scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.


2014 ◽  
Vol 21 (1) ◽  
pp. 127-142 ◽  
Author(s):  
B. O. Ogunsua ◽  
J. A. Laoye ◽  
I. A. Fuwape ◽  
A. B. Rabiu

Abstract. The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.


1998 ◽  
Author(s):  
A. Mutou ◽  
S. Mizuki ◽  
Y. Komatsubara ◽  
H. Tsujita

A dynamical system analysis method is presented, that permits the characterization of unsteady phenomena in a centrifugal compression system. The method maps one experimental time series of data into a state space in which behaviors of the compression system should be represented, and reconstructs an attractor that geometrically characterizes a state of the compression system. The time series of data were obtained by using a high response pressure transducer and an analog to digital converter at surge condition. For the reconstruction of attractors, a noise free differentiation method in time was employed. The differentiation was made by high order finite difference methods. To remove the influence of noise, the data were passed through a filter using a third order spline interpolation. In this study, the dimension of the state space was restricted to three. The measured data itself and their first and second derivatives in time are used to represent an attractor in the state space. The modeling of the system behavior from the time series of data by second order ordinary differential equations was attempted. It is assumed that the data and their derivatives satisfy the equations at each time. Then, appropriate coefficients are determined by a least square method. The reconstructed attractor showed complex cyclic trajectories at a first glance. However, by applying a band pass filter to the original signal, it was found that the attractor consisted of three independent wave forms and formed an attractor with torus-like behavior. In contrast, the solution by the modeled equations showed a type of limit cycle.


2019 ◽  
Vol 11 (3) ◽  
pp. 661-665 ◽  
Author(s):  
Ekta Hooda ◽  
Urmil Verma

Unlike classical regression analysis, the state space models have time-dependent parameters and provide a flexible class of dynamic and structural time series models. The unobserved component model (UCM) is a special type of state space models widely used to analyze and forecast time series. The present investigation has been carried out to study the trend of sugarcane(gur) yield in five districts (Ambala, Karnal, Panipat, Yamunanagar and Kurukshetra) of Haryana state using the unobserved component models with level, trend and irregular components. For this purpose, the time series data on sugarcane yield from 1966-67 to 2016-17 of Ambala and Karnal, 1971-72 to 2016-17 of Kurukshetra and 1980-81 to 2016-17 of Panipat and Yamunanagar districts have been used.   For all the districts, the irregular component was found to be highly significant (p=0.01) while both level and trend component variances were observed non-significant. Significance analysis of the individual component(s) has also been performed for possible dropping of the level and trend components by setting their variances equal to zero. The state space models may be effectively used pertaining to Indian agriculture data, as it takes into account the time dependency of the underlying parameters which may further enhance the predictive accuracy of the most popularly used ARIMA models with parameter constancy. Moreover, the unobserved component model is capable of handling both stationary as well as non-stationary time series and thus found more suitable for sugarcane yield modeling which is a trended yield (i.e. non-stationary in nature).


Author(s):  
Inna Koblianska ◽  
Larysa Kalachevska ◽  
Stanisław Minta ◽  
Nataliia Strochenko ◽  
Svitlana Lukash

