Model order reduction using sparse coding exemplified for the lid-driven cavity

2016 ◽  
Vol 808 ◽  
pp. 189-223 ◽  
Author(s):  
Rohit Deshmukh ◽  
Jack J. McNamara ◽  
Zongxian Liang ◽  
J. Zico Kolter ◽  
Abhijit Gogulapati
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Sparse Coding ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Driven Cavity ◽  
Reduced Order ◽  
Multi Scale ◽  
Small Set ◽  
Proper Orthogonal

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

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.

Inverse design of aircraft cabin environment using computational fluid dynamics-based proper orthogonal decomposition method

2017 ◽  
Vol 27 (10) ◽  
pp. 1379-1391 ◽  
Author(s):  
Jihong Wang ◽  
Tengfei (Tim) Zhang ◽  
Hongbiao Zhou ◽  
Shugang Wang
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Proper Orthogonal Decomposition ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Air Supply ◽  
Spatial Modes ◽  
Cabin Environment ◽  
Proper Orthogonal

To design a comfortable aircraft cabin environment, designers conventionally follow an iterative guess-and-correction procedure to determine the air-supply parameters. The conventional method has an extremely low efficiency but does not guarantee an optimal design. This investigation proposed an inverse design method based on a proper orthogonal decomposition of the thermo-flow data provided by full computational fluid dynamics simulations. The orthogonal spatial modes of the thermo-flow fields and corresponding coefficients were firstly extracted. Then, a thermo-flow field was expressed into a linear combination of the spatial modes with their coefficients. The coefficients for each spatial mode are functions of air-supply parameters, which can be interpolated. With a quick map of the cause–effect relationship between the air-supply parameters and the exhibited thermo-flow fields, the optimal air-supply parameters were determined from specific design targets. By setting the percentage of dissatisfied and the predicted mean vote as design targets, the proposed method was implemented for inverse determination of air-supply parameters in two aircraft cabins. The results show that the inverse design using computational fluid dynamics-based proper orthogonal decomposition method is viable. Most of computing time lies in the construction of data samples of thermo-flow fields, while the proper orthogonal decomposition analysis and data interpolation is efficient.

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.

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.

Analysis of Unsteady Flow Structures in a Radial Turbomachine by Using Proper Orthogonal Decomposition

2018 ◽  
Author(s):  
Matthias Witte ◽  
Benjamin Torner ◽  
Frank-Hendrik Wurm
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Flow Structures ◽  
Periodic Flow ◽  
Noise Emission ◽  
Turbulent Flow Field ◽  
Proper Orthogonal

Tonalities in hydro and airborne noise emission are a known problem of turbomachines, wherein the tonalities in the noise spectrum are associated with the different orders of the blade passing frequency (BPF). The proper orthogonal decomposition (POD) method was utilized to find the relationship between the fluctuations in the pressure field at the BPF orders which are the origin of the noise emission and the correlated fluctuations in the turbulent velocity field in terms of coherent, periodic flow structures. In order the provide the input data for the POD analysis, a URANS k-ω-SST scale adaptive simulation (SAS) of the turbulent flow field in a single stage radial pump under part load conditions was performed. Compared to traditional two equation turbulence models this approach is less dissipative and allows the development of small scale turbulence structures and is therefore an appropriate method for this study. In order to compute the POD correlation matrix Sirovich’s “Methods of Snapshots” was applied to the unsteady pressure and velocity fields from the CFD simulation. The discrimination of coherent, periodic flow structures and the incoherent, chaotic turbulence was carried out by analyzing the POD eigenvalue distributions, the POD mode shapes and the spectral properties of the POD time coefficients. Five coupled POD mode pairs were identified in total, which were strictly correlated with the 1st, 2nd, 3rd, 4th and 5th order of the BPF and therefore responsible for the noise emission at these discrete frequencies. The coherent structures were explored on the basis of the spatial POD velocity und pressure mode shapes and in terms of vortical structures after an additional phase averaging. The scope of this study is to introduce an enhanced collection of post processing techniques which are capable of analyzing highly unsteady flow fields from numerical simulations in a better way than is possible by just using traditional techniques like the evaluation of integral or time averaged quantities. The identified coherent flow structures and their associated pressure fluctuations are key elements for a proper comprehension of the internal dynamics of the turbulent flow field in a turbomachine and therefore essential for the understanding of the noise generation processes and the optimization of such machines.

Patterns and Reduced-order Reconstruction of Impinging Wiping Jet Pressure Profile Fluctuation Using Proper Orthogonal Decomposition

2021 ◽  
Author(s):  
Le Quang Phan ◽  
Andrew Johnstone ◽  
P. Buyung Kosasih ◽  
Wayne Renshaw
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Jet Impingement ◽  
Pressure Profile ◽  
Orthogonal Decomposition ◽  
Maximum Pressure ◽  
Frequency Spectra ◽  
Reduced Order ◽  
Order Reconstruction ◽  
Pressure Profiles ◽  
Proper Orthogonal

Abstract Wiping jet impingement pressure is important in controlling the coating mass (thickness) and influencing the smoothness of the thin metallic coating produced in continuous galvanizing lines (CGLs). However, the fluctuation of the impingement pressure profile that directly impacts the coating smoothness has not been adequately understood. To study key features of the impingement pressure fluctuation, the instantaneous impingement pressure profiles obtained from Large Eddy Simulations were analyzed using Proper Orthogonal Decomposition (POD). Dominant fluctuation modes of pressure profiles can be differentiated from the energy contents of the modes corresponding to different jet types namely mixing, non-mixing, and transitional mixing jet. The dominant modes of mixing jets in the wiping region contain comparable strength of all modes (flapping, pulsing, and out-of-phase multi pulsing). Non-mixing jets do not show discernable fluctuation modes and transitional mixing jets show pulsing and flapping modes only. Additionally, instantaneous maximum pressure gradient and their location were determined from the reduced-order reconstruction of the pressure profiles. From the analysis, frequency spectra of the magnitude and location fluctuations of the maximum pressure gradients associated with each of the jet types can be clearly distinguished. This is a knowledge that may be helpful for CGL operators in the operation of wiping jets.

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