Abstract
This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting events. The proposed scheme consists of the following two successive steps: decomposing the data using a wavelet packet, representing the GW signal and noise using the derived decomposition coeficients; and determining the existence of any GW event using a convolutional neural network (CNN) with a logistic regression output layer. The characteristic of this work is its comprehensive investigations on CNN structure, detection window width, data resolution, wavelet packet decomposition and detection window overlap scheme. Extensive simulation experiments show excellent performances for reliable detection of signals with a range of GW model parameters and signal-to-noise ratios. While we use a simple waveform model in this study, we expect the method to be particularly valuable when the potential GW shapes are too complex to be characterized with a template bank.
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B. P. Abbott, R. Abbott, T. D. Abbott, et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116(6), 061102 (2016)
B. P. Abbott, R. Abbott, and T. D. Abbott, Binary black hole mergers in the first advanced LIGO observing run, Phys. Rev. X 6(4), 041015 (2016)
B. P. Abbott, R. Abbott, T. D. Abbott, et al., GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2, Phys. Rev. Lett. 118, 221101 (2017)
B. P. Abbott, R. Abbott, T. D. Abbott, et al., GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119(16), 161101 (2017)
B. P. Abbott, R. Abbott, T. D. Abbott, et al., GW170814: A three-detector observation of gravitational waves from a binary black hole coalescence, Phys. Rev. Lett. 119(14), 141101 (2017)
B. P. Abbott, R. Abbott, and R. X. Adhikari, et al., Multi-messenger observations of a binary neutron star merger, Astrophys. J. Lett. 848(2), L12 (2017)
B. P. Abbott, R. Abbott, T. D. Abbott, et al., Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A, Astrophys. J. Lett. 848(2), L13 (2017)
B. P. Abbott, et al., A gravitational-wave standard siren measurement of the Hubble constant, Nature 551(7678), 85 (2017)
S. Adrián-Martínez, M. G. Aartsen, B. Abbott, et al., High-energy neutrino follow-up search of gravitational wave event GW150914 with ANTARES and IceCube, Phys. Rev. D 93, 122010
B. Abbott, R. Abbott, T. D. Abbott, et al., All-sky search for short gravitational-wave bursts in the first advanced LIGO run, Phys. Rev. D 95, 042003 (2017)
B. P. Abbott, G. Cagnoli, J. Degallaix, et al., Observing gravitational-wave transient GW150914 with minimal assumptions, Phys. Rev. D 93, 122004 (2016)
C. Vishveshwara, Scattering of gravitational radiation by a Schwarzschild black-hole, Nature 227, 936 (1970)
O. Benhar, V. Ferrari, and L. Gualtieri, Gravitational wave asteroseismology revisited, Phys. Rev. D 70, 124015 (2004)
J. Powell, D. Trifirò, E. Cuoco, et al., Classification methods for noise transients in advanced gravitational-wave detectors, Class. Quantum Grav. 32, 215012 (2015)
M. Zevin, S. Couǵhlin, et al., Gravity spy: Integrating advanced LIGO detector characterization, machine learning, and citizen science, Class. Quantum Grav. 34, 064003 (2017)
J. Powell, A. Torres-Forné, et al., Classification methods for noise transients in advanced gravitational-wave detectors II: Performance tests on advanced LIGO data, Class. Quantum Grav. 34, 034002 (2017)
B. Allen, W. G. Anderson, P. R. Brady, D. A. Brown, and J. D. E. Creighton, FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries, Phys. Rev. D 85(12), 122006 (2012)
S. Babak, R. Biswas, et al., Searching for gravitational waves from binary coalescence, Phys. Rev. D 87, 024033 (2013)
K. Cannon, R. Cariou, A. Chapman, et al., Toward early warning detection of gravitational waves from compact binary coalescence, Astrophys. J. 748(2), 136 (2012)
S. A. Usman, A. H. Nitz, I. W. Harry, et al., The PyCBC search for gravitational waves from compact binary coalescence, Class. Quantum Grav. 33(21), 215004 (2016)
