Numerical and Experimental Dynamic Characteristics of Thin-Film Membranes

NASA Technical Reports Server (NTRS)

Young, Leyland G.; Ramanathan, Suresh; Hu, Jia-Zhu; Pai, P. Frank

2004-01-01

Presented is a total-Lagrangian displacement-based non-linear finite-element model of thin-film membranes for static and dynamic large-displacement analyses. The membrane theory fully accounts for geometric non-linearities. Fully non-linear static analysis followed by linear modal analysis is performed for an inflated circular cylindrical Kapton membrane tube under different pressures, and for a rectangular membrane under different tension loads at four comers. Finite element results show that shell modes dominate the dynamics of the inflated tube when the inflation pressure is low, and that vibration modes localized along four edges dominate the dynamics of the rectangular membrane. Numerical dynamic characteristics of the two membrane structures were experimentally verified using a Polytec PI PSV-200 scanning laser vibrometer and an EAGLE-500 8-camera motion analysis system.

Dynamics of elastic nonlinear rotating composite beams with embedded actuators

NASA Astrophysics Data System (ADS)

Ghorashi, Mehrdaad

2009-08-01

A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.

Verification of nonlinear dynamic structural test results by combined image processing and acoustic analysis

NASA Astrophysics Data System (ADS)

Tene, Yair; Tene, Noam; Tene, G.

1993-08-01

An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

NASA Technical Reports Server (NTRS)

Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

1988-01-01

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Nonlinear analysis of NPP safety against the aircraft attack

DOE Office of Scientific and Technical Information (OSTI.GOV)

Králik, Juraj, E-mail: juraj.kralik@stuba.sk; Králik, Juraj, E-mail: kralik@fa.stuba.sk

The paper presents the nonlinear probabilistic analysis of the reinforced concrete buildings of nuclear power plant under the aircraft attack. The dynamic load is defined in time on base of the airplane impact simulations considering the real stiffness, masses, direction and velocity of the flight. The dynamic response is calculated in the system ANSYS using the transient nonlinear analysis solution method. The damage of the concrete wall is evaluated in accordance with the standard NDRC considering the spalling, scabbing and perforation effects. The simple and detailed calculations of the wall damage are compared.

Nonlinear Earthquake Analysis of Reinforced Concrete Frames with Fiber and Bernoulli-Euler Beam-Column Element

PubMed Central

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

1992-01-01

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

NASA Astrophysics Data System (ADS)

Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

PubMed Central

Porta, Alberto; Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Cysarz, Dirk; Van Leeuwen, Peter; Takahashi, Anielle C. M.; Catai, Aparecida M.; Gnecchi-Ruscone, Tomaso

2015-01-01

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales. PMID:25806002

Blade loss transient dynamics analysis, volume 1. Task 2: TETRA 2 theoretical development

NASA Technical Reports Server (NTRS)

Gallardo, Vincente C.; Black, Gerald

1986-01-01

The theoretical development of the forced steady state analysis of the structural dynamic response of a turbine engine having nonlinear connecting elements is discussed. Based on modal synthesis, and the principle of harmonic balance, the governing relations are the compatibility of displacements at the nonlinear connecting elements. There are four displacement compatibility equations at each nonlinear connection, which are solved by iteration for the principle harmonic of the excitation frequency. The resulting computer program, TETRA 2, combines the original TETRA transient analysis (with flexible bladed disk) with the steady state capability. A more versatile nonlinear rub or bearing element which contains a hardening (or softening) spring, with or without deadband, is also incorporated.

Nonlinear analysis of pupillary dynamics.

PubMed

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1985-01-01

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

The dynamics of a stabilised Wien bridge oscillator

NASA Astrophysics Data System (ADS)

Lerner, L.

2016-11-01

We present for the first time analytic solutions for the nonlinear dynamics of a Wien bridge oscillator stabilised by three common methods: an incandescent lamp, signal diodes, and the field effect transistor. The results can be used to optimise oscillator design, and agree well with measurements. The effect of operational amplifier marginal nonlinearity on oscillator performance at high frequencies is clarified. The oscillator circuits and their analysis can be used to demonstrate nonlinear dynamics in the undergraduate laboratory.

Non-linear controls influence functions in an aircraft dynamics simulator

NASA Technical Reports Server (NTRS)

Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.

2006-01-01

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

NASA Technical Reports Server (NTRS)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

NASA Technical Reports Server (NTRS)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

PubMed

Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

2008-03-01

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.

Modelling Nonlinear Dynamic Textures using Hybrid DWT-DCT and Kernel PCA with GPU

NASA Astrophysics Data System (ADS)

Ghadekar, Premanand Pralhad; Chopade, Nilkanth Bhikaji

2016-12-01

Most of the real-world dynamic textures are nonlinear, non-stationary, and irregular. Nonlinear motion also has some repetition of motion, but it exhibits high variation, stochasticity, and randomness. Hybrid DWT-DCT and Kernel Principal Component Analysis (KPCA) with YCbCr/YIQ colour coding using the Dynamic Texture Unit (DTU) approach is proposed to model a nonlinear dynamic texture, which provides better results than state-of-art methods in terms of PSNR, compression ratio, model coefficients, and model size. Dynamic texture is decomposed into DTUs as they help to extract temporal self-similarity. Hybrid DWT-DCT is used to extract spatial redundancy. YCbCr/YIQ colour encoding is performed to capture chromatic correlation. KPCA is applied to capture nonlinear motion. Further, the proposed algorithm is implemented on Graphics Processing Unit (GPU), which comprise of hundreds of small processors to decrease time complexity and to achieve parallelism.

Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient

NASA Astrophysics Data System (ADS)

Li, Huanhuan; Chen, Diyi; Zhang, Hao; Wang, Feifei; Ba, Duoduo

2016-12-01

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Nonlinear dynamic analysis of D α signals for type I edge localized modes characterization on JET with a carbon wall

NASA Astrophysics Data System (ADS)

Cannas, Barbara; Fanni, Alessandra; Murari, Andrea; Pisano, Fabio; Contributors, JET

2018-02-01

In this paper, the dynamic characteristics of type-I ELM time-series from the JET tokamak, the world’s largest magnetic confinement plasma physics experiment, have been investigated. The dynamic analysis has been focused on the detection of nonlinear structure in D α radiation time series. Firstly, the method of surrogate data has been applied to evaluate the statistical significance of the null hypothesis of static nonlinear distortion of an underlying Gaussian linear process. Several nonlinear statistics have been evaluated, such us the time delayed mutual information, the correlation dimension and the maximal Lyapunov exponent. The obtained results allow us to reject the null hypothesis, giving evidence of underlying nonlinear dynamics. Moreover, no evidence of low-dimensional chaos has been found; indeed, the analysed time series are better characterized by the power law sensitivity to initial conditions which can suggest a motion at the ‘edge of chaos’, at the border between chaotic and regular non-chaotic dynamics. This uncertainty makes it necessary to further investigate about the nature of the nonlinear dynamics. For this purpose, a second surrogate test to distinguish chaotic orbits from pseudo-periodic orbits has been applied. In this case, we cannot reject the null hypothesis which means that the ELM time series is possibly pseudo-periodic. In order to reproduce pseudo-periodic dynamical properties, a periodic state-of-the-art model, proposed to reproduce the ELM cycle, has been corrupted by a dynamical noise, obtaining time series qualitatively in agreement with experimental time series.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

NASA Astrophysics Data System (ADS)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.

PubMed

Gotoda, Hiroshi; Nikimoto, Hiroyuki; Miyano, Takaya; Tachibana, Shigeru

2011-03-01

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Nonlinearities of heart rate variability in animal models of impaired cardiac control: contribution of different time scales.

PubMed

Silva, Luiz Eduardo Virgilio; Lataro, Renata Maria; Castania, Jaci Airton; Silva, Carlos Alberto Aguiar; Salgado, Helio Cesar; Fazan, Rubens; Porta, Alberto

2017-08-01

Heart rate variability (HRV) has been extensively explored by traditional linear approaches (e.g., spectral analysis); however, several studies have pointed to the presence of nonlinear features in HRV, suggesting that linear tools might fail to account for the complexity of the HRV dynamics. Even though the prevalent notion is that HRV is nonlinear, the actual presence of nonlinear features is rarely verified. In this study, the presence of nonlinear dynamics was checked as a function of time scales in three experimental models of rats with different impairment of the cardiac control: namely, rats with heart failure (HF), spontaneously hypertensive rats (SHRs), and sinoaortic denervated (SAD) rats. Multiscale entropy (MSE) and refined MSE (RMSE) were chosen as the discriminating statistic for the surrogate test utilized to detect nonlinearity. Nonlinear dynamics is less present in HF animals at both short and long time scales compared with controls. A similar finding was found in SHR only at short time scales. SAD increased the presence of nonlinear dynamics exclusively at short time scales. Those findings suggest that a working baroreflex contributes to linearize HRV and to reduce the likelihood to observe nonlinear components of the cardiac control at short time scales. In addition, an increased sympathetic modulation seems to be a source of nonlinear dynamics at long time scales. Testing nonlinear dynamics as a function of the time scales can provide a characterization of the cardiac control complementary to more traditional markers in time, frequency, and information domains. NEW & NOTEWORTHY Although heart rate variability (HRV) dynamics is widely assumed to be nonlinear, nonlinearity tests are rarely used to check this hypothesis. By adopting multiscale entropy (MSE) and refined MSE (RMSE) as the discriminating statistic for the nonlinearity test, we show that nonlinear dynamics varies with time scale and the type of cardiac dysfunction. Moreover, as complexity metrics and nonlinearities provide complementary information, we strongly recommend using the test for nonlinearity as an additional index to characterize HRV. Copyright © 2017 the American Physiological Society.

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Computational Methods for Structural Mechanics and Dynamics

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

Topics addressed include: transient dynamics; transient finite element method; transient analysis in impact and crash dynamic studies; multibody computer codes; dynamic analysis of space structures; multibody mechanics and manipulators; spatial and coplanar linkage systems; flexible body simulation; multibody dynamics; dynamical systems; and nonlinear characteristics of joints.

New Representation of Bearings in LS-DYNA

NASA Technical Reports Server (NTRS)

Carney, Kelly S.; Howard, Samuel A.; Miller, Brad A.; Benson, David J.

2014-01-01

Non-linear, dynamic, finite element analysis is used in various engineering disciplines to evaluate high-speed, dynamic impact and vibration events. Some of these applications require connecting rotating to stationary components. For example, bird impacts on rotating aircraft engine fan blades are a common analysis performed using this type of analysis tool. Traditionally, rotating machines utilize some type of bearing to allow rotation in one degree of freedom while offering constraints in the other degrees of freedom. Most times, bearings are modeled simply as linear springs with rotation. This is a simplification that is not necessarily accurate under the conditions of high-velocity, high-energy, dynamic events such as impact problems. For this reason, it is desirable to utilize a more realistic non-linear force-deflection characteristic of real bearings to model the interaction between rotating and non-rotating components during dynamic events. The present work describes a rolling element bearing model developed for use in non-linear, dynamic finite element analysis. This rolling element bearing model has been implemented in LS-DYNA as a new element, *ELEMENT_BEARING.

An introduction to chaos theory in CFD

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

The brain as a dynamic physical system.

PubMed

McKenna, T M; McMullen, T A; Shlesinger, M F

1994-06-01

The brain is a dynamic system that is non-linear at multiple levels of analysis. Characterization of its non-linear dynamics is fundamental to our understanding of brain function. Identifying families of attractors in phase space analysis, an approach which has proven valuable in describing non-linear mechanical and electrical systems, can prove valuable in describing a range of behaviors and associated neural activity including sensory and motor repertoires. Additionally, transitions between attractors may serve as useful descriptors for analysing state changes in neurons and neural ensembles. Recent observations of synchronous neural activity, and the emerging capability to record the spatiotemporal dynamics of neural activity by voltage-sensitive dyes and electrode arrays, provide opportunities for observing the population dynamics of neural ensembles within a dynamic systems context. New developments in the experimental physics of complex systems, such as the control of chaotic systems, selection of attractors, attractor switching and transient states, can be a source of powerful new analytical tools and insights into the dynamics of neural systems.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS

PubMed Central

MIAO, HONGYU; XIA, XIAOHUA; PERELSON, ALAN S.; WU, HULIN

2011-01-01

Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice. PMID:21785515

Nonlinear stability and control study of highly maneuverable high performance aircraft

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1993-01-01

This project is intended to research and develop new nonlinear methodologies for the control and stability analysis of high-performance, high angle-of-attack aircraft such as HARV (F18). Past research (reported in our Phase 1, 2, and 3 progress reports) is summarized and more details of final Phase 3 research is provided. While research emphasis is on nonlinear control, other tasks such as associated model development, system identification, stability analysis, and simulation are performed in some detail as well. An overview of various models that were investigated for different purposes such as an approximate model reference for control adaptation, as well as another model for accurate rigid-body longitudinal motion is provided. Only a very cursory analysis was made relative to type 8 (flexible body dynamics). Standard nonlinear longitudinal airframe dynamics (type 7) with the available modified F18 stability derivatives, thrust vectoring, actuator dynamics, and control constraints are utilized for simulated flight evaluation of derived controller performance in all cases studied.

The "Chaos Theory" and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease?

PubMed

Krstacic, Goran; Krstacic, Antonija; Smalcelj, Anton; Milicic, Davor; Jembrek-Gostovic, Mirjana

2007-04-01

Dynamic analysis techniques may quantify abnormalities in heart rate variability (HRV) based on nonlinear and fractal analysis (chaos theory). The article emphasizes clinical and prognostic significance of dynamic changes in short-time series applied on patients with coronary heart disease (CHD) during the exercise electrocardiograph (ECG) test. The subjects were included in the series after complete cardiovascular diagnostic data. Series of R-R and ST-T intervals were obtained from exercise ECG data after sampling digitally. The range rescaled analysis method determined the fractal dimension of the intervals. To quantify fractal long-range correlation's properties of heart rate variability, the detrended fluctuation analysis technique was used. Approximate entropy (ApEn) was applied to quantify the regularity and complexity of time series, as well as unpredictability of fluctuations in time series. It was found that the short-term fractal scaling exponent (alpha(1)) is significantly lower in patients with CHD (0.93 +/- 0.07 vs 1.09 +/- 0.04; P < 0.001). The patients with CHD had higher fractal dimension in each exercise test program separately, as well as in exercise program at all. ApEn was significant lower in CHD group in both RR and ST-T ECG intervals (P < 0.001). The nonlinear dynamic methods could have clinical and prognostic applicability also in short-time ECG series. Dynamic analysis based on chaos theory during the exercise ECG test point out the multifractal time series in CHD patients who loss normal fractal characteristics and regularity in HRV. Nonlinear analysis technique may complement traditional ECG analysis.

A recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure.

PubMed

Liao, Fuyuan; Jan, Yih-Kuen

2012-06-01

This paper presents a recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure. Recurrence is a fundamental property of many dynamical systems, which can be explored in phase spaces constructed from observational time series. A visualization tool of recurrence analysis called recurrence plot (RP) has been proved to be highly effective to detect transitions in the dynamics of the system. However, it was found that delay embedding can produce spurious structures in RPs. Network-based concepts have been applied for the analysis of nonlinear time series recently. We demonstrate that time series with different types of dynamics exhibit distinct global clustering coefficients and distributions of local clustering coefficients and that the global clustering coefficient is robust to the embedding parameters. We applied the approach to study skin blood flow oscillations (BFO) response to loading pressure. The results showed that global clustering coefficients of BFO significantly decreased in response to loading pressure (p<0.01). Moreover, surrogate tests indicated that such a decrease was associated with a loss of nonlinearity of BFO. Our results suggest that the recurrence network approach can practically quantify the nonlinear dynamics of BFO.

Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Batch process fault detection and identification based on discriminant global preserving kernel slow feature analysis.

PubMed

Zhang, Hanyuan; Tian, Xuemin; Deng, Xiaogang; Cao, Yuping

2018-05-16

As an attractive nonlinear dynamic data analysis tool, global preserving kernel slow feature analysis (GKSFA) has achieved great success in extracting the high nonlinearity and inherently time-varying dynamics of batch process. However, GKSFA is an unsupervised feature extraction method and lacks the ability to utilize batch process class label information, which may not offer the most effective means for dealing with batch process monitoring. To overcome this problem, we propose a novel batch process monitoring method based on the modified GKSFA, referred to as discriminant global preserving kernel slow feature analysis (DGKSFA), by closely integrating discriminant analysis and GKSFA. The proposed DGKSFA method can extract discriminant feature of batch process as well as preserve global and local geometrical structure information of observed data. For the purpose of fault detection, a monitoring statistic is constructed based on the distance between the optimal kernel feature vectors of test data and normal data. To tackle the challenging issue of nonlinear fault variable identification, a new nonlinear contribution plot method is also developed to help identifying the fault variable after a fault is detected, which is derived from the idea of variable pseudo-sample trajectory projection in DGKSFA nonlinear biplot. Simulation results conducted on a numerical nonlinear dynamic system and the benchmark fed-batch penicillin fermentation process demonstrate that the proposed process monitoring and fault diagnosis approach can effectively detect fault and distinguish fault variables from normal variables. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

NASA Technical Reports Server (NTRS)

Brenner, Martin J.; Prazenica, Richard J.

2003-01-01

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

COMBINED DELAY AND GRAPH EMBEDDING OF EPILEPTIC DISCHARGES IN EEG REVEALS COMPLEX AND RECURRENT NONLINEAR DYNAMICS.

PubMed

Erem, B; Hyde, D E; Peters, J M; Duffy, F H; Brooks, D H; Warfield, S K

2015-04-01

The dynamical structure of the brain's electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem.

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1980-01-01

A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.

Non-Linear Vibroisolation Pads Design, Numerical FEM Analysis and Introductory Experimental Investigations

NASA Astrophysics Data System (ADS)

Zielnica, J.; Ziółkowski, A.; Cempel, C.

2003-03-01

Design and theoretical and experimental investigation of vibroisolation pads with non-linear static and dynamic responses is the objective of the paper. The analytical investigations are based on non-linear finite element analysis where the load-deflection response is traced against the shape and material properties of the analysed model of the vibroisolation pad. A new model of vibroisolation pad of antisymmetrical type was designed and analysed by the finite element method based on the second-order theory (large displacements and strains) with the assumption of material's non-linearities (Mooney-Rivlin model). Stability loss phenomenon was used in the design of the vibroisolators, and it was proved that it would be possible to design a model of vibroisolator in the form of a continuous pad with non-linear static and dynamic response, typical to vibroisolation purposes. The materials used for the vibroisolator are those of rubber, elastomers, and similar ones. The results of theoretical investigations were examined experimentally. A series of models made of soft rubber were designed for the test purposes. The experimental investigations of the vibroisolation models, under static and dynamic loads, confirmed the results of the FEM analysis.

Efficient loads analyses of Shuttle-payloads using dynamic models with linear or nonlinear interfaces

NASA Technical Reports Server (NTRS)

Spanos, P. D.; Cao, T. T.; Hamilton, D. A.; Nelson, D. A. R.

1989-01-01

An efficient method for the load analysis of Shuttle-payload systems with linear or nonlinear attachment interfaces is presented which allows the kinematics of the interface degrees of freedom at a given time to be evaluated without calculating the combined system modal representation of the Space Shuttle and its payload. For the case of a nonlinear dynamic model, an iterative procedure is employed to converge the nonlinear terms of the equations of motion to reliable values. Results are presented for a Shuttle abort landing event.

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen in those plots. The movement of shock changes the aerodynamic load distribution on the wing. The effect of viscous on aeroelastic analysis is also discussed. Also compared are the flutter solutions with, or without the structural nonlinearity. As can be seen, linear structural solution goes to infinite, which can not be true in reality. The nonlinear solution is more realistic and can be used to understand the fluid and structure interaction behavior, to control, or prevent disastrous events. (Abstract shortened by UMI.)

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

NASA Technical Reports Server (NTRS)

Sidwell, K.

1976-01-01

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

NASA Technical Reports Server (NTRS)

Barut, A.; Madenci, Erdogan; Tessler, A.

1997-01-01

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

General description and understanding of the nonlinear dynamics of mode-locked fiber lasers.

PubMed

Wei, Huai; Li, Bin; Shi, Wei; Zhu, Xiushan; Norwood, Robert A; Peyghambarian, Nasser; Jian, Shuisheng

2017-05-02

As a type of nonlinear system with complexity, mode-locked fiber lasers are known for their complex behaviour. It is a challenging task to understand the fundamental physics behind such complex behaviour, and a unified description for the nonlinear behaviour and the systematic and quantitative analysis of the underlying mechanisms of these lasers have not been developed. Here, we present a complexity science-based theoretical framework for understanding the behaviour of mode-locked fiber lasers by going beyond reductionism. This hierarchically structured framework provides a model with variable dimensionality, resulting in a simple view that can be used to systematically describe complex states. Moreover, research into the attractors' basins reveals the origin of stochasticity, hysteresis and multistability in these systems and presents a new method for quantitative analysis of these nonlinear phenomena. These findings pave the way for dynamics analysis and system designs of mode-locked fiber lasers. We expect that this paradigm will also enable potential applications in diverse research fields related to complex nonlinear phenomena.

A new similarity index for nonlinear signal analysis based on local extrema patterns

NASA Astrophysics Data System (ADS)

Niknazar, Hamid; Motie Nasrabadi, Ali; Shamsollahi, Mohammad Bagher

2018-02-01

Common similarity measures of time domain signals such as cross-correlation and Symbolic Aggregate approximation (SAX) are not appropriate for nonlinear signal analysis. This is because of the high sensitivity of nonlinear systems to initial points. Therefore, a similarity measure for nonlinear signal analysis must be invariant to initial points and quantify the similarity by considering the main dynamics of signals. The statistical behavior of local extrema (SBLE) method was previously proposed to address this problem. The SBLE similarity index uses quantized amplitudes of local extrema to quantify the dynamical similarity of signals by considering patterns of sequential local extrema. By adding time information of local extrema as well as fuzzifying quantized values, this work proposes a new similarity index for nonlinear and long-term signal analysis, which extends the SBLE method. These new features provide more information about signals and reduce noise sensitivity by fuzzifying them. A number of practical tests were performed to demonstrate the ability of the method in nonlinear signal clustering and classification on synthetic data. In addition, epileptic seizure detection based on electroencephalography (EEG) signal processing was done by the proposed similarity to feature the potentials of the method as a real-world application tool.

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Robustness Analysis of Integrated LPV-FDI Filters and LTI-FTC System for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Khong, Thuan H.; Shin, Jong-Yeob

2007-01-01

This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) micro-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closed-loop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.

Nonlinear dynamics of the magnetosphere and space weather

NASA Technical Reports Server (NTRS)

Sharma, A. Surjalal

1996-01-01

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Directed dynamical influence is more detectable with noise

PubMed Central

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-01-01

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence. PMID:27066763

Directed dynamical influence is more detectable with noise.

PubMed

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-04-12

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

Aerodynamic and Nonlinear Dynamic Acoustic Analysis of Tension Asymmetry in Excised Canine Larynges

ERIC Educational Resources Information Center

Devine, Erin E.; Bulleit, Erin E.; Hoffman, Matthew R.; McCulloch, Timothy M.; Jiang, Jack J.

2012-01-01

Purpose: To model tension asymmetry caused by superior laryngeal nerve paralysis (SLNP) in excised larynges and apply perturbation, nonlinear dynamic, and aerodynamic analyses. Method: SLNP was modeled in 8 excised larynges using sutures and weights to mimic cricothyroid (CT) muscle function. Weights were removed from one side to create tension…

Down syndrome's brain dynamics: analysis of fractality in resting state.

PubMed

Hemmati, Sahel; Ahmadlou, Mehran; Gharib, Masoud; Vameghi, Roshanak; Sajedi, Firoozeh

2013-08-01

To the best knowledge of the authors there is no study on nonlinear brain dynamics of down syndrome (DS) patients, whereas brain is a highly complex and nonlinear system. In this study, fractal dimension of EEG, as a key characteristic of brain dynamics, showing irregularity and complexity of brain dynamics, was used for evaluation of the dynamical changes in the DS brain. The results showed higher fractality of the DS brain in almost all regions compared to the normal brain, which indicates less centrality and higher irregular or random functioning of the DS brain regions. Also, laterality analysis of the frontal lobe showed that the normal brain had a right frontal laterality of complexity whereas the DS brain had an inverse pattern (left frontal laterality). Furthermore, the high accuracy of 95.8 % obtained by enhanced probabilistic neural network classifier showed the potential of nonlinear dynamic analysis of the brain for diagnosis of DS patients. Moreover, the results showed that the higher EEG fractality in DS is associated with the higher fractality in the low frequencies (delta and theta), in broad regions of the brain, and the high frequencies (beta and gamma), majorly in the frontal regions.

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

Serebryannikov, E E; Zheltikov, A M

2014-07-25

Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.

Digit replacement: A generic map for nonlinear dynamical systems.

PubMed

García-Morales, Vladimir

2016-09-01

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

PubMed

Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime

2016-12-01

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

Analysis of railroad tank car shell impacts using finite element method

DOT National Transportation Integrated Search

2008-04-22

This paper examines impacts to the side of railroad tank : cars by a ram car with a rigid indenter using dynamic, : nonlinear finite element analysis (FEA). Such impacts are : referred to as shell impacts. Here, nonlinear means elasticplastic : mater...

Transient and chaotic low-energy transfers in a system with bistable nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romeo, F., E-mail: francesco.romeo@uniroma1.it; Manevitch, L. I.; Bergman, L. A.

2015-05-15

The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensionalmore » projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.« less

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, Christopher A.

In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulatemore » the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

A Computer Code for Dynamic Stress Analysis of Media-Structure Problems with Nonlinearities (SAMSON). Volume III. User’s Manual.

