CHARACTERIZATION OF RUNNING-IN ATTRACTORS RECONSTRUCTED FROM FRICTION SIGNALS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850088 ◽  
Author(s):  
YUANKAI ZHOU ◽  
XUE ZUO ◽  
HUA ZHU ◽  
HAIFENG FANG
Keyword(s):  
Friction Force ◽  
Chaos Theory ◽  
Correlation Dimension ◽  
Average Distance ◽  
Nonlinear Property ◽  
Force Vibration ◽  
Well Correlation ◽  
Two Parameters

Friction tests were conducted by sliding a ring against a disc under oil lubricated condition. The running-in attractor was generated from measured friction force, vibration and noise signals. On the basis of correlation dimension, predictability was introduced from chaos theory to characterize the running-in attractor. Two parameters, i.e. enclosing radius and average distance were proposed innovatively. The algorithms for the proposed parameters were given as well. Correlation dimension, predictability, enclosing radius and average distance were used to describe the complexity, randomness, bound and convergence degree of a running-in attractor, respectively. This study provides new parameters to quantify the running-in attractor and is meaningful for revealing the nonlinear property of the attractor.

scholarly journals Singular perturbations of the unicritical polynomials with two parameters

2016 ◽  
Vol 37 (6) ◽  
pp. 1997-2016 ◽  
Author(s):  
YINGQING XIAO ◽  
FEI YANG
Keyword(s):  
Julia Set ◽  
Dynamical Behavior ◽  
Rational Maps ◽  
Topological Properties ◽  
Fatou Set ◽  
The Family ◽  
Image Position ◽  
Two Parameters ◽  
Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

scholarly journals Bending of an Infinite beam on a base with two parameters in the absence of a part of the base

2018 ◽  
Vol 33 ◽  
pp. 02074
Author(s):  
Maxim Aleksandrovskiy ◽  
Lidiya Zaharova
Keyword(s):  
Rapid Development ◽  
Fourier Integral ◽  
Infinite Length ◽  
Degenerate Kernel ◽  
Shift Parameter ◽  
Approximate Methods ◽  
Concentrated Force ◽  
High Rise ◽  
Two Parameters

Currently, in connection with the rapid development of high-rise construction and the improvement of joint operation of high-rise structures and bases models, the questions connected with the use of various calculation methods become topical. The rigor of analytical methods is capable of more detailed and accurate characterization of the structures behavior, which will affect the reliability of objects and can lead to a reduction in their cost. In the article, a model with two parameters is used as a computational model of the base that can effectively take into account the distributive properties of the base by varying the coefficient reflecting the shift parameter. The paper constructs the effective analytical solution of the problem of a beam of infinite length interacting with a two-parameter voided base. Using the Fourier integral equations, the original differential equation is reduced to the Fredholm integral equation of the second kind with a degenerate kernel, and all the integrals are solved analytically and explicitly, which leads to an increase in the accuracy of the computations in comparison with the approximate methods. The paper consider the solution of the problem of a beam loaded with a concentrated force applied at the point of origin with a fixed value of the length of the dip section. The paper gives the analysis of the obtained results values for various parameters of coefficient taking into account cohesion of the ground.

Invariants of Chaotic Attractor in a Nonlinearly Damped System

1998 ◽  
Vol 65 (4) ◽  
pp. 875-879 ◽  
Author(s):  
B. Ravindra ◽  
P. Hagedorn
Keyword(s):  
Power Law ◽  
Chaotic Attractor ◽  
Correlation Dimension ◽  
Ml Estimation ◽  
State Space Reconstruction ◽  
Damped System ◽  
Building Models ◽  
Prediction And Control ◽  
And Control

The characterization of a chaotic attractor in a driven, Duffing-Holmes oscillator with power-law damping is considered. State space reconstruction of the time series of the attractor is carried out to investigate its structure. The invariants associated with the attractor such as correlation dimension and entropy are computed. Also the maximum-likelihood (ML) estimation of dimension and entropy are carried out. The use of obtained invariants in building models for prediction and control using power-law dampers is discussed.

scholarly journals Persistent Liquidity Effects and Long-Run Money Demand

2014 ◽  
Vol 6 (2) ◽  
pp. 71-107 ◽  
Author(s):  
Fernando Alvarez ◽  
Francesco Lippi
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Asset Markets ◽  
Propagation Mechanism ◽  
Monetary Model ◽  
Long Run ◽  
Short Run ◽  
The Stability ◽  
Two Parameters

