. Future.

Soma Mukherjee LSC, Hanford, Aug.19 '04 Model description Each data segment is divided into three independent components viz. lines, transients and noise floor. Each component is characterized by low order ARMA model with mutual exclusion in time domain. Modeled noise generated from the three independent components are added back together to construct the final product.

Soma Mukherjee LSC, Hanford, Aug.19 '04 Characterizing noise floor variation Results obtained by running MNFT 1 on a stretch of LIGO S2 data.[ 1 Mukherjee, CQG, 2003 ] Low pass and resample Estimate spectral Noise floor with Running Median Use estimate to whiten data using FIR whitening Filter. Clean lines and Highpass Compute Running Median of the Squared output Set threshold

Soma Mukherjee LSC, Hanford, Aug.19 '04

II : Modeling ALL lines MBLT: Non-parametric Line estimation. [ Mohanty CQG, 2001 ]

Soma Mukherjee LSC, Hanford, Aug.19 '04 Non-parametric change point detector. KSCD : Kolmogorv-Smirnov test based Change point Detector Mohanty, GWDAW (2002); PSDCD, Mohanty, PRD (2000); III : Transient Classification 12 top wavelet coefficients of data surrounding each KSCD trigger. Visualized using GGobi. (Preliminary). Mukherjee, 2003, Amaldi, Pisa

Soma Mukherjee LSC, Hanford, Aug.19 '04 Algorithm 1. Low pass and resample given time series x(k). 2. Construct FIR filter that whitens the noise floor. Resulting time series : w(k) 3. Remove lines using notch filter. Cleaned time series : c(k) 4. Model variation in second moment of c(k) using Running Median and apply smoothing (SRM).

Soma Mukherjee LSC, Hanford, Aug.19 '04 Model Noise Generation Estimate lines using MBLT, ARMA model amplitude and phase, add reconstructed lines to synthetic data. Classify transients, model and add. Use MNFT to model variation in second moment Fit ARMA to it Characterize MNFT output with low order ARMA. Pass white noise thru’ this filter

Soma Mukherjee LSC, Hanford, Aug.19 '04 ARMA (p,q) A(T) y[k]= C(T) e[k] Y[k]: Output e[k] : White noise T: Time shift operator, T(x[k])=x[k-1] A and C : Polynomials of order p and q respectively. Example ARMA(2,1): A 1 y[k-1] + A 0 y[k]= C 0 e[k]

Soma Mukherjee LSC, Hanford, Aug.19 '04 Testing the model Apply statistical test of hypothesis Kolmogorov-Smirnov To avoid overfitting : Akaike Information criterion (AIC) I akaike (p,q) = ln  2 p,q + 2 (p+q)/N

Soma Mukherjee LSC, Hanford, Aug.19 '04 Result I : Noise floor model – ARMA (12,7)

Soma Mukherjee LSC, Hanford, Aug.19 '04

More work To add transients in the modeled data. Generation of band limited noise if required. To write the output in Frames. To generate S3/S4 segments. To carry out known waveform injection studies.

Soma Mukherjee LSC, Hanford, Aug.19 '04 Existing modeled data 20,000 s modeled S2 data generated in April Contains 330 s.mat files of noise floor and lines separately. Script exists to allow the user to combine the noise floor and lines in the desired way.