Nonlinear analysis of time series of vibration data from a friction brake: SSA, PCA, and MFDFA

TL;DR

This paper applies SSA, PCA, and MFDFA to analyze vibration data from a friction brake, revealing low-dimensional chaos in long-term dynamics and multi-scale features in fast processes.

Contribution

It introduces a combined nonlinear analysis approach to characterize the complex dynamics of brake vibrations, highlighting the dominance of low-dimensional chaos and multi-scale behavior.

Findings

Long time-scale dynamics are dominated by few active dimensions.

Brake vibrations exhibit low-dimensional chaotic attractors.

Fast friction interface processes are multi-scale in nature.

Abstract

We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake. SSA and PCA are used to study the long time-scale characteristics of the time series. MFDFA is applied for investigating all time scales up to the smallest recorded one. It turns out that the majority of the long time-scale dynamics, that is presumably dominated by the structural dynamics of the brake system, is dominated by very few active dimensions only and can well be understood in terms of low dimensional chaotic attractors. The multi-fractal analysis shows that the fast dynamical processes originating in the friction interface are in turn truly multi-scale in nature.