We present a monetary model with segmented asset markets that implies a persistent fall in interest rates after a once-and-for-all increase in liquidity. The gradual propagation mechanism produced by our model is novel in the literature. We provide an analytical characterization of this mechanism, showing that the magnitude of the liquidity effect on impact, and its persistence, depend on the ratio of two parameters: the long-run interest rate elasticity of money demand and the intertemporal substitution elasticity. The model simultaneously explains the short-run “instability” of money demand estimates as well as the stability of long-run interest-elastic money demand. (JEL E13, E31, E41, E43, E52, E62)

Soft Computing Based Statistical Time Series Analysis, Characterization of Chaos Theory, and Theory of Fractals

2013 ◽  
pp. 30-61 ◽  
Author(s):  
Mofazzal H. Khondekar ◽  
Dipendra N. Ghosh ◽  
Koushik Ghosh ◽  
Anup Kumar Bhattacharya
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Time Series Analysis ◽  
Soft Computing ◽  
Chaos Theory ◽  
Filter Design ◽  
Theoretical Perspective ◽  
Series Analysis ◽  
Statistical Time

The present work is an attempt to analyze the various researches already carried out from the theoretical perspective in the field of soft computing based time series analysis, characterization of chaos, and theory of fractals. Emphasis has been given in the analysis on soft computing based study in prediction, data compression, explanatory analysis, signal processing, filter design, tracing chaotic behaviour, and estimation of fractal dimension of time series. The present work is a study as a whole revealing the effectiveness as well as the shortcomings of the various techniques adapted in this regard.

Development of a new empirical method for Tunnel Squeezing Classification (TSC)

2020 ◽  
Vol 53 (4) ◽  
pp. 655-660 ◽  
Author(s):  
Hadi Farhadian ◽  
Arash Nikvar-Hassani
Keyword(s):  
Quality Index ◽  
Empirical Method ◽  
Point Of View ◽  
Geological Hazard ◽  
Case Histories ◽  
Proposed Model ◽  
Two Parameters ◽  
Classification Tool ◽  
Selection Of

The characterization of squeezing phenomena as a geological hazard is of great importance because squeezing has a crucial role in the selection of the route and type of tunnels and in the characteristics of the excavation device. Tunnel squeezing is also the basis for the designation and construction of tunnelling-related structures. We present a new tunnel squeezing classification tool to predict tunnel squeezing based on two parameters: Q, the tunnelling quality index; and H, the depth of the tunnel. We used data collected from published papers to train the model; these data included 225 case histories from different countries, including Andorra, India, Iran, Japan, Nepal, Spain, Turkey and Venezuela. Validation of the model indicated that our tunnel squeezing classification tool is more accurate than the speculative and analytical methods currently in use. The proposed model will help tunnelling experts to classify tunnelling media from the point of view of squeezing hazards.

scholarly journals Achieving Fairness in the Stochastic Multi-Armed Bandit Problem

2020 ◽  
Vol 34 (04) ◽  
pp. 5379-5386
Author(s):  
Vishakha Patil ◽  
Ganesh Ghalme ◽  
Vineet Nair ◽  
Y. Narahari
Keyword(s):  
Learning Algorithm ◽  
Complete Characterization ◽  
Bandit Problem ◽  
Fairness Constraints ◽  
Two Parameters ◽  
The Cost ◽  
Primary Contribution ◽  
Theoretical Results ◽  
Natural Way

We study an interesting variant of the stochastic multi-armed bandit problem, which we call the Fair-MAB problem, where, in addition to the objective of maximizing the sum of expected rewards, the algorithm also needs to ensure that at any time, each arm is pulled at least a pre-specified fraction of times. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, which we call r-Regret, that takes into account the above fairness constraints and extends the conventional notion of regret in a natural way. Our primary contribution is to obtain a complete characterization of a class of Fair-MAB algorithms via two parameters: the unfairness tolerance and the learning algorithm used as a black-box. For this class of algorithms, we provide a fairness guarantee that holds uniformly over time, irrespective of the choice of the learning algorithm. Further, when the learning algorithm is UCB1, we show that our algorithm achieves constant r-Regret for a large enough time horizon. Finally, we analyze the cost of fairness in terms of the conventional notion of regret. We conclude by experimentally validating our theoretical results.

Quantitative characterization of surface wettability by friction force

2021 ◽  
Vol 536 ◽  
pp. 147788
Author(s):  
Kui Shi ◽  
Qian Li ◽  
Jinhong Zhang ◽  
Lijun Li ◽  
Baisong Yang ◽  
...  
Keyword(s):  
Friction Force ◽  
Surface Wettability ◽  
Quantitative Characterization
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