Study on State Recognition of ASCE Benchmark Based on Lyapunov Exponent Spectrum Entropy

2011 ◽  
Vol 243-249 ◽  
pp. 5435-5439 ◽  
Author(s):  
Jian Xi Yang ◽  
Jian Ting Zhou ◽  
Yue Chen
Keyword(s):  
Lyapunov Exponent ◽  
Time Sequence ◽  
Maximum Lyapunov Exponent ◽  
Entropy Analysis ◽  
Structural System ◽  
Time Duration ◽  
State Recognition ◽  
Chaotic Characteristic ◽  
Lyapunov Exponent Spectrum ◽  
Maximum Lyapunov Exponents

The paper has made a maximum Lyapunov exponent and Lyapunov exponent spectrum entropy analysis of ASCE Benchmark using non-linear theory and chaos time sequence. The maximum Lyapunov exponents in the two kinds of structural monitored data are both over zero, indicating that in the structural system chaos phenomenon has appeared. And, experiments have shown that the maximum Lyapunov exponent is sensitive of the amount of samples and the time delay. So, to compute the chaos index, the amount of samples and the time duration are of importance. Meanwhile, the Lyapunov exponent spectrum entropy is effective to measure the chaotic characteristic of the system, but ,the entropy is less sensitive to state recognition more than the max Lyapunov exponent.

Study on State Recognition of ASCE Benchmark FEM Based on Lyapunov Exponent Spectrum Entropy

2011 ◽  
Vol 117-119 ◽  
pp. 1526-1530
Author(s):  
Jian Xi Yang ◽  
Jian Ting Zhou ◽  
Feng Qing Han
Keyword(s):  
Finite Element ◽  
Lyapunov Exponent ◽  
Finite Element Model ◽  
Linear Theory ◽  
Element Model ◽  
Time Sequence ◽  
State Recognition ◽  
Structure State ◽  
Lyapunov Index ◽  
Lyapunov Exponent Spectrum

In this paper, ASCE Benchmark Finite Element Model was established and analyzed. Also, The MLI(the max Lyapunov Index) and LISE(Lyapunov Index Spectrum Entropy) has made to recognize state of the FEM using non-linear theory and chaos time sequence. The results show that MLI and LISE are sensitive with the structure state, and the structure system is chaotic.

A Study on the State Recognition of Frame Structure Based on the Maximum Lyapunov Exponent

2012 ◽  
Vol 166-169 ◽  
pp. 1230-1236 ◽  
Author(s):  
Juan Yang ◽  
Jian Ting Zhou ◽  
Jian Xi Yang ◽  
Yue Chen
Keyword(s):  
Lyapunov Exponent ◽  
Safety Assessment ◽  
Element Model ◽  
Structural Condition ◽  
Time Sequence ◽  
Frame Structure ◽  
Maximum Lyapunov Exponent ◽  
State Recognition ◽  
Characteristic Index ◽  
New Ideas

Based on the analysis of chaotic time sequence and the characterization to the system chaotic property from it’s characteristic index, we established finite element model about ASCE Benchmark. Then we got 4 acceleration time sequence of Benchmark model by simulation of instantaneous excitation. At last, we made a experimental analysis on the maximum Lyapunov exponent. As the result shows, all maximum Lyapunov exponents are above zero. It means that chaotic phenomenon appears in the structure system. At the same time, maximum Lyapunov exponent shows it’s sensitivity along with the evolution of structural condition. That is to say, the statement of structure could be reflected by the chaotic index of chaotic time sequence. Then we get new ideas on the study of safety assessment relied on the structural health monitoring.

