scholarly journals A parametric and feasibility study for data sampling of the dynamic mode decomposition: range, resolution, and universal convergence states

2022 ◽  
Author(s):  
Cruz Y. Li ◽  
Zengshun Chen ◽  
Tim K. T. Tse ◽  
Asiri U. Weerasuriya ◽  
Xuelin Zhang ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Spatial Dimension ◽  
Test Subject ◽  
Dynamic Mode Decomposition ◽  
Engineering Practice ◽  
Dynamic Mode ◽  
Data Sampling ◽  
Temporal Dimension ◽  
Range Resolution ◽  
Mode Decomposition

AbstractScientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The dynamic mode decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear systems into periodically distinct constituents on reduced-order subspaces. As a novel mathematical hatchling, the DMD bears vast potentials yet an equal degree of unknown. This effort investigates the nuances of DMD sampling with an engineering-oriented emphasis. It aimed at elucidating how sampling range and resolution affect the convergence of DMD modes. We employed the most classical nonlinear system in fluid mechanics as the test subject—the turbulent free-shear flow over a prism—for optimal pertinency. We numerically simulated the flow by the dynamic-stress Large-Eddies Simulation with Near-Wall Resolution. With the large-quantity, high-fidelity data, we parametrized and identified four global convergence states: Initialization, Transition, Stabilization, and Divergence with increasing sampling range. Results showed that Stabilization is the optimal state for modal convergence, in which DMD output becomes independent of the sampling range. The Initialization state also yields sufficient accuracy for most system reconstruction tasks. Moreover, defying popular beliefs, over-sampling causes algorithmic instability: as the temporal dimension, n, approaches and transcends the spatial dimension, m (i.e., m < n), the output diverges and becomes meaningless. Additionally, the convergence of the sampling resolution depends on the mode-specific dynamics, such that the resolution of 15 frames per cycle for target activities is suggested for most engineering implementations. Finally, a bi-parametric study revealed that the convergence of the sampling range and resolution are mutually independent.

scholarly journals Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1119
Author(s):  
Camilo Garcia-Tenorio ◽  
Gilles Delansnay ◽  
Eduardo Mojica-Nava ◽  
Alain Vande-Wouwer
Keyword(s):  
Nonlinear Systems ◽  
Orthogonal Polynomials ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Real Life ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Trigonometric Functions ◽  
Maximum Order ◽  
Mode Decomposition

The extended dynamic mode decomposition algorithm is a tool for accurately approximating the point spectrum of the Koopman operator. This algorithm provides an approximate linear expansion of non-linear discrete-time systems, which can be useful for system analysis and controller design. The accuracy of this algorithm depends heavily on the availability of a set of basis functions that provide the ability to capture the nonlinear dynamics of the underlying system. Recently, the use of orthogonal polynomials, along with reduction techniques for the dimension and maximum order of the polynomial basis, have been successfully used to approximate nonlinear systems with the additional benefit of using smaller datasets. This paper expands the current methods for selecting the set of observables for nonlinear systems with periodic behavior, which is prone to a representation in terms of trigonometric functions. The benefit of working with orthogonal polynomials is preserved by embedding the trigonometric functions into the orthogonal basis. The algorithm is illustrated with the data-driven modelling of an inverted pendulum in simulation and real-life experiments.

Experimental Measurement of In-Plane Rolling Nonpneumatic Tire Vibrations Using High-Speed Imaging

2019 ◽  
Vol 47 (3) ◽  
pp. 196-210
Author(s):  
Meghashyam Panyam ◽  
Beshah Ayalew ◽  
Timothy Rhyne ◽  
Steve Cron ◽  
John Adcox
Keyword(s):  
High Speed ◽  
Image Correlation ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
High Speed Imaging ◽  
Correlation Algorithm ◽  
Mode Decomposition ◽  
Series Of Experiments ◽  
Plane Deformations ◽  
Dominant Frequencies

ABSTRACT This article presents a novel experimental technique for measuring in-plane deformations and vibration modes of a rotating nonpneumatic tire subjected to obstacle impacts. The tire was mounted on a modified quarter-car test rig, which was built around one of the drums of a 500-horse power chassis dynamometer at Clemson University's International Center for Automotive Research. A series of experiments were conducted using a high-speed camera to capture the event of the rotating tire coming into contact with a cleat attached to the surface of the drum. The resulting video was processed using a two-dimensional digital image correlation algorithm to obtain in-plane radial and tangential deformation fields of the tire. The dynamic mode decomposition algorithm was implemented on the deformation fields to extract the dominant frequencies that were excited in the tire upon contact with the cleat. It was observed that the deformations and the modal frequencies estimated using this method were within a reasonable range of expected values. In general, the results indicate that the method used in this study can be a useful tool in measuring in-plane deformations of rolling tires without the need for additional sensors and wiring.

Oscillatory flow around a vertical wall-mounted cylinder: Dynamic mode decomposition

2021 ◽  
Vol 33 (2) ◽  
pp. 025113
Author(s):  
H. K. Jang ◽  
C. E. Ozdemir ◽  
J.-H. Liang ◽  
M. Tyagi
Keyword(s):  
Oscillatory Flow ◽  
Vertical Wall ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

scholarly journals Analysis of transonic buffet using dynamic mode decomposition

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Antje Feldhusen-Hoffmann ◽  
Christian Lagemann ◽  
Simon Loosen ◽  
Pascal Meysonnat ◽  
Michael Klaas ◽  
...  
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Measurement Data ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Transonic Buffet

AbstractThe buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by a feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. High-speed particle-image velocimetry measurements are performed to investigate this feedback loop in transonic buffet flow over a supercritical DRA 2303 airfoil. The freestream Mach number is $$M_{\infty } = 0.73$$ M ∞ = 0.73 , the angle of attack is $$\alpha = 3.5^{\circ }$$ α = 3 . 5 ∘ , and the chord-based Reynolds number is $${\mathrm{Re}}_{c} = 1.9\times 10^6$$ Re c = 1.9 × 10 6 . The obtained velocity fields are processed by sparsity-promoting dynamic mode decomposition to identify the dominant dynamic features contributing strongest to the buffet flow field. Two pronounced dynamic modes are found which confirm the presence of two main features of the proposed feedback loop. One mode is related to the shock wave oscillation frequency and its shape includes the movement of the shock wave and the coupled pulsation of the recirculation region downstream of the shock wave. The other pronounced mode represents the disturbances which form the downstream propagating part of the proposed feedback loop. The frequency of this mode corresponds to the frequency of the acoustic waves which are generated by these downstream traveling disturbances and which form the upstream propagating part of the proposed feedback loop. In this study, the post-processing, i.e., the DMD, is highlighted to substantiate the existence of this vortex mode. It is this vortex mode that via the Lamb vector excites the shock oscillations. The measurement data based DMD results confirm numerical findings, i.e., the dominant buffet and vortex modes are in good agreement with the feedback loop suggested by Lee. Graphic abstract

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