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

Abstract

Segregating noise from chaos in a dynamical system has been one of the most challenging work for the researchers across the globe due to their seemingly similar statistical properties. Even the most used tools such as 0-1 test and Lyapunov exponents fail to distinguish chaos from regular dynamics 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 chaotic signal from regular signal mixed with noise has been established. Second, the underexplored Benford’s Law and its application to the vibratory dynamical rotor-stator rub system has been introduced for the first time. Using the Benford’s 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 Benford’s Law to separate chaos from noise. Moreover, for moderate bands of noise in signals, we have shown that the Schreiber’s 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 regular dynamics from chaotic dynamics in noisy environment has been proposed.