Study of efficient methods of detection and reconstruction of gravitational waves from nonrotating 3D general relativistic core collapse supernovae explosion using multilayer signal estimation method

In the post-detection era of gravitational wave (GW) astronomy, core collapse supernovae (CCSN) are one of the most interesting potential sources of signals arriving at the Advanced LIGO detectors. Mukherjee et al. have developed and implemented a new method to search for GW signals from the CCSN search based on a multistage, high accuracy spectral estimation to effectively achieve higher detection signal to noise ratio (SNR). The study has been further enhanced by incorporation of a convolutional neural network (CNN) to significantly reduce false alarm rates (FAR). The combined pipeline is termed multilayer signal estimation (MuLaSE) that works in an integrative manner with the coherent wave burst (cWB) pipeline. In order to compare the performance of this new search pipeline, termed “MuLaSECC”, with the cWB, an extensive analysis has been performed with two families of core collapse supernova waveforms corresponding to two different three dimensional (3D) general relativistic CCSN explosion models, viz. Kuroda 2017 and the Ott 2013. The performance of this pipeline has been characterized through receiver operating characteristics (ROC) and the reconstruction of the detected signals. The MuLaSECC is found to have higher efficiency in low false alarm range, a higher detection probability of weak signals and an improved reconstruction, especially in the lower frequency domain.

Figure 1

This figure shows the main steps involved in a typical CNN. A CNN convolves learned features with input data and uses 2D convolutional layers, making it suitable for processing 2D images. CNN has an input layer, and output layer, and hidden layers. The hidden layers usually consist of convolutional layers that pass information to following layers, ReLU layers, pooling layers that combine the outputs of clusters of neurons into a single neuron, and fully connected layers that connect every neuron in one layer to the next level.

Figure 2

The figure shows accuracy of training on the glitches and the Ott 2013 waveform.

Figure 3

The figure shows Loss of accuracy vs the number of iterations on the glitches and the Kuroda 2017 s11 waveform.

Figure 4

The search pipeline is shown here. The pipeline can be viewed to have two main parts. The two left side boxes represent the identification of glitches, training and testing of the CNN components and classification, while the second part deals with an actual detection and parameter estimation resulting from data with glitches removed. Details of the pipeline is given in the Search Algorithm and Pipeline section.

Figure 5

The figure shows the $h_{+}$ and $h_x$ components of the Kuroda 2017 S11 waveform. The waveform is 0.16 s in duration.

Figure 6

The figure shows the spectrogram of the Kuroda 2017 S11 waveform. Only $h_{+}$ is seen here.

Figure 7

The figure shows the spectrogram of the Kuroda 2017 S11 waveform. Only $h_X$ is seen here.

Figure 8

The figure shows the $h_{+}$ and $h_x$ components of the Ott 2013 S27 waveform. The waveform is 0.16 s in duration.

Figure 9

The figure shows the spectrogram of the Ott 2013 S27 waveform. Only $h_{+}$ is seen here.

Figure 10

The figure shows the spectrogram of the Ott 2013 S27 waveform. Only $h_X$ is seen here.

Figure 11

The figure shows spectrograms of the different types of background glitches obtained in the analysis. These glitches were identified to be non-CCSN signals by the trained CNN.

Figure 12

The figure shows spectrograms of the Ott 2013 s27 waveforms as recovered by the pipeline.

Figure 13

The figure shows spectrograms of the Kuroda 2017 s11 waveforms as recovered by the pipeline.

Figure 14

The figure shows the receiver operating characteristics (ROC) of the Ott 2013 s27 waveform.

Figure 15

The figure shows the receiver operating characteristics (ROC) of the Kuroda 2017 s11 waveform.

Figure 16

This figure shows the spectrogram of the Ott 2013 s27 signal detected at an output SNR of 7.8 by the MuLaSECC pipeline for the L1 (bottom panel) and the H1 (top panel) detectors.

Figure 17

The figure shows the reconstruction of the detected Ott 2013 s27 signal waveform at the H1 and L1 detectors. In this figure, the L1 results are in the left hand column and the H1 results are in the right hand column. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 18

The figure shows the reconstruction of the Ott 2013 s27 detected signal spectrum at the H1 and L1 detectors. In this figure, the L1 results are in the right hand column and the H1 results are in the left hand column. The top panels show the injected signal time frequency maps, while the bottom panels show the same for the reconstructed signal.

