scholarly journals On the Investigation of State Space Reconstruction of Nonlinear Aeroelastic Response Time Series

2006 ◽  
Vol 13 (4-5) ◽  
pp. 393-407 ◽  
Author(s):  
Flávio D. Marques ◽  
Eduardo M. Belo ◽  
Vilma A. Oliveira ◽  
José R. Rosolen ◽  
Andréia R. Simoni
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Response Time ◽  
State Space ◽  
The State ◽  
Aeroelastic Response ◽  
State Space Reconstruction ◽  
Wing Model ◽  
Linear Behavior ◽  
Non Linear

Stall-induced aeroelastic motion may present severe non-linear behavior. Mathematical models for predicting such phenomena are still not available for practical applications and they are not enough reliable to capture physical effects. Experimental data can provide suitable information to help the understanding of typical non-linear aeroelastic phenomena. Dynamic systems techniques based on time series analysis can be adequately applied to non-linear aeroelasticity. When experimental data are available, the methods of state space reconstruction have been widely considered. This paper presents the state space reconstruction approach for the characterization of the stall-induced aeroelastic non-linear behavior. A wind tunnel scaled wing model has been tested. The wing model is subjected to different airspeeds and dynamic incidence angle variations. The method of delays is used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. To obtain an estimate of the time delay used in the state space reconstruction from time series, the autocorrelation function analyis is used. For the calculation of the embedding dimension the correlation integral approach is considered. The reconstructed attractors can reveal typical non-linear structures associated, for instance, to chaos or limit cycles.

scholarly journals Detección de fallas en máquinas rotatorias utilizando parámetros no lineales

2019 ◽  
pp. 25-33
Author(s):  
Erick Eduardo Huesca-Lazcano ◽  
Oscar Flores-Ramirez ◽  
Gabriel Romero-Rodriguez ◽  
Karla Cecilia Apan-Araujo
Keyword(s):  
Time Series ◽  
Dynamic Systems ◽  
Rotating Machinery ◽  
The State ◽  
Single Type ◽  
Nonlinear Parameters ◽  
Processing Power ◽  
Linear Behavior ◽  
Non Linear ◽  
Alternative Methodology

With the development of modern electronics and the increase in processing power it is now possible to install many and diverse sensors in a single type of machinery. Temperature, vibration, pressure, voltage, etc. they are variables that are commonly monitored in rotating machinery. These variables together contain all the information related to the condition of the machine. In case of a malfunction, this will be reflected in one or more of the monitored variables. These changes can be so subtle that they can not be noticed directly in the time series. Therefore, it is necessary to transform this information into a new and more useful representation. In the present work an alternative methodology is exposed for the analysis and diagnosis of malfunctions present in components of rotating machinery. This methodology is based on the processing of time series obtained from the sensors installed in the machinery, without considering the model of this. The extraction of nonlinear parameters is presented as an alternative, among which the maximum exponent of Lyapunov stands out, as an indicator of the state of the machine. In conjunction with traditional parameters it makes it possible to detect faults masked due to non-linear behavior of dynamic systems.

Nonlinear Time Series Analysis with R

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Particle Physics ◽  
Linear Time ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Linear Behavior ◽  
Non Linear ◽  
Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

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.

Non-linear controller applied to boost DC-DC converters using the state space average model

2009 ◽  
Author(s):  
Luigi Galotto ◽  
Carlos A. Canesin ◽  
Raimundo Cordero ◽  
Cristiano A. Quevedo ◽  
Rubenz Gazineu
Keyword(s):  
State Space ◽  
The State ◽  
Average Model ◽  
Linear Controller ◽  
Non Linear

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

scholarly journals Behavior of Attractors During Surge in Centrifugal Compression System

1998 ◽  
Author(s):  
A. Mutou ◽  
S. Mizuki ◽  
Y. Komatsubara ◽  
H. Tsujita
Keyword(s):  
Time Series ◽  
State Space ◽  
System Analysis ◽  
Spline Interpolation ◽  
Finite Difference Methods ◽  
The State ◽  
Least Square ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Compression System

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.

scholarly journals Unobserved Components Model for Forecasting Sugarcane Yield in Haryana

2019 ◽  
Vol 11 (3) ◽  
pp. 661-665 ◽  
Author(s):  
Ekta Hooda ◽  
Urmil Verma
Keyword(s):  
Time Series ◽  
State Space ◽  
The State ◽  
State Space Models ◽  
Stationary Time Series ◽  
Component Model ◽  
Series Data ◽  
Unobserved Component ◽  
Sugarcane Yield ◽  
Unobserved Component Model

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).

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