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

Composite Test inclusive of Benfords Law, Noise reduction and 0-1 Test for effective detection of Chaos in Rotor-Stator Rub