DTIC Science & Technology

NONLINEAR SYSTEMS, LINEAR SYSTEMS, SUBROUTINES , SOIL MECHANICS, INTERFACES, DYNAMICS, LOADS(FORCES), FORCE(MECHANICS), DAMPING, ACCELERATION, ELASTIC...PROPERTIES, PLASTIC PROPERTIES, CRACKS , REINFORCING MATERIALS , COMPOSITE MATERIALS , FAILURE(MECHANICS), MECHANICAL PROPERTIES, INSTRUCTION MANUALS, DIGITAL COMPUTERS...STRESSES, *COMPUTER PROGRAMS), (*STRUCTURES, STRESSES), (*DATA PROCESSING, STRUCTURAL PROPERTIES), SOILS , STRAIN(MECHANICS), MATHEMATICAL MODELS

A case study in nonlinear dynamics and control of articulated spacecraft: The Space Station Freedom with a mobile remote manipulator system

NASA Technical Reports Server (NTRS)

Bennett, William H.; Kwatny, Harry G.; Lavigna, Chris; Blankenship, Gilmer

1994-01-01

The following topics are discussed: (1) modeling of articulated spacecraft as multi-flex-body systems; (2) nonlinear attitude control by adaptive partial feedback linearizing (PFL) control; (3) attitude dynamics and control for SSF/MRMS; and (4) performance analysis results for attitude control of SSF/MRMS.

NASA LeRC/Akron University Graduate Cooperative Fellowship Program and Graduate Student Researchers Program

NASA Technical Reports Server (NTRS)

Fertis, D. G.; Simon, A. L.

1981-01-01

The requisite methodology to solve linear and nonlinear problems associated with the static and dynamic analysis of rotating machinery, their static and dynamic behavior, and the interaction between the rotating and nonrotating parts of an engine is developed. Linear and nonlinear structural engine problems are investigated by developing solution strategies and interactive computational methods whereby the man and computer can communicate directly in making analysis decisions. Representative examples include modifying structural models, changing material, parameters, selecting analysis options and coupling with interactive graphical display for pre- and postprocessing capability.

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

NASA Astrophysics Data System (ADS)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Neural Networks for Rapid Design and Analysis

NASA Technical Reports Server (NTRS)

Sparks, Dean W., Jr.; Maghami, Peiman G.

1998-01-01

Artificial neural networks have been employed for rapid and efficient dynamics and control analysis of flexible systems. Specifically, feedforward neural networks are designed to approximate nonlinear dynamic components over prescribed input ranges, and are used in simulations as a means to speed up the overall time response analysis process. To capture the recursive nature of dynamic components with artificial neural networks, recurrent networks, which use state feedback with the appropriate number of time delays, as inputs to the networks, are employed. Once properly trained, neural networks can give very good approximations to nonlinear dynamic components, and by their judicious use in simulations, allow the analyst the potential to speed up the analysis process considerably. To illustrate this potential speed up, an existing simulation model of a spacecraft reaction wheel system is executed, first conventionally, and then with an artificial neural network in place.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

NASA Astrophysics Data System (ADS)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental approaches

NASA Astrophysics Data System (ADS)

Doedel, Eusebius J.; Panayotaros, Panayotis; Lambruschini, Carlos L. Pando

2016-11-01

This special issue contains a concise account of significant research results presented at the international workshop on Advanced Computational and Experimental Techniques in Nonlinear Dynamics, which was held in Cusco, Peru in August 2015. The meeting gathered leading experts, as well as new researchers, who have contributed to different aspects of Nonlinear Dynamics. Particularly significant was the presence of many active scientists from Latin America. The topics covered in this special issue range from advanced numerical techniques to novel physical experiments, and reflect the present state of the art in several areas of Nonlinear Dynamics. It contains seven review articles, followed by twenty-one regular papers that are organized in five categories, namely (1) Nonlinear Evolution Equations and Applications, (2) Numerical Continuation in Self-sustained Oscillators, (3) Synchronization, Control and Data Analysis, (4) Hamiltonian Systems, and (5) Scaling Properties in Maps.

Analysis of helicopter flight dynamics through modeling and simulation of primary flight control actuation system

NASA Astrophysics Data System (ADS)

Nelson, Hunter Barton

A simplified second-order transfer function actuator model used in most flight dynamics applications cannot easily capture the effects of different actuator parameters. The present work integrates a nonlinear actuator model into a nonlinear state space rotorcraft model to determine the effect of actuator parameters on key flight dynamics. The completed actuator model was integrated with a swashplate kinematics where step responses were generated over a range of key hydraulic parameters. The actuator-swashplate system was then introduced into a nonlinear state space rotorcraft simulation where flight dynamics quantities such as bandwidth and phase delay analyzed. Frequency sweeps were simulated for unique actuator configurations using the coupled nonlinear actuator-rotorcraft system. The software package CIFER was used for system identification and compared directly to the linearized models. As the actuator became rate saturated, the effects on bandwidth and phase delay were apparent on the predicted handling qualities specifications.

Investigation of complexity dynamics in a DC glow discharge magnetized plasma using recurrence quantification analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitra, Vramori; Sarma, Bornali; Sarma, Arun

Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, L{sub max}, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time seriesmore » is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.« less

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal

PubMed Central

Mohapatra, Biswajit

2018-01-01

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis. PMID:29854361

A Review on the Nonlinear Dynamical System Analysis of Electrocardiogram Signal.

PubMed

Nayak, Suraj K; Bit, Arindam; Dey, Anilesh; Mohapatra, Biswajit; Pal, Kunal

2018-01-01

Electrocardiogram (ECG) signal analysis has received special attention of the researchers in the recent past because of its ability to divulge crucial information about the electrophysiology of the heart and the autonomic nervous system activity in a noninvasive manner. Analysis of the ECG signals has been explored using both linear and nonlinear methods. However, the nonlinear methods of ECG signal analysis are gaining popularity because of their robustness in feature extraction and classification. The current study presents a review of the nonlinear signal analysis methods, namely, reconstructed phase space analysis, Lyapunov exponents, correlation dimension, detrended fluctuation analysis (DFA), recurrence plot, Poincaré plot, approximate entropy, and sample entropy along with their recent applications in the ECG signal analysis.

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

PubMed Central

Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.

2016-01-01

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the third subtopic we extend our periodic orbit analysis to the dissociation of diatomic molecules driven by a bichromatic laser. In this problem, our results based on periodic orbit analysis again show good agreement with previous work, and hence promise more potential applications of this approach in molecular physics.

Limit Cycle Analysis Applied to the Oscillations of Decelerating Blunt-Body Entry Vehicles

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Queen, Eric M.

2008-01-01

Many blunt-body entry vehicles have nonlinear dynamic stability characteristics that produce self-limiting oscillations in flight. Several different test techniques can be used to extract dynamic aerodynamic coefficients to predict this oscillatory behavior for planetary entry mission design and analysis. Most of these test techniques impose boundary conditions that alter the oscillatory behavior from that seen in flight. Three sets of test conditions, representing three commonly used test techniques, are presented to highlight these effects. Analytical solutions to the constant-coefficient planar equations-of-motion for each case are developed to show how the same blunt body behaves differently depending on the imposed test conditions. The energy equation is applied to further illustrate the governing dynamics. Then, the mean value theorem is applied to the energy rate equation to find the effective damping for an example blunt body with nonlinear, self-limiting dynamic characteristics. This approach is used to predict constant-energy oscillatory behavior and the equilibrium oscillation amplitudes for the various test conditions. These predictions are verified with planar simulations. The analysis presented provides an overview of dynamic stability test techniques and illustrates the effects of dynamic stability, static aerodynamics and test conditions on observed dynamic motions. It is proposed that these effects may be leveraged to develop new test techniques and refine test matrices in future tests to better define the nonlinear functional forms of blunt body dynamic stability curves.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant

NASA Astrophysics Data System (ADS)

Feng, Jingjing; Zhang, Qichang; Wang, Wei; Hao, Shuying

2017-03-01

Tendril-bearing plants appear to have a spiraling shape when tendrils climb along a support during growth. The growth characteristics of a tendril-bearer can be simplified to a model of a thin elastic rod with a cylindrical constraint. In this paper, the connection between some typical configuration characteristics of tendrils and complex nonlinear dynamic behavior are qualitatively analyzed. The space configuration problem of tendrils can be explained through the study of the nonlinear dynamic behavior of the thin elastic rod system equation. In this study, the complex non-Z2 symmetric critical orbits in the system equation under critical parameters were presented. A new function transformation method that can effectively maintain the critical orbit properties was proposed, and a new nonlinear differential equations system containing complex nonlinear terms can been obtained to describe the cross section position and direction of a rod during climbing. Numerical simulation revealed that the new system can describe the configuration of a rod with reasonable accuracy. To adequately explain the growing regulation of the rod shape, the critical orbit and configuration of rod are connected in a direct way. The high precision analytical expressions of these complex non-Z2 symmetric critical orbits are obtained by introducing a suitable analytical method, and then these expressions are used to draw the corresponding three-dimensional configuration figures of an elastic thin rod. Combined with actual tendrils on a live plant, the space configuration of the winding knots of tendril is explained by the concept of heteroclinic orbit from the perspective of nonlinear dynamics, and correctness of the theoretical analysis was verified. This theoretical analysis method could also be effectively applied to other similar slender structures.

Nonlinear bivariate dependency of price-volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

NASA Astrophysics Data System (ADS)

He, Ling-Yun; Chen, Shu-Peng

2011-01-01

Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.

Swarming behaviors in multi-agent systems with nonlinear dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Wenwu, E-mail: wenwuyu@gmail.com; School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001; Chen, Guanrong

2013-12-15

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agentmore » is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.« less

Nonlinear Dynamics and Control of Flexible Structures

DTIC Science & Technology

1991-03-01

of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers and...methods for vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally... electrical and mechanical engineers and resulted in nine doctoral dissertations and two masters theses wholly or partially supported by this grant

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Shake, Rattle, and Roll: Nonlinear Dynamics in Mechanical Engineering

NASA Astrophysics Data System (ADS)

Shaw, Steven

1997-03-01

This presentation will focus on three mechanical engineering applications in which methods from nonlinear dynamics have been applied with success. Each topic will be briefly surveyed by outlining the development of a mathematical model, providing a description of the analysis tools employed, and showing the main results obtained. The applications are: vibration reduction in internal combustion engines, impact dynamics of mechanical components, and the dynamics of ship capsize. The first topic demonstrates a novel arrangement of dynamic absorbers that can be used for attenuating torsional vibrations in rotating machinery. The operation of this device takes advantage of a purely nonlinear system response that results from a period doubling bifurcation. This configuration is more effective than existing absorbers and it cannot be imagined by using naive extensions of linear vibration theory. The second topic deals with the dynamics of mechanical systems in which components make intermittent contact with each another. Such dynamics are often the source of undesirable noise and wear in machinery and can be extremely complicated. Results obtained from simple predictive models and some application areas will be presented for these impacting systems. The final topic deals with the gross motions of seagoing vessels and their stability against capsize. Existing safety regulations for ship stability are based on purely static measures, whereas capsize is an inherently nonlinear dynamic event. An overview will be given that considers some basic modeling issues, dynamic analysis techniques (based on the concept of chaotic phase-space transport), and the resulting predictive tools that have been developed for this class of problems.

A nonlinear dynamical system for combustion instability in a pulse model combustor

NASA Astrophysics Data System (ADS)

Takagi, Kazushi; Gotoda, Hiroshi

2016-11-01

We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.

Nonlinear dynamics of motor learning.

PubMed

Mayer-Kress, Gottfried; Newell, Karl M; Liu, Yeou-Teh

2009-01-01

In this paper we review recent work from our studies of a nonlinear dynamics of motor learning that is grounded in the construct of an evolving attractor landscape. With the assumption that learning is goal-directed, we can quantify the observed performance as a score or measure of the distance to the learning goal. The structure of the dynamics of how the goal is approached has been traditionally studied through an analysis of learning curves. Recent years have seen a gradual paradigm shift from a 'universal power law of practice' to an analysis of performance dynamics that reveals multiple processes that include adaption and learning as well as changes in performance due to factors such as fatigue. Evidence has also been found for nonlinear phenomena such as bifurcations, hysteresis and even a form of self-organized criticality. Finally, we present a quantitative measure for the dual concepts of skill and difficulty that allows us to unfold a learning process in order to study universal properties of learning transitions.

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

NASA Astrophysics Data System (ADS)

Anderies, J. M.; Carpenter, S. R.; Steffen, Will; Rockström, Johan

2013-12-01

We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries.

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

Computational analysis of nonlinearities within dynamics of cable-based driving systems

NASA Astrophysics Data System (ADS)

Anghelache, G. D.; Nastac, S.

2017-08-01

This paper deals with computational nonlinear dynamics of mechanical systems containing some flexural parts within the actuating scheme, and, especially, the situations of the cable-based driving systems were treated. It was supposed both functional nonlinearities and the real characteristic of the power supply, in order to obtain a realistically computer simulation model being able to provide very feasible results regarding the system dynamics. It was taken into account the transitory and stable regimes during a regular exploitation cycle. The authors present a particular case of a lift system, supposed to be representatively for the objective of this study. The simulations were made based on the values of the essential parameters acquired from the experimental tests and/or the regular practice in the field. The results analysis and the final discussions reveal the correlated dynamic aspects within the mechanical parts, the driving system, and the power supply, whole of these supplying potential sources of particular resonances, within some transitory phases of the working cycle, and which can affect structural and functional dynamics. In addition, it was underlines the influences of computational hypotheses on the both quantitative and qualitative behaviour of the system. Obviously, the most significant consequence of this theoretical and computational research consist by developing an unitary and feasible model, useful to dignify the nonlinear dynamic effects into the systems with cable-based driving scheme, and hereby to help an optimization of the exploitation regime including a dynamics control measures.

Linear and nonlinear dynamic analysis by boundary element method. Ph.D. Thesis, 1986 Final Report

NASA Technical Reports Server (NTRS)

Ahmad, Shahid

1991-01-01

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations.

PubMed

Abney, Drew H; Warlaumont, Anne S; Haussman, Anna; Ross, Jessica M; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations

PubMed Central

Abney, Drew H.; Warlaumont, Anne S.; Haussman, Anna; Ross, Jessica M.; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior. PMID:25161629

Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

NASA Technical Reports Server (NTRS)

Bacon, Barton J.; Ostroff, Aaron J.

2000-01-01

This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications

NASA Technical Reports Server (NTRS)

Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)

2002-01-01

The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.

Transient analysis techniques in performing impact and crash dynamic studies

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.

1989-01-01

Because of the emphasis being placed on crashworthiness as a design requirement, increasing demands are being made by various organizations to analyze a wide range of complex structures that must perform safely when subjected to severe impact loads, such as those generated in a crash event. The ultimate goal of crashworthiness design and analysis is to produce vehicles with the ability to reduce the dynamic forces experienced by the occupants to specified levels, while maintaining a survivable envelope around them during a specified crash event. DYCAST is a nonlinear structural dynamic finite element computer code that started from the plans systems of a finite element program for static nonlinear structural analysis. The essential features of DYCAST are outlined.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study.

PubMed

Li, Nianqiang; Susanto, H; Cemlyn, B R; Henning, I D; Adams, M J

2018-02-19

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

Modeling of dielectric elastomer as electromechanical resonator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Bo, E-mail: liboxjtu@mail.xjtu.edu.cn; Liu, Lei; Chen, Hualing

Dielectric elastomers (DEs) feature nonlinear dynamics resulting from an electromechanical coupling. Under alternating voltage, the DE resonates with tunable performances. We present an analysis of the nonlinear dynamics of a DE as electromechanical resonator (DEER) configured as a pure shear actuator. A theoretical model is developed to characterize the complex performance under different boundary conditions. Physical mechanisms are presented and discussed. Chaotic behavior is also predicted, illustrating instabilities in the dynamics. The results provide a guide to the design and application of DEER in haptic devices.

Development of a simulation model for dynamic derailment analysis of high-speed trains

NASA Astrophysics Data System (ADS)

Ling, Liang; Xiao, Xin-Biao; Jin, Xue-Song

2014-12-01

The running safety of high-speed trains has become a major concern of the current railway research with the rapid development of high-speed railways around the world. The basic safety requirement is to prevent the derailment. The root causes of the dynamic derailment of high-speed trains operating in severe environments are not easy to identify using the field tests or laboratory experiments. Numerical simulation using an advanced train-track interaction model is a highly efficient and low-cost approach to investigate the dynamic derailment behavior and mechanism of high-speed trains. This paper presents a three-dimensional dynamic model of a high-speed train coupled with a ballast track for dynamic derailment analysis. The model considers a train composed of multiple vehicles and the nonlinear inter-vehicle connections. The ballast track model consists of rails, fastenings, sleepers, ballasts, and roadbed, which are modeled by Euler beams, nonlinear spring-damper elements, equivalent ballast bodies, and continuous viscoelastic elements, in which the modal superposition method was used to reduce the order of the partial differential equations of Euler beams. The commonly used derailment safety assessment criteria around the world are embedded in the simulation model. The train-track model was then used to investigate the dynamic derailment responses of a high-speed train passing over a buckled track, in which the derailment mechanism and train running posture during the dynamic derailment process were analyzed in detail. The effects of train and track modelling on dynamic derailment analysis were also discussed. The numerical results indicate that the train and track modelling options have a significant effect on the dynamic derailment analysis. The inter-vehicle impacts and the track flexibility and nonlinearity should be considered in the dynamic derailment simulations.

Nonlinear dynamics analysis of a low-temperature-differential kinematic Stirling heat engine

NASA Astrophysics Data System (ADS)

Izumida, Yuki

2018-03-01

The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.

Nonlinear analysis of dynamic signature

NASA Astrophysics Data System (ADS)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique.

PubMed

Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan

2009-01-01

The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region.

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Stratified rotating Boussinesq equations in geophysical fluid dynamics: Dynamic bifurcation and periodic solutions

NASA Astrophysics Data System (ADS)

Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong

2007-06-01

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than 1, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than 1, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Sciences Vol. 53 (World Scientific, Singapore, 2005)].

Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull

NASA Astrophysics Data System (ADS)

Xiang, Changle; Liu, Feng; Liu, Hui; Han, Lijin; Zhang, Xun

2016-06-01

Unbalanced magnetic pull (UMP) plays a key role in nonlinear dynamic behaviors of permanent magnet synchronous motors (PMSM) in electric vehicles. Based on Jeffcott rotor model, the stiffness characteristics of the rotor system of the PMSM are analyzed and the nonlinear dynamic behaviors influenced by UMP are investigated. In free vibration study, eigenvalue-based stability analysis for multiple equilibrium points is performed which offers an insight in system stiffness. Amplitude modulation effects are discovered of which the mechanism is explained and the period of modulating signal is carried out by phase analysis and averaging method. The analysis indicates that the effects are caused by the interaction of the initial phases of forward and backward whirling motions. In forced vibration study, considering dynamic eccentricity, frequency characteristics revealing softening type are obtained by harmonic balance method, and the stability of periodic solution is investigated by Routh-Hurwitz criterion. The frequency characteristics analysis indicates that the response amplitude is limited in the range between the amplitudes of the two kinds of equilibrium points. In the vicinity of the continuum of equilibrium points, the system hardly provides resistance to bending, and hence external disturbances easily cause loss of stability. It is useful for the design of the PMSM with high stability and low vibration and acoustic noise.

Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

NASA Astrophysics Data System (ADS)

Al-Hindawi, Mohammed M.; Abusorrah, Abdullah; Al-Turki, Yusuf; Giaouris, Damian; Mandal, Kuntal; Banerjee, Soumitro

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v-i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v-i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v-i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v-i characteristics of the PV panel. The theoretical results are validated experimentally.

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Preliminary assessment of the robustness of dynamic inversion based flight control laws

NASA Technical Reports Server (NTRS)

Snell, S. A.

1992-01-01

Dynamic-inversion-based flight control laws present an attractive alternative to conventional gain-scheduled designs for high angle-of-attack maneuvering, where nonlinearities dominate the dynamics. Dynamic inversion is easily applied to the aircraft dynamics requiring a knowledge of the nonlinear equations of motion alone, rather than an extensive set of linearizations. However, the robustness properties of the dynamic inversion are questionable especially when considering the uncertainties involved with the aerodynamic database during post-stall flight. This paper presents a simple analysis and some preliminary results of simulations with a perturbed database. It is shown that incorporating integrators into the control loops helps to improve the performance in the presence of these perturbations.

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region

NASA Astrophysics Data System (ADS)

Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib

2018-03-01

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.

Nonlinear dynamic phase contrast microscopy for microfluidic and microbiological applications

NASA Astrophysics Data System (ADS)

Denz, C.; Holtmann, F.; Woerdemann, M.; Oevermann, M.

2008-08-01

In live sciences, the observation and analysis of moving living cells, molecular motors or motion of micro- and nano-objects is a current field of research. At the same time, microfluidic innovations are needed for biological and medical applications on a micro- and nano-scale. Conventional microscopy techniques are reaching considerable limits with respect to these issues. A promising approach for this challenge is nonlinear dynamic phase contrast microscopy. It is an alternative full field approach that allows to detect motion as well as phase changes of living unstained micro-objects in real-time, thereby being marker free, without contact and non destructive, i.e. fully biocompatible. The generality of this system allows it to be combined with several other microscope techniques such as conventional bright field or fluorescence microscopy. In this article we will present the dynamic phase contrast technique and its applications in analysis of micro organismic dynamics, micro flow velocimetry and micro-mixing analysis.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

The symbolic computation and automatic analysis of trajectories

NASA Technical Reports Server (NTRS)

Grossman, Robert

1991-01-01

Research was generally done on computation of trajectories of dynamical systems, especially control systems. Algorithms were further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear control systems. An initial design was completed of the system architecture for software to analyze nonlinear control systems using data base computing.

Assessing Spontaneous Combustion Instability with Recurrence Quantification Analysis

NASA Technical Reports Server (NTRS)

Eberhart, Chad J.; Casiano, Matthew J.

2016-01-01

Spontaneous instabilities can pose a significant challenge to verification of combustion stability, and characterizing its onset is an important avenue of improvement for stability assessments of liquid propellant rocket engines. Recurrence Quantification Analysis (RQA) is used here to explore nonlinear combustion dynamics that might give insight into instability. Multiple types of patterns representative of different dynamical states are identified within fluctuating chamber pressure data, and markers for impending instability are found. A class of metrics which describe these patterns is also calculated. RQA metrics are compared with and interpreted against another metric from nonlinear time series analysis, the Hurst exponent, to help better distinguish between stable and unstable operation.

Nonlinear optimal control for the synchronization of chaotic and hyperchaotic finance systems

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Ademi, S.; Ghosh, T.

2017-11-01

It is possible to make specific finance systems get synchronized to other finance systems exhibiting chaotic and hyperchaotic dynamics, by applying nonlinear optimal (H-infinity) control. This signifies that chaotic behavior can be generated in finance systems by exerting a suitable control input. Actually, a lead financial system is considered which exhibits inherently chaotic dynamics. Moreover, a follower finance system is introduced having parameters in its model that inherently prohibit the appearance of chaotic dynamics. Through the application of a suitable nonlinear optimal (H-infinity) control input it is proven that the follower finance system can replicate the chaotic dynamics of the lead finance system. By applying Lyapunov analysis it is proven that asymptotically the follower finance system gets synchronized with the lead system and that the tracking error between the state variables of the two systems vanishes.

Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

NASA Astrophysics Data System (ADS)

Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David

2018-05-01

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

Nonlinear field equations for aligning self-propelled rods.

PubMed

Peshkov, Anton; Aranson, Igor S; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

2012-12-28

We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

Dynamic performance and mechanical model analysis of a shear thickening fluid damper

NASA Astrophysics Data System (ADS)

Zhao, Qian; He, Yonghui; Yao, Hongliang; Wen, Bangchun

2018-07-01

This paper presents an experimental study of the dynamic performance of a self-developed shear thickening fluid (STF) damper and its mechanical model was proposed by nonlinear fitting. First, STF samples with different mass fraction and dispersion medium were fabricated by nano fumed silica and polyethylene glycol, and its rheological properties were investigated by a rheometer. Second, a smart STF damper was developed and manufactured. Its dynamic properties were experimentally investigated by establishing a vibration test bench, and results indicated that the STF damper can output variable damping force by controlling the loading frequency, loading amplitude and fluid gap. Third, the Bouc–Wen model was proposed to address the dynamic properties of STF damper, and mechanical model analysis was carried out by comparing several fitting functions. It verified that the Bouc–Wen hysteresis model can be better used to describe the nonlinear stiffness, nonlinear damping and rate-dependence characteristics of the STF damper. All these investigations can offer an effective guidance for further theoretical and application study of the smart STF damper in energy dissipation fields.

On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients

NASA Astrophysics Data System (ADS)

Raza, Nauman; Murtaza, Isma Ghulam; Sial, Sultan; Younis, Muhammad

2018-07-01

The article studies the dynamics of solitons in electrical microtubule ? model, which describes the propagation of waves in nonlinear dynamical system. Microtubules are not only a passive support of a cell but also they have highly dynamic structures involved in cell motility, intracellular transport and signaling. The underlying model has been considered with constant and variable coefficients of time function. The solitary wave ansatz has been applied successfully to extract these solitons. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow

NASA Astrophysics Data System (ADS)

Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.

2014-12-01

Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Does preprocessing change nonlinear measures of heart rate variability?

PubMed

Gomes, Murilo E D; Guimarães, Homero N; Ribeiro, Antônio L P; Aguirre, Luis A

2002-11-01

This work investigated if methods used to produce a uniformly sampled heart rate variability (HRV) time series significantly change the deterministic signature underlying the dynamics of such signals and some nonlinear measures of HRV. Two methods of preprocessing were used: the convolution of inverse interval function values with a rectangular window and the cubic polynomial interpolation. The HRV time series were obtained from 33 Wistar rats submitted to autonomic blockade protocols and from 17 healthy adults. The analysis of determinism was carried out by the method of surrogate data sets and nonlinear autoregressive moving average modelling and prediction. The scaling exponents alpha, alpha(1) and alpha(2) derived from the detrended fluctuation analysis were calculated from raw HRV time series and respective preprocessed signals. It was shown that the technique of cubic interpolation of HRV time series did not significantly change any nonlinear characteristic studied in this work, while the method of convolution only affected the alpha(1) index. The results suggested that preprocessed time series may be used to study HRV in the field of nonlinear dynamics.

Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators

NASA Astrophysics Data System (ADS)

Naseradinmousavi, Peiman; Nataraj, C.