Figure 19

This figure shows the spectrogram of the Kuroda 2017 s11 signal detected at an output SNR of 7.8 by the MuLaSECC pipeline for the L1 (bottom panel) and the H1 (top panel) detectors.

Figure 20

The figure shows the reconstruction of the Kuroda 2017 s11 detected signal waveform at the H1 and L1 detectors. In this figure, the L1 results are in the left hand column and the H1 results are in the right hand column. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 21

The figure shows the reconstruction of the Kuroda 2017 s11 detected signal spectrum at the H1 and L1 detectors. In this figure, the L1 results are in the right hand column and the H1 results are in the left hand column. The top panels show the injected signal time frequency maps, while the bottom panels show the same for the reconstructed signal.

Figure 22

This figure shows the spectrogram of signal detected at an output SNR of 10.6 by the cWB pipeline (left column, H1 at the top and L1 at the bottom); MuLaSECC pipeline (right column, H1 at the top and L1 at the bottom) detected an output SNR of 11.9. The injected Kuroda 2017 s11 signal was at $\mathrm{SNR}=10$.

Figure 23

The figure shows a comparative picture of the reconstruction of the detected signal waveform at the H1 and L1 detectors for Kuroda 2017 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 10. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 24

The figure shows the reconstruction of the detected signal spectrum at the H1 and L1 detectors for Kuroda 2017 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 10. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the time-frequency plots for the band-limited signal. The bottom panels display the same for the reconstructed signal.

Figure 25

This figure shows the spectrogram of signal detected at an output SNR of 10.6 by the cWB pipeline (left column, H1 at the top and L1 at the bottom); MuLaSECC pipeline (right column, H1 at the top and L1 at the bottom) detected an output SNR of 11.9. The injected Ott 2013 s11 signal was at $\mathrm{SNR}=10$.

Figure 26

The figure shows a comparative picture of the reconstruction of the detected signal waveform at the H1 and L1 detectors for Ott 2013 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 10. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 27

The figure shows the reconstruction of the detected signal spectrum at the H1 and L1 detectors for Ott 2013 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 10. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the time-frequency plots for the band-limited signal. The bottom panels display the same for the reconstructed signal.

Figure 28

This figure shows the spectrogram of signal detected at an output SNR of 14.7 by the cWB pipeline (left column, H1 at the top and L1 at the bottom); MuLaSECC pipeline (right column, H1 at the top and L1 at the bottom) detected an output SNR of 20.8. The injected Kuroda 2017 s11 signal was at $\mathrm{SNR}=15$.

Figure 29

The figure shows a comparative picture of the reconstruction of the detected signal waveform at the H1 and L1 detectors for Kuroda 2017 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 15. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 30

The figure shows the reconstruction of the detected signal spectrum at the H1 and L1 detectors for Kuroda 2017 s11 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 15. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the time-frequency plots for the band-limited signal. The bottom panels display the same for the reconstructed signal.

Figure 31

This figure shows the spectrogram of signal detected at an output SNR of 14.7 by the cWB pipeline (left column, H1 at the top and L1 at the bottom); MuLaSECC pipeline (right column, H1 at the top and L1 at the bottom) detected an output SNR of 20.8. The injected Ott 2013 s27 signal was at $\mathrm{SNR}=15$.

Figure 32

The figure shows a comparative picture of the reconstruction of the detected signal waveform at the H1 and L1 detectors for Ott 2013 s27 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 15. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the band-limited signal with the original in black and the reconstructed signal in red. The middle panels show the injected (in black) vs reconstructed (in red) whitened signal time series. The bottom panels display the amplitude spectra of the injected (black) vs reconstructed (red) whitened signal data.

Figure 33

The figure shows the reconstruction of the detected signal spectrum at the H1 and L1 detectors for Ott 2013 s27 waveforms as obtained by the cWB and the MuLaSECC pipelines for an injection with SNR 15. In this figure, the cWB results are in the two left hand columns and the MuLaSECC results are in the two right hand columns. For each pipeline, the left hand column presents results from H1 and the right hand column present results from L1. The top panels show the time-frequency plots for the band-limited signal. The bottom panels display the same for the reconstructed signal.