Identifying noise transients in gravitational-wave data arising from nonlinear couplings

Noise in various interferometer systems can sometimes couple non-linearly to create excess noise in the gravitational wave (GW) strain data. Third-order statistics, such as bicoherence and biphase, can identify these couplings and help discriminate those occurrences from astrophysical GW signals. However, the conventional analysis can yield large bicoherence values even when no phase-coupling is present, thereby, resulting in false identifications. Introducing artificial phase randomization in computing the bicoherence reduces such occurrences with negligible impact on its effectiveness for detecting true phase-coupled disturbances. We demonstrate this property with simulated disturbances in this work. Statistical hypothesis testing is used for distinguishing phase-coupled disturbances from non-phase coupled ones when employing the phase-randomized bicoherence. We also obtain an expression for the bicoherence value that minimizes the sum of the probabilities of false positives and false negatives. This can be chosen as a threshold for shortlisting bicoherence triggers for further scrutiny for the presence of non-linear coupling. Finally, the utility of the phase-randomized bicoherence analysis in GW time-series data is demonstrated for the following three scenarios: (1) Finding third-order statistical similarities within categories of noise transients, such as blips and koi fish. If these non-Gaussian noise transients, or glitches, have a common source, their bicoherence maps can have similarities arising from common bifrequencies related to that source. (2) Differentiating linear or non-linear phase-coupled glitches from compact binary coalescence signals through their bicoherence maps. This is explained with a simulated signal. (3) Identifying repeated bifrequencies in the second and third observation runs (i.e., O2 and O3) of LIGO and Virgo.