Characterizing Nonlinear Dynamic Systems With Periodicity Ratio and Statistic Hypothesis

2011 ◽  
Author(s):  
Lu Han ◽  
Liming Dai
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Poincaré Map ◽  
Numerical Results ◽  
Present Approach ◽  
Nonlinear Dynamic Systems ◽  
Statistical Hypothesis ◽  
Poincare Map ◽  
Nonlinear Characteristics

By introducing a statistical hypothesis to Periodicity Ratio, the efficiency and accuracy of diagnosing the nonlinear characteristics of dynamic systems are improved. Overlapping points in a Poincare map are verified on a statistically sound basis. The characteristics of nonlinear systems are investigated by using the present approach. The numerical results generated by the approach are compared with that of the conventional approaches.

PARAMETRIC IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS USING COMBINED LEVENBERG–MARQUARDT AND GENETIC ALGORITHM

2007 ◽  
Vol 07 (04) ◽  
pp. 715-725 ◽  
Author(s):  
R. KISHORE KUMAR ◽  
S. SANDESH ◽  
K. SHANKAR
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Parametric Identification ◽  
Computational Effort ◽  
Technical Note ◽  
Nonlinear Dynamic Systems ◽  
Levenberg Marquardt ◽  
Time Accuracy

This technical note presents the parametric identification of multi-degree-of-freedom nonlinear dynamic systems in the time domain using a combination of Levenberg–Marquardt (LM) method and Genetic Algorithm (GA). Here the crucial initial values to the LM algorithm are supplied by GA with a small population size. Two nonlinear systems are studied, the complex one having two nonlinear spring-damper pairs. The springs have cubic nonlinearity (Duffing oscillator) and dampers have quadratic nonlinearity. The effects of noise in the acceleration measurements and sensitivity analysis are also studied. The performance of combined GA and LM method is compared with pure LM and pure GA in terms of solution time, accuracy and number of iterations, and convergence and great improvement is observed. This method is found to be suitable for the identification of complex nonlinear systems, where the repeated solution of the numerically difficult equations over many generations requires enormous computational effort.

Diagnosing Irregularities of Nonlinear Dynamic Systems With Implementation of Periodicity-Ratio

2008 ◽  
Author(s):  
Liming Dai ◽  
Guoqing Wang
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
The Other ◽  
Nonlinear Dynamic Systems ◽  
Deterministic System ◽  
Final States ◽  
Regular Motion ◽  
Chaotic Vibrations ◽  
Irregular Behavior

Among the irregular responses of nonlinear dynamic systems, chaotic responses of nonlinear systems are probably the most attractive phenomena along with the new observations in the last decades. A nonlinear deterministic system may behavior chaotically under regular such as periodic excitations. Regular motion of a system subjected to periodic exertions is usually periodic. In contrast with regular motions, final states of chaotic vibrations are extremely nonperiodic. This research is to analyzing the irregular behavior of dynamic systems with implementation of a newly developed criterion named Periodicity-Ratio. The development of a methodology for diagnosing the irregular motions from the regular motions of a dynamic system is presented. The Periodicity-Ratio describes the degree of periodicity of motion and can be conveniently used to distinguish a nonperiodic motion from a regular vibration or oscillation and to diagnose whether or not a motion is chaotic and the other irregular responses of the nonlinear dynamic systems, without plotting any figures. The analyses on the irregular behavior of nonlinear dynamic systems with the implementation of the Periodicity-Ratio will be demonstrated.

On the Control and Stability of One Class of Biped Locomotion Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 328-332 ◽  
Author(s):  
M. Vukobratovic´ ◽  
D. Juricˇic´ ◽  
A. A. Frank
Keyword(s):  
Nonlinear Systems ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Lower Limb ◽  
Nonlinear Dynamic ◽  
Point Mass ◽  
Nonlinear Dynamic Systems ◽  
Biped Locomotion ◽  
Gait Stability ◽  
Stability Properties

The control and stability properties of a “simplified dynamic system” representing a particular biped gait are discussed. The simplified dynamic system consists of an algorithmically controlled lower limb system and a movable point mass. The concepts of repeatability and cyclicity are introduced by means of this model. These concepts provide the basis for control considerations in this class of systems. They lead to conditions which guarantee the maintenance of a gait. Stability of such nonlinear systems cannot be considered by classical techniques. To study stability, the concept of disturbance to nonlinear dynamic systems is introduced. This concept leads to a measure of stability by a quantity termed an “index of capability.” A method of computation for this index for this class of machines is shown.

A Waveform Similarity Approach for Diagnosing Nonlinear Behavior of Vibratory Systems

2020 ◽  
Vol 20 (06) ◽  
pp. 2040012
Author(s):  
Changzhao Qian ◽  
Changping Chen
Keyword(s):  
Lyapunov Exponent ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Behavior ◽  
Nonlinear Dynamic Systems ◽  
Chaotic Motions ◽  
Nonlinear Characteristics ◽  
New Approach ◽  
Duffing System ◽  
Waveform Similarity

A new approach is proposed for diagnosing the nonlinear characteristics of vibratory systems in engineering applications. The correlation coefficient of two periods’ response wave is used in this approach and a new concept named similarity degree of waveform (SDW) is proposed to describe the correlations of the responses and therefore the characteristics of the nonlinear dynamic systems. A Duffing system is used in this research as an example to demonstrate the application and efficiency of the proposed approach. The approach has shown effectiveness in diagnosing periodic, multi-periodic, quasi-periodic and chaotic motions. The characterization with implementing the proposed approach is compared with that of the Lyapunov exponent method. The advantages of the proposed approach are demonstrated.

Model Checking Control Software for Nonlinear Dynamic Systems

2008 ◽  
Author(s):  
James Kapinski ◽  
Alexandre Donze ◽  
Flavio Lerda ◽  
Hitashyam Maka ◽  
Edmund Clarke ◽  
...  
Keyword(s):  
Model Checking ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Control Software

Emulation of Ensembles of Nonlinear Dynamic Systems in Ultrawideband Active Wireless Direct Chaotic Networks

2018 ◽  
Vol 7 (3) ◽  
pp. 38-49
Author(s):  
Yu.V. Andreyev ◽  
◽  
M.Yu. Gerasimov ◽  
A.S. Dmitriev ◽  
R.Yu. Yemelyanov ◽  
...  
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems
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