Identification of Linear Time-Varying Dynamical Systems Using Hilbert Transform and Empirical Mode Decomposition Method

This paper addresses the identification of linear time-varying multi-degrees-of-freedom systems. The identification approach is based on the Hilbert transform and the empirical mode decomposition method with free vibration response signals. Three-different types of time-varying systems, i.e., smoothly varying, periodically varying, and abruptly varying stiffness and damping of a linear time-varying system, are studied. Numerical simulations demonstrate the effectiveness and accuracy of the proposed method with single- and multi-degrees-of-freedom dynamical systems.

Download Full-text

Application of the Empirical Mode Decomposition Method to the Identification of Disc Brake Squeal

Design Engineering ◽

10.1115/imece2002-39224 ◽

2002 ◽

Cited By ~ 1

Author(s):

Fulun Yang ◽

Chin An Tan ◽

Frank Chen

Keyword(s):

Empirical Mode Decomposition ◽

Decomposition Method ◽

Disc Brake ◽

Intrinsic Mode Functions ◽

Brake Squeal ◽

Mode Decomposition ◽

Out Of Plane ◽

Empirical Mode Decomposition Method ◽

Original Application ◽

The Hilbert Transform

This paper investigates the identification of mechanisms of disc brake squeal by the application of a recently developed Empirical Mode Decomposition method (EMD). A known strength of the EMD is its adaptive nature in analyzing nonstationary data, with success in its original application to ocean mechanics. The EMD decomposes an original signal into a number of intrinsic mode functions (IMFs), with each IMF often containing distinct physical significance. Several sets of disc brake squeal data were obtained and processed by EMD. A typical set data is presented in this paper for discussion. Employing a sifting process in the EMD, four prominent squeal-related IMFs are identified in this set of data. The Hilbert transform is then used to analyze the frequency and amplitude contents of the four IMFs, and it is shown that the first IMF is dominant. The spectrogram method is applied to analyze the time-evolution of the frequency components of the IMFs in the squeal process. This analysis procedure confirms an important squeal mechanism, i.e., the squeal condition is governed by the coupling of in-plane and out-of-plane vibration modes of the rotor and the coalescence of their natural frequencies. The inverse approach outlined in this paper is shown to be useful for providing new insights and confirming established hypotheses of disc brake squeal.

Download Full-text

Identification of MDOF Non-Linear Uncoupled Dynamical Systems Using Hilbert Transform and Empirical Mode Decomposition Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.255-260.1676 ◽

2011 ◽

Vol 255-260 ◽

pp. 1676-1680

Author(s):

Tian Li Huang ◽

Wei Xin Ren ◽

Meng Lin Lou

Keyword(s):

Dynamical Systems ◽

Empirical Mode Decomposition ◽

Hilbert Transform ◽

Degree Of Freedom ◽

Intrinsic Mode Functions ◽

Nonlinear Properties ◽

Identification Method ◽

Mode Decomposition ◽

Non Linear ◽

The Hilbert Transform

A non-linear dynamical system identification method using Hilbert transform (HT) and empirical mode decomposition (EMD) is proposed. For a single-degree-of-freedom (SDOF) nonlinear system, the Hilbert transform identification method is good at identifying the instantaneous modal parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency). For the multi-degree-of-freedom (MDOF) non-linear uncoupled dynamical systems, the EMD method is attempting for the decomposition of response signals into a collection of mono-components signals, termed intrinsic mode functions (IMFs). Considering the IMFs admit a well-behaved Hilbert transform, the HT identification method has been applied for the identification of nonlinear properties. The numerical simulation of a 2-dof shear-beam building model with nonlinear stiffness illustrated the proposed technique.

Download Full-text