  The gravitational-wave detector is a complex and sensitive collection of
advanced instruments that are impacted not only by mechanical/electronics
systems but also by the surrounding environment. Hence, it is of great
importance to classify and mitigate noises to detect gravitational-wave signals
by using information from many auxiliary channels related to such devices and
surroundings. This improves the signal-to-noise ratio and reduces false alarms
from coincident loud events. For this reason, it is essential for identifying
coherent relationships between complex channels. This study presents a way of
identifying (non-) linear couplings between associated channels by using the
method of correlation coefficients. And we show that the method can be applied
to practical problems in the gravitational-wave detector, such as noises by
lightning strokes, air compressors vibrations, and noises caused by wind
effects.
