scholarly journals Data-driven spectral analysis for coordinative structures in periodic human locomotion

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Keisuke Fujii ◽  
Naoya Takeishi ◽  
Benio Kibushi ◽  
Motoki Kouzaki ◽  
Yoshinobu Kawahara
Keyword(s):  
Spectral Analysis ◽  
Nonlinear Dynamical Systems ◽  
Model Simulation ◽  
Human Locomotion ◽  
Data Driven ◽  
Limit Cycle Oscillation ◽  
Double Pendulum ◽  
Control Mechanisms ◽  
Dynamical Properties ◽  
Low Dimensional

AbstractLiving organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not reflect dynamical properties in principle. Here we regard coordinative structures in biological periodic systems with unknown and redundant dynamics as a nonlinear limit-cycle oscillation, and apply a data-driven operator-theoretic spectral analysis, which obtains dynamical properties of coordinative structures such as frequency and phase from the estimated eigenvalues and eigenfunctions of a composition operator. Using segmental angle series during human walking as an example, we first extracted the coordinative structures based on dynamics; e.g. the speed-independent coordinative structures in the harmonics of gait frequency. Second, we discovered the speed-dependent time-evolving behaviours of the phase by estimating the eigenfunctions via our approach on the conventional low-dimensional structures. We also verified our approach using the double pendulum and walking model simulation data. Our results of locomotion analysis suggest that our approach can be useful to analyse biological periodic phenomena from the perspective of nonlinear dynamical systems.

scholarly journals Data-driven spectral analysis for coordinative structures in periodic systems with unknown and redundant dynamics

2019 ◽  
Author(s):  
Keisuke Fujii ◽  
Naoya Takeishi ◽  
Benio Kibushi ◽  
Motoki Kouzaki ◽  
Yoshinobu Kawahara
Keyword(s):  
Spectral Analysis ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Periodic Systems ◽  
Limit Cycle Oscillation ◽  
Control Mechanisms ◽  
Nonlinear Dynamical ◽  
Reduction Methods ◽  
Dynamical Properties ◽  
Low Dimensional

AbstractLiving organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not reflect dynamical properties in principle. Here we regard coordinative structures in biological periodic systems with unknown and redundant dynamics as a nonlinear limit-cycle oscillation, and apply a data-driven operator-theoretic spectral analysis, which obtains dynamical properties of coordinative structures such as frequency and phase from the estimated eigenvalues and eigenfunctions of a composition operator. First, from intersegmental angles during human walking, we extracted the speed-independent harmonics of gait frequency. Second, we discovered the speed-dependent time-evolving behaviors of the phase on the conventional low-dimensional structures by estimating the eigenfunctions. Our approach contributes to the understanding of biological periodic phenomena with unknown and redundant dynamics from the perspective of nonlinear dynamical systems.

scholarly journals Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

2019 ◽  
Author(s):  
Xuping Xie ◽  
Guannan Zhang ◽  
Clayton G. Webster
Keyword(s):  
Differential Operators ◽  
Nonlinear Dynamical Systems ◽  
Dimensional Space ◽  
Fluid Dynamic ◽  
Data Driven ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Highly Nonlinear ◽  
Low Dimensional

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams-Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches

scholarly journals Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 757 ◽  
Author(s):  
Xuping Xie ◽  
Guannan Zhang ◽  
Clayton G. Webster
Keyword(s):  
Differential Operators ◽  
Nonlinear Dynamical Systems ◽  
Dimensional Space ◽  
Fluid Dynamic ◽  
Data Driven ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Highly Nonlinear ◽  
Low Dimensional

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.

