Time-Varying and Non-Linear Dynamical System Identification Using the Hilbert Transform

2005 ◽  
Author(s):  
Michael Feldman
Keyword(s):  
Hilbert Transform ◽  
Special Kind ◽  
Harmonic Signal ◽  
Dynamic Structure ◽  
Forced Vibrations ◽  
Time Varying ◽  
Transform Method ◽  
Non Linear ◽  
Force Signal ◽  
The Hilbert Transform

The objective of the paper is to explain a modern Hilbert transform method for analysis and identification of mechanical non-linear vibration structures in the case of quasiperiodic signals. This special kind of periodicity arises in experimental vibration signals. The method is based on the Hilbert transform of input and output signals in a time domain to extract the instantaneous dynamic structure characteristics. The paper focuses on the dynamic analysis and identification of three groups of dynamics systems: • Forced vibrations of linear and non-linear SDOF systems excited with quasiperiodic force signal. • Combined forced vibrations of quasiperiodic time varying linear and non-linear SDOF systems excited with harmonic signal. • Combined self-excited and forced vibrations of non-linear SDOF systems excited with harmonic signal. The study focuses on signal processing techniques for nonlinear system investigation, which enable us to estimate instantaneous system dynamic parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency) for different kinds of system excitation.

scholarly journals PORTRAIT AND HILBERT TRANSFORM METHODS FOR EVALUATING CONTINUOUS RELATIVE PHASE BETWEEN LOWER-LIMB JOINTS IN THE ELDERLY DURING WALKING

2021 ◽  
pp. 2140038
Author(s):  
HYUK-JAE CHOI ◽  
GYOOSUK KIM ◽  
CHANG-YONG KO
Keyword(s):  
Angular Velocity ◽  
Hilbert Transform ◽  
Lower Limb ◽  
Cross Correlation ◽  
Relative Phase ◽  
The Elderly ◽  
Transform Method ◽  
Transform Methods ◽  
Continuous Relative Phase ◽  
The Hilbert Transform

In order to calculate the continuous relative phase (CRP) between joints, the portrait method based on the joint angle and angular velocity and the Hilbert transform method based on the analytical signal have been widely used. However, there are few comparisons of these methods. Therefore, the aim of this study is to quantitatively compare these methods by calculating the CRP in the lower-limb joints of the elderly during level free walking. Eighteen elderly female adults ([Formula: see text] year-old, [Formula: see text][Formula: see text]cm, [Formula: see text][Formula: see text]kg) wearing a Helen Hayes full-body marker set walked 10[Formula: see text]m on level ground at a self-selected velocity. The angles of the hip, knee, and ankle were measured. To calculate the CRP using the portrait method, the angular velocities were measured. Then, the phases between the angle and the angular velocity were calculated. To calculate the CRP using the Hilbert transform method, analytical signals were acquired. Then, the phases between the real and imaginary parts were calculated. A CRP was calculated as the difference between the phase in the proximal joint and the phase in the distal joint. To evaluate the similarity in the shape between the portrait and Hilbert transform methods, the cross-correlation was calculated. Bland–Altman plot analyses were performed to assess the agreement between these methods. For the root mean squares (RMSs) and standard deviations (SDs), a paired [Formula: see text]-test and the Pearson correlation between methods were evaluated. There were similarities in the in-phase or out-of-phase features and in the RMS and SD between the methods. Additionally, a higher cross-correlation and agreement between them were found. These results indicated the similarity between the portrait and Hilbert transform methods for the calculation of the CRP. Therefore, either method can be used to evaluate joint coordination.

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

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.

Non-Linear Spring and Damping Forces Estimation During Free Vibration

1995 ◽  
Author(s):  
Michael Feldman ◽  
Simon Braun
Keyword(s):  
Free Vibration ◽  
Hilbert Transform ◽  
Time Domain ◽  
Free Vibration Analysis ◽  
Single Degree Of Freedom ◽  
Non Linear ◽  
Linear Spring ◽  
The Time Domain ◽  
The Hilbert Transform ◽  
Vibrating Systems

Abstract A method for dynamic analysis of sophisticated nonlinear single-degree-of-freedom systems, based on the Hilbert transform in the time domain is described. Using the Hilbert transform together with the proposed method for system identification, we obtain both instantaneous modal parameters together with non-linear force characteristics during free vibration analysis under impulse excitation without long resonance testing. Using the Hilbert transform in the time domain is a new method of studying linear and non-linear vibrating systems exposed to impulse or shock inputs.

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

2006 ◽  
Vol 74 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Z. Y. Shi ◽  
S. S. Law
Keyword(s):  
Dynamical Systems ◽  
Empirical Mode Decomposition ◽  
Hilbert Transform ◽  
Decomposition Method ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Time Varying ◽  
Mode Decomposition ◽  
Empirical Mode Decomposition Method ◽  
The Hilbert Transform

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.

scholarly journals WAVE GROUP ANALYSIS BY THE HILBERT TRANSFORM

1988 ◽  
Vol 1 (21) ◽  
pp. 66 ◽  
Author(s):  
Robert T. Hudspeth ◽  
Josep R. Medina
Keyword(s):  
Hilbert Transform ◽  
Group Analysis ◽  
Height Function ◽  
Sea Surface ◽  
Frequency Function ◽  
Wave Group ◽  
Transform Method ◽  
Wave Groups ◽  
The Mean ◽  
The Hilbert Transform

A methodology based on linear theory is presented for analyzing wave groups from a random sea representation in the complex plane. A wave height function [H(t)], a local frequency function, [0(t)] , and an orbital velocity function [V(t)] are defined from the Hilbert transform of the sea surface elevation. Envelopes computed by the Hilbert transform are compared with the SIWEH. A three axes representation of the mean lengths of runs of waves is employed to compare the lengths of runs computed by the discrete wave method with runs computed by the Hilbert transform method.

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