scholarly journals Parallel kd-Tree Based Approach for Computing the Prediction Horizon Using Wolf’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
J. J. Águila ◽  
E. Arias ◽  
M. M. Artigao ◽  
J. J. Miralles
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Measurement Data ◽  
Original System ◽  
Model Parameters ◽  
Maximal Lyapunov Exponent ◽  
Science And Engineering ◽  
Prediction Horizon ◽  
Means Of Measurement

In different fields of science and engineering, a model of a given underlying dynamical system can be obtained by means of measurement data records called time series. This model becomes very important to understand the original system behaviour and to predict the future values of that system. From the model, parameters such as the prediction horizon can be computed to obtain the point where the prediction becomes useless. In this work, a new parallel kd-tree based approach for computing the prediction horizon is presented. The parallel approach uses the maximal Lyapunov exponent, which is computed by Wolf’s method, as an estimator of the prediction horizon.

Dynamic Data-Driven Spatiotemporal System Behavior Prediction With Simulations and Sensor Measurement Data

2018 ◽  
Author(s):  
Xiangxue Zhao ◽  
Shapour Azarm ◽  
Balakumar Balachandran
Keyword(s):  
Dynamical System ◽  
Real Time ◽  
Measurement Data ◽  
Data Driven ◽  
Sensor Data ◽  
Model Parameters ◽  
High Fidelity ◽  
System Behavior ◽  
Sensor Measurement

Online prediction of dynamical system behavior based on a combination of simulation data and sensor measurement data has numerous applications. Examples include predicting safe flight configurations, forecasting storms and wildfire spread, estimating railway track and pipeline health conditions. In such applications, high-fidelity simulations may be used to accurately predict a system’s dynamical behavior offline (“non-real time”). However, due to the computational expense, these simulations have limited usage for online (“real-time”) prediction of a system’s behavior. To remedy this, one possible approach is to allocate a significant portion of the computational effort to obtain data through offline simulations. The obtained offline data can then be combined with online sensor measurements for online estimation of the system’s behavior with comparable accuracy as the off-line, high-fidelity simulation. The main contribution of this paper is in the construction of a fast data-driven spatiotemporal prediction framework that can be used to estimate general parametric dynamical system behavior. This is achieved through three steps. First, high-order singular value decomposition is applied to map high-dimensional offline simulation datasets into a subspace. Second, Gaussian processes are constructed to approximate model parameters in the subspace. Finally, reduced-order particle filtering is used to assimilate sparsely located sensor data to further improve the prediction. The effectiveness of the proposed approach is demonstrated through a case study. In this case study, aeroelastic response data obtained for an aircraft through simulations is integrated with measurement data obtained from a few sparsely located sensors. Through this case study, the authors show that along with dynamic enhancement of the state estimates, one can also realize a reduction in uncertainty of the estimates.

scholarly journals The Study of the Chaotic Behavior in Retailer's Demand Model

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Yun Feng
Keyword(s):  
Lyapunov Exponent ◽  
Systems Theory ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Deterministic Chaos ◽  
Model Parameters ◽  
Initial Condition ◽  
Maximal Lyapunov Exponent ◽  
Demand Model

Based on the work of domestic and foreign scholars and the application of chaotic systems theory, this paper presents an investigation simulation of retailer's demand and stock. In simulation of the interaction, the behavior of the system exhibits deterministic chaos with consideration of system constraints. By the method of space's reconstruction, the maximal Lyapunov exponent of retailer's demand model was calculated. The result shows the model is chaotic. By the results of bifurcation diagram of model parameters , and changing initial condition, the system can be led to chaos.

Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

scholarly journals Stochastic Approach to a Rain Attenuation Time Series Synthesizer for Heavy Rain Regions

2016 ◽  
Vol 6 (5) ◽  
pp. 2379
Author(s):  
Masoud Mohebbi Nia ◽  
Jafri Din ◽  
Hong Yin Lam ◽  
Athanasios D. Panagopoulos
Keyword(s):  
Time Series ◽  
Communication Systems ◽  
Measurement Data ◽  
Likelihood Estimation ◽  
Heavy Rain ◽  
Stochastic Approach ◽  
Rain Attenuation ◽  
Least Square ◽  
Model Parameters ◽  
Cir Model

<p>In this work, a new rain attenuation time series synthesizer based on the stochastic approach is presented. The model combines a well-known interest-rate prediction model in finance namely the Cox-Ingersoll-Ross (CIR) model, and a stochastic differential equation approach to generate a long-term gamma distributed rain attenuation time series, particularly appropriate for heavy rain regions. The model parameters were derived from maximum-likelihood estimation (MLE) and Ordinary Least Square (OLS) methods. The predicted statistics from the CIR model with the OLS method are in good agreement with the measurement data collected in equatorial Malaysia while the MLE method overestimated the result. The proposed stochastic model could provide radio engineers an alternative solution for the design of propagation impairment mitigation techniques (PIMTs) to improve the Quality of Service (QoS) of wireless communication systems such as 5G propagation channel, in particular in heavy rain regions.</p>

Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Kaan Atak ◽  
Ozgur Aybar ◽  
Gokhan Şahin ◽  
Avadis Hacınlıyan ◽  
Yani Skarlatos
Keyword(s):  
Thin Films ◽  
Time Series ◽  
Polyethylene Glycol ◽  
Lyapunov Exponent ◽  
Relative Humidity ◽  
Time Series Analysis ◽  
Maximal Lyapunov Exponent ◽  
Series Analysis ◽  
Hydrophobically Modified ◽  
Irregular Behavior

AbstractPolyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.

scholarly journals Bayesian Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors

2021 ◽  
Vol 5 (1) ◽  
pp. 20
Author(s):  
Alexander Dorndorf ◽  
Boris Kargoll ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Time Series ◽  
Nonlinear Models ◽  
Multivariate Time Series ◽  
Functional Model ◽  
Measurement Data ◽  
Model Parameters ◽  
Correlated Noise ◽  
Posterior Density ◽  
Stochastic Properties ◽  
T Distribution

Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usually nonlinear regarding the trend parameters. To deal with these characteristics, a time series model, which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autoregressive (AR) processes the white noise components of which obey independent, scaled t-distributions, was proposed by the authors in previous research papers. In this paper, we extend the aforementioned model to include prior knowledge regarding various model parameters, the information about which is often available in practical situations. We develop an algorithm based on Bayesian inference that provides a robust and reliable estimation of the functional parameters, the coefficients of the AR process and the parameters of the underlying t-distribution. We approximate the resulting posterior density using Markov chain Monte Carlo (MCMC) techniques consisting of a Metropolis-within-Gibbs algorithm.

scholarly journals Chaotic Dynamics of Flags from Recurring Values of Flapping Moment

2017 ◽  
Vol 27 (02) ◽  
pp. 1750020 ◽  
Author(s):  
Emmanuel Virot ◽  
Davide Faranda ◽  
Xavier Amandolese ◽  
Pascal Hémon
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Point Of View ◽  
Experimental Point ◽  
Maximal Lyapunov Exponent ◽  
Limited Size ◽  
Energy Harvesters ◽  
Large Oscillation ◽  
Strong Winds

The performance of recently proposed flag-based energy harvesters is strongly limited by the chaotic response of flags to strong winds. From an experimental point of view, the detection of flag chaotic dynamics were scarce, based on the flapping amplitude and the maximal Lyapunov exponent. In practice, tracking the flapping amplitude is difficult and flawed in the large oscillation limit. Also, computing the maximal Lyapunov exponent from time series of limited size requires strong assumptions on the attractor geometry, without getting insurance of their reliability. For bypassing these issues, (1) we use a time series which takes into account the whole dynamics of the flag, by using the flapping moment which integrates its displacements, and (2) we apply an algorithm of detection of chaos based on recurring values in time series.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

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