Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

2008 ◽  
Author(s):  
G. Y. Xu ◽  
W. D. Zhu
Keyword(s):  
High Dimensional ◽  
Structural Systems ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Included Trial ◽  
Frequency Responses ◽  
Linear And Nonlinear ◽  
Dimensional Models ◽  
Low Dimensional

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially-discretized models, and the results obtained from the low-dimensional models may not accurately represent the behavior of the distributed systems. In this work the incremental harmonic balance method is used for the first time to handle a variety of problems for high-dimensional models of distributed structural systems, including determination of linear and nonlinear frequency responses, optimization of system parameters, determination of simple parametric instability region boundaries, analysis of parametrically-excited nonlinear systems, and determination of linear and nonlinear frequency responses under combined parametric and forcing excitations. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from non-proportionarity of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially-discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.

Nonlinear and Time-Varying Dynamics of High-Dimensional Models of a Translating Beam With a Stationary Load Subsystem

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
G. Y. Xu ◽  
W. D. Zhu
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
High Dimensional ◽  
Structural Systems ◽  
Time Varying ◽  
Incremental Harmonic Balance Method ◽  
Included Trial ◽  
Incremental Harmonic Balance ◽  
Dimensional Models ◽  
Low Dimensional

Nonlinear vibration and dynamic stability analyses of distributed structural systems have often been conducted for their low-dimensional spatially discretized models, and the results obtained from the low-dimensional models may not accurately represent the behaviors of the distributed systems. In this work the incremental harmonic balance method is used to handle a variety of problems pertaining to determining periodic solutions of high-dimensional models of distributed structural systems. The methodology is demonstrated on a translating tensioned beam with a stationary load subsystem and some related systems. With sufficient numbers of included trial functions and harmonic terms, convergent and accurate results are obtained in all the cases. The effect of nonlinearities due to the vibration-dependent friction force between the translating beam and the stationary load subsystem, which results from nonproportionality of the load parameters, decreases as the number of included trial functions increases. A low-dimensional spatially discretized model of the nonlinear distributed system can yield quantitatively and qualitatively inaccurate predictions. The methodology can be applied to other nonlinear and/or time-varying distributed structural systems.

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

2015 ◽  
Vol 82 (10) ◽  
Author(s):  
Ioannis A. Kougioumtzoglou ◽  
Alberto Di Matteo ◽  
Pol D. Spanos ◽  
Antonina Pirrotta ◽  
Mario Di Paola
Keyword(s):  
Path Integral ◽  
Computational Cost ◽  
High Dimensional ◽  
System Response ◽  
Stochastic Response ◽  
Mdof Systems ◽  
Low Dimensional ◽  
Response Determination ◽  
Efficiency And Reliability

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF. It is shown that, for the case of relatively high-dimensional systems, the herein proposed implementation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard WPI technique and an MCS approach. Several numerical examples are included, whereas comparisons with pertinent MCS data demonstrate the efficiency and reliability of the technique.

scholarly journals Characterizing neural phase-space trajectories via Principal Louvain Clustering

2021 ◽  
Author(s):  
Mark M. Dekker ◽  
Arthur S. C. França ◽  
Debabrata Panja ◽  
Michael X Cohen
Keyword(s):  
Field Potential ◽  
High Dimensional ◽  
Time Varying ◽  
Ongoing Behavior ◽  
Reduction Methods ◽  
Novel Method ◽  
High Consistency ◽  
Low Dimensional ◽  
High Dimensional Datasets ◽  
Local Field Potential Lfp

AbstractBackgroundWith the growing size and richness of neuroscience datasets in terms of dimension, volume, and resolution, identifying spatiotemporal patterns in those datasets is increasingly important. Multivariate dimension-reduction methods are particularly adept at addressing these challenges.New MethodIn this paper, we propose a novel method, which we refer to as Principal Louvain Clustering (PLC), to identify clusters in a low-dimensional data subspace, based on time-varying trajectories of spectral dynamics across multisite local field potential (LFP) recordings in awake behaving mice. Data were recorded from prefrontal cortex, hippocampus, and parietal cortex in eleven mice while they explored novel and familiar environments.ResultsPLC-identified subspaces and clusters showed high consistency across animals, and were modulated by the animals’ ongoing behavior.ConclusionsPLC adds to an important growing literature on methods for characterizing dynamics in high-dimensional datasets, using a smaller number of parameters. The method is also applicable to other kinds of datasets, such as EEG or MEG.

scholarly journals Identifying limits of linear control design validity in nonlinear systems: a continuation-based approach

2021 ◽  
Author(s):  
D. H. Nguyen ◽  
M. H. Lowenberg ◽  
S. A. Neild
Keyword(s):  
Limit Cycle ◽  
Equations Of Motion ◽  
Numerical Continuation ◽  
Limit Cycle Oscillation ◽  
Nonlinear Frequency ◽  
Multiple Attractors ◽  
Chaotic Motions ◽  
Frequency Responses ◽  
Linear And Nonlinear ◽  
Cycle Oscillation

AbstractIt is well known that a linear-based controller is only valid near the point from which the linearised system is obtained. The question remains as to how far one can move away from that point before the linear and nonlinear responses differ significantly, resulting in the controller failing to achieve the desired performance. In this paper, we propose a method to quantify these differences. By appending a harmonic oscillator to the equations of motion, the frequency responses at different operating points of a nonlinear system can be generated using numerical continuation. In the presence of strong nonlinearities, subtle differences exist between the linear and nonlinear frequency responses, and these variations are also reflected in the step responses. A systematic way of comparing the discrepancies between the linear and the nonlinear frequency responses is presented, which can determine whether the controller performs as predicted by linear-based design. We demonstrate the method on a simple fixed-gain Duffing system and a gain-scheduled reduced-order aircraft model with a manoeuvre-demand controller; the latter presents a case where strong nonlinearities exist in the form of multiple attractors. The analysis is then expanded to include actuator rate saturation, which creates a limit-cycle isola, coexisting multiple solutions (corresponding to the so-called flying qualities cliff), and chaotic motions. The proposed method can infer the influence of these additional attractors even when there is no systematic way to detect them. Finally, when severe rate saturation is present, reducing the controller gains can mitigate—but not eliminate—the risk of limit-cycle oscillation.

scholarly journals Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals

2020 ◽  
Vol 10 (5) ◽  
pp. 1797 ◽  
Author(s):  
Mera Kartika Delimayanti ◽  
Bedy Purnama ◽  
Ngoc Giang Nguyen ◽  
Mohammad Reza Faisal ◽  
Kunti Robiatul Mahmudah ◽  
...  
Keyword(s):  
Machine Learning ◽  
Sleep Stage ◽  
Machine Learning Algorithms ◽  
High Dimensional ◽  
Sleep Stages ◽  
Eeg Signals ◽  
Stage Classification ◽  
Sleep Stage Classification ◽  
Low Dimensional

Manual classification of sleep stage is a time-consuming but necessary step in the diagnosis and treatment of sleep disorders, and its automation has been an area of active study. The previous works have shown that low dimensional fast Fourier transform (FFT) features and many machine learning algorithms have been applied. In this paper, we demonstrate utilization of features extracted from EEG signals via FFT to improve the performance of automated sleep stage classification through machine learning methods. Unlike previous works using FFT, we incorporated thousands of FFT features in order to classify the sleep stages into 2–6 classes. Using the expanded version of Sleep-EDF dataset with 61 recordings, our method outperformed other state-of-the art methods. This result indicates that high dimensional FFT features in combination with a simple feature selection is effective for the improvement of automated sleep stage classification.

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