H. Gabbard, M. Williams, F. Hayes, and C. Messenger, Matching matched filtering with deep networks for gravitational-wave astronomy, Phys. Rev. Lett. 120(14), 141103 (2018)
D. George and E. A. Huerta, Deep learning for real-time gravitational wave detection and parameter estimation: Results with Advanced LIGO data, Phys. Lett. B 778, 64 (2018)
B. J. Lin, X. R. Li, and W. L. Yu, Binary neutron stars gravitational wave detection based on wavelet packet analysis and convolutional neural networks, Front. Phys 15(2), 24602 (2020)
H. M. Luo, W. B. Lin, Z. C. Chen, and Q. G. Huang, Extraction of gravitational wave signals with optimized convolutional neural network, Front. Phys. 15(1), 14601 (2020)
D. George and E. A. Huerta, Deep neural networks to enable real-time multimessenger astrophysics, Phys. Rev. D 97, 044039 (2018)
T. D. Gebhard, N. Kilbertus, G. Parascandolo, I. Harry, and B. Schlkopf, CONVWAVE: Searching for gravitational waves with fully convolutional Neural Nets, in: Workshop on Deep Learning for Physical Sciences (DLPS) at the 31st Conference on Neural Information Processing Systems (NIPS), 2017
T. D. Gebhard, N. Kilbertus, I. Harry, and B. Schlkopf, Convolutional neural networks: A magic bullet for gravitational-wave detection? Phys. Rev. D 100(6), 063015 (2019)
S. Chatterji, L. Blackburn, G. Martin, and E. Katsavounidis, Multiresolution techniques for the detection of gravitational-wave bursts, Class. Quantum Grav 21(20), S1809 (2004)
P. J. Sutton, G. Jones, S. Chatterji, et al., X-Pipeline: An analysis package for autonomous gravitational-wave burst searches, New J. Phys. 12(5), 053034 (2010)
S. Bahaadini, N. Rohani, S. Coughlin, M. Zevin, V. Kalogera, and A. K. Katsaggelos, Deep multi-view models for glitch classification, IEEE ICASSP, 2931–2935 (2017)
S. Bahaadini, V. Noroozi, N. Rohani, S. Coughlin, M. Zevein, J. R. Smith, V. Kalogera, and A. Katsaggelos, Machine learning for Gravity Spy: Glitch classification and dataset, Information Sciences 444, pp 172–186 (2018)
D. George, H. Shen, and E. A. Huerta, Classification and unsupervised clustering of LIGO data with deep transfer learning, Phys. Rev. D 97, 101501 (2018)
N. Mukund, S. Abraham, S. Kandhasamy, and N. S. Philip, Transient classification in LIGO data using difference boosting neural network, Phys. Rev. D 95, 104059 (2017)
J. C. Brown, Calculation of a constant Q-spectral transform, J. Acoust. Soc. Am. 89(1), 425 (1991)
S. Klimenko, I. Yakushin, A. Mercer, and G. Mitselmakher, Coherent method for detection of gravitational wave bursts, Class. Quantum Grav. 25, 114029 (2008)
S. Klimenko, G. Vedovato, M. Drago, F. Salemi, V. Tiwari, G. A. Prodi, C. Lazzaro, S. Tiwari, F. Da Silva, and G. Mitselmakher, Method for detection and reconstruction of gravitational wave transients with networks of advanced detectors, Phys. Rev. D 93, 042004 (2016)
R. S. Lynch, S. Vitale, R. C. Essick, E. Katsavounidis, and F. Robinet, An information-theoretic approach to the gravitational-wave burst detection problem, Phys. Rev. D 95, 104046 (2017)
N. J. Cornish and T. B. Littenberg, BayesWave: Bayesian Inference for Gravitational Wave Bursts and Instrument Glitches, Class. Quantum Grav. 32, 135012 (2015)
T. B. Littenberg and N. J. Cornish, Bayesian inference for spectral estimation of gravitational wave detector noise, Phys. Rev. D 91, 084034 (2015)
S. Chatterji, A. Lazzarini, L. Stein, P. Sutton, A. Searle, and M. Tinto, Coherent network analysis technique for discriminating gravitational-wave bursts from instrumental noise, Phys. Rev. D 74, 082005 (2006)
S. Bose, S. Dhurandhar, et al., Towards mitigating the effect of sine-Gaussian noise transients on searches for gravitational waves from compact binary coalescences, Phys. Rev. D 94, 122004 (2016)
B. J. Owen and B. S. Sathyaprakash, Matched filtering of gravitational waves from inspiraling compact binaries: Computational cost and template placement, Phys. Rev. D 60(2), 022002 (1999)
pwelch: Welch’s power spectral density estimate.
