  Segregating noise from chaos in dynamic systems has been one of the
challenging work for the researchers across the globe due to their seemingly
similar statistical properties. Even the most used tools such 0-1 test and
Lyapunov exponents fail to distinguish chaos when signal is mixed with noise.
This paper addresses the issue of segregating the dynamics in a rotor-stator
rub system when the vibrations are subjected to different levels of noise.
First, the limitation of 0-1 test in segregating chaos from signal mixed with
noise has been established. Second, the underexplored Benfords Law and its
application to the vibratory dynamical rotor-stator rub system has been
introduced for the first time. Using the Benfords Law Compliance Test (BLCT),
successful segregation of not only noise from chaos but also very low Signal to
Noise Ratio (SNR) signals which are mainly stochastic has been achieved. The
Euclidean Distance concept has been used to explore the scale-invariant
probability distribution of systems that comply with Benfords Law to separate
chaos from noise. Moreover, for moderate bands of noise in signals, we have
shown that the Schreibers Nonlinear Noise Reduction technique works effectively
in reducing the noise without damaging the dynamic properties of the system.
Combining these individual layers (0-1 Test, BLCT and Noise reduction) on a
rotor system, a Decision Tree based method to effectively segregate noise from
chaos and identify the correct dynamics of any system with time series data set
has been proposed.