2012-11-01

Chilled water systems used in the industry and on board ships are critical for safe and reliable operation. It is hence important to understand the fundamental physics of these systems. This paper focuses in particular on a critical part of the automation system, namely, actuators and valves that are used in so-called "smart valve" systems. The system is strongly nonlinear, and necessitates a nonlinear dynamic analysis to be able to predict all critical phenomena that affect effective operation and efficient design. The derived mathematical model includes electromagnetics, fluid mechanics, and mechanical dynamics. Nondimensionalization has been carried out in order to reduce the large number of parameters to a few critical independent sets to help carry out a broad parametric analysis. The system stability analysis is then carried out with the aid of the tools from nonlinear dynamic analysis. This reveals that the system is unstable in a certain region of the parameter space. The system is also shown to exhibit crisis and transient chaotic responses; this is characterized using Lyapunov exponents and power spectra. Knowledge and avoidance of these dangerous regimes is necessary for successful and safe operation.

Market Orientation within University Schools of Business: Can a Dynamical Systems Viewpoint Applied to a Non-Temporal Data Set Yield Valuable Insights for University Managers?

ERIC Educational Resources Information Center

Cox, John C.; Webster, Robert L.; Hammond, Kevin L.

2009-01-01

This study investigates the use of using complexity theory--the study of nonlinear dynamical systems of which chaos and catastrophe theory are subsets--in the analysis of a non temporal data set to derive valuable insights into the functioning of university schools of business. The approach is unusual in that studies of nonlinearity in complex…

Nonlinear systems dynamics in cardiovascular physiology: The heart rate delay map and lower body negative pressure

NASA Technical Reports Server (NTRS)

Hooker, John C.

1990-01-01

A preliminary study of the applicability of nonlinear dynamic systems analysis techniques to low body negative pressure (LBNP) studies. In particular, the applicability of the heart rate delay map is investigated. It is suggested that the heart rate delay map has potential as a supplemental tool in the assessment of subject performance in LBNP tests and possibly in the determination of susceptibility to cardiovascular deconditioning with spaceflight.

Numerical Analysis of the Dynamics of Nonlinear Solids and Structures

DTIC Science & Technology

2008-08-01

to arrive to a new numerical scheme that exhibits rigorously the dissipative character of the so-called canonical free en - ergy characteristic of...UCLA), February 14 2006. 5. "Numerical Integration of the Nonlinear Dynamics of Elastoplastic Solids," keynote lecture , 3rd European Conference on...Computational Mechanics (ECCM 3), Lisbon, Portugal, June 5-9 2006. 6. "Energy-Momentum Schemes for Finite Strain Plasticity," keynote lecture , 7th

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

PubMed Central

Tajima, Satohiro; Yanagawa, Toru; Fujii, Naotaka; Toyoizumi, Taro

2015-01-01

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness. PMID:26584045

Development of a rotorcraft. Propulsion dynamics interface analysis, volume 2

NASA Technical Reports Server (NTRS)

Hull, R.

1982-01-01

A study was conducted to establish a coupled rotor/propulsion analysis that would be applicable to a wide range of rotorcraft systems. The effort included the following tasks: (1) development of a model structure suitable for simulating a wide range of rotorcraft configurations; (2) defined a methodology for parameterizing the model structure to represent a particular rotorcraft; (3) constructing a nonlinear coupled rotor/propulsion model as a test case to use in analyzing coupled system dynamics; and (4) an attempt to develop a mostly linear coupled model derived from the complete nonlinear simulations. Documentation of the computer models developed is presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodriguez, Mario E.

An area in earthquake risk reduction that needs an urgent examination is the selection of earthquake records for nonlinear dynamic analysis of structures. An often-mentioned shortcoming from results of nonlinear dynamic analyses of structures is that these results are limited to the type of records that these analyses use as input data. This paper proposes a procedure for selecting earthquake records for nonlinear dynamic analysis of structures. This procedure uses a seismic damage index evaluated using the hysteretic energy dissipated by a Single Degree of Freedom System (SDOF) representing a multi-degree-of freedom structure responding to an earthquake record, and themore » plastic work capacity of the system at collapse. The type of structural system is considered using simple parameters. The proposed method is based on the evaluation of the damage index for a suite of earthquake records and a selected type of structural system. A set of 10 strong ground motion records is analyzed to show an application of the proposed procedure for selecting earthquake records for structural design.« less

Analysis of Instantaneous Linear, Nonlinear and Complex Cardiovascular Dynamics from Videophotoplethysmography.

PubMed

Valenza, Gaetano; Iozzia, Luca; Cerina, Luca; Mainardi, Luca; Barbieri, Riccardo

2018-05-01

There is a fast growing interest in the use of non-contact devices for health and performance assessment in humans. In particular, the use of non-contact videophotoplethysmography (vPPG) has been recently demonstrated as a feasible way to extract cardiovascular information. Nevertheless, proper validation of vPPG-derived heartbeat dynamics is still missing. We aim to an in-depth validation of time-varying, linear and nonlinear/complex dynamics of the pulse rate variability extracted from vPPG. We apply inhomogeneous pointprocess nonlinear models to assess instantaneous measures defined in the time, frequency, and bispectral domains as estimated through vPPG and standard ECG. Instantaneous complexity measures, such as the instantaneous Lyapunov exponents and the recently defined inhomogeneous point-process approximate and sample entropy, were estimated as well. Video recordings were processed using our recently proposed method based on zerophase principal component analysis. Experimental data were gathered from 60 young healthy subjects (age: 24±3 years) undergoing postural changes (rest-to-stand maneuver). Group averaged results show that there is an overall agreement between linear and nonlinear/complexity indices computed from ECG and vPPG during resting state conditions. However, important differences are found, particularly in the bispectral and complexity domains, in recordings where the subjects has been instructed to stand up. Although significant differences exist between cardiovascular estimates from vPPG and ECG, it is very promising that instantaneous sympathovagal changes, as well as time-varying complex dynamics, were correctly identified, especially during resting state. In addition to a further improvement of the video signal quality, more research is advocated towards a more precise estimation of cardiovascular dynamics by a comprehensive nonlinear/complex paradigm specifically tailored to the non-contact quantification. Schattauer GmbH.

Visualization of system dynamics using phasegrams

PubMed Central

Herbst, Christian T.; Herzel, Hanspeter; Švec, Jan G.; Wyman, Megan T.; Fitch, W. Tecumseh

2013-01-01

A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine. PMID:23697715

Nonlinear amplitude dynamics in flagellar beating

NASA Astrophysics Data System (ADS)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating.

PubMed

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating

PubMed Central

Casademunt, Jaume

2017-01-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. PMID:28405357

NASA Workshop on Computational Structural Mechanics 1987, part 3

NASA Technical Reports Server (NTRS)

Sykes, Nancy P. (Editor)

1989-01-01

Computational Structural Mechanics (CSM) topics are explored. Algorithms and software for nonlinear structural dynamics, concurrent algorithms for transient finite element analysis, computational methods and software systems for dynamics and control of large space structures, and the use of multi-grid for structural analysis are discussed.

Nonlinear aspects of the EEG during sleep in children

NASA Astrophysics Data System (ADS)

Berryman, Matthew J.; Coussens, Scott W.; Pamula, Yvonne; Kennedy, Declan; Lushington, Kurt; Shalizi, Cosma; Allison, Andrew; Martin, A. James; Saint, David; Abbott, Derek

2005-05-01

Electroencephalograph (EEG) analysis enables the dynamic behavior of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal children and children with mild OSAS are evaluated for nonlinear brain behaviour. We found that there were differences in the nonlinearity of the brain behaviour between different sleep stages, and between the two groups of children.

Nonlinear dynamic analysis of voices before and after surgical excision of vocal polyps

NASA Astrophysics Data System (ADS)

Zhang, Yu; McGilligan, Clancy; Zhou, Liang; Vig, Mark; Jiang, Jack J.

2004-05-01

Phase space reconstruction, correlation dimension, and second-order entropy, methods from nonlinear dynamics, are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps. Two conventional acoustic perturbation parameters, jitter and shimmer, are also employed to analyze voices before and after surgery. Presurgical and postsurgical analyses of jitter, shimmer, correlation dimension, and second-order entropy are statistically compared. Correlation dimension and second-order entropy show a statistically significant decrease after surgery, indicating reduced complexity and higher predictability of postsurgical voice dynamics. There is not a significant postsurgical difference in shimmer, although jitter shows a significant postsurgical decrease. The results suggest that jitter and shimmer should be applied to analyze disordered voices with caution; however, nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

NASA Astrophysics Data System (ADS)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

Flexible traffic control of the synfire-mode transmission by inhibitory modulation: Nonlinear noise reduction

NASA Astrophysics Data System (ADS)

Shinozaki, Takashi; Okada, Masato; Reyes, Alex D.; Câteau, Hideyuki

2010-01-01

Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propagating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the degree of synchrony of population firing of neurons as well as controlling the size of the population firing bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.

Research in structures, structural dynamics and materials, 1989

NASA Technical Reports Server (NTRS)

Hunter, William F. (Compiler); Noor, Ahmed K. (Compiler)

1989-01-01

Topics addressed include: composite plates; buckling predictions; missile launch tube modeling; structural/control systems design; optimization of nonlinear R/C frames; error analysis for semi-analytic displacement; crack acoustic emission; and structural dynamics.

Evaluation and Analysis of F-16XL Wind Tunnel Data From Static and Dynamic Tests

NASA Technical Reports Server (NTRS)

Kim, Sungwan; Murphy, Patrick C.; Klein, Vladislav

2004-01-01

A series of wind tunnel tests were conducted in the NASA Langley Research Center as part of an ongoing effort to develop and test mathematical models for aircraft rigid-body aerodynamics in nonlinear unsteady flight regimes. Analysis of measurement accuracy, especially for nonlinear dynamic systems that may exhibit complicated behaviors, is an essential component of this ongoing effort. In this report, tools for harmonic analysis of dynamic data and assessing measurement accuracy are presented. A linear aerodynamic model is assumed that is appropriate for conventional forced-oscillation experiments, although more general models can be used with these tools. Application of the tools to experimental data is demonstrated and results indicate the levels of uncertainty in output measurements that can arise from experimental setup, calibration procedures, mechanical limitations, and input errors.

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

NASA Astrophysics Data System (ADS)

Kanjilal, Oindrila; Manohar, C. S.

2017-07-01

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

Detecting chaos in particle accelerators through the frequency map analysis method.

PubMed

Papaphilippou, Yannis

2014-06-01

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

Development of Nonlinear Flight Mechanical Model of High Aspect Ratio Light Utility Aircraft

NASA Astrophysics Data System (ADS)

Bahri, S.; Sasongko, R. A.

2018-04-01

The implementation of Flight Control Law (FCL) for Aircraft Electronic Flight Control System (EFCS) aims to reduce pilot workload, while can also enhance the control performance during missions that require long endurance flight and high accuracy maneuver. In the development of FCL, a quantitative representation of the aircraft dynamics is needed for describing the aircraft dynamics characteristic and for becoming the basis of the FCL design. Hence, a 6 Degree of Freedom nonlinear model of a light utility aircraft dynamics, also called the nonlinear Flight Mechanical Model (FMM), is constructed. This paper shows the construction of FMM from mathematical formulation, the architecture design of FMM, the trimming process and simulations. The verification of FMM is done by analysis of aircraft behaviour in selected trimmed conditions.

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.

PubMed

Venkataraman, Vinay; Turaga, Pavan

2016-12-01

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

Dynamical principles in neuroscience

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.; Abarbanel, Henry D. I.

2006-10-01

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?

Dynamical principles in neuroscience

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only amore » few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?.« less

Experimental evaluation of four ground-motion scaling methods for dynamic response-history analysis of nonlinear structures

USGS Publications Warehouse

O'Donnell, Andrew P.; Kurama, Yahya C.; Kalkan, Erol; Taflanidis, Alexandros A.

2017-01-01

This paper experimentally evaluates four methods to scale earthquake ground-motions within an ensemble of records to minimize the statistical dispersion and maximize the accuracy in the dynamic peak roof drift demand and peak inter-story drift demand estimates from response-history analyses of nonlinear building structures. The scaling methods that are investigated are based on: (1) ASCE/SEI 7–10 guidelines; (2) spectral acceleration at the fundamental (first mode) period of the structure, Sa(T1); (3) maximum incremental velocity, MIV; and (4) modal pushover analysis. A total of 720 shake-table tests of four small-scale nonlinear building frame specimens with different static and dynamic characteristics are conducted. The peak displacement demands from full suites of 36 near-fault ground-motion records as well as from smaller “unbiased” and “biased” design subsets (bins) of ground-motions are included. Out of the four scaling methods, ground-motions scaled to the median MIV of the ensemble resulted in the smallest dispersion in the peak roof and inter-story drift demands. Scaling based on MIValso provided the most accurate median demands as compared with the “benchmark” demands for structures with greater nonlinearity; however, this accuracy was reduced for structures exhibiting reduced nonlinearity. The modal pushover-based scaling (MPS) procedure was the only method to conservatively overestimate the median drift demands.

Nonlinear dynamics in cardiac conduction

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Detecting dynamic causal inference in nonlinear two-phase fracture flow

NASA Astrophysics Data System (ADS)

Faybishenko, Boris

2017-08-01

Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time, but can then become spontaneously decoupled or non-correlated. In his 2002 paper (Faybishenko, 2002), the author performed a nonlinear dynamical and chaotic analysis of time-series data obtained from the fracture flow experiment conducted by Persoff and Pruess (1995), and, based on the visual examination of time series data, hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. In the current paper, the author explores an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author infers that his hypothesis is correct, and presents a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes, for example, infiltration and pumping tests in heterogeneous subsurface media, and climatic processes, for example, to find correlations between various meteorological parameters, such as temperature, solar radiation, barometric pressure, etc.

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

PubMed

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle-slab track systems

NASA Astrophysics Data System (ADS)

Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.

2015-01-01

A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Stochastic modular analysis for gene circuits: interplay among retroactivity, nonlinearity, and stochasticity.

PubMed

Kim, Kyung Hyuk; Sauro, Herbert M

2015-01-01

This chapter introduces a computational analysis method for analyzing gene circuit dynamics in terms of modules while taking into account stochasticity, system nonlinearity, and retroactivity. (1) ANALOG ELECTRICAL CIRCUIT REPRESENTATION FOR GENE CIRCUITS: A connection between two gene circuit components is often mediated by a transcription factor (TF) and the connection signal is described by the TF concentration. The TF is sequestered to its specific binding site (promoter region) and regulates downstream transcription. This sequestration has been known to affect the dynamics of the TF by increasing its response time. The downstream effect-retroactivity-has been shown to be explicitly described in an electrical circuit representation, as an input capacitance increase. We provide a brief review on this topic. (2) MODULAR DESCRIPTION OF NOISE PROPAGATION: Gene circuit signals are noisy due to the random nature of biological reactions. The noisy fluctuations in TF concentrations affect downstream regulation. Thus, noise can propagate throughout the connected system components. This can cause different circuit components to behave in a statistically dependent manner, hampering a modular analysis. Here, we show that the modular analysis is still possible at the linear noise approximation level. (3) NOISE EFFECT ON MODULE INPUT-OUTPUT RESPONSE: We investigate how to deal with a module input-output response and its noise dependency. Noise-induced phenotypes are described as an interplay between system nonlinearity and signal noise. Lastly, we provide the comprehensive approach incorporating the above three analysis methods, which we call "stochastic modular analysis." This method can provide an analysis framework for gene circuit dynamics when the nontrivial effects of retroactivity, stochasticity, and nonlinearity need to be taken into account.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

PubMed

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Finite element for rotor/stator interactive forces in general engine dynamic simulation. Part 1: Development of bearing damper element

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1980-01-01

A general purpose squeeze-film damper interactive force element was developed, coded into a software package (module) and debugged. This software package was applied to nonliner dynamic analyses of some simple rotor systems. Results for pressure distributions show that the long bearing (end sealed) is a stronger bearing as compared to the short bearing as expected. Results of the nonlinear dynamic analysis, using a four degree of freedom simulation model, showed that the orbit of the rotating shaft increases nonlinearity to fill the bearing clearance as the unbalanced weight increases.

Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1975-01-01

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Solar Dynamic Power System Stability Analysis and Control

NASA Technical Reports Server (NTRS)

Momoh, James A.; Wang, Yanchun

1996-01-01

The objective of this research is to conduct dynamic analysis, control design, and control performance test of solar power system. Solar power system consists of generation system and distribution network system. A bench mark system is used in this research, which includes a generator with excitation system and governor, an ac/dc converter, six DDCU's and forty-eight loads. A detailed model is used for modeling generator. Excitation system is represented by a third order model. DDCU is represented by a seventh order system. The load is modeled by the combination of constant power and constant impedance. Eigen-analysis and eigen-sensitivity analysis are used for system dynamic analysis. The effects of excitation system, governor, ac/dc converter control, and the type of load on system stability are discussed. In order to improve system transient stability, nonlinear ac/dc converter control is introduced. The direct linearization method is used for control design. The dynamic analysis results show that these controls affect system stability in different ways. The parameter coordination of controllers are recommended based on the dynamic analysis. It is concluded from the present studies that system stability is improved by the coordination of control parameters and the nonlinear ac/dc converter control stabilize system oscillation caused by the load change and system fault efficiently.

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

PubMed

Lu, Tao

2016-01-01

The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

An extended car-following model to describe connected traffic dynamics under cyberattacks

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Yu, Guizhen; Wu, Xinkai; Qin, Hongmao; Wang, Yunpeng

2018-04-01

In this paper, the impacts of the potential cyberattacks on vehicles are modeled through an extended car-following model. To better understand the mechanism of traffic disturbance under cyberattacks, the linear and nonlinear stability analysis are conducted respectively. Particularly, linear stability analysis is performed to obtain different neutral stability conditions with various parameters; and nonlinear stability analysis is carried out by using reductive perturbation method to derive the soliton solution of the modified Korteweg de Vries equation (mKdV) near the critical point, which is used to draw coexisting stability lines. Furthermore, by applying linear and nonlinear stability analysis, traffic flow state can be divided into three states, i.e., stable, metastable and unstable states which are useful to describe shockwave dynamics and driving behaviors under cyberattacks. The theoretical results show that the proposed car-following model is capable of successfully describing the car-following behavior of connected vehicles with cyberattacks. Finally, numerical simulation using real values has confirmed the validity of theoretical analysis. The results further demonstrate our model can be used to help avoid collisions and relieve traffic congestion with cybersecurity threats.

A 1-D model of the nonlinear dynamics of the human lumbar intervertebral disc

NASA Astrophysics Data System (ADS)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J.

2017-01-01

Lumped parameter models of the spine have been developed to investigate its response to whole body vibration. However, these models assume the behaviour of the intervertebral disc to be linear-elastic. Recently, the authors have reported on the nonlinear dynamic behaviour of the human lumbar intervertebral disc. This response was shown to be dependent on the applied preload and amplitude of the stimuli. However, the mechanical properties of a standard linear elastic model are not dependent on the current deformation state of the system. The aim of this study was therefore to develop a model that is able to describe the axial, nonlinear quasi-static response and to predict the nonlinear dynamic characteristics of the disc. The ability to adapt the model to an individual disc's response was a specific focus of the study, with model validation performed against prior experimental data. The influence of the numerical parameters used in the simulations was investigated. The developed model exhibited an axial quasi-static and dynamic response, which agreed well with the corresponding experiments. However, the model needs further improvement to capture additional peculiar characteristics of the system dynamics, such as the change of mean point of oscillation exhibited by the specimens when oscillating in the region of nonlinear resonance. Reference time steps were identified for specific integration scheme. The study has demonstrated that taking into account the nonlinear-elastic behaviour typical of the intervertebral disc results in a predicted system oscillation much closer to the physiological response than that provided by linear-elastic models. For dynamic analysis, the use of standard linear-elastic models should be avoided, or restricted to study cases where the amplitude of the stimuli is relatively small.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Chaos in plasma simulation and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, C.; Newman, D.E.; Sprott, J.C.

1993-09-01

We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFPmore » dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

NASA Astrophysics Data System (ADS)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

Engine dynamic analysis with general nonlinear finite element codes

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1991-01-01

A general engine dynamic analysis as a standard design study computational tool is described for the prediction and understanding of complex engine dynamic behavior. Improved definition of engine dynamic response provides valuable information and insights leading to reduced maintenance and overhaul costs on existing engine configurations. Application of advanced engine dynamic simulation methods provides a considerable cost reduction in the development of new engine designs by eliminating some of the trial and error process done with engine hardware development.

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1978-01-01

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

Assessment of the Structural Conditions of the San Clemente a Vomano Abbey

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benedettini, Francesco; Alaggio, Rocco; Fusco, Felice

2008-07-08

The simultaneous use of a Finite Element (FE) accurate modeling, dynamical tests, model updating and nonlinear analysis are used to describe the integrated approach used by the authors to assess the structural conditions and the seismic vulnerability of an historical masonry structure: the Abbey Church of San Clemente al Vomano, situated in the Notaresco territory (TE, Italy) commissioned by Ermengarda, daughter of the Emperor Ludovico II, and built at the end of IX century together with a monastery to host a monastic community. Dynamical tests 'in operational conditions' and modal identification have been used to perform the FE model validation.more » Both a simple and direct method as the kinematic analysis applied on meaningful sub-structures and a nonlinear 3D dynamic analysis conducted by using the FE model have been used to forecast the seismic performance of the Church.« less

Three dimensional modeling and dynamic analysis of four-wheel-steering vehicles

NASA Astrophysics Data System (ADS)

Hu, Haiyan; Han, Qiang

2003-02-01

The paper presents a nonlinear dynamic model of 9 degrees of freedom for four-wheel-steering vehicles. Compared with those in previous studies, this model includes the pitch and roll of the vehicle body, the motion of 4 wheels in the accelerating or braking process, the nonlinear coupling of vehicle body and unsprung part, as well as the air drag and wind effect. As a result, the model can be used for the analysis of various maneuvers of the four-wheel-steering vehicles. In addition, the previous models can be considered as a special case of this model. The paper gives some case studies for the dynamic performance of a four-wheel-steering vehicle under step input and saw-tooth input of steering angle applied on the front wheels, respectively.

The contribution of reorientational nonlinearity of CS2 liquid in supercontinuum generation

NASA Astrophysics Data System (ADS)

Porsezian, K.; Raja, R. Vasantha Jayakantha; Husakou, Anton; Hermann, Joachim

2011-08-01

We aim to study the nonlinear optical phenomena with femtosecond pulse propagation in liquid-core photonic crystal fibers filled with CS2. In particular, we intend to study the effect of slow nonlinearity due to reorientational contribution of liquid molecules on broadband supercontinuum generation in the femtosecond regime using appropriately modified nonlinear Schrödinger equation. We show that the response of the slow nonlinearity enhances broadening of the pulse and changes the dynamics of the generated solitons. To analyse the quality of the pulse, the stability analysis and coherence of the SCG are studied numerically.

Recent advances in reduction methods for nonlinear problems. [in structural mechanics

NASA Technical Reports Server (NTRS)

Noor, A. K.

1981-01-01

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Aircraft Accident Prevention: Loss-of-Control Analysis

NASA Technical Reports Server (NTRS)

Kwatny, Harry G.; Dongmo, Jean-Etienne T.; Chang, Bor-Chin; Bajpai, Guarav; Yasar, Murat; Belcastro, Christine M.

2009-01-01

The majority of fatal aircraft accidents are associated with loss-of-control . Yet the notion of loss-of-control is not well-defined in terms suitable for rigorous control systems analysis. Loss-of-control is generally associated with flight outside of the normal flight envelope, with nonlinear influences, and with an inability of the pilot to control the aircraft. The two primary sources of nonlinearity are the intrinsic nonlinear dynamics of the aircraft and the state and control constraints within which the aircraft must operate. In this paper we examine how these nonlinearities affect the ability to control the aircraft and how they may contribute to loss-of-control. Examples are provided using NASA s Generic Transport Model.

Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling

NASA Astrophysics Data System (ADS)

Dumeige, Yannick; Féron, Patrice

2011-10-01

Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.

Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

NASA Astrophysics Data System (ADS)

Zhang, Wei-Ya; Li, Yong-Li; Chang, Xiao-Yong; Wang, Nan

2013-09-01

In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis

NASA Astrophysics Data System (ADS)

Ogunjo, Samuel T.; Adediji, Adekunle T.; Dada, Joseph B.

2017-01-01

The use of solar energy for power generation and other uses is on the increase. This demand necessitate a better understanding of the underlying dynamics for better prediction. Nonlinear dynamics and its associated tools readily lend itself for such analysis. In this paper, nonlinearity in solar radiation data is tested using recurrence plot (RP) and recurrence quantification analysis (RQA) in a tropical station. The data used was obtained from an ongoing campaign at the Federal University of Technology, Akure, Southwestern Nigeria using an Integrated Sensor Suite (Vantage2 Pro). Half hourly and daily values were tested for each month of the year. Both were found to be nonlinear. The dry months of the year exhibit higher chaoticity compared to the wet months of the year. The daily average values were found to be mildly chaotic. Using RQA, features due to external effects such as harmattan and intertropical discontinuity (ITD) on solar radiation data were uniquely identified.

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kadtke, J.B.; Bulsara, A.

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

Modeling of Nonlinear Dynamics and Synchronized Oscillations of Microbial Populations, Carbon and Oxygen Concentrations, Induced by Root Exudation in the Rhizosphere

NASA Astrophysics Data System (ADS)

Molz, F. J.; Faybishenko, B.; Jenkins, E. W.

2012-12-01

Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.

Automated diagnosis of autism: in search of a mathematical marker.

PubMed

Bhat, Shreya; Acharya, U Rajendra; Adeli, Hojjat; Bairy, G Muralidhar; Adeli, Amir

2014-01-01

Autism is a type of neurodevelopmental disorder affecting the memory, behavior, emotion, learning ability, and communication of an individual. An early detection of the abnormality, due to irregular processing in the brain, can be achieved using electroencephalograms (EEG). The variations in the EEG signals cannot be deciphered by mere visual inspection. Computer-aided diagnostic tools can be used to recognize the subtle and invisible information present in the irregular EEG pattern and diagnose autism. This paper presents a state-of-the-art review of automated EEG-based diagnosis of autism. Various time domain, frequency domain, time-frequency domain, and nonlinear dynamics for the analysis of autistic EEG signals are described briefly. A focus of the review is the use of nonlinear dynamics and chaos theory to discover the mathematical biomarkers for the diagnosis of the autism analogous to biological markers. A combination of the time-frequency and nonlinear dynamic analysis is the most effective approach to characterize the nonstationary and chaotic physiological signals for the automated EEG-based diagnosis of autism spectrum disorder (ASD). The features extracted using these nonlinear methods can be used as mathematical markers to detect the early stage of autism and aid the clinicians in their diagnosis. This will expedite the administration of appropriate therapies to treat the disorder.

Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors

NASA Astrophysics Data System (ADS)

Green, K.; Champneys, A. R.; Lieven, N. J.

2006-04-01

We present a nonlinear bifurcation analysis of the dynamics of an automatic dynamic balancing mechanism for rotating machines. The principle of operation is to deploy two or more masses that are free to travel around a race at a fixed distance from the hub and, subsequently, balance any eccentricity in the rotor. Mathematically, we start from a Lagrangian description of the system. It is then shown how under isotropic conditions a change of coordinates into a rotating frame turns the problem into a regular autonomous dynamical system, amenable to a full nonlinear bifurcation analysis. Using numerical continuation techniques, curves are traced of steady states, limit cycles and their bifurcations as parameters are varied. These results are augmented by simulations of the system trajectories in phase space. Taking the case of a balancer with two free masses, broad trends are revealed on the existence of a stable, dynamically balanced steady-state solution for specific rotation speeds and eccentricities. However, the analysis also reveals other potentially attracting states—non-trivial steady states, limit cycles, and chaotic motion—which are not in balance. The transient effects which lead to these competing states, which in some cases coexist, are investigated.

Nonlinear Dynamics of a Foil Bearing Supported Rotor System: Simulation and Analysis

NASA Technical Reports Server (NTRS)

Li, Feng; Flowers, George T.

1996-01-01

Foil bearings provide noncontacting rotor support through a number of thin metal strips attached around the circumference of a stator and separated from the rotor by a fluid film. The resulting support stiffness is dominated by the characteristics of the foils and is a nonlinear function of the rotor deflection. The present study is concerned with characterizing this nonlinear effect and investigating its influence on rotordynamical behavior. A finite element model is developed for an existing bearing, the force versus deflection relation characterized, and the dynamics of a sample rotor system are studied. Some conclusions are discussed with regard to appropriate ranges of operation for such a system.

Unbalance response of a two spool gas turbine engine with squeeze film bearings

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Barrett, L. E.; Li, D. F.

1981-01-01

This paper presents a dynamic analysis of a two-spool gas turbine helicopter engine incorporating intershaft rolling element bearings between the gas generator and power turbine rotors. The analysis includes the nonlinear effects of a squeeze film bearing incorporated on the gas generator rotor. The analysis includes critical speeds and forced response of the system and indicates that substantial dynamic loads may be imposed on the intershaft bearings and main bearing supports with an improperly designed squeeze film bearing. A comparison of theoretical and experimental gas generator rotor response is presented illustrating the nonlinear characteristics of the squeeze film bearing. It was found that large intershaft bearing forces may occur even though the engine is not operating at a resonant condition.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Nonlinear differential system applied of a mechanical plan model of the automotives used for the nonlinear stability analysis

NASA Astrophysics Data System (ADS)

Simniceanu, Loreta; Mihaela, Bogdan; Otat, Victor; Trotea, Mario

2017-10-01

This paper proposes a plan mechanical model for the vehicles with two axles, taking into account the lateral deflection of the tire. For this mechanical model are determined two mathematical models under the nonlinear differential equations systems form without taking into account the action of the driver and taking into account. The analysis of driver-vehicle system consists in the mathematical description of vehicle dynamics, coupled with the possibilities and limits of the human factor. Description seeks to emphasize the significant influence of the driver in handling and stability analyzes of vehicles and vehicle-driver system stability until the advent of skidding. These mathematical models are seen as very useful tools to analyzing the vehicles stability. The paper analyzes the influence of some parameters of the vehicle on its behavior in terms of stability of dynamic systems.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Structure Detection of Nonlinear Aeroelastic Systems with Application to Aeroelastic Flight Test Data. Part 2

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Brenner, martin J.

2006-01-01

This viewgraph presentation reviews the 1. Motivation for the study 2. Nonlinear Model Form 3. Structure Detection 4. Least Absolute Shrinkage and Selection Operator (LASSO) 5. Objectives 6. Results 7. Assess LASSO as a Structure Detection Tool: Simulated Nonlinear Models 8. Applicability to Complex Systems: F/A-18 Active Aeroelastic Wing Flight Test Data. The authors conclude that 1. this is a novel approach for detecting the structure of highly over-parameterised nonlinear models in situations where other methods may be inadequate 2. that it is a practical significance in the analysis of aircraft dynamics during envelope expansion and could lead to more efficient control strategies and 3. this could allow greater insight into the functionality of various systems dynamics, by providing a quantitative model which is easily interpretable

Nonlinear dynamical modes of climate variability: from curves to manifolds

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2016-04-01

The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

Zhang, Yan; Holt, Tim A; Khovanova, Natalia

2016-03-01

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

New insights into sucking, swallowing and breathing central generators: A complexity analysis of rhythmic motor behaviors.

PubMed

Samson, Nathalie; Praud, Jean-Paul; Quenet, Brigitte; Similowski, Thomas; Straus, Christian

2017-01-18

Sucking, swallowing and breathing are dynamic motor behaviors. Breathing displays features of chaos-like dynamics, in particular nonlinearity and complexity, which take their source in the automatic command of breathing. In contrast, buccal/gill ventilation in amphibians is one of the rare motor behaviors that do not display nonlinear complexity. This study aimed at assessing whether sucking and swallowing would also follow nonlinear complex dynamics in the newborn lamb. Breathing movements were recorded before, during and after bottle-feeding. Sucking pressure and the integrated EMG of the thyroartenoid muscle, as an index of swallowing, were recorded during bottle-feeding. Nonlinear complexity of the whole signals was assessed through the calculation of the noise limit value (NL). Breathing and swallowing always exhibited chaos-like dynamics. The NL of breathing did not change significantly before, during or after bottle-feeding. On the other hand, sucking inconsistently and significantly less frequently than breathing exhibited a chaos-like dynamics. Therefore, the central pattern generator (CPG) that drives sucking may be functionally different from the breathing CPG. Furthermore, the analogy between buccal/gill ventilation and sucking suggests that the latter may take its phylogenetic origin in the gill ventilation CPG of the common ancestor of extant amphibians and mammals. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis.

PubMed

Ding, Hang

2014-01-01

Structures in recurrence plots (RPs), preserving the rich information of nonlinear invariants and trajectory characteristics, have been increasingly analyzed in dynamic discrimination studies. The conventional analysis of RPs is mainly focused on quantifying the overall diagonal and vertical line structures through a method, called recurrence quantification analysis (RQA). This study extensively explores the information in RPs by quantifying local complex RP structures. To do this, an approach was developed to analyze the combination of three major RQA variables: determinism, laminarity, and recurrence rate (DLR) in a metawindow moving over a RP. It was then evaluated in two experiments discriminating (1) ideal nonlinear dynamic series emulated from the Lorenz system with different control parameters and (2) data sets of human heart rate regulations with normal sinus rhythms (n = 18) and congestive heart failure (n = 29). Finally, the DLR was compared with seven major RQA variables in terms of discriminatory power, measured by standardized mean difference (DSMD). In the two experiments, DLR resulted in the highest discriminatory power with DSMD = 2.53 and 0.98, respectively, which were 7.41 and 2.09 times the best performance from RQA. The study also revealed that the optimal RP structures for the discriminations were neither typical diagonal structures nor vertical structures. These findings indicate that local complex RP structures contain some rich information unexploited by RQA. Therefore, future research to extensively analyze complex RP structures would potentially improve the effectiveness of the RP analysis in dynamic discrimination studies.

Non-linear dynamical classification of short time series of the rössler system in high noise regimes.

PubMed

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E; Poizner, Howard; Sejnowski, Terrence J

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to -30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.

Non-Linear Dynamical Classification of Short Time Series of the Rössler System in High Noise Regimes

PubMed Central

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E.; Poizner, Howard; Sejnowski, Terrence J.

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data. PMID:24379798

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

State Anxiety and Nonlinear Dynamics of Heart Rate Variability in Students.

PubMed

Dimitriev, Dimitriy A; Saperova, Elena V; Dimitriev, Aleksey D

2016-01-01

Clinical and experimental research studies have demonstrated that the emotional experience of anxiety impairs heart rate variability (HRV) in humans. The present study investigated whether changes in state anxiety (SA) can also modulate nonlinear dynamics of heart rate. A group of 96 students volunteered to participate in the study. For each student, two 5-minute recordings of beat intervals (RR) were performed: one during a rest period and one just before a university examination, which was assumed to be a real-life stressor. Nonlinear analysis of HRV was performed. The Spielberger's State-Trait Anxiety Inventory was used to assess the level of SA. Before adjusting for heart rate, a Wilcoxon matched pairs test showed significant decreases in Poincaré plot measures, entropy, largest Lyapunov exponent (LLE), and pointwise correlation dimension (PD2), and an increase in the short-term fractal-like scaling exponent of detrended fluctuation analysis (α1) during the exam session, compared with the rest period. A Pearson analysis indicated significant negative correlations between the dynamics of SA and Poincaré plot axes ratio (SD1/SD2), and between changes in SA and changes in entropy measures. A strong negative correlation was found between the dynamics of SA and LLE. A significant positive correlation was found between the dynamics of SA and α1. The decreases in Poincaré plot measures (SD1, complex correlation measure), entropy measures, and LLE were still significant after adjusting for heart rate. Corrected α1 was increased during the exam session. As before, the dynamics of adjusted LLE was significantly correlated with the dynamics of SA. The qualitative increase in SA during academic examination was related to the decrease in the complexity and size of the Poincaré plot through a reduction of both the interbeat interval and its variation.

Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

PubMed Central

Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

2013-01-01

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

Nonlinear effects of electromagnetic forces on primary resonance of a levitated elastic bar supported by high- Tc superconducting bearings

NASA Astrophysics Data System (ADS)

Iori, T.; Ogawa, S.; Sugiura, T.

2007-10-01

This research investigates nonlinear dynamics of an elastic body supported at both its ends by electromagnetic forces between superconductors and magnets. We focus on the primary resonance of each eigenmode under vertical excitation of superconducting bulks. Experiment and numerical analysis show the softening tendency in the resonance of the 3rd mode consisting of mainly deflection and slightly translation. This nonlinear response can be theoretically explained only by nonlinear coupling between the 1st and 3rd modes through their quadratic terms.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Projective formulation of Maggi's method for nonholonomic systems analysis

NASA Astrophysics Data System (ADS)

Blajer, Wojciech

1992-04-01

A projective interpretation of Maggi'a approach to dynamic analysis of nonholonomic systems is presented. Both linear and nonlinear constraint cases are treatment in unified fashion, using the language of vector spaces and tensor algebra analysis.

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

NASA Technical Reports Server (NTRS)

Peterson, Lee D.

1991-01-01

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Off-Policy Integral Reinforcement Learning Method to Solve Nonlinear Continuous-Time Multiplayer Nonzero-Sum Games.

PubMed

Song, Ruizhuo; Lewis, Frank L; Wei, Qinglai

2017-03-01

This paper establishes an off-policy integral reinforcement learning (IRL) method to solve nonlinear continuous-time (CT) nonzero-sum (NZS) games with unknown system dynamics. The IRL algorithm is presented to obtain the iterative control and off-policy learning is used to allow the dynamics to be completely unknown. Off-policy IRL is designed to do policy evaluation and policy improvement in the policy iteration algorithm. Critic and action networks are used to obtain the performance index and control for each player. The gradient descent algorithm makes the update of critic and action weights simultaneously. The convergence analysis of the weights is given. The asymptotic stability of the closed-loop system and the existence of Nash equilibrium are proved. The simulation study demonstrates the effectiveness of the developed method for nonlinear CT NZS games with unknown system dynamics.

Complexity of EEG-signal in Time Domain - Possible Biomedical Application

NASA Astrophysics Data System (ADS)

Klonowski, Wlodzimierz; Olejarczyk, Elzbieta; Stepien, Robert

2002-07-01

Human brain is a highly complex nonlinear system. So it is not surprising that in analysis of EEG-signal, which represents overall activity of the brain, the methods of Nonlinear Dynamics (or Chaos Theory as it is commonly called) can be used. Even if the signal is not chaotic these methods are a motivating tool to explore changes in brain activity due to different functional activation states, e.g. different sleep stages, or to applied therapy, e.g. exposure to chemical agents (drugs) and physical factors (light, magnetic field). The methods supplied by Nonlinear Dynamics reveal signal characteristics that are not revealed by linear methods like FFT. Better understanding of principles that govern dynamics and complexity of EEG-signal can help to find `the signatures' of different physiological and pathological states of human brain, quantitative characteristics that may find applications in medical diagnostics.

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

NASA Astrophysics Data System (ADS)

Imani Masouleh, Mehdi; Limebeer, David J. N.

2018-07-01

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-02-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-06-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

On the coupling of nonlinear macro-fiber composite piezoelectric cantilever dynamics with hydrodynamic loads

NASA Astrophysics Data System (ADS)

Tan, D.; Erturk, A.

2018-03-01

For bio-inspired, fish-like robotic propulsion, the Macro-Fiber Composite (MFC) piezoelectric technology offers noiseless actuation with a balance between actuation force and velocity response. However, internal nonlinear- ities within the MFCs, such as piezoelectric softening, geometric hardening, inertial softening, and nonlinear dissipation, couple with the hydrodynamic loading on the structure from the surrounding fluid. In the present work, we explore nonlinear actuation of MFC cantilevers underwater and develop a mathematical framework for modeling and analysis. In vacuo resonant actuation experiments are conducted for a set of MFC cantilevers of varying length to width aspect ratios to validate the structural model in the absence of fluid loading. These MFC cantilevers are then subjected to underwater resonant actuation experiments, and model simulations are compared with nonlinear experimental frequency response functions. It is observed that semi-empirical hydro- dynamic loads obtained from quasilinear experiments have to be modified to account for amplitude dependent added mass, and additional nonlinear hydrodynamic effects might be present, yielding qualitative differences in the resulting underwater frequency respones curves with increased excitation amplitude.

Estimation of Spatial Dynamic Nonparametric Durbin Models with Fixed Effects

ERIC Educational Resources Information Center

Qian, Minghui; Hu, Ridong; Chen, Jianwei

2016-01-01

Spatial panel data models have been widely studied and applied in both scientific and social science disciplines, especially in the analysis of spatial influence. In this paper, we consider the spatial dynamic nonparametric Durbin model (SDNDM) with fixed effects, which takes the nonlinear factors into account base on the spatial dynamic panel…

Dynamic analysis of clamp band joint system subjected to axial vibration

NASA Astrophysics Data System (ADS)

Qin, Z. Y.; Yan, S. Z.; Chu, F. L.

2010-10-01

Clamp band joints are commonly used for connecting circular components together in industry. Some of the systems jointed by clamp band are subjected to dynamic load. However, very little research on the dynamic characteristics for this kind of joint can be found in the literature. In this paper, a dynamic model for clamp band joint system is developed. Contact and frictional slip between the components are accommodated in this model. Nonlinear finite element analysis is conducted to identify the model parameters. Then static experiments are carried out on a scaled model of the clamp band joint to validate the joint model. Finally, the model is adopted to study the dynamic characteristics of the clamp band joint system subjected to axial harmonic excitation and the effects of the wedge angle of the clamp band joint and the preload on the response. The model proposed in this paper can represent the nonlinearity of the clamp band joint and be used conveniently to investigate the effects of the structural and loading parameters on the dynamic characteristics of this type of joint system.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

PubMed Central

Friedman, Alexander; Slocum, Joshua F.; Tyulmankov, Danil; Gibb, Leif G.; Altshuler, Alex; Ruangwises, Suthee; Shi, Qinru; Toro Arana, Sebastian E.; Beck, Dirk W.; Sholes, Jacquelyn E. C.; Graybiel, Ann M.

2016-01-01

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain. PMID:27222584

Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumeige, Yannick; Feron, Patrice

Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processingmore » or ternary optical logic applications.« less

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Nonlinear analysis of heart rate variability within independent frequency components during the sleep-wake cycle.

PubMed

Vigo, Daniel E; Dominguez, Javier; Guinjoan, Salvador M; Scaramal, Mariano; Ruffa, Eduardo; Solernó, Juan; Siri, Leonardo Nicola; Cardinali, Daniel P

2010-04-19

Heart rate variability (HRV) is a complex signal that results from the contribution of different sources of oscillation related to the autonomic nervous system activity. Although linear analysis of HRV has been applied to sleep studies, the nonlinear dynamics of HRV underlying frequency components during sleep is less known. We conducted a study to evaluate nonlinear HRV within independent frequency components in wake status, slow-wave sleep (SWS, stages III or IV of non-rapid eye movement sleep), and rapid-eye-movement sleep (REM). The sample included 10 healthy adults. Polysomnography was performed to detect sleep stages. HRV was studied globally during each phase and then very low frequency (VLF), low frequency (LF) and high frequency (HF) components were separated by means of the wavelet transform algorithm. HRV nonlinear dynamics was estimated with sample entropy (SampEn). A higher SampEn was found when analyzing global variability (Wake: 1.53+/-0.28, SWS: 1.76+/-0.32, REM: 1.45+/-0.19, p=0.005) and VLF variability (Wake: 0.13+/-0.03, SWS: 0.19+/-0.03, REM: 0.14+/-0.03, p<0.001) at SWS. REM was similar to wake status regarding nonlinear HRV. We propose nonlinear HRV is a useful index of the autonomic activity that characterizes the different sleep-wake cycle stages. 2009 Elsevier B.V. All rights reserved.

NASA automatic system for computer program documentation, volume 2

NASA Technical Reports Server (NTRS)

Simmons, D. B.

1972-01-01

The DYNASOR 2 program is used for the dynamic nonlinear analysis of shells of revolution. The equations of motion of the shell are solved using Houbolt's numerical procedure. The displacements and stress resultants are determined for both symmetrical and asymmetrical loading conditions. Asymmetrical dynamic buckling can be investigated. Solutions can be obtained for highly nonlinear problems utilizing as many as five of the harmonics generated by SAMMSOR program. A restart capability allows the user to restart the program at a specified time. For Vol. 1, see N73-22129.

Comparison of heaving buoy and oscillating flap wave energy converters

NASA Astrophysics Data System (ADS)

Abu Bakar, Mohd Aftar; Green, David A.; Metcalfe, Andrew V.; Najafian, G.

2013-04-01

Waves offer an attractive source of renewable energy, with relatively low environmental impact, for communities reasonably close to the sea. Two types of simple wave energy converters (WEC), the heaving buoy WEC and the oscillating flap WEC, are studied. Both WECs are considered as simple energy converters because they can be modelled, to a first approximation, as single degree of freedom linear dynamic systems. In this study, we estimate the response of both WECs to typical wave inputs; wave height for the buoy and corresponding wave surge for the flap, using spectral methods. A nonlinear model of the oscillating flap WEC that includes the drag force, modelled by the Morison equation is also considered. The response to a surge input is estimated by discrete time simulation (DTS), using central difference approximations to derivatives. This is compared with the response of the linear model obtained by DTS and also validated using the spectral method. Bendat's nonlinear system identification (BNLSI) technique was used to analyze the nonlinear dynamic system since the spectral analysis was only suitable for linear dynamic system. The effects of including the nonlinear term are quantified.

Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics.

PubMed

Wang, Huanqing; Liu, Peter Xiaoping; Li, Shuai; Wang, Ding

2017-08-29

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Nonlinear dynamic analysis of rigid rotor supported by gas foil bearings: Effects of gas film and foil structure on subsynchronous vibrations

NASA Astrophysics Data System (ADS)

Guo, Zhiyang; Feng, Kai; Liu, Tianyu; Lyu, Peng; Zhang, Tao

2018-07-01

Highly nonlinear subsynchronous vibrations are the main causing factors of failure in gas foil bearing (GFB)-rotor systems. Thus, investigating the vibration generation mechanisms and the relationship between subsynchronous vibrations and GFBs is necessary to ensure the healthy operation of rotor systems. In this study, an integrated nonlinear dynamic model with the consideration of shaft motion, unsteady gas film, and deformations of foil structure is established to investigate the effect of gas film and foil structure on system subsynchronous response. One test rig of GFB-rotor system is developed for model comparison. High agreement is shown between the prediction and test data, especially in the frequency domain. The nonlinear dynamic response is analyzed using waterfall plots, operation deflection shapes, journal orbits, Poincaré maps, and fast Fourier transforms. The parameter studies reveal that subsynchronous vibrations are highly related to gas film and foil structure. Subsynchronous vibrations can be adjusted by parameters such as bump stiffness, nominal clearance, and static loads. Therefore, gas foil bearing parameters should be carefully adjusted by system manufacturers to achieve the best rotordynamic performance.

Experimental and numerical investigation of the nonlinear dynamics of compliant mechanisms for deployable structures

NASA Astrophysics Data System (ADS)

Dewalque, Florence; Schwartz, Cédric; Denoël, Vincent; Croisier, Jean-Louis; Forthomme, Bénédicte; Brüls, Olivier

2018-02-01

This paper studies the dynamics of tape springs which are characterised by a highly geometrical nonlinear behaviour including buckling, the formation of folds and hysteresis. An experimental set-up is designed to capture these complex nonlinear phenomena. The experimental data are acquired by the means of a 3D motion analysis system combined with a synchronised force plate. Deployment tests show that the motion can be divided into three phases characterised by different types of folds, frequencies of oscillation and damping behaviours. Furthermore, the reproducibility quality of the dynamic and quasi-static results is validated by performing a large number of tests. In parallel, a nonlinear finite element model is developed. The required model parameters are identified based on simple experimental tests such as static deformed configurations and small amplitude vibration tests. In the end, the model proves to be well correlated with the experimental results in opposite sense bending, while in equal sense, both the experimental set-up and the numerical model are particularly sensitive to the initial conditions.

Nonlinear dynamics of a two-dimensional Wigner solid on superfluid helium

NASA Astrophysics Data System (ADS)

Monarkha, Yu. P.

2018-04-01

Nonlinear dynamics and transport properties of a 2D Wigner solid (WS) on the free surface of superfluid helium are theoretically studied. The analysis is nonperturbative in the amplitude of the WS velocity. An anomalous nonlinear response of the liquid helium surface to the oscillating motion of the WS is shown to appear when the driving frequency is close to subharmonics of the frequency of a capillary wave (ripplon) whose wave vector coincides with a reciprocal-lattice vector. As a result, the effective mass of surface dimples formed under electrons and the kinetic friction acquire sharp anomalies in the low-frequency range, which affects the mobility and magnetoconductivity of the WS. The results obtained here explain a variety of experimental observations reported previously.

Investigation of the dynamics of a nonlinear optical response in glassy chalcogenide semiconductors by the pump–probe method

NASA Astrophysics Data System (ADS)

Romanova, E. A.; Kuzyutkina, Yu S.; Shiryaev, V. S.; Guizard, S.

2018-03-01

An analysis of the results of measurements by using the pump–probe method with a femtosecond resolution in time and computer simulation of the charge carrier kinetics have revealed two types of a nonlinear optical response in samples of chalcogenide glasses belonging to the As – S – Se system, irradiated by 50-fs laser pulses with a wavelength of 0.79 μm. The difference in the nonlinear dynamics is due to the difference in the photoexcitation character, because laser radiation can be absorbed either through bound states in the band gap or without their participation, depending on the ratio of the pump photon energy to the bandgap energy.

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

PubMed

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

Nonlinear heart rate variability measures under electromagnetic fields produced by GSM cellular phones.

PubMed

Parazzini, Marta; Ravazzani, Paolo; Thuroczy, György; Molnar, Ferenc B; Ardesi, Gianluca; Sacchettini, Alessio; Mainardi, Luca Tommaso

2013-06-01

This study was designed to assess the nonlinear dynamics of heart rate variability (HRV) during exposure to low-intensity EMFs. Twenty-six healthy young volunteers were subjected to a rest-to-stand protocol to evaluate autonomic nervous system in quiet condition (rest, vagal prevalence) and after a sympathetic activation (stand). The procedure was conducted twice in a double-blind design: once with a genuine EMFs exposure (GSM cellular phone at 900 MHz, 2 W) and once with a sham exposure (at least 24 h apart). During each session, three-lead electrocardiograms were recorded and RR series extracted off-line. The RR series were analyzed by nonlinear deterministic techniques in every phase of the protocol and during the different exposures. The analysis of the data shows there was no statistically significant effect due to GSM exposure on the nonlinear dynamics of HRV.

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Dynamic analysis of a flexible spacecraft with rotating components. Volume 1: Analytical developments

NASA Technical Reports Server (NTRS)

Bodley, C. S.; Devers, A. D.; Park, A. C.

1975-01-01

Analytical procedures and digital computer code are presented for the dynamic analysis of a flexible spacecraft with rotating components. Topics, considered include: (1) nonlinear response in the time domain, and (2) linear response in the frequency domain. The spacecraft is assumed to consist of an assembly of connected rigid or flexible subassemblies. The total system is not restricted to a topological connection arrangement and may be acting under the influence of passive or active control systems and external environments. The analytics and associated digital code provide the user with the capability to establish spacecraft system nonlinear total response for specified initial conditions, linear perturbation response about a calculated or specified nominal motion, general frequency response and graphical display, and spacecraft system stability analysis.

Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets

NASA Astrophysics Data System (ADS)

Chen, Shu-Peng; He, Ling-Yun

2010-04-01

Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in China’s agricultural futures markets.

Continuation Methods for Qualitative Analysis of Aircraft Dynamics

NASA Technical Reports Server (NTRS)

Cummings, Peter A.

2004-01-01

A class of numerical methods for constructing bifurcation curves for systems of coupled, non-linear ordinary differential equations is presented. Foundations are discussed, and several variations are outlined along with their respective capabilities. Appropriate background material from dynamical systems theory is presented.

Use of recurrence plots in the analysis of pupil diameter dynamics in narcoleptics

NASA Astrophysics Data System (ADS)

Keegan, Andrew P.; Zbilut, J. P.; Merritt, S. L.; Mercer, P. J.

1993-11-01

Recurrence plots were used to evaluate pupil dynamics of subjects with narcolepsy. Preliminary data indicate that this nonlinear method of analyses may be more useful in revealing underlying deterministic differences than traditional methods like FFT and counting statistics.