Extended-Range Prediction with Low-Dimensional, Stochastic-Dynamic Models: A Data-driven Approach

2012 ◽  
Author(s):  
Michael Ghil ◽  
Mickael D. Chekroun ◽  
Dmitri Kondrashov ◽  
Michael K. Tippett ◽  
Andrew Robertson ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Data Driven ◽  
Stochastic Dynamic ◽  
Extended Range ◽  
Data Driven Approach ◽  
Low Dimensional

scholarly journals COVID-19 Brings Data Equity Challenges to the Fore

2021 ◽  
Author(s):  
H.V. Jagadish ◽  
Julia Stoyanovich ◽  
Bill Howe
Keyword(s):  
Quality Control ◽  
Government Policy ◽  
Data Driven ◽  
Contact Tracing ◽  
Control Mechanisms ◽  
Sources Of Information ◽  
Decision Systems ◽  
Physical Resources ◽  
Multiple Levels ◽  
Data Driven Decisions

The COVID-19 pandemic is compelling us to make crucial data-driven decisions quickly, bringing together diverse and unreliable sources of information without the usual quality control mechanisms we may employ. These decisions are consequential at multiple levels: they can inform local, state and national government policy, be used to schedule access to physical resources such as elevators and workspaces within an organization, and inform contact tracing and quarantine actions for individuals. In all these cases, significant inequities are likely to arise, and to be propagated and reinforced by data-driven decision systems. In this article, we propose a framework, called FIDES, for surfacing and reasoning about data equity in these systems.

scholarly journals Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Zhe Bai ◽  
Liqian Peng
Keyword(s):  
Machine Learning ◽  
Nonlinear Dynamical Systems ◽  
Reduced Order Models ◽  
Simulation Code ◽  
Nonlinear Dynamical ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Regression Techniques ◽  
Low Dimensional ◽  
Modern Machine

AbstractAlthough projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

scholarly journals Lower complexity of motor primitives ensures robust control of high-speed human locomotion

2020 ◽  
Author(s):  
Alessandro Santuz ◽  
Antonis Ekizos ◽  
Yoko Kunimasa ◽  
Kota Kijima ◽  
Masaki Ishikawa ◽  
...  
Keyword(s):  
High Speed ◽  
Muscle Activation ◽  
Human Locomotion ◽  
Muscle Synergies ◽  
Activation Patterns ◽  
Motor Primitives ◽  
Muscle Activation Patterns ◽  
Relative Contribution ◽  
Muscle Activations ◽  
Low Dimensional

AbstractWalking and running are mechanically and energetically different locomotion modes. For selecting one or another, speed is a parameter of paramount importance. Yet, both are likely controlled by similar low-dimensional neuronal networks that reflect in patterned muscle activations called muscle synergies. Here, we investigated how humans synergistically activate muscles during locomotion at different submaximal and maximal speeds. We analysed the duration and complexity (or irregularity) over time of motor primitives, the temporal components of muscle synergies. We found that the challenge imposed by controlling high-speed locomotion forces the central nervous system to produce muscle activation patterns that are wider and less complex relative to the duration of the gait cycle. The motor modules, or time-independent coefficients, were redistributed as locomotion speed changed. These outcomes show that robust locomotion control at challenging speeds is achieved by modulating the relative contribution of muscle activations and producing less complex and wider control signals, whereas slow speeds allow for more irregular control.

Wave-Based Control of a Crane System With Complex Loads

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Jiao Zhou ◽  
Kai Zhang ◽  
Gengkai Hu
Keyword(s):  
Wave Scattering ◽  
Control Method ◽  
Model Simulation ◽  
Double Pendulum ◽  
Time Varying ◽  
Pendulum Model ◽  
Simulation And Experiment ◽  
Special Case ◽  
Transmission And Reflection ◽  
Load Mass

In the framework of wave-based method, we have examined swing motion control for double-pendulum and load-hoist models. Emphases are placed on wave scattering by the middle load mass in the double-pendulum model and on time-varying configuration in the load-hoist model. By analyzing wave transmission and reflection, trolley's motion to alleviate swing is designed by absorbing reflected wave through adjusting the velocity of trolley. Simulation and experiment are also conducted to validate the proposed control method. The results show that with the designed trolley's motion swings of load can be significantly reduced for both double-pendulum model, suspended rod model which is demonstrated a special case of double-pendulum model, and load-hoist model. Simulation results agree well with the experimental measurement. Launch velocity profiles may have important impact on motion design, especially on force necessary to displace trolley. Finally, a wave-based feedback control is also discussed to demonstrate the flexibility of method.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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