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

TL;DR

This paper introduces a composite approach combining Benfords Law, noise reduction, and the 0-1 test to effectively distinguish chaos from noise in rotor-stator systems, even under low SNR conditions.

Contribution

It pioneers the application of Benfords Law to vibratory systems and develops a layered decision tree method for robust chaos detection in noisy signals.

Findings

Benfords Law effectively segregates chaos from noise at low SNR.

Schreibers Nonlinear Noise Reduction preserves system dynamics.

Combined method outperforms traditional chaos detection tools.

Abstract

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.