Spin-current emission governed by nonlinear spin dynamics.

PubMed

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-10-16

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

Spin-current emission governed by nonlinear spin dynamics

PubMed Central

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-01-01

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators. PMID:26472712

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Hui, E-mail: huiyang@usf.edu; Chen, Yun

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., valuesmore » and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Experimental Modal Analysis and Dynamic Component Synthesis. Volume 2. Measurement Techniques for Experimental Modal Analysis

DTIC Science & Technology

1987-12-01

A- -- HZ LIN 3.0 . Be-I. •,% •4’ 20.. 0-p -4 -0 30a 4a j0 O0 100a 10 4140 iSo 130 20C. 2210 140 M* LIN g•" %g Figur 19. Cyli Avergin (N4,M 0 -3- 40...shows that the degree of nonlinearity of a structure varies according to the characteristics of the system. That is, welded structures will usually...exhibit a linear response; where a riveted or spot welded structure exhibits a very nonlinear response [52]. As an example of a nonlinear system

Nonlinear dynamics and numerical uncertainties in CFD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Nonlinear flutter analysis of composite panels

NASA Astrophysics Data System (ADS)

An, Xiaomin; Wang, Yan

2018-05-01

Nonlinear panel flutter is an interesting subject of fluid-structure interaction. In this paper, nonlinear flutter characteristics of curved composite panels are studied in very low supersonic flow. The composite panel with geometric nonlinearity is modeled by a nonlinear finite element method; and the responses are computed by the nonlinear Newmark algorithm. An unsteady aerodynamic solver, which contains a flux splitting scheme and dual time marching technology, is employed in calculating the unsteady pressure of the motion of the panel. Based on a half-step staggered coupled solution, the aeroelastic responses of two composite panels with different radius of R = 5 and R = 2.5 are computed and compared with each other at different dynamic pressure for Ma = 1.05. The nonlinear flutter characteristics comprising limited cycle oscillations and chaos are analyzed and discussed.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin

PubMed Central

Jaksic, V.; O'Shea, R.; Cahill, P.; Murphy, J.; Mandic, D. P.; Pakrashi, V.

2015-01-01

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson–Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. PMID:25583866

Dynamic Modeling Accuracy Dependence on Errors in Sensor Measurements, Mass Properties, and Aircraft Geometry

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2013-01-01

A nonlinear simulation of the NASA Generic Transport Model was used to investigate the effects of errors in sensor measurements, mass properties, and aircraft geometry on the accuracy of dynamic models identified from flight data. Measurements from a typical system identification maneuver were systematically and progressively deteriorated and then used to estimate stability and control derivatives within a Monte Carlo analysis. Based on the results, recommendations were provided for maximum allowable errors in sensor measurements, mass properties, and aircraft geometry to achieve desired levels of dynamic modeling accuracy. Results using other flight conditions, parameter estimation methods, and a full-scale F-16 nonlinear aircraft simulation were compared with these recommendations.

Analyses of Multishaft Rotor-Bearing Response

NASA Technical Reports Server (NTRS)

Nelson, H. D.; Meacham, W. L.

1985-01-01

Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).

Flocking with connectivity preservation for disturbed nonlinear multi-agent systems by output feedback

NASA Astrophysics Data System (ADS)

Li, Ping; Zhang, Baoyong; Ma, Qian; Xu, Shengyuan; Chen, Weimin; Zhang, Zhengqiang

2018-05-01

This paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi-agent systems. In order to deal with the nonlinearities in the dynamic of all agents, some auxiliary variables are introduced into the state observer for stability analysis. By proposing a bounded potential function and using adaptive theory, a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation.

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

NASA Technical Reports Server (NTRS)

Sreekantamurthy, Tham; Gaspar, James L.; Mann, Troy; Behun, Vaughn; Pearson, James C., Jr.; Scarborough, Stephen

2007-01-01

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Rotor systems research aircraft risk-reduction shake test

NASA Technical Reports Server (NTRS)

Wellman, J. Brent

1990-01-01

A shake test and an extensive analysis of results were performed to evaluate the possibility of and the method for dynamically calibrating the Rotor Systems Research Aircraft (RSRA). The RSRA airframe was subjected to known vibratory loads in several degrees of freedom and the responses of many aircraft transducers were recorded. Analysis of the transducer responses using the technique of dynamic force determination showed that the RSRA, when used as a dynamic measurement system, could predict, a posteriori, an excitation force in a single axis to an accuracy of about 5 percent and sometimes better. As the analysis was broadened to include multiple degrees of freedom for the excitation force, the predictive ability of the measurement system degraded to about 20 percent, with the error occasionally reaching 100 percent. The poor performance of the measurement system is explained by the nonlinear response of the RSRA to vibratory forces and the inadequacy of the particular method used in accounting for this nonlinearity.

Review of Dynamic Modeling and Simulation of Large Scale Belt Conveyor System

NASA Astrophysics Data System (ADS)

He, Qing; Li, Hong

Belt conveyor is one of the most important devices to transport bulk-solid material for long distance. Dynamic analysis is the key to decide whether the design is rational in technique, safe and reliable in running, feasible in economy. It is very important to study dynamic properties, improve efficiency and productivity, guarantee conveyor safe, reliable and stable running. The dynamic researches and applications of large scale belt conveyor are discussed. The main research topics, the state-of-the-art of dynamic researches on belt conveyor are analyzed. The main future works focus on dynamic analysis, modeling and simulation of main components and whole system, nonlinear modeling, simulation and vibration analysis of large scale conveyor system.

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics.

PubMed

Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo

2015-01-01

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.

Nonlinear dynamics of global atmospheric and Earth-system processes

NASA Technical Reports Server (NTRS)

Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel

1990-01-01

Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.

Lifespan differences in nonlinear dynamics during rest and auditory oddball performance.

PubMed

Müller, Viktor; Lindenberger, Ulman

2012-07-01

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an indicator of cortical reactivity. During rest, both nonlinear coupling and spectral alpha power decreased with age, whereas dimensional complexity increased. In contrast, when attending to the deviant stimulus, nonlinear coupling increased with age, and complexity decreased. Correlational analyses showed that nonlinear measures assessed during auditory oddball performance were reliably related to an independently assessed measure of perceptual speed. We conclude that cortical dynamics during rest and stimulus processing undergo substantial reorganization from childhood to old age, and propose that lifespan age differences in nonlinear dynamics during stimulus processing reflect lifespan changes in the functional organization of neuronal cell assemblies. © 2012 Blackwell Publishing Ltd.

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

NASA Technical Reports Server (NTRS)

Noor, A. K.

1983-01-01

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2014-05-01

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

Slackline dynamics and the Helmholtz-Duffing oscillator

NASA Astrophysics Data System (ADS)

Athanasiadis, Panos J.

2018-01-01

Slacklining is a new, rapidly expanding sport, and understanding its physics is paramount for maximizing fun and safety. Yet, compared to other sports, very little has been published so far on slackline dynamics. The equations of motion describing a slackline are fundamentally nonlinear, and assuming linear elasticity, they lead to a form of the Duffing equation. Following this approach, characteristic examples of slackline motion are simulated, including trickline bouncing, leash falls and longline surfing. The time-dependent solutions of the differential equations describing the system are acquired by numerical integration. A simple form of energy dissipation (linear drag) is added in some cases. It is recognized in this study that geometric nonlinearity is a fundamental aspect characterizing the dynamics of slacklines. Sports, and particularly slackline, is an excellent way of engaging young people with physics. A slackline is a simple yet insightful example of a nonlinear oscillator. It is very easy to model in the laboratory, as well as to rig and try on a university campus. For instructive purposes, its behaviour can be explored by numerically integrating the respective equations of motion. A form of the Duffing equation emerges naturally in the analysis and provides a powerful introduction to nonlinear dynamics. The material is suitable for graduate students and undergraduates with a background in classical mechanics and differential equations.

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

Dimensionless embedding for nonlinear time series analysis

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; Aihara, Kazuyuki

2017-09-01

Recently, infinite-dimensional delay coordinates (InDDeCs) have been proposed for predicting high-dimensional dynamics instead of conventional delay coordinates. Although InDDeCs can realize faster computation and more accurate short-term prediction, it is still not well-known whether InDDeCs can be used in other applications of nonlinear time series analysis in which reconstruction is needed for the underlying dynamics from a scalar time series generated from a dynamical system. Here, we give theoretical support for justifying the use of InDDeCs and provide numerical examples to show that InDDeCs can be used for various applications for obtaining the recurrence plots, correlation dimensions, and maximal Lyapunov exponents, as well as testing directional couplings and extracting slow-driving forces. We demonstrate performance of the InDDeCs using the weather data. Thus, InDDeCs can eventually realize "dimensionless embedding" while we enjoy faster and more reliable computations.

Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Yaguang

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

Mastodon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

A Program for Solving the Brain Ischemia Problem

PubMed Central

DeGracia, Donald J.

2013-01-01

Our recently described nonlinear dynamical model of cell injury is here applied to the problems of brain ischemia and neuroprotection. We discuss measurement of global brain ischemia injury dynamics by time course analysis. Solutions to proposed experiments are simulated using hypothetical values for the model parameters. The solutions solve the global brain ischemia problem in terms of “master bifurcation diagrams” that show all possible outcomes for arbitrary durations of all lethal cerebral blood flow (CBF) decrements. The global ischemia master bifurcation diagrams: (1) can map to a single focal ischemia insult, and (2) reveal all CBF decrements susceptible to neuroprotection. We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection. Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery. We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature. The hypothetical examples studied here illustrate the use of the nonlinear cell injury model as a fresh avenue of approach that has the potential, not only to solve the brain ischemia problem, but also to advance the technology of neuroprotection. PMID:24961411

Nonlinear dynamics that appears in the dynamical model of drying process of a polymer solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2007-01-01

We have proposed and modified the dynamical model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication and have presented the fruits through some meetings and so on. Though basic equations of the dynamical model have characteristic nonlinearity, character of the nonlinearity has not been studied enough yet. In this paper, at first, we derive nonlinear equations from the dynamical model of drying process of polymer solution. Then we introduce results of numerical simulations of the nonlinear equations and consider roles of various parameters. Some of them are indirectly concerned in strength of non-equilibriumity. Through this study, we approach essential qualities of nonlinearity in non-equilibrium process of drying process.

SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michalski, D; Huq, M; Bednarz, G

Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same ismore » for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for 4D-based clinical technologies, can be better controlled if nonlinear-based methodology, which reflects respiration characteristic, is applied. Funding provided by Varian Medical Systems via Investigator Initiated Research Project.« less

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Characterizing psychological dimensions in non-pathological subjects through autonomic nervous system dynamics

PubMed Central

Nardelli, Mimma; Valenza, Gaetano; Cristea, Ioana A.; Gentili, Claudio; Cotet, Carmen; David, Daniel; Lanata, Antonio; Scilingo, Enzo P.

2015-01-01

The objective assessment of psychological traits of healthy subjects and psychiatric patients has been growing interest in clinical and bioengineering research fields during the last decade. Several experimental evidences strongly suggest that a link between Autonomic Nervous System (ANS) dynamics and specific dimensions such as anxiety, social phobia, stress, and emotional regulation might exist. Nevertheless, an extensive investigation on a wide range of psycho-cognitive scales and ANS non-invasive markers gathered from standard and non-linear analysis still needs to be addressed. In this study, we analyzed the discerning and correlation capabilities of a comprehensive set of ANS features and psycho-cognitive scales in 29 non-pathological subjects monitored during resting conditions. In particular, the state of the art of standard and non-linear analysis was performed on Heart Rate Variability, InterBreath Interval series, and InterBeat Respiration series, which were considered as monovariate and multivariate measurements. Experimental results show that each ANS feature is linked to specific psychological traits. Moreover, non-linear analysis outperforms the psychological assessment with respect to standard analysis. Considering that the current clinical practice relies only on subjective scores from interviews and questionnaires, this study provides objective tools for the assessment of psychological dimensions. PMID:25859212

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems

NASA Astrophysics Data System (ADS)

Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay

2017-01-01

In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.

Modelling chaotic vibrations using NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1993-01-01

Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

NASA Technical Reports Server (NTRS)

Tang, D. M.; Dowell, E. H.

1985-01-01

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.

Mathematical modeling of the aerodynamic characteristics in flight dynamics

NASA Technical Reports Server (NTRS)

Tobak, M.; Chapman, G. T.; Schiff, L. B.

1984-01-01

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

Spectral decomposition of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

2016-02-01

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

Development of a helicopter rotor/propulsion system dynamics analysis

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Hull, R.

1982-01-01

A time-domain analysis of coupled engine/drive train/rotor dynamics of a twin-engine, single main rotor helicopter model has been performed. The analysis incorporates an existing helicopter model with nonlinear simulations of a helicopter turboshaft engine and its fuel controller. System dynamic behavior is studied using the resulting simulation which included representations for the two engines and their fuel controllers, drive system, main rotor, tail rotor, and aircraft rigid body motions. Time histories of engine and rotor RPM response to pilot control inputs are studied for a baseline rotor and propulsion system model. Sensitivity of rotor RPM droop to fuel controller gain changes and collective input feed-forward gain changes are studied. Torque-load-sharing between the two engines is investigated by making changes in the fuel controller feedback paths. A linear engine model is derived from the nonlinear engine simulation and used in the coupled system analysis. This four-state linear engine model is then reduced to a three-state model. The effect of this simplification on coupled system behavior is shown.

Influence of a Levelness Defect in a Thrust Bearing on the Dynamic Behaviour of AN Elastic Shaft

NASA Astrophysics Data System (ADS)

BERGER, S.; BONNEAU, O.; FRÊNE, J.

2002-01-01

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.

Some Aspects of Nonlinear Dynamics and CFD

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Retrieving hydrological connectivity from empirical causality in karst systems

NASA Astrophysics Data System (ADS)

Delforge, Damien; Vanclooster, Marnik; Van Camp, Michel; Poulain, Amaël; Watlet, Arnaud; Hallet, Vincent; Kaufmann, Olivier; Francis, Olivier

2017-04-01

Because of their complexity, karst systems exhibit nonlinear dynamics. Moreover, if one attempts to model a karst, the hidden behavior complicates the choice of the most suitable model. Therefore, both intense investigation methods and nonlinear data analysis are needed to reveal the underlying hydrological connectivity as a prior for a consistent physically based modelling approach. Convergent Cross Mapping (CCM), a recent method, promises to identify causal relationships between time series belonging to the same dynamical systems. The method is based on phase space reconstruction and is suitable for nonlinear dynamics. As an empirical causation detection method, it could be used to highlight the hidden complexity of a karst system by revealing its inner hydrological and dynamical connectivity. Hence, if one can link causal relationships to physical processes, the method should show great potential to support physically based model structure selection. We present the results of numerical experiments using karst model blocks combined in different structures to generate time series from actual rainfall series. CCM is applied between the time series to investigate if the empirical causation detection is consistent with the hydrological connectivity suggested by the karst model.

Analysis and simulation of a magnetic bearing suspension system for a laboratory model annular momentum control device

NASA Technical Reports Server (NTRS)

Groom, N. J.; Woolley, C. T.; Joshi, S. M.

1981-01-01

A linear analysis and the results of a nonlinear simulation of a magnetic bearing suspension system which uses permanent magnet flux biasing are presented. The magnetic bearing suspension is part of a 4068 N-m-s (3000 lb-ft-sec) laboratory model annular momentum control device (AMCD). The simulation includes rigid body rim dynamics, linear and nonlinear axial actuators, linear radial actuators, axial and radial rim warp, and power supply and power driver current limits.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

The Shock and Vibration Bulletin. Part 2. Structural Analysis, Design Techniques

DTIC Science & Technology

1973-06-01

FLOATING SHOCK PLATFORM SUBJECTED TO UNDERWATER EXPLOSIONS R. P. Brooks, and B. C, McNalght Naval Air Engineering Center Philadelphia, Pa, A lumped...Lohwasser, Air Force Flight Dynamics Laboratory, Wright -Patterson APB, Ohio AN ALGORITHM FOR SEMI-INVERSE ANALYSIS OF NONLINEAR DYNAMIC SYSTEMS ... 65 R...MATHEMATICAL MODEL OF A TYPICAL.FOATING SHOCK PLATFORM SSUBJECTED TO-UNDERWATE- EXPLOSIONS .......... ...................... 143 R. P. Brooks and B. C

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

A simulation of atomic force microscope microcantilever in the tapping mode utilizing couple stress theory.

PubMed

Abbasi, Mohammad

2018-04-01

The nonlinear vibration behavior of a Tapping mode atomic force microscopy (TM-AFM) microcantilever under acoustic excitation force has been modeled and investigated. In dynamic AFM, the tip-surface interactions are strongly nonlinear, rapidly changing and hysteretic. First, the governing differential equation of motion and boundary conditions for dynamic analysis are obtained using the modified couple stress theory. Afterwards, closed-form expressions for nonlinear frequency and effective nonlinear damping ratio are derived utilizing perturbation method. The effect of tip connection position on the vibration behavior of the microcantilever are also analyzed. The results show that nonlinear frequency is size dependent. According to the results, an increase in the equilibrium separation between the tip and the sample surface reduces the overall effect of van der Waals forces on the nonlinear frequency, but its effect on the effective nonlinear damping ratio is negligible. The results also indicate that both the change in the distance between tip and cantilever free end and the reduction of tip radius have significant effects on the accuracy and sensitivity of the TM-AFM in the measurement of surface forces. The hysteretic behavior has been observed in the near resonance frequency response due to softening and hardening of the forced vibration response. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Slew maneuvers of Spacecraft Control Laboratory Experiment (SCOLE)

NASA Technical Reports Server (NTRS)

Kakad, Yogendra P.

1992-01-01

This is the final report on the dynamics and control of slew maneuvers of the Spacecraft Control Laboratory Experiment (SCOLE) test facility. The report documents the basic dynamical equation derivations for an arbitrary large angle slew maneuver as well as the basic decentralized slew maneuver control algorithm. The set of dynamical equations incorporate rigid body slew maneuver and three dimensional vibrations of the complete assembly comprising the rigid shuttle, the flexible beam, and the reflector with an offset mass. The analysis also includes kinematic nonlinearities of the entire assembly during the maneuver and the dynamics of the interactions between the rigid shuttle and the flexible appendage. The equations are simplified and evaluated numerically to include the first ten flexible modes to yield a model for designing control systems to perform slew maneuvers. The control problem incorporates the nonlinear dynamical equations and is expressed in terms of a two point boundary value problem.

Comparing Consider-Covariance Analysis with Sigma-Point Consider Filter and Linear-Theory Consider Filter Formulations

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2007-01-01

Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to nonlinear sequential consider covariance analysis, i.e. in the presence of nonlinear dynamics and nonlinear measurements. A simple SPCF for orbit determination, exemplifying an algorithm hosted in the guidance, navigation and control (GN&C) computer processor of a hypothetical robotic spacecraft, was implemented, and compared with an identically-parameterized (standard) extended, consider-parameterized Kalman filter. The onboard filtering scenario examined is a hypothetical spacecraft orbit about a small natural body with imperfectly-known mass. The formulations, relative complexities, and performances of the filters are compared and discussed.

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

NASA Astrophysics Data System (ADS)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Modeling, numerical simulation, and nonlinear dynamic behavior analysis of PV microgrid-connected inverter with capacitance catastrophe

NASA Astrophysics Data System (ADS)

Li, Sichen; Liao, Zhixian; Luo, Xiaoshu; Wei, Duqu; Jiang, Pinqun; Jiang, Qinghong

2018-02-01

The value of the output capacitance (C) should be carefully considered when designing a photovoltaic (PV) inverter since it can cause distortion in the working state of the circuit, and the circuit produces nonlinear dynamic behavior. According to Kirchhoff’s laws and the characteristics of an ideal operational amplifier for a strict piecewise linear state equation, a circuit simulation model is constructed to study the system parameters (time, C) for the current passing through an inductor with an inductance of L and the voltage across the capacitor with a capacitance of C. The developed simulation model uses Runge-Kutta methods to solve the state equations. This study focuses on predicting the fault of the circuit from the two aspects of the harmonic distortion and simulation results. Moreover, the presented model is also used to research the working state of the system in the case of a load capacitance catastrophe. The nonlinear dynamic behaviors in the inverter are simulated and verified.

Dynamical characteristics of surface EMG signals of hand grasps via recurrence plot.

PubMed

Ouyang, Gaoxiang; Zhu, Xiangyang; Ju, Zhaojie; Liu, Honghai

2014-01-01

Recognizing human hand grasp movements through surface electromyogram (sEMG) is a challenging task. In this paper, we investigated nonlinear measures based on recurrence plot, as a tool to evaluate the hidden dynamical characteristics of sEMG during four different hand movements. A series of experimental tests in this study show that the dynamical characteristics of sEMG data with recurrence quantification analysis (RQA) can distinguish different hand grasp movements. Meanwhile, adaptive neuro-fuzzy inference system (ANFIS) is applied to evaluate the performance of the aforementioned measures to identify the grasp movements. The experimental results show that the recognition rate (99.1%) based on the combination of linear and nonlinear measures is much higher than those with only linear measures (93.4%) or nonlinear measures (88.1%). These results suggest that the RQA measures might be a potential tool to reveal the sEMG hidden characteristics of hand grasp movements and an effective supplement for the traditional linear grasp recognition methods.

Joint symbolic dynamic analysis of cardiorespiratory interactions in patients on weaning trials.

PubMed

Caminal, P; Giraldo, B; Zabaleta, H; Vallverdu, M; Benito, S; Ballesteros, D; Lopez-Rodriguez, L; Esteban, A; Baumert, M; Voss, A

2005-01-01

Assessing autonomic control provides information about patho-physiological imbalances. Measures of variability of the cardiac interbeat duration RR(n) and the variability of the breath duration TTot(n) are sensitive to those changes. The interactions between RR(n) and TTot(n) are complex and strongly non-linear. A study of joint symbolic dynamics is presented as a new short-term non-linear analysis method to investigate these interactions in patients on weaning trials. 78 patients from mechanical ventilation are studied: Group A (patients that failed to maintain spontaneous breathing and were reconnected) and Group B (patients with successful trials). Using the concept of joint symbolic dynamics, cardiac and respiratory changes were transformed into a word series, and the probability of occurrence of each word type was calculated and compared between both groups. Significant differences were found in 13 words, and the most significant pn(Wc010, r010): 0.0041 ± 0.0036 (group A) against 0.0012 ± 0.0024 (group B), p-value = 0.00001. The number of seldom occurring word types (forbidden words) also presents significant differences fwcr: 6.9 ± 6.6 against 13.5 ± 5.3, p-value = 0.00004. Joint symbolic dynamics provides an efficient non-linear representation of cardiorespiratory interactions that offers simple physiological interpretations.

The cortical focus in childhood absence epilepsy; evidence from nonlinear analysis of scalp EEG recordings.

PubMed

Sarrigiannis, Ptolemaios G; Zhao, Yifan; He, Fei; Billings, Stephen A; Baster, Kathleen; Rittey, Chris; Yianni, John; Zis, Panagiotis; Wei, Hualiang; Hadjivassiliou, Marios; Grünewald, Richard

2018-03-01

To determine the origin and dynamic characteristics of the generalised hyper-synchronous spike and wave (SW) discharges in childhood absence epilepsy (CAE). We applied nonlinear methods, the error reduction ratio (ERR) causality test and cross-frequency analysis, with a nonlinear autoregressive exogenous (NARX) model, to electroencephalograms (EEGs) from CAE, selected with stringent electro-clinical criteria (17 cases, 42 absences). We analysed the pre-ictal and ictal strength of association between homologous and heterologous EEG derivations and estimated the direction of synchronisation and corresponding time lags. A frontal/fronto-central onset of the absences is detected in 13 of the 17 cases with the highest ictal strength of association between homologous frontal followed by centro-temporal and fronto-central areas. Delays consistently in excess of 4 ms occur at the very onset between these regions, swiftly followed by the emergence of "isochronous" (0-2 ms) synchronisation but dynamic time lag changes occur during SW discharges. In absences an initial cortico-cortical spread leads to dynamic lag changes to include periods of isochronous interhemispheric synchronisation, which we hypothesize is mediated by the thalamus. Absences from CAE show ictal epileptic network dynamics remarkably similar to those observed in WAG/Rij rats which guided the formulation of the cortical focus theory. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

NASA Astrophysics Data System (ADS)

Koh, Heeyuen; Cannon, James; Chiashi, Shohei; Shiomi, Junichiro; Maruyama, Shigeo

2013-03-01

Based on the finding that the lowest frequency mode of cantilevered SWNT is described by the continuum beam theory in frequency domain, we considered its effect of the symmetric structure for the coupling of orthogonal transverse modes to explain the nonlinear motion of free thermal vibration. This nonlinear motion calculated by our molecular dynamics simulation, once regarded as noise, is observed to have the periodic order with duffing and beating, which is dependent on aspect ratio and temperature. It could be dictated by the governing equation from the Green Lagrangian strain tensor. The nonlinear beam equation from strain tensor described the motion well for various models which has different aspect ratio in molecular dynamics simulation. Since this motion is nothing but the interaction between 2nd mode of radial, tangential mode and 1st longitudinal mode, it was found that Green Lagrangian strain tensor is capable to deal such coupling. The free thermal motion of suspended SWNT is also considered without temperature gradient. The Q factor measured by this theoretical analysis will be discussed. Part of this work was financially supported by Grant-in-Aid for Scientific Research (19054003 and 22226006), and Global COE Program 'Global Center for Excellence for Mechanical Systems Innovation'

Nonlinear dynamics of cardiovascular ageing

PubMed Central

Shiogai, Y.; Stefanovska, A.; McClintock, P.V.E.

2010-01-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing. PMID:20396667

Nonlinear dynamics of cardiovascular ageing

NASA Astrophysics Data System (ADS)

Shiogai, Y.; Stefanovska, A.; McClintock, P. V. E.

2010-03-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

State Anxiety and Nonlinear Dynamics of Heart Rate Variability in Students

PubMed Central

Dimitriev, Aleksey D.

