Parametric Identification of Chaotic Systems Via a Long-Period Harmonic Balance

2005 ◽  
Author(s):  
Yang Liang ◽  
B. F. Feeny
Keyword(s):  
Harmonic Balance ◽  
Chaotic Systems ◽  
Harmonic Balance Method ◽  
Parametric Identification ◽  
Model Parameters ◽  
Unstable Periodic Orbits ◽  
Ideal Model ◽  
Domain Identification ◽  
Long Period ◽  
Countable Infinity

Hyperbolic chaotic sets are composed of a countable infinity of unstable periodic orbits (UPOs). Symbol dynamics reveals that any long chaotic segment can be approximated by a UPO, which is a periodic solution to an ideal model of the system. Treated as such, the harmonic balance method is applied to the long chaotic segments to identify model parameters. Ultimately, this becomes a frequency domain identification method applied to chaotic systems.

scholarly journals Validation of Friction Model Parameters Identified Using the IHB Method Using Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Abdallah Hadji ◽  
Njuki Mureithi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Friction Force ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Balance Method ◽  
Model Parameters ◽  
Friction Models ◽  
Element Method

A hybrid friction model was recently developed by Azizian and Mureithi (2013) to simulate the friction behavior of tube-support interaction. However, identification and validation of the model parameters remains unresolved. In previous work, the friction model parameters were identified using the reverse harmonic method, where the following quantities were indirectly obtained by measuring the vibration response of a beam: friction force, sliding speed of the force of impact, and local displacement at the contact point. In the present work, the numerical simulation by the finite element method (FEM) of a beam clamped at one end and simply supported with the consideration of friction effect at the other is conducted. This beam is used to validate the inverse harmonic balance method and the parameters of the friction models identified previously. Two static friction models (the Coulomb model and Stribeck model) are tested. The two models produce friction forces of the correct order of magnitude compared to the friction force calculated using the inverse harmonic balance method. However, the models cannot accurately reproduce the beam response; the Stribeck friction model is shown to give the response closest to experiments. The results demonstrate some of the challenges associated with accurate friction model parameter identification using the inverse harmonic balance method. The present work is an intermediate step toward identification of the hybrid friction model parameters and, longer-term, improved analysis of tube-support dynamic behavior under the influence of friction.

Validation of Friction Model Parameters Identified Using the Inverse Harmonic Balance Method

2015 ◽  
Author(s):  
Abdallah Hadji ◽  
Njuki Mureithi
Keyword(s):  
Friction Force ◽  
Harmonic Balance ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Balance Method ◽  
Model Parameters ◽  
Intermediate Step ◽  
Friction Forces ◽  
Friction Models

A hybrid friction model was recently developed by Azizian and Mureithi [1] to simulate the friction behavior of tube-support interaction. However, identification of the model parameters remains unresolved. In previous work, the friction model parameters were identified using reverse the harmonic method, where the following quantities were indirectly obtained by measuring the vibration response of a beam: friction force, sliding speed of the force of impact and local displacement at the contact point. In the present work, the simulation by the finite element method (FEM) of a beam clamped at one end and simply supported with the consideration of friction effect at the other is conducted. This beam is used to validate the inverse harmonic balance method and the parameters of the friction models identified previously. Two static friction models (the Coulomb model and Stribeck model) are tested. The two models produce friction forces of the correct order of magnitude compared to the friction force calculated using the inverse harmonic balance method. However, the models cannot accurately reproduce the beam response; the Stribeck friction model is shown to give the response closer to experiments. The results demonstrate some of the challenges associated with accurate friction model parameter identification using the inverse harmonic balance method. The present work is an intermediate step toward identification of the hybrid friction model parameters and, longer term, improved analysis of tube-support dynamic behavior under the influence of friction.

scholarly journals Parametric Identification of Chaotic Base-Excited Double Pendulum Experiment

2004 ◽  
Author(s):  
Yang Liang ◽  
B. F. Feeny
Keyword(s):  
Harmonic Balance ◽  
Parametric Identification ◽  
Identification Algorithm ◽  
Double Pendulum ◽  
Unstable Periodic Orbits ◽  
Identification Process ◽  
Response Data ◽  
Regression Techniques ◽  
Linearized System ◽  
Pendulum Experiment

An improved parametric identification of chaotic systems was investigated for a double pendulum. From recorded experimental response data, the unstable periodic orbits were extracted and later used in a harmonic balance identification process. By applying digital filtering, digital differentiation and linear regression techniques for optimization, the results were improved. Verification of the related simulation system and linearized system also corroborated the success of the identification algorithm.

Harmonic balance method for time–delay chaotic systems design

2011 ◽  
Vol 44 (1) ◽  
pp. 5112-5117 ◽  
Author(s):  
A. Buscarino ◽  
L. Fortuna ◽  
M. Frasca ◽  
G. Sciuto ◽  
M.G. Xibilia
Keyword(s):  
Time Delay ◽  
Harmonic Balance ◽  
Chaotic Systems ◽  
Harmonic Balance Method ◽  
Systems Design ◽  
Balance Method

Parametric Identification of an Experimental Two-Well Oscillator

1999 ◽  
Author(s):  
B. F. Feeny ◽  
C.-M. Yuan
Keyword(s):  
Periodic Orbits ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Parametric Identification ◽  
Equation Model ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Identification Process ◽  
Nonlinear Force ◽  
Force Displacement

Abstract The identification of parameters in an experimental two-well chaotic system is presented. The method involves the extraction of periodic orbits from a chaotic set. The form of the differential-equation model is assumed, with unknown coefficients on the terms in the model. The harmonic-balance method is applied to these periodic orbits, resulting in a linear equation in the unknown parameters, which can then be solved in the least-squares sense. The identification process reveals the nonlinear force-displacement characteristic of the oscillator. The results are cross-checked with various sets of extracted periodic orbits. The model is validated by examining simulated responses.

scholarly journals Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

2021 ◽  
Vol 6 (3) ◽  
pp. 25
Author(s):  
Jan Philipp Heners ◽  
Stephan Stotz ◽  
Annette Krosse ◽  
Detlef Korte ◽  
Maximilian Beck ◽  
...  
Keyword(s):  
Turbulence Model ◽  
Harmonic Balance ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Filter Method ◽  
Turbine Cascade ◽  
Transient Pressure ◽  
Low Pressure Turbine

Unsteady pressure fluctuations measured by fast-response pressure transducers mounted in a low-pressure turbine cascade are compared to unsteady simulation results. Three differing simulation approaches are considered, one time-integration method and two harmonic balance methods either resolving or averaging the time-dependent components within the turbulence model. The observations are used to evaluate the capability of the harmonic balance solver to predict the transient pressure fluctuations acting on the investigated stator surface. Wakes of an upstream rotor are generated by moving cylindrical bars at a prescribed rotational speed that refers to a frequency of f∼500 Hz. The excitation at the rear part of the suction side is essentially driven by the presence of a separation bubble and is therefore highly dependent on the unsteady behavior of turbulence. In order to increase the stability of the investigated harmonic balance solver, a developed Lanczos-type filter method is applied if the turbulence model is considered in an unsteady fashion.

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