Purpose. Under the background of the climate change and other crises, the world food system is becoming increasingly vulnerable to price fluctuations. This highlights the need to consider and better manage the risks associated with price volatility in accordance with the principles of a market economy and simultaneously protecting the most vulnerable groups of population. Responding to these challenges, in this study we aim to determine the main parameters of time series of potato sales prices in agricultural enterprises in Ukraine, to build an appropriate model, and to form a short-term (one-year) forecast. Methodology / approach. We used in the research the data from the State Statistics Service of Ukraine on average monthly sales prices of potatoes in agricultural enterprises from December 2012 to July 2021 (104 observations) adjusted for the price index of crop products sold by enterprises for the month (with December 2012 base period). Decomposition was used to determine the characteristics of the time series; exponential smoothing methods (Holt-Winters and State Space Framework – ETS) and autoregressive-moving average were used to find the model that fits the actual data the best and has high prognostic quality. We applied the Rstudio forecast package to model and to forecast the time series. Results. The time series of potato sales prices in enterprises is characterized by seasonality (mainly related to seasonal production) with the lowest prices in November, and the highest – in June; although, other periods of price growth were identified during the year: in January and April. The ARMA (2, 2) (1,0)12 with a non-zero mean was found to be the best model for forecasting potatoes sales prices. ARMA (2, 2) (1,0)12, compared to the state-space exponential smoothing model with additive errors – ETS (A), better fits the observed data and provides more accurate forecasting model (with lower errors). Forecast made with ARMA (2, 2) (1,0)12 shows that potato sale prices in agricultural enterprises in November 2021 (months with the lowest price) will range from 2154.76 UAH/t to 7414.57 UAH/t, in June 2022 – from 3016.72 UAH/t to 14051.63 UAH/t (prices of July 2021) with a probability of 95%. The forecast’s mean absolute percentage error is 14.87%. Originality / scientific novelty. This research deepens the methodological basis for food prices modelling and forecasting, thus contributing to the agricultural economics science development. The obtained results confirm the previous research findings on the better quality of food prices forecasts made with autoregressive models (for univariate time series) compared with exponential smoothing. Additionally, the study reveals advantages of the state space framework for exponential smoothing (ETS) compared to Holt-Winters methods in case of time series with seasonality: although the ETS model overlaps with the observed (train) data, it is better in terms of information criteria and forecasting (for the test data). Practical value / implications. The obtained results can serve as an information basis for decision-making on potato production and sales by producers, on more efficient use of resources by the population, on more effective measures to support industrial potato growing, to implement social programs and food security policy by the government.


2017 ◽  
Vol 28 (14) ◽  
pp. 1941-1956 ◽  
Author(s):  
Mehrisadat Makki Alamdari ◽  
Bijan Samali ◽  
Jianchun Li ◽  
Ye Lu ◽  
Samir Mustapha

We present a time-series-based algorithm to identify structural damage in the structure. The method is in the context of non-model-based approaches; hence, it eliminates the need of any representative numerical model of the structure to be built. The method starts by partitioning the state space into a finite number of subsets which are mutually exclusive and exhaustive and each subset is identified by a distinct symbol. Partitioning is performed based on a maximum entropy approach which takes into account the sparsity and distribution of information in the time series. After constructing the symbol space, the time series data are uniquely transformed from the state space into the constructed symbol space to create the symbol sequences. Symbol sequences are the simplified abstractions of the complex system and describe the evolution of the system. Each symbol sequence is statistically characterized by its entropy which is obtained based on the probability of occurrence of the symbols in the sequence. As a consequence of damage occurrence, the entropy of the symbol sequences changes; this change is implemented to define a damage indicative feature. The method shows promising results using data from two experimental case studies subject to varying excitation. The first specimen is a reinforced concrete jack arch which replicates one of the major structural components of the Sydney Harbor Bridge and the second specimen is a three-story frame structure model which has been tested at Los Alamos National Laboratory. The method not only could successfully identify the presence of damage but also has potential to localize it.


2010 ◽  
Vol 13 (1) ◽  
pp. 244-256 ◽  
Author(s):  
José Navarro ◽  
Carlos Arrieta

This study considers the complex dynamics of work motivation. Forty-eight employees completed a work-motivation diary several times per day over a period of four weeks. The obtained time series were analysed using different methodologies derived from chaos theory (i.e. recurrence plots, Lyapunov exponents, correlation dimension and surrogate data). Results showed chaotic dynamics in 75% of cases. The findings confirm the universality of chaotic behavior within human behavior, challenge some of the underlying assumptions on which work motivation theories are based, and suggest that chaos theory may offer useful and relevant information on how this process is managed within organizations.


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