2016-01-01

Objectives Clinical and experimental research studies have demonstrated that the emotional experience of anxiety impairs heart rate variability (HRV) in humans. The present study investigated whether changes in state anxiety (SA) can also modulate nonlinear dynamics of heart rate. Methods A group of 96 students volunteered to participate in the study. For each student, two 5-minute recordings of beat intervals (RR) were performed: one during a rest period and one just before a university examination, which was assumed to be a real-life stressor. Nonlinear analysis of HRV was performed. The Spielberger’s State-Trait Anxiety Inventory was used to assess the level of SA. Results Before adjusting for heart rate, a Wilcoxon matched pairs test showed significant decreases in Poincaré plot measures, entropy, largest Lyapunov exponent (LLE), and pointwise correlation dimension (PD2), and an increase in the short-term fractal-like scaling exponent of detrended fluctuation analysis (α1) during the exam session, compared with the rest period. A Pearson analysis indicated significant negative correlations between the dynamics of SA and Poincaré plot axes ratio (SD1/SD2), and between changes in SA and changes in entropy measures. A strong negative correlation was found between the dynamics of SA and LLE. A significant positive correlation was found between the dynamics of SA and α1. The decreases in Poincaré plot measures (SD1, complex correlation measure), entropy measures, and LLE were still significant after adjusting for heart rate. Corrected α1 was increased during the exam session. As before, the dynamics of adjusted LLE was significantly correlated with the dynamics of SA. Conclusions The qualitative increase in SA during academic examination was related to the decrease in the complexity and size of the Poincaré plot through a reduction of both the interbeat interval and its variation. PMID:26807793

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Adaptive integral dynamic surface control of a hypersonic flight vehicle

NASA Astrophysics Data System (ADS)

Aslam Butt, Waseem; Yan, Lin; Amezquita S., Kendrick

2015-07-01

In this article, non-linear adaptive dynamic surface air speed and flight path angle control designs are presented for the longitudinal dynamics of a flexible hypersonic flight vehicle. The tracking performance of the control design is enhanced by introducing a novel integral term that caters to avoiding a large initial control signal. To ensure feasibility, the design scheme incorporates magnitude and rate constraints on the actuator commands. The uncertain non-linear functions are approximated by an efficient use of the neural networks to reduce the computational load. A detailed stability analysis shows that all closed-loop signals are uniformly ultimately bounded and the ? tracking performance is guaranteed. The robustness of the design scheme is verified through numerical simulations of the flexible flight vehicle model.

Theoretical investigation of the force and dynamically coupled torsional-axial-lateral dynamic response of eared rotors

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1982-01-01

Difficulties in solution methodology to be used to deal with the potentially higher nonlinear rotor equations when dynamic coupling is included. A solution methodology is selected to solve the nonlinear differential equations. The selected method was verified to give good results even at large nonlinearity levels. The transfer matrix methodology is extended to the solution of nonlinear problems.

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

PubMed

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Y.; Borland, Michael

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling

DTIC Science & Technology

1999-12-31

incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

EPA Science Inventory

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

Modelling, validation and analysis of a three-dimensional railway vehicle-track system model with linear and nonlinear track properties in the presence of wheel flats

NASA Astrophysics Data System (ADS)

Uzzal, R. U. A.; Ahmed, A. K. W.; Bhat, R. B.

2013-11-01

This paper presents dynamic contact loads at wheel-rail contact point in a three-dimensional railway vehicle-track model as well as dynamic response at vehicle-track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel-rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle-track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel-rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel-rail impact forces that arise in the wheel-rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary-wave solutions, and the numerical results are in very good agreement with the collective-coordinate approach.

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Improved Design of Tunnel Supports : Volume 3 : Finite Element Analysis of the Peachtree Center Station in Atlanta

DOT National Transportation Integrated Search

1980-06-01

Volume 3 contains the application of the three-dimensional (3-D) finite element program, Automatic Dynamic Incremental Nonlinear Analysis (ADINA), which was designed to replace the traditional 2-D plane strain analysis, to a specific location. The lo...

Study on longitudinal force simulation of heavy-haul train

NASA Astrophysics Data System (ADS)

Chang, Chongyi; Guo, Gang; Wang, Junbiao; Ma, Yingming

2017-04-01

The longitudinal dynamics model of heavy-haul trains and air brake model used in the longitudinal train dynamics (LTDs) are established. The dry friction damping hysteretic characteristic of steel friction draft gears is simulated by the equation which describes the suspension forces in truck leaf springs. The model of draft gears introduces dynamic loading force, viscous friction of steel friction and the damping force. Consequently, the numerical model of the draft gears is brought forward. The equation of LTDs is strongly non-linear. In order to solve the response of the strongly non-linear system, the high-precision and equilibrium iteration method based on the Newmark-β method is presented and numerical analysis is made. Longitudinal dynamic forces of the 20,000 tonnes heavy-haul train are tested, and models and solution method provided are verified by the test results.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

Dynamic response signatures of a scaled model platform for floating wind turbines in an ocean wave basin.

PubMed

Jaksic, V; O'Shea, R; Cahill, P; Murphy, J; Mandic, D P; Pakrashi, V

2015-02-28

Understanding of dynamic behaviour of offshore wind floating substructures is extremely important in relation to design, operation, maintenance and management of floating wind farms. This paper presents assessment of nonlinear signatures of dynamic responses of a scaled tension-leg platform (TLP) in a wave tank exposed to different regular wave conditions and sea states characterized by the Bretschneider, the Pierson-Moskowitz and the JONSWAP spectra. Dynamic responses of the TLP were monitored at different locations using load cells, a camera-based motion recognition system and a laser Doppler vibrometer. The analysis of variability of the TLP responses and statistical quantification of their linearity or nonlinearity, as non-destructive means of structural monitoring from the output-only condition, remains a challenging problem. In this study, the delay vector variance (DVV) method is used to statistically study the degree of nonlinearity of measured response signals from a TLP. DVV is observed to create a marker estimating the degree to which a change in signal nonlinearity reflects real-time behaviour of the structure and also to establish the sensitivity of the instruments employed to these changes. The findings can be helpful in establishing monitoring strategies and control strategies for undesirable levels or types of dynamic response and can help to better estimate changes in system characteristics over the life cycle of the structure. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Databases for the Global Dynamics of Multiparameter Nonlinear Systems

DTIC Science & Technology

2014-03-05

AFRL-OSR-VA-TR-2014-0078 DATABASES FOR THE GLOBAL DYNAMICS OF MULTIPARAMETER NONLINEAR SYSTEMS Konstantin Mischaikow RUTGERS THE STATE UNIVERSITY OF...University of New Jersey ASB III, Rutgers Plaza New Brunswick, NJ 08807 DATABASES FOR THE GLOBAL DYNAMICS OF MULTIPARAMETER NONLINEAR SYSTEMS ...dynamical systems . We refer to the output as a Database for Global Dynamics since it allows the user to query for information about the existence and

A nonlinear delayed model for the immune response in the presence of viral mutation

NASA Astrophysics Data System (ADS)

Messias, D.; Gleria, Iram; Albuquerque, S. S.; Canabarro, Askery; Stanley, H. E.

2018-02-01

We consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains a wild-type virus and a mutant. We consider the finite response time of the immune system and find sustained oscillatory behavior as well as chaotic behavior triggered by the presence of delays. We present a numeric analysis and some analytical results.

The commodity terms of trade, unit roots, and nonlinear alternatives: a smooth transition approach

Treesearch

Barry K. Goodwin; Matthew T. Holt; Jeffrey P. Prestemon

2008-01-01

Market price dynamics for North American oriented strand board markets are examined.  Specifically, the role of transactions costs are examined vis-a-vis the law of one price. Weekly data for the January 3rd, 1995 through April 14th, 2006 period are used in the analysis. Nonlinearities induced by unobservable transactions costs are modelled by estimating smooth...

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Josiński, Henryk; Świtoński, Adam; Silesian University of Technology, Akademicka 16, 44-100 Gliwice

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

Sobol’ sensitivity analysis for stressor impacts on honeybee colonies

EPA Science Inventory

We employ Monte Carlo simulation and nonlinear sensitivity analysis techniques to describe the dynamics of a bee exposure model, VarroaPop. Daily simulations are performed of hive population trajectories, taking into account queen strength, foraging success, mite impacts, weather...

Nonlinear time series analysis of electrocardiograms

NASA Astrophysics Data System (ADS)

Bezerianos, A.; Bountis, T.; Papaioannou, G.; Polydoropoulos, P.

1995-03-01

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's ``dimension.'' We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three ``normal'' subjects and three ``heavy smokers'' at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics.

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

NASA Astrophysics Data System (ADS)

Xian, Bin; Zhang, Yao

2016-06-01

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.

A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band

NASA Astrophysics Data System (ADS)

Sun, Xiuting; Jing, Xingjian

2016-12-01

This study investigates theoretically and experimentally a vibration isolator constructed by an n-layer Scissor-Like Structure (SLS), focusing on the analysis and design of nonlinear stiffness and damping characteristics for advantageous isolation performance in both orthogonal directions. With the mathematical modeling, the influence incurred by different structural parameters on system isolation performance is studied. It is shown that, (a) nonlinear high-static-low-dynamic stiffness and damping characteristics can be seen such that the system can achieve good isolation performance in both directions, (b) an anti-resonance frequency band exists due to the coupling effect between the linear and nonlinear stiffness in the two orthogonal directions within the structure, and (c) all these performances are designable with several structural parameters. The advantages of the proposed system are shown through comparisons with an existing quasi-zero-stiffness vibration isolator (QZS-VI) and a traditional mass-spring-damper vibration isolator (MSD-VI), and further validated by experimental results.

Computational Aeroelastic Modeling of Airframes and TurboMachinery: Progress and Challenges

NASA Technical Reports Server (NTRS)

Bartels, R. E.; Sayma, A. I.

2006-01-01

Computational analyses such as computational fluid dynamics and computational structural dynamics have made major advances toward maturity as engineering tools. Computational aeroelasticity is the integration of these disciplines. As computational aeroelasticity matures it too finds an increasing role in the design and analysis of aerospace vehicles. This paper presents a survey of the current state of computational aeroelasticity with a discussion of recent research, success and continuing challenges in its progressive integration into multidisciplinary aerospace design. This paper approaches computational aeroelasticity from the perspective of the two main areas of application: airframe and turbomachinery design. An overview will be presented of the different prediction methods used for each field of application. Differing levels of nonlinear modeling will be discussed with insight into accuracy versus complexity and computational requirements. Subjects will include current advanced methods (linear and nonlinear), nonlinear flow models, use of order reduction techniques and future trends in incorporating structural nonlinearity. Examples in which computational aeroelasticity is currently being integrated into the design of airframes and turbomachinery will be presented.

The analysis on nonlinear control of the aircraft arresting system

NASA Astrophysics Data System (ADS)

Song, Jinchun; Du, Tianrong

2005-12-01

The aircraft arresting system is a complicated nonlinear system. This paper analyzes the mechanical-hydraulic structure of aircraft arresting system composed of electro hydraulic valve and establishes the dynamic equation of the aircraft arresting system. Based on the state-feedback linearization of nonlinear system, a PD-based controller is synthesized. Simulation studies indicate, while arresting the different type aircraft, the proposed controller has fast response, good tracking performance and strong robustness. By tuning the parameters of the PD controller, a satisfactory control performance can be guaranteed.

Pupil movements to light and accommodative stimulation - A comparative study.

NASA Technical Reports Server (NTRS)

Semmlow, J.; Stark, L.

1973-01-01

Isolation and definition of specific response components in pupil reflexes through comparison of the dynamic features of light-induced and accommodation-induced pupil movements. A quantitative analysis of the behavior of the complex nonlinear pupil responses reveals the presence of two independent nonlinear characteristics: a range-dependent gain and a direction dependence or movement asymmetry. These nonlinear properties are attributed to motor processes because they are observable in pupil responses to both light and accommodation stimuli. The possible mechanisms and consequences of these pupil response characteristics are quantitatively defined and discussed.

Potential for wind extraction from 4D-Var assimilation of aerosols and moisture

NASA Astrophysics Data System (ADS)

Zaplotnik, Žiga; Žagar, Nedjeljka

2017-04-01

We discuss the potential of the four-dimensional variational data assimilation (4D-Var) to retrieve the unobserved wind field from observations of atmospheric tracers and the mass field through internal model dynamics and the multivariate relationships in the background-error term for 4D-Var. The presence of non-linear moist dynamics makes the wind retrieval from tracers very difficult. On the other hand, it has been shown that moisture observations strongly influence both tropical and mid-latitude wind field in 4D-Var. We present an intermediate complexity model that describes nonlinear interactions between the wind, temperature, aerosols and moisture including their sinks and sources in the framework of the so-called first baroclinic mode atmosphere envisaged by A. Gill. Aerosol physical processes, which are included in the model, are the non-linear advection, diffusion and sources and sinks that exist as dry and wet deposition and diffusion. Precipitation is parametrized according to the Betts-Miller scheme. The control vector for 4D-Var includes aerosols, moisture and the three dynamical variables. The former is analysed univariately whereas wind field and mass field are analysed in a multivariate fashion taking into account quasi-geostrophic and unbalanced dynamics. The OSSE type of studies are performed for the tropical region to assess the ability of 4D-Var to extract wind-field information from the time series of observations of tracers as a function of the flow nonlinearity, the observations density and the length of the assimilation window (12 hours and 24 hours), in dry and moist environment. Results show that the 4D-Var assimilation of aerosols and temperature data is beneficial for the wind analysis with analysis errors strongly dependent on the moist processes and reliable background-error covariances.

Empirical Investigation of Critical Transitions in Paleoclimate

NASA Astrophysics Data System (ADS)

Loskutov, E. M.; Mukhin, D.; Gavrilov, A.; Feigin, A.

2016-12-01

In this work we apply a new empirical method for the analysis of complex spatially distributed systems to the analysis of paleoclimate data. The method consists of two general parts: (i) revealing the optimal phase-space variables and (ii) construction the empirical prognostic model by observed time series. The method of phase space variables construction based on the data decomposition into nonlinear dynamical modes which was successfully applied to global SST field and allowed clearly separate time scales and reveal climate shift in the observed data interval [1]. The second part, the Bayesian approach to optimal evolution operator reconstruction by time series is based on representation of evolution operator in the form of nonlinear stochastic function represented by artificial neural networks [2,3]. In this work we are focused on the investigation of critical transitions - the abrupt changes in climate dynamics - in match longer time scale process. It is well known that there were number of critical transitions on different time scales in the past. In this work, we demonstrate the first results of applying our empirical methods to analysis of paleoclimate variability. In particular, we discuss the possibility of detecting, identifying and prediction such critical transitions by means of nonlinear empirical modeling using the paleoclimate record time series. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep155102. Ya. I. Molkov, D. N. Mukhin, E. M. Loskutov, A.M. Feigin, (2012) : Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.3. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962-1976. http://doi.org/10.1175/JCLI-D-14-00240.1

Perturbation and Nonlinear Dynamic Analysis of Different Singing Styles

PubMed Central

Butte, Caitlin J.; Zhang, Yu; Song, Huangqiang; Jiang, Jack J.

2012-01-01

Summary Previous research has used perturbation analysis methods to study the singing voice. Using perturbation and nonlinear dynamic analysis (NDA) methods in conjunction may provide more accurate information on the singing voice and may distinguish vocal usage in different styles. Acoustic samples from different styles of singing were compared using nonlinear dynamic and perturbation measures. Twenty-six songs from different musical styles were obtained from an online music database (Rhapsody, RealNetworks, Inc., Seattle, WA). One-second samples were selected from each song for analysis. Perturbation analyses of jitter, shimmer, and signal-to-noise ratio and NDA of correlation dimension (D2) were performed on samples from each singing style. Percent jitter and shimmer median values were low normal for country (0.32% and 3.82%), musical theater (MT) (0.280% and 2.80%), jazz (0.440% and 2.34%), and soul (0.430% and 6.42%). The popular style had slightly higher median jitter and shimmer values (1.13% and 6.78%) than other singing styles, although this was not statistically significant. The opera singing style had median jitter of 0.520%, and yielded significantly high shimmer (P = 0.001) of 7.72%. All six singing styles were measured reliably using NDA, indicating that operatic singing is notably more chaotic than other singing styles. Median correlation dimension values were low to normal, compared to healthy voices, in country (median D2 = 2.14), jazz (median D2 = 2.24), pop (median D2 = 2.60), MT (median D2 = 2.73), and soul (mean D2 = 3.26). Correlation dimension was significantly higher in opera (P < 0.001) with median D2 = 6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D2, suggesting that it is more irregular than other singing styles; a previously unknown quality of opera singing. Perturbation analysis also suggested significant differences in vocal output in different singing styles. This preliminary study using acoustic analysis with nonlinear dynamic measures and perturbation measures may represent a valuable procedure in quantitatively describing the properties of the singing voice. Further research with human test subjects may allow us to characterize singing styles and diagnose vocal dysfunction in the singing voice. PMID:18504114

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

PubMed

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Advances in engineering science, volume 2

NASA Technical Reports Server (NTRS)

1976-01-01

Papers are presented dealing with structural dynamics; structural synthesis; and the nonlinear analysis of structures, structural members, and composite structures and materials. Applications of mathematics and computer science are included.

Protein Aggregation/Folding: The Role of Deterministic Singularities of Sequence Hydrophobicity as Determined by Nonlinear Signal Analysis of Acylphosphatase and Aβ(1–40)

PubMed Central

Zbilut, Joseph P.; Colosimo, Alfredo; Conti, Filippo; Colafranceschi, Mauro; Manetti, Cesare; Valerio, MariaCristina; Webber, Charles L.; Giuliani, Alessandro

2003-01-01

The problem of protein folding vs. aggregation was investigated in acylphosphatase and the amyloid protein Aβ(1–40) by means of nonlinear signal analysis of their chain hydrophobicity. Numerical descriptors of recurrence patterns provided the basis for statistical evaluation of folding/aggregation distinctive features. Static and dynamic approaches were used to elucidate conditions coincident with folding vs. aggregation using comparisons with known protein secondary structure classifications, site-directed mutagenesis studies of acylphosphatase, and molecular dynamics simulations of amyloid protein, Aβ(1–40). The results suggest that a feature derived from principal component space characterized by the smoothness of singular, deterministic hydrophobicity patches plays a significant role in the conditions governing protein aggregation. PMID:14645049

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kanjilal, Oindrila, E-mail: oindrila@civil.iisc.ernet.in; Manohar, C.S., E-mail: manohar@civil.iisc.ernet.in

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the secondmore » explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations. - Highlights: • The distance minimizing control forces minimize a bound on the sampling variance. • Establishing Girsanov controls via solution of a two-point boundary value problem. • Girsanov controls via Volterra's series representation for the transfer functions.« less

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Emergent geometries and nonlinear-wave dynamics in photon fluids.

PubMed

Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D

2016-03-22

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Emergent geometries and nonlinear-wave dynamics in photon fluids

NASA Astrophysics Data System (ADS)

Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.

2016-03-01

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

PubMed

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

GPU-based acceleration of computations in nonlinear finite element deformation analysis.

PubMed

Mafi, Ramin; Sirouspour, Shahin

2014-03-01

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.

Synthesizing Virtual Oscillators to Control Islanded Inverters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged modelsmore » reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.« less

Nonlinear dynamic range transformation in visual communication channels.

PubMed

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

Recent Progress in Heliogyro Solar Sail Structural Dynamics

NASA Technical Reports Server (NTRS)

Wilkie, William K.; Warren, Jerry E.; Horta, Lucas G.; Juang, Jer-Nan; Gibbs, Samuel C.; Dowell, E.; Guerrant, Daniel; Lawrence Dale

2014-01-01

Results from recent National Aeronautics and Space Administration (NASA) research on the structural dynamics and control characteristics of heliogyro solar sails are summarized. Specific areas under investigation include coupled nonlinear finite element analysis of heliogyro membrane blade with solar radiation pressure effects, system identification of spinning membrane structures, solarelastic stability analysis of heliogyro solar sails, including stability during blade deployment, and results from small-scale in vacuo dynamics experiments with spinning high-aspect ratio membranes. A low-cost, rideshare payload heliogyro technology demonstration mission concept, used as a mission context for these heliogyro structural dynamics and solarelasticity investigations, is also described.

Nonlinear histogram binning for quantitative analysis of lung tissue fibrosis in high-resolution CT data

NASA Astrophysics Data System (ADS)

Zavaletta, Vanessa A.; Bartholmai, Brian J.; Robb, Richard A.

2007-03-01

Diffuse lung diseases, such as idiopathic pulmonary fibrosis (IPF), can be characterized and quantified by analysis of volumetric high resolution CT scans of the lungs. These data sets typically have dimensions of 512 x 512 x 400. It is too subjective and labor intensive for a radiologist to analyze each slice and quantify regional abnormalities manually. Thus, computer aided techniques are necessary, particularly texture analysis techniques which classify various lung tissue types. Second and higher order statistics which relate the spatial variation of the intensity values are good discriminatory features for various textures. The intensity values in lung CT scans range between [-1024, 1024]. Calculation of second order statistics on this range is too computationally intensive so the data is typically binned between 16 or 32 gray levels. There are more effective ways of binning the gray level range to improve classification. An optimal and very efficient way to nonlinearly bin the histogram is to use a dynamic programming algorithm. The objective of this paper is to show that nonlinear binning using dynamic programming is computationally efficient and improves the discriminatory power of the second and higher order statistics for more accurate quantification of diffuse lung disease.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Econometric testing on linear and nonlinear dynamic relation between stock prices and macroeconomy in China

NASA Astrophysics Data System (ADS)

Borjigin, Sumuya; Yang, Yating; Yang, Xiaoguang; Sun, Leilei

2018-03-01

Many researchers have realized that there is a strong correlation between stock prices and macroeconomy. In order to make this relationship clear, a lot of studies have been done. However, the causal relationship between stock prices and macroeconomy has still not been well explained. A key point is that, most of the existing research adopts linear and stable models to investigate the correlation of stock prices and macroeconomy, while the real causality of that may be nonlinear and dynamic. To fill this research gap, we investigate the nonlinear and dynamic causal relationships between stock prices and macroeconomy. Based on the case of China's stock prices and acroeconomy measures from January 1992 to March 2017, we compare the linear Granger causality test models with nonlinear ones. Results demonstrate that the nonlinear dynamic Granger causality is much stronger than linear Granger causality. From the perspective of nonlinear dynamic Granger causality, China's stock prices can be viewed as "national economic barometer". On the one hand, this study will encourage researchers to take nonlinearity and dynamics into account when they investigate the correlation of stock prices and macroeconomy; on the other hand, our research can guide regulators and investors to make better decisions.

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Nonlinear analysis and dynamic structure in the energy market

NASA Astrophysics Data System (ADS)

Aghababa, Hajar

This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non-OPEC production time series data does not reveal signs of nonlinearity. The third essay explores nonlinear structure in the case of high dimensionality of the observations, different frequencies of sample sizes, and division of the samples into sub-samples. It systematically examines the robustness of the inference methods at various levels of time aggregation by employing daily spot prices on crude oil for 26 years as well as monthly spot price index on crude oil for 41 years. The daily and monthly samples are divided into sub-samples as well. All the tests detect strong evidence of nonlinear structure in the daily spot price of crude oil; whereas in monthly observations the evidence of nonlinear dependence is less dramatic, indicating that the nonlinear serial dependence will not be as intense when the time aggregation increase in time series observations.

Quantitative EEG analysis using error reduction ratio-causality test; validation on simulated and real EEG data.

PubMed

Sarrigiannis, Ptolemaios G; Zhao, Yifan; Wei, Hua-Liang; Billings, Stephen A; Fotheringham, Jayne; Hadjivassiliou, Marios

2014-01-01

To introduce a new method of quantitative EEG analysis in the time domain, the error reduction ratio (ERR)-causality test. To compare performance against cross-correlation and coherence with phase measures. A simulation example was used as a gold standard to assess the performance of ERR-causality, against cross-correlation and coherence. The methods were then applied to real EEG data. Analysis of both simulated and real EEG data demonstrates that ERR-causality successfully detects dynamically evolving changes between two signals, with very high time resolution, dependent on the sampling rate of the data. Our method can properly detect both linear and non-linear effects, encountered during analysis of focal and generalised seizures. We introduce a new quantitative EEG method of analysis. It detects real time levels of synchronisation in the linear and non-linear domains. It computes directionality of information flow with corresponding time lags. This novel dynamic real time EEG signal analysis unveils hidden neural network interactions with a very high time resolution. These interactions cannot be adequately resolved by the traditional methods of coherence and cross-correlation, which provide limited results in the presence of non-linear effects and lack fidelity for changes appearing over small periods of time. Copyright © 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Describing Function Techniques for the Non-Linear Analysis of the Dynamics of a Rail Vehicle Wheelset

DOT National Transportation Integrated Search

1975-07-01

The describing function method of analysis is applied to investigate the influence of parametric variations on wheelset critical velocity. In addition, the relationship between the amplitude of sustained lateral oscillations and critical speed is der...

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

NASA Astrophysics Data System (ADS)

Jokhio, G. A.; Izzuddin, B. A.

2015-05-01

This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

Simulation of crash tests for high impact levels of a new bridge safety barrier

NASA Astrophysics Data System (ADS)

Drozda, Jiří; Rotter, Tomáš

2017-09-01

The purpose is to show the opportunity of a non-linear dynamic impact simulation and to explain the possibility of using finite element method (FEM) for developing new designs of safety barriers. The main challenge is to determine the means to create and validate the finite element (FE) model. The results of accurate impact simulations can help to reduce necessary costs for developing of a new safety barrier. The introductory part deals with the creation of the FE model, which includes the newly-designed safety barrier and focuses on the application of an experimental modal analysis (EMA). The FE model has been created in ANSYS Workbench and is formed from shell and solid elements. The experimental modal analysis, which was performed on a real pattern, was employed for measuring the modal frequencies and shapes. After performing the EMA, the FE mesh was calibrated after comparing the measured modal frequencies with the calculated ones. The last part describes the process of the numerical non-linear dynamic impact simulation in LS-DYNA. This simulation was validated after comparing the measured ASI index with the calculated ones. The aim of the study is to improve professional public knowledge about dynamic non-linear impact simulations. This should ideally lead to safer, more accurate and profitable designs.

On the origin of nonlinear elasticity in disparate rocks

DOE PAGES

Riviere, Jacques Vincent; Shokouhi, Parisa; Guyer, Robert A.; ...

