Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method

2003 ◽  
Vol 18 (2) ◽  
pp. 227-250 ◽  
Author(s):  
M. Amabili ◽  
A. Sarkar ◽  
M.P. Paı̈doussis
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Decomposition Method ◽  
Nonlinear Vibrations ◽  
Cylindrical Shells ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Proper Orthogonal

scholarly journals Constrained reduced-order models based on proper orthogonal decomposition

2017 ◽  
Vol 321 ◽  
pp. 18-34 ◽  
Author(s):  
Sohail R. Reddy ◽  
Brian A. Freno ◽  
Paul G.A. Cizmas ◽  
Seckin Gokaltun ◽  
Dwayne McDaniel ◽  
...  
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Proper Orthogonal

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

scholarly journals Comparison of the Atmospheric 200 hPa Jet’s Analyses between Proper Orthogonal Decomposition and Advanced Dynamic Mode Decomposition Method

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Mei Gao ◽  
Xiao-Qun Cao ◽  
Bai-Nian Liu ◽  
Zi-Hang Han ◽  
Shi-Cheng Hou ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Jet Flow ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reduced Order Models ◽  
Dynamic Information ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

In this paper, a frequently employed technique named the sparsity-promoting dynamic mode decomposition (SPDMD) is proposed to analyze the velocity fields of atmospheric motion. The dynamic mode decomposition method (DMD) is an effective technique to extract dynamic information from flow fields that is generated from direct experiment measurements or numerical simulation and has been broadly employed to study the dynamics of the flow, to achieve a reduced-order model (ROM) of the complex high dimensional flow field, and even to predict the evolution of the flow in a short time in the future. However, for standard DMD, it is hard to determine which modes are the most physically relevant, unlike the proper orthogonal decomposition (POD) method which ranks the decomposed modes according to their energy content. The advanced modal decomposition method SPDMD is a variant of the standard DMD, which is capable of determining the modes that can be used to achieve a high-quality approximation of the given field. It is novel to introduce the SPDMD to analyze the atmospheric flow field. In this study, SPDMD is applied to extract essential dynamic information from the 200 hPa jet flow, and the decomposed results are compared with the POD method. To further demonstrate the extraction effect of POD/SPDMD methods on the 200 hPa jet flow characteristics, the POD/SPDMD reduced-order models are constructed, respectively. The results show that both modal decomposition methods successfully extract the underlying coherent structures from the 200 hPa jet flow. And the DMD method provides additional information on the modal properties, such as temporal frequency and growth rate of each mode which can be used to identify the stability of the modes. It is also found that a fewer order of modes determined by the SPDMD method can capture nearly the same dynamic information of the jet flow as the POD method. Furthermore, from the quantitative comparisons between the POD and SPDMD reduced-order models, the latter provides a higher precision than the former, especially when the number of modes is small.

A Parametric Analysis of Reduced Order Models of Potential Flows in Turbomachinery Using Proper Orthogonal Decomposition

2001 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Mach Number ◽  
Proper Orthogonal Decomposition ◽  
Steady Flow ◽  
Inviscid Flow ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Spatial Gradients ◽  
Potential Flows ◽  
Proper Orthogonal

An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced order models.

Reduced Order Models of Viscous Flows in Turbomachinery Using Proper Orthogonal Decomposition

1999 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Frequency Domain ◽  
Degrees Of Freedom ◽  
Orthogonal Decomposition ◽  
Full Potential ◽  
Reduced Order Models ◽  
Full System ◽  
Integral Boundary ◽  
Reduced Order ◽  
Proper Orthogonal

Abstract The proper orthogonal decomposition technique is applied in the frequency domain to obtain reduced order models (ROM) of the flow in a cascade of airfoils. The flow is described by a inviscid-viscous interaction model where the inviscid part is described by the full potential equation and the viscous part is described by an integral boundary layer model. The fully nonlinear steady flow is computed and the unsteady flow is linearized about the steady solution. A frequency domain model is constructed and validated showing to provide similar results when compared with previous computational and experimental data presented in the literature. A cascade of airfoils forming a slightly modified Tenth Standard Configuration is numerically investigated. We show that the ROMs with only 10 to 40 degrees of freedom predict accurately the unsteady response of the full system with approximately 10,000 degrees of freedom for the subsonic case. We also show that the ROMs with 15 to 75 degrees of freedom predict accurately the unsteady response of the full system with approximately 17, 500 degrees of freedom for the transonic case. The ROMs are shown to be accurate both for a broad range of reduced frequencies and a full spectrum of interblade phase angles.

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