  The mechanism and characteristics of the irregular variations of red
supergiants (RSGs) are studied based on the RSG samples in Small Magellanic
Cloud (SMC), Large Magellanic Cloud (LMC) and M31. With the time-series data
from All-Sky Automated Survey for SuperNovae (ASAS-SN) and Intermediate Palomar
Transient Factory survey, we use the continuous time autoregressive moving
average model to estimate the variability features of the light curves and
their power spectral density. The characteristic evolution timescale and
amplitude of granulations are further derived from fitting the posterior power
spectral density with the COR function, which is a Harvey-like granulation
model. The consistency of theoretical predictions and results is checked to
verify the correctness of the assumption that granulations on RSGs contribute
to irregular variation. The relations between granulation and stellar
parameters are obtained and compared with the results of red giant branch stars
and Betelgeuse. It is found that the relations are in agreement with
predictions from basic physical process of granulation and fall close to the
extrapolated relations of RGB stars. The granulations in most of the RSGs
evolve at a timescale of several days to a year with the characteristic
amplitude of 10-1000 mmag. The results imply that the irregular variations of
RSGs can be attributed to the evolution of granulations. When comparing the
results from SMC, LMC and M31, the timescale and amplitude of granulation seem
to increase with metallicity. The analytical relations of the granulation
parameters with stellar parameters are derived for the RSG sample of each
galaxy.
