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 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.

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.

Response of Hysteretic Multidegree-of-Freedom Systems Using Harmonic Balance Method

1999 ◽  
Author(s):  
Danilo Capecchi ◽  
Renato Masiani ◽  
Fabrizio Vestroni
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Elastic Model ◽  
Hysteretic Model ◽  
Response Curves ◽  
Periodic Response ◽  
Nonlinear Elastic ◽  
Force Displacement ◽  
Two Degree Of Freedom ◽  
System Characteristics

Abstract This article illustrates the nonlinear response of a hysteretic two degree of freedom system. The constitutive laws which define the force-displacement relation are based on a hysteretic model with Masing rules linked to a suitable nonlinear elastic model. Attention is focused on the periodic response, though an insight is also given to the non-periodic response. The method of analysis used is the harmonic balance with many components. Frequency-response curves are evaluated for different system characteristics. Ratios of small amplitude vibration frequency 3 and 2 are considered, with different hysteresis degree. Notwithstanding the dissipation due to hysteresis usually destroys most of the phenomena evidenced by the classical nonlinear oscillators, in the present analysis a rich behavior is found: IT symmetric and non symmetric, 2T periodic responses are found and so on.

Parameter estimation of a susceptible–infected–recovered–dead computer worm model

SIMULATION ◽  
2021 ◽  
pp. 003754972110095
Author(s):  
Yue Deng ◽  
Yongzhen Pei ◽  
Changguo Li
Keyword(s):  
Parameter Estimation ◽  
Equation Model ◽  
Internet Security ◽  
Economic Losses ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Computer Worms ◽  
Computer Worm ◽  
Worm Model ◽  
Ensemble Kalman Filtering

Computer worms are serious threats to Internet security and have caused billions of dollars of economic losses during the past decades. In this study, we implemented a susceptible–infected–recovered–dead (SIRD) model of computer worms and analyzed the characteristics and mechanisms of worm transmission. We applied the ordinary differential equation model to simulate the transmission process of computer worms and estimated the unknown parameters of the SIRD model through the methods of least squares, Markov chain Monte Carlo, and ensemble Kalman filtering (ENKF). The results reveal that the proposed SIRD model is more accurate than the susceptible–exposed–infected–recovered–susceptible model with respect to parameter estimation.

COALESCENCE OF THE TWO SECONDARY RESPONSES IN COUPLED DUFFING EQUATIONS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250149
Author(s):  
TING-YU LAI ◽  
PI-CHENG TUNG ◽  
YUNG-CHIA HSIAO
Keyword(s):  
Periodic Orbits ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Harmonic Balance Method ◽  
The Novel ◽  
Duffing Equations ◽  
Duffing System ◽  
Parametric Continuation ◽  
Continuation Algorithm ◽  
The Stability

The novel coalescence of the secondary responses for the coupled Duffing equations are observed in this study. Two secondary responses that do not bifurcate from the primary responses merge into one due to saddle-node bifurcation generation within a specific parameter range. The frequency responses of the coupled Duffing equations are calculated using the harmonic balance method while the periodic orbits are detected by the shooting method. The stability of the periodic orbits is determined on utilizing Floquet theory. The parametric continuation algorithm is used to obtain the bifurcation points and bifurcation lines for a Duffing system with two varying parameters. The analytical results demonstrate the novel phenomenon that occurs in the Duffing equations.

scholarly journals A nonlinear model of the hand-arm system and parameters identification using vibration transmissibility

2018 ◽  
Vol 241 ◽  
pp. 01014
Author(s):  
Nahid Hida ◽  
Mohamed Abid ◽  
Faouzi Lakrad
Keyword(s):  
Nonlinear Model ◽  
Harmonic Balance ◽  
Grip Force ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Single Degree Of Freedom ◽  
Identification Process ◽  
Harmonic Vibrations ◽  
Single Degree ◽  
Vibration Transmissibility

In the present paper a lumped single degree-of-freedom nonlinear model is used to study biodynamic responses of the hand arm system (HAS) under harmonic vibrations. Then, the harmonic balance method is implemented to derive the vibration transmissibility. Furthermore,Padé approximations are used in the identification process of biodynamic characteristics of the HAS model. This process is based on minimizing the distance between the theoretical and the experimentally measured transmissibilities. The proposed identification workflow is applied to vibrations at the wrist in two cases: 1) the transmissibility versus the grip force for fixed excitation frequencies, and 2) the transmissibility versus the excitation frequency for fixed grip force.

HOPF BIFURCATION IN A CALCIUM OSCILLATION MODEL AND ITS CONTROL: FREQUENCY DOMAIN APPROACH

2013 ◽  
Vol 23 (01) ◽  
pp. 1350012 ◽  
Author(s):  
YU CHANG ◽  
LILI ZHOU ◽  
JINLIANG WANG
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Periodic Orbits ◽  
Harmonic Balance ◽  
Bifurcation Theory ◽  
Harmonic Balance Method ◽  
Calcium Oscillation ◽  
Control Frequency ◽  
Oscillation Model ◽  
Frequency Domain Approach

The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

scholarly journals Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Xiaoxia Zhao ◽  
Wei Li ◽  
Yanyang Wang ◽  
Lihong Jiang
Keyword(s):  
Differential Equation ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Equation Model ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Differential Equation Model ◽  
Number Of Visits ◽  
Positive Equilibrium Point

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

scholarly journals A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems

2016 ◽  
Vol 63 (2) ◽  
pp. 297-314 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco I. Leine
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Harmonic Balance ◽  
Degrees Of Freedom ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Constrained Mechanical Systems ◽  
Nonlinear Force

Abstract In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

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