  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.