G. D. Meadors, K. Kawabe, and K. Riles, Increasing LIGO sensitivity by feed forward subtraction of auxiliary length control noise, Class. Quantum Grav. 31, 105014 (2014)
P. D. Welch, The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms, IEEE Transactions on Audio and Electroacoustics 15(2), 70 (1967)
J. Abadie, B. P. Abbott, R. Abbott, et al., All-sky search for gravitational-wave bursts in the second joint LIGOVirgo run, Phys. Rev. D 85, 122007 (2012)
S. Mallat, A Wavelet Tour of Signal Processing, Boston: Academic Press, 2009
K. B. Howell, Principles of Fourier analysis, CRC Press, 2016
I. Daubechies, Ten Lectures on Wavelets, Philadelphia: Society for Industrial and Applied Mathematics, 1992
S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. on Pattern Analysis and Machine Intel. 11(7), 674 (1989)
S. Rampone, V. Pierro, L. Troiano, et al., Neural network aided glitch-burst discrimination and glitch classification, Inter. J. Mod. Phys. 24(11), 1350084 (2013)
S. Vinciguerra, M. Drago, G. A. Prodi, et al., Enhancing the significance of gravitational wave bursts through signal classification, Class. Quantum Grav. 34, 094003 (2017)
MATLAB and Wavelet Toolbox Release 2013b, The MathWorks, Inc., Natick, Massachusetts, United States
X. R. Li, Y. Lu, G. Comte, AL. Luo, Y. H. Zhao, and Y. J. Wang, Linearly Supporting feature extraction for automated estimation of stellar atmospheric parameters, Astrophys. J. Suppl. S. 218(1), 3 (2015)
Y. LeCun, B. E. Boser, J. S. Denker, et al., Handwritten digit recognition with a back-propagation network, in Advances in Neural Information Processing Systems, 396 (1990)
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proceedings of the IEEE 86, pp 2278–2324 (1998)
Y. LeCun, Y. Bengio, and G. E. Hinton, Deep learning, Nature 521(7553), 436 (2015)
D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Learning representations by back-propagating errors, Nature 323(6088), 533 (1986)
I. Goodfellow, Y. Bengio, and A. Courville, Deep learning, Cambridge: MIT Press, 2016
H. Wang, Z. J. Cao, X. L. Liu, S. C. Wu, and J. Y. Zhu, Gravitational wave signal recognition of O1 data by deep learning, arXiv: 1909.13442 (2019)
Acknowledgements
Authors thank H. Gabbard, M. Williams, F. Hayes, and C. Messenger very much for their enthusiastic discussions and sharing of their experimental code. We are grateful for valuable suggestions and corrections from anonymous reviewers, Eric D. Feigelson, Dr. Jin Li and B. S. Sathyaprakash. X. L. and W. Y. were supported by the National Natural Science Foundation of China (Grant Nos. 11973022 and U1811464), the Natural Science Foundation of Guangdong Province (No. 2020A1515010710), and China Scholarship Council (No. 201706755006), and the Joint Research Fund in Astronomy (No. U1531242) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS). Xilong Fan was supported by the National Natural Science Foundation of China (Grant Nos. 11673008 and 11922303) and Hubei Province Natural Science Fund for the Distinguished Young Scholars.
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Li, XR., Yu, WL., Fan, XL. et al. Some optimizations on detecting gravitational wave using convolutional neural network. Front. Phys. 15, 54501 (2020). https://doi.org/10.1007/s11467-020-0966-4
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DOI: https://doi.org/10.1007/s11467-020-0966-4