Modal Reduction of Mathematical Models of Biological Molecules

2005 ◽  
Author(s):  
Aiqin Li ◽  
Earl H. Dowell
Keyword(s):  
Low Frequency ◽  
Biological Molecules ◽  
Computational Time ◽  
Strong Nonlinearity ◽  
Reduced Order ◽  
Modal Reduction ◽  
Modal Synthesis ◽  
Frequency Excitation ◽  
A Chain ◽  
Proper Orthogonal

This paper reports a detailed study of modal reduction based on either linear normal mode(LNM) analysis or proper orthogonal decomposition(POD) for modeling a single α-D glucopyranose monomer as well as a chain of monomers. Also a modal reduction method combining POD and component modal synthesis(CMS) is developed. The accuracy and efficiency of these methods are reported. The focus of this study is to determine to what extent these methods can reduce the time and cost of molecular modeling and simultaneously provide the required accuracy. It has been demonstrated that a linear reduced order model(ROM) is valid for small amplitude excitation and low frequency excitation. It is found that a nonlinear ROM based on POD modes provides a good approximation even for large excitation while the nonlinear ROM using linear eigenmodes as the basis vectors is less effective for modeling molecules with a strong nonlinearity. The ROM based on CMS using POD modes for each component also gives a good approximation. With the reduction in the dimension of the system using these methods the computational time and cost can be reduced significantly.

Reduced-Order Model of Unsteady Flows in a Turbomachinery Fan Modeled Using a Novel Proper Orthogonal Decomposition

2019 ◽  
Author(s):  
Elizabeth H. Krath ◽  
Forrest L. Carpenter ◽  
Paul G. A. Cizmas ◽  
David A. Johnston
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Reference Conditions ◽  
Stable Solution ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Model Rotor

Abstract This paper presents a novel, more efficient reduced-order model based on the proper orthogonal decomposition (POD) for the prediction of flows in turbomachinery. To further reduce the computational time, the governing equations were written as a function of specific volume instead of density. This allowed for the pre-computation of the coefficients of the system of ordinary differential equations that describe the reduced-order model. A penalty method was developed to implement time-dependent boundary conditions and achieve a stable solution for the reduced-order model. Rotor 67 was used as a validation case for the reduced-order model, which was tested for both on- and off-reference conditions. This reduced-order model was shown to be more than 10,000 times faster than the full-order model.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

scholarly journals A Step Towards a Reduced Order Modelling of Flow Characterized by Wakes Using Proper Orthogonal Decomposition

2017 ◽  
Author(s):  
Eivind Fonn ◽  
Adil Rasheed ◽  
Mandar Tabib ◽  
Trond Kvamsdal
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Degrees Of Freedom ◽  
Orthogonal Decomposition ◽  
Computational Time ◽  
High Fidelity ◽  
Partial Differential ◽  
Navier Stokes Equation ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Proper Orthogonal

High fidelity simulations of flow might be quite demanding, because they involve up to O(106 – 109) degrees of freedom and several hours (or even days) of computational time, also on powerful hardware parallel architectures. Thus, high-fidelity techniques can become prohibitive when we expect them to deal quickly and efficiently with the repetitive solution of partial differential equations. One set of partial differential equation that we encounter on a regular basis is the Navier Stokes Equation which is used to simulate flow around complex geometries like sub-sea structures. To address the issues associated with computational efficiency, a field of Reduced Order Modelling is evolving fast. In this paper we investigate Proper Orthogonal Decomposition as a potential method for constructing reduced bases for Reduced Order Models. In the case of flows around cylindrical bodies we found that only a few modes were sufficient to represent the dominant flow structures and energies associated with them making POD to be an attractive candidate for bases construction.

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.

Modal Reduced Order Model for Vision Sensing of IPMC Actuator

2006 ◽  
Vol 326-328 ◽  
pp. 1523-1526
Author(s):  
Il Kweon Oh ◽  
Seong Won Yeom ◽  
Dong Weon Lee
Keyword(s):  
Reduced Order Model ◽  
Mode Shapes ◽  
Computational Time ◽  
Transverse Displacement ◽  
Metal Composite ◽  
Motion Generation ◽  
Order Model ◽  
Lower Mode ◽  
Reduced Order ◽  
Vision Sensing

In order to control the IPMC (Ionic Polymer Metal Composite) actuators, it is necessary to use a vision sensing system and a reduced order model from the vision sensing data. In this study, the MROVS (Modal Reduced Order Vision Sensing) model using the least square method has been developed for implementation of the biomimetic motion generation. The simulated transverse displacement is approximated with a sum of the lower mode shapes of the cantilever beam. The NIPXI 1409 image acquisition board and CCD camera (XC-HR50) are used in the experimental setup. Present results show that the MROVS model can efficiently process the vision sensing of the biomimetic IPMC actuator with cost-effective computational time.

Very low frequency electromagnetic phenomena: ‘whistlers’ and micropulsations

1977 ◽  
Vol 279 (963) ◽  
pp. 225-238 ◽  
Keyword(s):  
Low Frequency ◽  
Dynamical Behaviour ◽  
Weddell Sea ◽  
Particle Interactions ◽  
Terrestrial Environment ◽  
Wave Amplification ◽  
A Chain ◽  
Magnetic Conjugacy ◽  
Sea Area ◽  
The Antarctic

Observations of natural electromagnetic phenomena, embracing frequencies ranging from millihertz to tens of kilohertz, have made a major contribution to our knowledge of the terrestrial environment extending out to many Earth’s radii. The Antarctic has offered exceptional opportunities in this field for a number of reasons, including: (i) the location of Antarctic bases (including Halley Bay) at key magnetic latitudes, (ii) magnetic conjugacy to Northern Hemisphere thunderstorm sources, (iii) low interference levels. Important aspects of this research are the investigation of the role of wave-particle interactions in the magnetosphere and that of the structure and dynamical behaviour of the plasmapause, using both passive and active techniques. Comparisons of observations made at antarctic stations and their northern geomagnetic conjugates show close similarities in dominant pulsation periods and demonstrate the uniqueness of the Weddell Sea area in relation to magnetospheric wave amplification at the higher frequencies. An extra dimension to this work is being added, during the International Magnetospheric Study (1976-8), through the development of a chain of stations employing the goniometer (direction-finding) technique pioneered at Halley Bay by Sheffield University.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

The essential role of early-spring westerly wind burst in generating the centennial extreme 1997/98 El Niño

2021 ◽  
pp. 1-38
Author(s):  
Tao Lian ◽  
Dake Chen
Keyword(s):  
El Niño ◽  
El Nino ◽  
Southern Oscillation ◽  
Low Frequency ◽  
Coupled Model ◽  
Early Spring ◽  
Strong Nonlinearity ◽  
Westerly Wind ◽  
Enso Dynamics

AbstractWhile both intrinsic low-frequency atmosphere–ocean interaction and multiplicative burst-like event affect the development of the El Niño–Southern Oscillation (ENSO), the strong nonlinearity in ENSO dynamics has prevented us from separating their relative contributions. Here we propose an online filtering scheme to estimate the role of the westerly wind bursts (WWBs), a type of aperiodic burst-like atmospheric perturbation over the western-central tropical Pacific, in the genesis of the centennial extreme 1997/98 El Niño using the CESM coupled model. This scheme highlights the deterministic part of ENSO dynamics during model integration, and clearly demonstrates that the strong and long-lasting WWB in March 1997 was essential for generating the 1997/98 El Niño. Without this WWB, the intrinsic low-frequency coupling would have only produced a weak warm event in late 1997 similar to the 2014/15 El Niño.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

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