Non-Linearity and Chaotic Behaviour in Cyprus Stock Market

2015 ◽  
Vol 5 (4) ◽  
Author(s):  
Athina Bougioukou
Keyword(s):  
Lyapunov Exponent ◽  
Stock Market ◽  
Chaos Theory ◽  
Linear Dependence ◽  
Chaotic Behavior ◽  
Efficient Market Hypothesis ◽  
Chaotic Behaviour ◽  
Maximum Lyapunov Exponent ◽  
Efficient Market ◽  
General Index

The intention of this research is to investigate the aspect of non-linearity and chaotic behavior of the Cyprus stock market. For this purpose, we use non-linearity and chaos theory. We perform BDS, Hinich-Bispectral tests and compute Lyapunov exponent of the Cyprus General index. The results show that existence of non-linear dependence and chaotic features as the maximum Lyapunov exponent was found to be positive. This study is important because chaos and efficient market hypothesis are mutually exclusive aspects. The efficient market hypothesis which requires returns to be independent and identically distributed (i.i.d.) cannot be accepted.

scholarly journals An investigation of EEG dynamics in an animal model of temporal lobe epilepsy using the maximum Lyapunov exponent

2009 ◽  
Vol 216 (1) ◽  
pp. 115-121 ◽  
Author(s):  
Sandeep P. Nair ◽  
Deng-Shan Shiau ◽  
Jose C. Principe ◽  
Leonidas D. Iasemidis ◽  
Panos M. Pardalos ◽  
...  
Keyword(s):  
Animal Model ◽  
Lyapunov Exponent ◽  
Temporal Lobe Epilepsy ◽  
Temporal Lobe ◽  
Maximum Lyapunov Exponent

Chaotic Dynamics of Piezoelectric MEMS Based on Maximum Lyapunov Exponent and Smaller Alignment Index Computations

2020 ◽  
Vol 30 (09) ◽  
pp. 2030025
Author(s):  
M. V. Tchakui ◽  
P. Woafo ◽  
Ch. Skokos
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Detection Method ◽  
Dynamical Behavior ◽  
Time Dependent ◽  
Maximum Lyapunov Exponent ◽  
Nonconservative System ◽  
Surface Of Section ◽  
Chaos Detection ◽  
Piezoelectric Mems

We characterize the dynamical states of a piezoelectric micrcoelectromechanical system (MEMS) using several numerical quantifiers including the maximum Lyapunov exponent, the Poincaré Surface of Section and a chaos detection method called the Smaller Alignment Index (SALI). The analysis makes use of the MEMS Hamiltonian. We start our study by considering the case of a conservative piezoelectric MEMS model and describe the behavior of some representative phase space orbits of the system. We show that the dynamics of the piezoelectric MEMS becomes considerably more complex as the natural frequency of the system’s mechanical part decreases. This refers to the reduction of the stiffness of the piezoelectric transducer. Then, taking into account the effects of damping and time-dependent forces on the piezoelectric MEMS, we derive the corresponding nonautonomous Hamiltonian and investigate its dynamical behavior. We find that the nonconservative system exhibits a rich dynamics, which is strongly influenced by the values of the parameters that govern the piezoelectric MEMS energy gain and loss. Our results provide further evidences of the ability of the SALI to efficiently characterize the chaoticity of dynamical systems.

Research of Extracting Information about Reservoir Logging Signals Based on Chaos Characteristics

2013 ◽  
Vol 380-384 ◽  
pp. 3742-3745
Author(s):  
Chun Yan Nie ◽  
Rui Li ◽  
Wan Li Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Correlation Dimension ◽  
Approximate Entropy ◽  
Water Layer ◽  
Time Correlation ◽  
Largest Lyapunov Exponent ◽  
Characteristic Parameters ◽  
Chaotic Characteristic ◽  
Oil Water

The mechanism of logging signals generating was researched. In the same time, correlation dimension, largest Lyapunov exponent and approximate entropy of chaotic characteristics were extracted. On this basis, chaotic characteristic parameters were applied in processing, analysis and interpretation, try to find chaotic characteristics of different of reservoirs for example oil, water layer and the dry layer. The results showed that chaos characteristics in different reservoir is different, therefore, we can distinguish the different natures of reservoirs by extracting chaos characteristics.

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