2015-03-31

Dynamic acousto-elastic (DAE) studies are performed on a set of 6 rock samples (four sandstones, one soapstone, and one granite). From these studies, at 20 strain levels 10 -7 < ϵ < 10 -5, four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy (NRUS) and a fth measure of nonlinear elastic response is found. The ve measures of the nonlinear elastic response of the samples (approximately 3 x 6 x 20 x 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis usingmore » model independent statistical methods, principal component analysis and fuzzy clustering. This analysis reveals di erences among the samples and di erences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fth is seeing something di erent. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classi cation of the samples into two groups. The numbers in this study and the classi cation of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.« less

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations

NASA Astrophysics Data System (ADS)

Kishor, Ram; Kushvah, Badam Singh

2017-09-01

For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which is very helpful to obtain the information as regards a realistic solution of the problem. In the present study, normalization of the Hamiltonian and analysis of nonlinear stability in non-resonance case, in the Chermnykh-like problem under the influence of perturbations in the form of radiation pressure, oblateness, and a disc is performed. To describe nonlinear stability, initially, quadratic part of the Hamiltonian is normalized in the neighborhood of triangular equilibrium point and then higher order normalization is performed by computing the fourth order normalized Hamiltonian with the help of Lie transforms. In non-resonance case, nonlinear stability of the system is discussed using the Arnold-Moser theorem. Again, the effects of radiation pressure, oblateness and the presence of the disc are analyzed separately and it is observed that in the absence as well as presence of perturbation parameters, triangular equilibrium point is unstable in the nonlinear sense within the stability range 0<μ<μ1=\\bar{μc} due to failure of the Arnold-Moser theorem. However, perturbation parameters affect the values of μ at which D4=0, significantly. This study may help to analyze more generalized cases of the problem in the presence of some other types of perturbations such as P-R drag and solar wind drag. The results are limited to the regular symmetric disc but it can be extended in the future.

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Dynamic Stiffness Transfer Function of an Electromechanical Actuator Using System Identification

NASA Astrophysics Data System (ADS)

Kim, Sang Hwa; Tahk, Min-Jea

2018-04-01

In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.

[Recurrence plot analysis of HRV for brain ischemia and asphyxia].

PubMed

Chen, Xiaoming; Qiu, Yihong; Zhu, Yisheng

2008-02-01

Heart rate variability (HRV) is the tiny variability existing in the cycles of the heart beats, which reflects the corresponding balance between sympathetic and vagus nerves. Since the nonlinear characteristic of HRV is confirmed, the Recurrence Plot method, a nonlinear dynamic analysis method based on the complexity, could be used to analyze HRV. The results showed the recurrence plot structures and some quantitative indices (L-Mean, L-Entr) during asphyxia insult vary significantly as compared to those in normal conditions, which offer a new method to monitor brain asphyxia injury.

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor.

PubMed

Gotoda, Hiroshi; Amano, Masahito; Miyano, Takaya; Ikawa, Takuya; Maki, Koshiro; Tachibana, Shigeru

2012-12-01

We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.

Rogue-wave pattern transition induced by relative frequency.

PubMed

Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying

2014-08-01

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

Nonlinear calculations of the time evolution of black hole accretion disks

NASA Technical Reports Server (NTRS)

Luo, C.

1994-01-01

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Application of Probabilistic Analysis to Aircraft Impact Dynamics

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Padula, Sharon L.; Stockwell, Alan E.

2003-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stressstrain behaviors, laminated composites, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the uncertainty in the simulated responses. Several criteria are used to determine that a response surface method is the most appropriate probabilistic approach. The work is extended to compare optimization results with and without probabilistic constraints.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Orbital stability analysis in biomechanics: a systematic review of a nonlinear technique to detect instability of motor tasks.

PubMed

Riva, F; Bisi, M C; Stagni, R

2013-01-01

Falls represent a heavy economic and clinical burden on society. The identification of individual chronic characteristics associated with falling is of fundamental importance for the clinicians; in particular, the stability of daily motor tasks is one of the main factors that the clinicians look for during assessment procedures. Various methods for the assessment of stability in human movement are present in literature, and methods coming from stability analysis of nonlinear dynamic systems applied to biomechanics recently showed promise. One of these techniques is orbital stability analysis via Floquet multipliers. This method allows to measure orbital stability of periodic nonlinear dynamic systems and it seems a promising approach for the definition of a reliable motor stability index, taking into account for the whole task cycle dynamics. Despite the premises, its use in the assessment of fall risk has been deemed controversial. The aim of this systematic review was therefore to provide a critical evaluation of the literature on the topic of applications of orbital stability analysis in biomechanics, with particular focus to methodologic aspects. Four electronic databases have been searched for articles relative to the topic; 23 articles were selected for review. Quality of the studies present in literature has been assessed with a customised quality assessment tool. Overall quality of the literature in the field was found to be high. The most critical aspect was found to be the lack of uniformity in the implementation of the analysis to biomechanical time series, particularly in the choice of state space and number of cycles to include in the analysis. Copyright © 2012 Elsevier B.V. All rights reserved.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Archetypes for Organisational Safety

NASA Technical Reports Server (NTRS)

Marais, Karen; Leveson, Nancy G.

2003-01-01

We propose a framework using system dynamics to model the dynamic behavior of organizations in accident analysis. Most current accident analysis techniques are event-based and do not adequately capture the dynamic complexity and non-linear interactions that characterize accidents in complex systems. In this paper we propose a set of system safety archetypes that model common safety culture flaws in organizations, i.e., the dynamic behaviour of organizations that often leads to accidents. As accident analysis and investigation tools, the archetypes can be used to develop dynamic models that describe the systemic and organizational factors contributing to the accident. The archetypes help clarify why safety-related decisions do not always result in the desired behavior, and how independent decisions in different parts of the organization can combine to impact safety.

Vibration signature analysis of multistage gear transmission

NASA Technical Reports Server (NTRS)

Choy, F. K.; Tu, Y. K.; Savage, M.; Townsend, D. P.

1989-01-01

An analysis is presented for multistage multimesh gear transmission systems. The analysis predicts the overall system dynamics and the transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional model characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics coupling in the system. The method synthesizes the interaction of each modal component or stage with the nonlinear gear mesh dynamics and the modal support geometry characteristics. The analysis simulates transient and steady state vibration events to determine the resulting torque variations, speeds, changes, rotor imbalances, and support gear box motion excitations. A vibration signature analysis examines the overall dynamic characteristics of the system, and the individual model component responses. The gear box vibration analysis also examines the spectral characteristics of the support system.

Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Faybishenko, Boris

2002-11-27

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fracturedmore » rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.« less

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Detection of traffic incidents using nonlinear time series analysis

NASA Astrophysics Data System (ADS)

Fragkou, A. D.; Karakasidis, T. E.; Nathanail, E.

2018-06-01

In this study, we present results of the application of nonlinear time series analysis on traffic data for incident detection. More specifically, we analyze daily volume records of Attica Tollway (Greece) collected from sensors located at various locations. The analysis was performed using the Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) method of the volume data of the lane closest to the median. The results show that it is possible to identify, through the abrupt change of the dynamics of the system revealed by RPs and RQA, the occurrence of incidents on the freeway and differentiate from recurrent traffic congestion. The proposed methodology could be of interest for big data traffic analysis.

Empirical and Theoretical Aspects of Generation and Transfer of Information in a Neuromagnetic Source Network

PubMed Central

Vakorin, Vasily A.; Mišić, Bratislav; Krakovska, Olga; McIntosh, Anthony Randal

2011-01-01

Variability in source dynamics across the sources in an activated network may be indicative of how the information is processed within a network. Information-theoretic tools allow one not only to characterize local brain dynamics but also to describe interactions between distributed brain activity. This study follows such a framework and explores the relations between signal variability and asymmetry in mutual interdependencies in a data-driven pipeline of non-linear analysis of neuromagnetic sources reconstructed from human magnetoencephalographic (MEG) data collected as a reaction to a face recognition task. Asymmetry in non-linear interdependencies in the network was analyzed using transfer entropy, which quantifies predictive information transfer between the sources. Variability of the source activity was estimated using multi-scale entropy, quantifying the rate of which information is generated. The empirical results are supported by an analysis of synthetic data based on the dynamics of coupled systems with time delay in coupling. We found that the amount of information transferred from one source to another was correlated with the difference in variability between the dynamics of these two sources, with the directionality of net information transfer depending on the time scale at which the sample entropy was computed. The results based on synthetic data suggest that both time delay and strength of coupling can contribute to the relations between variability of brain signals and information transfer between them. Our findings support the previous attempts to characterize functional organization of the activated brain, based on a combination of non-linear dynamics and temporal features of brain connectivity, such as time delay. PMID:22131968

Nonlinearity in the vertical transmissibility of seating: the role of the human body apparent mass and seat dynamic stiffness

NASA Astrophysics Data System (ADS)

Tufano, Saverio; Griffin, Michael J.

2013-01-01

The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the dynamic characteristics of the seat, and the dynamic characteristics of the person sitting on the seat. However, it is not known whether seat cushions influence the dynamic response of the human body, whether the human body influences the dynamic response of seat cushions, or the relative importance of human body nonlinearity and seat nonlinearity in causing nonlinearity in measures of seat transmissibility. This study was designed to investigate the nonlinearity of the coupled seat and human body systems and to compare the apparent mass of the human body supported on rigid and foam seats. A frequency domain model was used to identify the dynamic parameters of seat foams and investigate their dependence on the subject-sitting weight and hip breadth. With 15 subjects, the force and acceleration at the seat base and acceleration at the subject interface were measured during random vertical vibration excitation (0.25-25 Hz) at each of five vibration magnitudes, (0.25-1.6 ms-2 r.m.s.) with four seating conditions (rigid flat seat and three foam cushions). The measurements are presented in terms of the subject's apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility. The apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. The foam dynamic stiffness showed complex correlations with characteristics of the human body, which differed between foams. The nonlinearities in cushion transmissibilities, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity.

Lifespan Differences in Nonlinear Dynamics during Rest and Auditory Oddball Performance

ERIC Educational Resources Information Center

Muller, Viktor; Lindenberger, Ulman

2012-01-01

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an…

Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Weinstein, M. I.; Xin, J.

1996-10-01

The dynamic stability of vortex solutions to the Ginzburg-Landau and nonlinear Schrödinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the Ginzburg-Landau dynamics we prove that all vortices are asymptotically nonlinearly stable relative to small radial perturbations. Initially finite energy perturbations of vortices decay to zero in L p (ℝ2) spaces with an algebraic rate as time tends to infinity. We also prove that under general (nonradial) perturbations, the plus and minus one-vortices are linearly dynamically stable in L 2; the linearized operator has spectrum equal to (-∞, 0] and generates a C 0 semigroup of contractions on L 2(ℝ2). The nature of the zero energy point is clarified; it is resonance, a property related to the infinite energy of planar vortices. Our results on the linearized operator are also used to show that the plus and minus one-vortices for the Schrödinger (Hamiltonian) dynamics are spectrally stable, i.e. the linearized operator about these vortices has ( L 2) spectrum equal to the imaginary axis. The key ingredients of our analysis are the Nash-Aronson estimates for obtaining Gaussian upper bounds for fundamental solutions of parabolic operator, and a combination of variational and maximum principles.

Differential flatness properties and multivariable adaptive control of ovarian system dynamics

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos

2016-12-01

The ovarian system exhibits nonlinear dynamics which is modeled by a set of coupled nonlinear differential equations. The paper proposes adaptive fuzzy control based on differential flatness theory for the complex dynamics of the ovarian system. It is proven that the dynamic model of the ovarian system, having as state variables the LH and the FSH hormones and their derivatives, is a differentially flat one. This means that all its state variables and its control inputs can be described as differential functions of the flat output. By exploiting differential flatness properties the system's dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop's Lyapunov function to be a negative one. Moreover, Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.

Nonlinear dynamics of team performance and adaptability in emergency response.

PubMed

Guastello, Stephen J

2010-04-01

The impact of team size and performance feedback on adaptation levels and performance of emergency response (ER) teams was examined to introduce a metric for quantifying adaptation levels based on nonlinear dynamical systems (NDS) theory. NDS principles appear in reports surrounding Hurricane Katrina, earthquakes, floods, a disease epidemic, and the Southeast Asian tsunami. They are also intrinsic to coordination within teams, adaptation levels, and performance in dynamic decision processes. Performance was measured in a dynamic decision task in which ER teams of different sizes worked against an attacker who was trying to destroy a city (total N = 225 undergraduates). The complexity of teams' and attackers' adaptation strategies and the role of the opponents' performance were assessed by nonlinear regression analysis. An optimal group size for team performance was identified. Teams were more readily influenced by the attackers' performance than vice versa. The adaptive capabilities of attackers and teams were impaired by their opponents in some conditions. ER teams should be large enough to contribute a critical mass of ideas but not so large that coordination would be compromised. ER teams used self-organized strategies that could have been more adaptive, whereas attackers used chaotic strategies. The model and results are applicable to ER processes or training maneuvers involving dynamic decisions but could be limited to nonhierarchical groups.

Multivariate moment closure techniques for stochastic kinetic models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

Non-linear principal component analysis applied to Lorenz models and to North Atlantic SLP

NASA Astrophysics Data System (ADS)

Russo, A.; Trigo, R. M.

2003-04-01

A non-linear generalisation of Principal Component Analysis (PCA), denoted Non-Linear Principal Component Analysis (NLPCA), is introduced and applied to the analysis of three data sets. Non-Linear Principal Component Analysis allows for the detection and characterisation of low-dimensional non-linear structure in multivariate data sets. This method is implemented using a 5-layer feed-forward neural network introduced originally in the chemical engineering literature (Kramer, 1991). The method is described and details of its implementation are addressed. Non-Linear Principal Component Analysis is first applied to a data set sampled from the Lorenz attractor (1963). It is found that the NLPCA approximations are more representative of the data than are the corresponding PCA approximations. The same methodology was applied to the less known Lorenz attractor (1984). However, the results obtained weren't as good as those attained with the famous 'Butterfly' attractor. Further work with this model is underway in order to assess if NLPCA techniques can be more representative of the data characteristics than are the corresponding PCA approximations. The application of NLPCA to relatively 'simple' dynamical systems, such as those proposed by Lorenz, is well understood. However, the application of NLPCA to a large climatic data set is much more challenging. Here, we have applied NLPCA to the sea level pressure (SLP) field for the entire North Atlantic area and the results show a slight imcrement of explained variance associated. Finally, directions for future work are presented.%}

Simulation Analysis of Helicopter Ground Resonance Nonlinear Dynamics

NASA Astrophysics Data System (ADS)

Zhu, Yan; Lu, Yu-hui; Ling, Ai-min

2017-07-01

In order to accurately predict the dynamic instability of helicopter ground resonance, a modeling and simulation method of helicopter ground resonance considering nonlinear dynamic characteristics of components (rotor lead-lag damper, landing gear wheel and absorber) is presented. The numerical integral method is used to calculate the transient responses of the body and rotor, simulating some disturbance. To obtain quantitative instabilities, Fast Fourier Transform (FFT) is conducted to estimate the modal frequencies, and the mobile rectangular window method is employed in the predictions of the modal damping in terms of the response time history. Simulation results show that ground resonance simulation test can exactly lead up the blade lead-lag regressing mode frequency, and the modal damping obtained according to attenuation curves are close to the test results. The simulation test results are in accordance with the actual accident situation, and prove the correctness of the simulation method. This analysis method used for ground resonance simulation test can give out the results according with real helicopter engineering tests.

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

Modeling and dynamic properties of dual-chamber solid and liquid mixture vibration isolator

NASA Astrophysics Data System (ADS)

Li, F. S.; Chen, Q.; Zhou, J. H.

2016-07-01

The dual-chamber solid and liquid mixture (SALiM) vibration isolator, mainly proposed for vibration isolation of heavy machines with low frequency, consists of four principle parts: SALiM working media including elastic elements and incompressible oil, multi-layers bellows container, rigid reservoir and the oil tube connecting the two vessels. The isolation system under study is governed by a two-degrees-of-freedom (2-DOF) nonlinear equation including quadratic damping. Simplifying the nonlinear damping into viscous damping, the equivalent stiffness and damping model is derived from the equation for the response amplitude. Theoretical analysis and numerical simulation reveal that the isolator's stiffness and damping have multiple properties with different parameters, among which the effects of exciting frequency, vibrating amplitude, quadratic damping coefficient and equivalent stiffness of the two chambers on the isolator's dynamics are discussed in depth. Based on the boundary characteristics of stiffness and damping and the main causes for stiffness hardening effect, improvement strategies are proposed to obtain better dynamic properties. At last, experiments were implemented and the test results were generally consistent with the theoretical ones, which verified the reliability of the nonlinear dynamic model.

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

Possibilities of fractal analysis of the competitive dynamics: Approaches and procedures

NASA Astrophysics Data System (ADS)

Zagornaya, T. O.; Medvedeva, M. A.; Panova, V. L.; Isaichik, K. F.; Medvedev, A. N.

2017-11-01

The possibilities of the fractal approach are used for the study of non-linear nature of the competitive dynamics of the market of trading intermediaries. Based on a statistical study of the functioning of retail indicators in the region, the approach to the analysis of the characteristics of the competitive behavior of market participants is developed. The authors postulate the principles of studying the dynamics of competition as a result of changes in the characteristics of the vector and the competitive behavior of market agents.

Current Results and Proposed Activities in Microgravity Fluid Dynamics

NASA Technical Reports Server (NTRS)

Polezhaev, V. I.

1996-01-01

The Institute for Problems in Mechanics' Laboratory work in mathematical and physical modelling of fluid mechanics develops models, methods, and software for analysis of fluid flow, instability analysis, direct numerical modelling and semi-empirical models of turbulence, as well as experimental research and verification of these models and their applications in technological fluid dynamics, microgravity fluid mechanics, geophysics, and a number of engineering problems. This paper presents an overview of the results in microgravity fluid dynamics research during the last two years. Nonlinear problems of weakly compressible and compressible fluid flows are discussed.

Interactive Finite Elements for General Engine Dynamics Analysis

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1984-01-01

General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.

Evaluation of the temporal structure of postural sway fluctuations based on a comprehensive set of analysis tools

NASA Astrophysics Data System (ADS)

Kirchner, M.; Schubert, P.; Schmidtbleicher, D.; Haas, C. T.

2012-10-01

The analysis of postural control has a long history. Traditionally, the amount of body sway is solely used as an index of postural stability. Although this leads to some extent to an effective evaluation of balance performance, the control mechanisms involved have not yet been fully understood. The concept of nonlinear dynamics suggests that variability in the motor output is not randomness but structure, providing the stimulus to reveal the functionality of postural sway. The present work evaluates sway dynamics by means of COP excursions in a quiet standing task versus a dual-task condition in three different test times (30, 60, 300 s). Besides the application of traditional methods-which estimate the overall size of sway-the temporal pattern of body sway was quantified via wavelet transform, multiscale entropy and fractal analysis. We found higher sensitivity of the structural parameters to modulations of postural control strategies and partly an improved evaluation of sway dynamics in longer recordings. It could be shown that postural control modifications take place on different timescales corresponding to the interplay of the sensory systems. A continued application of nonlinear analysis can help to better understand postural control mechanisms.

Bright breathers in nonlinear left-handed metamaterial lattices

NASA Astrophysics Data System (ADS)

Koukouloyannis, V.; Kevrekidis, P. G.; Veldes, G. P.; Frantzeskakis, D. J.; DiMarzio, D.; Lan, X.; Radisic, V.

2018-02-01

In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber k=π . Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.

A comparative robustness evaluation of feedforward neurofilters

NASA Technical Reports Server (NTRS)

Troudet, Terry; Merrill, Walter

1993-01-01

A comparative performance and robustness analysis is provided for feedforward neurofilters trained with back propagation to filter additive white noise. The signals used in this analysis are simulated pitch rate responses to typical pilot command inputs for a modern fighter aircraft model. Various configurations of nonlinear and linear neurofilters are trained to estimate exact signal values from input sequences of noisy sampled signal values. In this application, nonlinear neurofiltering is found to be more efficient than linear neurofiltering in removing the noise from responses of the nominal vehicle model, whereas linear neurofiltering is found to be more robust in the presence of changes in the vehicle dynamics. The possibility of enhancing neurofiltering through hybrid architectures based on linear and nonlinear neuroprocessing is therefore suggested as a way of taking advantage of the robustness of linear neurofiltering, while maintaining the nominal performance advantage of nonlinear neurofiltering.

Adaptive Event-Triggered Control Based on Heuristic Dynamic Programming for Nonlinear Discrete-Time Systems.

PubMed

Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo

2017-07-01

This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.

Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Tiwari, S. K.; Roy, Parimita

2015-06-01

In this paper, an attempt has been made to study the spatial and temporal dynamical interactions among the species of wetland ecosystem through a mathematical model. The model represents the population dynamics of phytoplankton, zooplankton and fish species found in Chilika lake, Odisha, India. Nonlinear stability analysis of both the temporal and spatial models has been carried out. Maximum sustainable yield and optimal harvesting policy have been studied for a nonspatial model system. Numerical simulation has been performed to figure out the parameters responsible for the complex dynamics of the wetland system. Significant outcomes of our numerical findings and their interpretations from an ecological point of view are provided in this paper. Numerical simulation of spatial model exhibits some interesting and beautiful patterns. We have also pointed out the parameters that are responsible for the good health of wetland ecosystem.

Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry

NASA Astrophysics Data System (ADS)

Ohtaki, Yasuaki; Arif, Muhammad; Suzuki, Akihiro; Fujita, Kazuki; Inooka, Hikaru; Nagatomi, Ryoichi; Tsuji, Ichiro

This study presents an assessment of walking stability in elderly people, focusing on local dynamic stability of walking. Its main objectives were to propose a technique to quantify local dynamic stability using nonlinear time-series analyses and a portable instrument, and to investigate their reliability in revealing the efficacy of an exercise training intervention for elderly people for improvement of walking stability. The method measured three-dimensional acceleration of the upper body, and computation of Lyapunov exponents, thereby directly quantifying the local stability of the dynamic system. Straight level walking of young and elderly subjects was investigated in the experimental study. We compared Lyapunov exponents of young and the elderly subjects, and of groups before and after the exercise intervention. Experimental results demonstrated that the exercise intervention improved local dynamic stability of walking. The proposed method was useful in revealing effects and efficacies of the exercise intervention for elderly people.

A Four-Dimensional Computed Tomography Comparison of Healthy vs. Asthmatic Human Lungs

PubMed Central

Jahani, Nariman; Choi, Sanghun; Choi, Jiwoong; Haghighi, Babak; Hoffman, Eric A.; Comellas, Alejandro P.; Kline, Joel N.; Lin, Ching-Long

2017-01-01

The purpose of this study was to explore new insights in non-linearity, hysteresis and ventilation heterogeneity of asthmatic human lungs using four-dimensional computed tomography (4D-CT) image data acquired during tidal breathing. Volumetric image data were acquired for 5 non-severe and one severe asthmatic volunteers. Besides 4D-CT image data, function residual capacity and total lung capacity image data during breath-hold were acquired for comparison with dynamic scans. Quantitative results were compared with the previously reported analysis of five healthy human lungs. Using an image registration technique, local variables such as regional ventilation and anisotropic deformation index (ADI) were estimated. Regional ventilation characteristics of non-severe asthmatic subjects were similar to those of healthy subjects, but different from the severe asthmatic subject. Lobar airflow fractions were also well correlated between static and dynamic scans (R2 > 0.84). However, local ventilation heterogeneity significantly increased during tidal breathing in both healthy and asthmatic subjects relative to that of breath-hold perhaps because of airway resistance present only in dynamic breathing. ADI was used to quantify non-linearity and hysteresis of lung motion during tidal breathing. Nonlinearity was greater on inhalation than exhalation among all subjects. However, exhalation nonlinearity among asthmatic subjects was greater than healthy subjects and the difference diminished during inhalation. An increase of non-linearity during exhalation in asthmatic subjects accounted for lower hysteresis relative to that of healthy ones. Thus, assessment of nonlinearity differences between healthy and asthmatic lungs during exhalation may provide quantitative metrics for subject identification and outcome assessment of new interventions. PMID:28372795

Three-Dimensional Numerical Analyses of Earth Penetration Dynamics

DTIC Science & Technology

1979-01-31

Lagrangian formulation based on the HEMP method and has been adapted and validated for treatment of normal-incidence (axisymmetric) impact and...code, is a detailed analysis of the structural response of the EPW. This analysis is generated using a nonlinear dynamic, elastic- plastic finite element...based on the HEMP scheme. Thus, the code has the same material modeling capabilities and abilities to track large scale motion found in the WAVE-L code

Nonlinear flight control design using backstepping methodology

NASA Astrophysics Data System (ADS)

Tran, Thanh Trung

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Nonlinear analysis and dynamic compensation of stylus scanning measurement with wide range

NASA Astrophysics Data System (ADS)

Hui, Heiyang; Liu, Xiaojun; Lu, Wenlong

2011-12-01

Surface topography is an important geometrical feature of a workpiece that influences its quality and functions such as friction, wearing, lubrication and sealing. Precision measurement of surface topography is fundamental for product quality characterizing and assurance. Stylus scanning technique is a widely used method for surface topography measurement, and it is also regarded as the international standard method for 2-D surface characterizing. Usually surface topography, including primary profile, waviness and roughness, can be measured precisely and efficiently by this method. However, by stylus scanning method to measure curved surface topography, the nonlinear error is unavoidable because of the difference of horizontal position of the actual measured point from given sampling point and the nonlinear transformation process from vertical displacement of the stylus tip to angle displacement of the stylus arm, and the error increases with the increasing of measuring range. In this paper, a wide range stylus scanning measurement system based on cylindrical grating interference principle is constructed, the originations of the nonlinear error are analyzed, the error model is established and a solution to decrease the nonlinear error is proposed, through which the error of the collected data is dynamically compensated.

Fractal dimension and nonlinear dynamical processes

NASA Astrophysics Data System (ADS)

McCarty, Robert C.; Lindley, John P.

1993-11-01

Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

Cardiovascular dynamics during space sickness and deconditioning

NASA Technical Reports Server (NTRS)

Goldberger, Ary L.; Rigney, David R.

1991-01-01

We are currently funded by NASA for the project, 'Cardiovascular Dynamics During Space Sickness and Deconditioning.' NASA has given priority to the investigation of two problems encountered in the long-term space flights currently being planned: (1) space motion sickness; and (2) cardiovascular deconditioning. We have proposed to use spectral and nonlinear dynamical analysis of heart rate data to quantify the presence of these problems and to evaluate countermeasures against them.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Neural network modelling and dynamical system theory: are they relevant to study the governing dynamics of association football players?

PubMed

Dutt-Mazumder, Aviroop; Button, Chris; Robins, Anthony; Bartlett, Roger

2011-12-01

Recent studies have explored the organization of player movements in team sports using a range of statistical tools. However, the factors that best explain the performance of association football teams remain elusive. Arguably, this is due to the high-dimensional behavioural outputs that illustrate the complex, evolving configurations typical of team games. According to dynamical system analysts, movement patterns in team sports exhibit nonlinear self-organizing features. Nonlinear processing tools (i.e. Artificial Neural Networks; ANNs) are becoming increasingly popular to investigate the coordination of participants in sports competitions. ANNs are well suited to describing high-dimensional data sets with nonlinear attributes, however, limited information concerning the processes required to apply ANNs exists. This review investigates the relative value of various ANN learning approaches used in sports performance analysis of team sports focusing on potential applications for association football. Sixty-two research sources were summarized and reviewed from electronic literature search engines such as SPORTDiscus, Google Scholar, IEEE Xplore, Scirus, ScienceDirect and Elsevier. Typical ANN learning algorithms can be adapted to perform pattern recognition and pattern classification. Particularly, dimensionality reduction by a Kohonen feature map (KFM) can compress chaotic high-dimensional datasets into low-dimensional relevant information. Such information would be useful for developing effective training drills that should enhance self-organizing coordination among players. We conclude that ANN-based qualitative analysis is a promising approach to understand the dynamical attributes of association football players.

A statistical state dynamics approach to wall turbulence.

PubMed

Farrell, B F; Gayme, D F; Ioannou, P J

2017-03-13

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

A statistical state dynamics approach to wall turbulence

PubMed Central

Gayme, D. F.; Ioannou, P. J.

2017-01-01

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation–perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or ‘band-limiting’ can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167577

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2002-01-01

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters: A Stability Margin

NASA Astrophysics Data System (ADS)

Kolokolov, Yury; Monovskaya, Anna

The popularity of systems of pulse energy conversion (PEC-systems) for practical applications is due to the heightened efficiency of energy conversion processes with comparatively simple realizations. Nevertheless, a PEC-system represents a nonlinear object with a variable structure, and the bifurcation analysis remains the basic tool to describe PEC dynamics evolution. The paper is devoted to the discussion on whether the scientific viewpoint on the natural nonlinear dynamics evolution can be involved in practical applications. We focus on the problems connected with stability boundaries of an operating regime. The results of both small-signal analysis and computational bifurcation analysis are considered in the parametrical space in comparison with the results of the experimental identification of the zonal heterogeneity of the operating process. This allows to propose an adapted stability margin as a sufficiently safe distance before the point after which the operating process begins to lose the stability. Such stability margin can extend the permissible operating domain in the parametrical space at the expense of using cause-and-effect relations in the context of natural regularities of nonlinear dynamics. Reasoning and discussion are based on the experimental and computational results for a synchronous buck converter with a pulse-width modulation. The presented results can be useful, first of all, for PEC-systems with significant variation of equivalent inductance and/or capacity. We believe that the discussion supports a viewpoint by which the contemporary methods of the computational and experimental bifurcation analyses possess both analytical abilities and experimental techniques for promising solutions which could be practice-oriented for PEC-systems.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

PubMed

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Recent developments in heterodyne laser interferometry at Harbin Institute of Technology

NASA Astrophysics Data System (ADS)

Hu, P. C.; Tan, J. B. B.; Yang, H. X. X.; Fu, H. J. J.; Wang, Q.

2013-01-01

In order to fulfill the requirements for high-resolution and high-precision heterodyne interferometric technologies and instruments, the laser interferometry group of HIT has developed some novel techniques for high-resolution and high-precision heterodyne interferometers, such as high accuracy laser frequency stabilization, dynamic sub-nanometer resolution phase interpolation and dynamic nonlinearity measurement. Based on a novel lock point correction method and an asymmetric thermal structure, the frequency stabilized laser achieves a long term stability of 1.2×10-8, and it can be steadily stabilized even in the air flowing up to 1 m/s. In order to achieve dynamic sub-nanometer resolution of laser heterodyne interferometers, a novel phase interpolation method based on digital delay line is proposed. Experimental results show that, the proposed 0.62 nm, phase interpolator built with a 64 multiple PLL and an 8-tap digital delay line achieves a static accuracy better than 0.31nm and a dynamic accuracy better than 0.62 nm over the velocity ranging from -2 m/s to 2 m/s. Meanwhile, an accuracy beam polarization measuring setup is proposed to check and ensure the light's polarization state of the dual frequency laser head, and a dynamic optical nonlinearity measuring setup is built to measure the optical nonlinearity of the heterodyne system accurately and quickly. Analysis and experimental results show that, the beam polarization measuring setup can achieve an accuracy of 0.03° in ellipticity angles and an accuracy of 0.04° in the non-orthogonality angle respectively, and the optical nonlinearity measuring setup can achieve an accuracy of 0.13°.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

NASA Astrophysics Data System (ADS)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

Do nonlinear dynamics in economics amount to a Kuhnian paradigm shift?

PubMed

Dore, Mohammed H I; Rosser, J Barkley

2007-01-01

Much empirical analysis and econometric work recognizes that there are nonlinearities, regime shifts or structural breaks, asymmetric adjustment costs, irreversibilities and lagged dependencies. Hence, empirical work has already transcended neoclassical economics. Some progress has also been made in modeling endogenously generated cyclical growth and fluctuations. All this is inconsistent with neoclassical general equilibrium. Hence there is growing evidence of Kuhnian anomalies. It therefore follows that there is a Kuhnian crisis in economics and further research in nonlinear dynamics and complexity can only increase the Kuhnian anomalies. This crisis can only deepen. However, there is an ideological commitment to general equilibrium that justifies "free enterprise" with only minimal state intervention that may still sustain neoclassical economics despite the growing evidence of Kuhnian anomalies. Thus, orthodox textbook theory continues to ignore this fact and static neoclassical theory remains a dogma with no apparent reformulation to replace it.

Linear and Nonlinear Dynamics of Heart Rate Variability are Correlated with Purpose in Life and Degree of Optimism in Anxiety Disorder Patients.

PubMed

Oh, Jihoon; Chae, Jeong-Ho

2018-04-01

Although heart rate variability (HRV) may be a crucial marker of mental health, how it is related to positive psychological factors (i.e. attitude to life and positive thinking) is largely unknown. Here we investigated the correlation of HRV linear and nonlinear dynamics with psychological scales that measured degree of optimism and happiness in patients with anxiety disorders. Results showed that low- to high-frequency HRV ratio (LF/HF) was increased and the HRV HF parameter was decreased in subjects who were more optimistic and who felt happier in daily living. Nonlinear analysis also showed that HRV dispersion and regulation were significantly correlated with the subjects' optimism and purpose in life. Our findings showed that HRV properties might be related to degree of optimistic perspectives on life and suggests that HRV markers of autonomic nervous system function could reflect positive human mind states.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

PubMed

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

Measuring the nonlinear elastic properties of tissue-like phantoms.

PubMed

Erkamp, Ramon Q; Skovoroda, Andrei R; Emelianov, Stanislav Y; O'Donnell, Matthew

2004-04-01

A direct mechanical system simultaneously measuring external force and deformation of samples over a wide dynamic range is used to obtain force-displacement curves of tissue-like phantoms under plain strain deformation. These measurements, covering a wide deformation range, then are used to characterize the nonlinear elastic properties of the phantom materials. The model assumes incompressible media, in which several strain energy potentials are considered. Finite-element analysis is used to evaluate the performance of this material characterization procedure. The procedures developed allow calibration of nonlinear elastic phantoms for elasticity imaging experiments and finite-element simulations.

Multibody dynamic simulation of knee contact mechanics

PubMed Central

Bei, Yanhong; Fregly, Benjamin J.

2006-01-01

Multibody dynamic musculoskeletal models capable of predicting muscle forces and joint contact pressures simultaneously would be valuable for studying clinical issues related to knee joint degeneration and restoration. Current three-dimensional multi-body knee models are either quasi-static with deformable contact or dynamic with rigid contact. This study proposes a computationally efficient methodology for combining multibody dynamic simulation methods with a deformable contact knee model. The methodology requires preparation of the articular surface geometry, development of efficient methods to calculate distances between contact surfaces, implementation of an efficient contact solver that accounts for the unique characteristics of human joints, and specification of an application programming interface for integration with any multibody dynamic simulation environment. The current implementation accommodates natural or artificial tibiofemoral joint models, small or large strain contact models, and linear or nonlinear material models. Applications are presented for static analysis (via dynamic simulation) of a natural knee model created from MRI and CT data and dynamic simulation of an artificial knee model produced from manufacturer’s CAD data. Small and large strain natural knee static analyses required 1 min of CPU time and predicted similar contact conditions except for peak pressure, which was higher for the large strain model. Linear and nonlinear artificial knee dynamic simulations required 10 min of CPU time and predicted similar contact force and torque but different contact pressures, which were lower for the nonlinear model due to increased contact area. This methodology provides an important step toward the realization of dynamic musculoskeletal models that can predict in vivo knee joint motion and loading simultaneously. PMID:15564115

Embedding of multidimensional time-dependent observations.

PubMed

Barnard, J P; Aldrich, C; Gerber, M

2001-10-01

A method is proposed to reconstruct dynamic attractors by embedding of multivariate observations of dynamic nonlinear processes. The Takens embedding theory is combined with independent component analysis to transform the embedding into a vector space of linearly independent vectors (phase variables). The method is successfully tested against prediction of the unembedded state vector in two case studies of simulated chaotic processes.

Embedding of multidimensional time-dependent observations

NASA Astrophysics Data System (ADS)

Barnard, Jakobus P.; Aldrich, Chris; Gerber, Marius

2001-10-01

A method is proposed to reconstruct dynamic attractors by embedding of multivariate observations of dynamic nonlinear processes. The Takens embedding theory is combined with independent component analysis to transform the embedding into a vector space of linearly independent vectors (phase variables). The method is successfully tested against prediction of the unembedded state vector in two case studies of simulated chaotic processes.

Simulation of stochastic wind action on transmission power lines

NASA Astrophysics Data System (ADS)

Wielgos, Piotr; Lipecki, Tomasz; Flaga, Andrzej

2018-01-01

The paper presents FEM analysis of the wind action on overhead transmission power lines. The wind action is based on a stochastic simulation of the wind field in several points of the structure and on the wind tunnel tests on aerodynamic coefficients of the single conductor consisting of three wires. In FEM calculations the section of the transmission power line composed of three spans is considered. Non-linear analysis with deadweight of the structure is performed first to obtain the deformed shape of conductors. Next, time-dependent wind forces are applied to respective points of conductors and non-linear dynamic analysis is carried out.

Nonlinear neural control with power systems applications

NASA Astrophysics Data System (ADS)

Chen, Dingguo

1998-12-01

Extensive studies have been undertaken on the transient stability of large interconnected power systems with flexible ac transmission systems (FACTS) devices installed. Varieties of control methodologies have been proposed to stabilize the postfault system which would otherwise eventually lose stability without a proper control. Generally speaking, regular transient stability is well understood, but the mechanism of load-driven voltage instability or voltage collapse has not been well understood. The interaction of generator dynamics and load dynamics makes synthesis of stabilizing controllers even more challenging. There is currently increasing interest in the research of neural networks as identifiers and controllers for dealing with dynamic time-varying nonlinear systems. This study focuses on the development of novel artificial neural network architectures for identification and control with application to dynamic electric power systems so that the stability of the interconnected power systems, following large disturbances, and/or with the inclusion of uncertain loads, can be largely enhanced, and stable operations are guaranteed. The latitudinal neural network architecture is proposed for the purpose of system identification. It may be used for identification of nonlinear static/dynamic loads, which can be further used for static/dynamic voltage stability analysis. The properties associated with this architecture are investigated. A neural network methodology is proposed for dealing with load modeling and voltage stability analysis. Based on the neural network models of loads, voltage stability analysis evolves, and modal analysis is performed. Simulation results are also provided. The transient stability problem is studied with consideration of load effects. The hierarchical neural control scheme is developed. Trajectory-following policy is used so that the hierarchical neural controller performs as almost well for non-nominal cases as they do for the nominal cases. The adaptive hierarchical neural control scheme is also proposed to deal with the time-varying nature of loads. Further, adaptive neural control, which is based on the on-line updating of the weights and biases of the neural networks, is studied. Simulations provided on the faulted power systems with unknown loads suggest that the proposed adaptive hierarchical neural control schemes should be useful for practical power applications.

Automatic network coupling analysis for dynamical systems based on detailed kinetic models.

PubMed

Lebiedz, Dirk; Kammerer, Julia; Brandt-Pollmann, Ulrich

2005-10-01

We introduce a numerical complexity reduction method for the automatic identification and analysis of dynamic network decompositions in (bio)chemical kinetics based on error-controlled computation of a minimal model dimension represented by the number of (locally) active dynamical modes. Our algorithm exploits a generalized sensitivity analysis along state trajectories and subsequent singular value decomposition of sensitivity matrices for the identification of these dominant dynamical modes. It allows for a dynamic coupling analysis of (bio)chemical species in kinetic models that can be exploited for the piecewise computation of a minimal model on small time intervals and offers valuable functional insight into highly nonlinear reaction mechanisms and network dynamics. We present results for the identification of network decompositions in a simple oscillatory chemical reaction, time scale separation based model reduction in a Michaelis-Menten enzyme system and network decomposition of a detailed model for the oscillatory peroxidase-oxidase enzyme system.

Brain-heart linear and nonlinear dynamics during visual emotional elicitation in healthy subjects.

PubMed

Valenza, G; Greco, A; Gentili, C; Lanata, A; Toschi, N; Barbieri, R; Sebastiani, L; Menicucci, D; Gemignani, A; Scilingo, E P

2016-08-01

This study investigates brain-heart dynamics during visual emotional elicitation in healthy subjects through linear and nonlinear coupling measures of EEG spectrogram and instantaneous heart rate estimates. To this extent, affective pictures including different combinations of arousal and valence levels, gathered from the International Affective Picture System, were administered to twenty-two healthy subjects. Time-varying maps of cortical activation were obtained through EEG spectral analysis, whereas the associated instantaneous heartbeat dynamics was estimated using inhomogeneous point-process linear models. Brain-Heart linear and nonlinear coupling was estimated through the Maximal Information Coefficient (MIC), considering EEG time-varying spectra and point-process estimates defined in the time and frequency domains. As a proof of concept, we here show preliminary results considering EEG oscillations in the θ band (4-8 Hz). This band, indeed, is known in the literature to be involved in emotional processes. MIC highlighted significant arousal-dependent changes, mediated by the prefrontal cortex interplay especially occurring at intermediate arousing levels. Furthermore, lower and higher arousing elicitations were associated to not significant brain-heart coupling changes in response to pleasant/unpleasant elicitations.

Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Zheng, Jinde; Pan, Haiyang; Yang, Shubao; Cheng, Junsheng

2018-01-01

Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Poster — Thur Eve — 44: Linearization of Compartmental Models for More Robust Estimates of Regional Hemodynamic, Metabolic and Functional Parameters using DCE-CT/PET Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blais, AR; Dekaban, M; Lee, T-Y

2014-08-15

Quantitative analysis of dynamic positron emission tomography (PET) data usually involves minimizing a cost function with nonlinear regression, wherein the choice of starting parameter values and the presence of local minima affect the bias and variability of the estimated kinetic parameters. These nonlinear methods can also require lengthy computation time, making them unsuitable for use in clinical settings. Kinetic modeling of PET aims to estimate the rate parameter k{sub 3}, which is the binding affinity of the tracer to a biological process of interest and is highly susceptible to noise inherent in PET image acquisition. We have developed linearized kineticmore » models for kinetic analysis of dynamic contrast enhanced computed tomography (DCE-CT)/PET imaging, including a 2-compartment model for DCE-CT and a 3-compartment model for PET. Use of kinetic parameters estimated from DCE-CT can stabilize the kinetic analysis of dynamic PET data, allowing for more robust estimation of k{sub 3}. Furthermore, these linearized models are solved with a non-negative least squares algorithm and together they provide other advantages including: 1) only one possible solution and they do not require a choice of starting parameter values, 2) parameter estimates are comparable in accuracy to those from nonlinear models, 3) significantly reduced computational time. Our simulated data show that when blood volume and permeability are estimated with DCE-CT, the bias of k{sub 3} estimation with our linearized model is 1.97 ± 38.5% for 1,000 runs with a signal-to-noise ratio of 10. In summary, we have developed a computationally efficient technique for accurate estimation of k{sub 3} from noisy dynamic PET data.« less

Application of the GRC Stirling Convertor System Dynamic Model

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.; Schreiber, Jeffrey G. (Technical Monitor)

2004-01-01

The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.

Nonlinear Dynamics of the Planar Pitch Attitude Motion for a Gravity- Gradient Satellite

DTIC Science & Technology

1994-08-01

distribution of the asteroid belt between Mars and Jupiter by nonlinear analysis and very clever long-term integration techniques, a problem that had...baffled scientists for over one hundred years. He showed that chaotic (and many quasiperiodic) astroid trajectories near the 3/1 Kirkwood gap had, over...millions of years, occasional spikes in eccentricity that caused either collisions with Mars or close enough passages for the astroid to be removed

Foldover effect and energy output from a nonlinear pseudo-maglev harvester

NASA Astrophysics Data System (ADS)

Kecik, Krzysztof; Mitura, Andrzej; Warminski, Jerzy; Lenci, Stefano

2018-01-01

Dynamics analysis and energy harvesting of a nonlinear magnetic pseudo-levitation (pseudo-maglev) harvester under harmonic excitation is presented in this paper. The system, for selected parameters, has two stable possible solutions with different corresponding energy outputs. The main goal is to analyse the influence of resistance load on the multi-stability zones and energy recovery which can help to tune the system to improve the energy harvesting efficiency.

Mathematical and Computational Foundations of Recurrence Quantifications

NASA Astrophysics Data System (ADS)

Marwan, Norbert; Webber, Charles L.

Real-world systems possess deterministic trajectories, phase singularities and noise. Dynamic trajectories have been studied in temporal and frequency domains, but these are linear approaches. Basic to the field of nonlinear dynamics is the representation of trajectories in phase space. A variety of nonlinear tools such as the Lyapunov exponent, Kolmogorov-Sinai entropy, correlation dimension, etc. have successfully characterized trajectories in phase space, provided the systems studied were stationary in time. Ubiquitous in nature, however, are systems that are nonlinear and nonstationary, existing in noisy environments all of which are assumption breaking to otherwise powerful linear tools. What has been unfolding over the last quarter of a century, however, is the timely discovery and practical demonstration that the recurrences of system trajectories in phase space can provide important clues to the system designs from which they derive. In this chapter we will introduce the basics of recurrence plots (RP) and their quantification analysis (RQA). We will begin by summarizing the concept of phase space reconstructions. Then we will provide the mathematical underpinnings of recurrence plots followed by the details of recurrence quantifications. Finally, we will discuss computational approaches that have been implemented to make recurrence strategies feasible and useful. As computers become faster and computer languages advance, younger generations of researchers will be stimulated and encouraged to capture nonlinear recurrence patterns and quantification in even better formats. This particular branch of nonlinear dynamics remains wide open for the definition of new recurrence variables and new applications untouched to date.

Osculating Keplerian Elements for Highly Non-Keplerian Orbits

DTIC Science & Technology

2017-03-27

1.52133 2 McInnes, C. R., “The Existence and Stability of Families of Displacement Two-Body Orbits”, Celestial Mechanics and Dynamical Astronomy , Vol...j.actaastro.2011.08.012 5 Xu, M. and Xu, S., “Nonlinear dynamical analysis for displaced orbits above a planet”, Celestial Mechanics and Dynamical Astronomy ...Celestial Mechanics and Dynamical Astronomy , Vol. 110, No. 3, 2011, pp. 199-215. doi: 10.1007/s10569-011-9351-5 7 Macdonald, M., McKay, R. J., Vasile, M

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings

NASA Astrophysics Data System (ADS)

Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis

2014-05-01

The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps.

Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms

NASA Technical Reports Server (NTRS)

Lee, Jeh Won

1991-01-01

The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.

PubMed

Linnemann, D; Strobel, H; Muessel, W; Schulz, J; Lewis-Swan, R J; Kheruntsyan, K V; Oberthaler, M K

2016-07-01

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Nonlinear Tides in Close Binary Systems

NASA Astrophysics Data System (ADS)

Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

2012-06-01

We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P <~ a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.

Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Panda, Satyajit; Ray, M. C.

2008-04-01

In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially uniform over the substrate plate surfaces and varied through the thickness of the host FG plates. The temperature-dependent material properties of the FG substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla-Hughes-McTavish (GHM) method. Based on the first-order shear deformation theory, a three-dimensional finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG substrate plates under the thermal environment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear vibrations of FG plates in the absence or the presence of the temperature gradient across the thickness of the plates. It is found that the ACLD treatment is more effective in controlling the geometrically nonlinear vibrations of FG plates than in controlling their linear vibrations. The analysis also reveals that the ACLD patch is more effective for controlling the nonlinear vibrations of FG plates when it is attached to the softest surface of the FG plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also discussed.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Nonlinear optical properties of thick composite media with vanadium dioxide nanoparticles. I. Self-defocusing of radiation in the visible and near-IR regions

NASA Astrophysics Data System (ADS)

Ostrosablina, A. A.; Sidorov, A. I.

2005-07-01

This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It establishes that the reversible semiconductor-metal phase transition that occurs in VO2 nanoparticles under the action of radiation can produce self-defocusing of radiation in the visible and near-IR regions because of the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of these processes. It is shown that photoinduced absorption and scattering play a role in forming the nonlinear optical response.

Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

NASA Astrophysics Data System (ADS)

Awais, M.; Hayat, T.; Muqaddass, N.; Ali, A.; Aqsa; Awan, Saeed Ehsan

2018-03-01

The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model) with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed.

Rayleigh-type parametric chemical oscillation.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

Decentralized adaptive control of robot manipulators with robust stabilization design

NASA Technical Reports Server (NTRS)

Yuan, Bau-San; Book, Wayne J.

1988-01-01

Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

NASA Astrophysics Data System (ADS)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.

PubMed

Aftab, Muhammad Saleheen; Shafiq, Muhammad

2015-11-01

This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamics identification of a piezoelectric vibrational energy harvester by image analysis with a high speed camera

NASA Astrophysics Data System (ADS)

Wolszczak, Piotr; Łygas, Krystian; Litak, Grzegorz

2018-07-01

This study investigates dynamic responses of a nonlinear vibration energy harvester. The nonlinear mechanical resonator consists of a flexible beam moving like an inverted pendulum between amplitude limiters. It is coupled with a piezoelectric converter, and excited kinematically. Consequently, the mechanical energy input is converted into the electrical power output on the loading resistor included in an electric circuit attached to the piezoelectric electrodes. The curvature of beam mode shapes as well as deflection of the whole beam are examined using a high speed camera. The visual identification results are compared with the voltage output generated by the piezoelectric element for corresponding frequency sweeps and analyzed by the Hilbert transform.

Parachute dynamics and stability analysis. [using nonlinear differential equations of motion

NASA Technical Reports Server (NTRS)

Ibrahim, S. K.; Engdahl, R. A.

1974-01-01

The nonlinear differential equations of motion for a general parachute-riser-payload system are developed. The resulting math model is then applied for analyzing the descent dynamics and stability characteristics of both the drogue stabilization phase and the main descent phase of the space shuttle solid rocket booster (SRB) recovery system. The formulation of the problem is characterized by a minimum number of simplifying assumptions and full application of state-of-the-art parachute technology. The parachute suspension lines and the parachute risers can be modeled as elastic elements, and the whole system may be subjected to specified wind and gust profiles in order to assess their effects on the stability of the recovery system.

Joint nonlinearity effects in the design of a flexible truss structure control system

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

Nonlinear analysis of EEGs of patients with major depression during different emotional states.

PubMed

Akdemir Akar, Saime; Kara, Sadık; Agambayev, Sümeyra; Bilgiç, Vedat

2015-12-01

Although patients with major depressive disorder (MDD) have dysfunctions in cognitive behaviors and the regulation of emotions, the underlying brain dynamics of the pathophysiology are unclear. Therefore, nonlinear techniques can be used to understand the dynamic behavior of the EEG signals of MDD patients. To investigate and clarify the dynamics of MDD patients׳ brains during different emotional states, EEG recordings were analyzed using nonlinear techniques. The purpose of the present study was to assess whether there are different EEG complexities that discriminate between MDD patients and healthy controls during emotional processing. Therefore, nonlinear parameters, such as Katz fractal dimension (KFD), Higuchi fractal dimension (HFD), Shannon entropy (ShEn), Lempel-Ziv complexity (LZC) and Kolmogorov complexity (KC), were computed from the EEG signals of two groups under different experimental states: noise (negative emotional content) and music (positive emotional content) periods. First, higher complexity values were generated by MDD patients relative to controls. Significant differences were obtained in the frontal and parietal scalp locations using KFD (p<0.001), HFD (p<0.05), and LZC (p=0.05). Second, lower complexities were observed only in the controls when they were subjected to music compared to the resting baseline state in the frontal (p<0.05) and parietal (p=0.005) regions. In contrast, the LZC and KFD values of patients increased in the music period compared to the resting state in the frontal region (p<0.05). Third, the patients׳ brains had higher complexities when they were exposed to noise stimulus than did the controls׳ brains. Moreover, MDD patients׳ negative emotional bias was demonstrated by their higher brain complexities during the noise period than the music stimulus. Additionally, we found that the KFD, HFD and LZC values were more sensitive in discriminating between patients and controls than the ShEn and KC measures, according to the results of ANOVA and ROC calculations. It can be concluded that the nonlinear analysis may be a useful and discriminative tool in investigating the neuro-dynamic properties of the brain in patients with MDD during emotional stimulation. Copyright © 2015 Elsevier Ltd. All rights reserved.