Practical Aspects of the Implementation of Proper Orthogonal Decomposition

Brenner, Thomas A.; Cizmas, Paul G. A.; O’Brien, Thomas J.; Breault, Ronald W.

doi:10.2514/6.2009-918

Cited by 3 publications

(8 citation statements)

References 26 publications

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“…Figure 6 demonstrate the extraction of flow information which characterise the EIT signal from dynamics point of view, and Figure 7 illustrate the capability of original image reconstruction according extracted basis function, with certain accuracy . Both attributes of POD techniques will be utilised for further flow regime recognition based on the developed reduce-order model [6,37].…”

Section: Resultsmentioning

confidence: 99%

“…Using POD, time independent basis functions were extracted from the EIT data and were projected onto the basis functions to generate reduced-order models. In the reduced-order models (ROMs) [6,15] the large amount of experimental data are replaced by a much smaller number of coefficients of ordinary differential equations. These reduced-order models were applied to several reference cases; Liquid mass flow rate between 1 − 1000 kg/sm 2 , gas mass flow rate between 0.1 − 20 kg/sm 2 simulating on water-air experimental loop, using the fast impedance camera system (FICA) [32].…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

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Proper Orthogonal Decomposition as a technique for identifying two-phase flow pattern based on electrical impedance tomography

Polanský

Wang

2017

Flow Measurement and Instrumentation

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Collecting very large amount of data from experimental measurement is a common practice in almost every scientific domain. There is a great need to have specific techniques capable of extracting synthetic information, which is essential to understand and model the specific phenomena. The Proper Orthogonal Decomposition (POD) is one of the most powerful data-analysis methods for multivariate and nonlinear phenomena. Generally, POD is a procedure that takes a given collection of input experimental or numerical data and creates an orthogonal basis constituted by functions estimated as the solutions of an integral eigenvalue problem known as a Fredholm equation. By utilising POD to identify flow structure in horizontal pipeline, specially, for slag, plug and wavy stratified air-water flow regimes, this paper proposes a novel approach, in which POD technique extends the current evaluation procedure of electrical impedance tomography applied on air-water flow measurement [32] . This extension is provided by implementation of the POD as an identifier of typical horizontal multiphase flow regimes. The POD snapshot matrices are reconstructed for electrical thomography measurement domain and specific flow conditions. Direct POD method introduced by Lumley and Snapshot POD method introduced by Sirovich are applied. It is expected that this study may provide new knowledge on two phase flow dynamics in a horizontal pipeline and supportive information for further prediction of multiphase flow regime.

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Section: Resultsmentioning

confidence: 99%

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Proper Orthogonal Decomposition as a technique for identifying two-phase flow pattern based on electrical impedance tomography

Polanský

Wang

2017

Flow Measurement and Instrumentation

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“…In view of the sampling point, the different sampling signal can obtain different POD reduced modes; therefore, what kind of sampling signal and how to sample can obtain the optimal reduced-order mode have become a research issue for scholars. By reviewing the relative literature about POD sampling, it is found that some scholars obtained POD reduced modes from chaos response signal [58,59,79,87,88,111,112], random response signal [87,[113][114][115], moment response signal [116][117][118][119][120][121][122][123][124][125], different sampling method [126][127][128][129][130][131][132][133], and constructing different autocorrelation matrix [134].…”

Section: Sampling Study Of Pod Methodmentioning

confidence: 99%

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

Zhang

et al. 2021

Shock and Vibration

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The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

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“…The paper titled "Practical Aspects of the Implementation of Proper Orthogonal Decomposition" was presented at the 47th AIAA Aerospace Sciences Meeting on January 7th, 2009 (Brenner et al, 2009). This paper described our investigation of the effect of time sampling on POD error and a brief study of the necessity of including inter-variable crosscorrelation terms in the computation of the POD basis functions.…”

Section: Dissemination Of Research Resultsmentioning

confidence: 99%

“…Additionally the extrapolation of the field variables in time has been studied (Richardson, 2007). The error in the POD approximation of the field variables has been computed as a function of time between snapshots in the snapshot database (Brenner et al, 2009). This error gives an estimate of the limits of interpolation in time on the dynamics of the flow that can be captured.…”

Section: Interpolation and Extrapolationmentioning

confidence: 99%

A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

Cizmas¹,

Richardson²,

Brenner³

et al. 2009

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This report summarizes the objectives and tasks of this project, and describes how they were achieved. The report presents the progress made towards the program milestones and deliverables and summarizes the additional work done in the pursuit of these goals.A reduced-order model based on proper orthogonal decomposition (POD) has been developed to simulate transient two-and three-dimensional isothermal and non-isothermal flows in a fluidized bed. Reduced-order models of void fraction, gas and solids temperatures, granular energy, and z-direction gas and solids velocity have been added to the previous version of the code. These algorithms are presented and their implementation is discussed. Verification studies are presented for each algorithm.A number of methods to accelerate the computations performed by the reduced-order model are presented. The errors associated with each acceleration method are computed and discussed. Using a combination of acceleration methods, a two-dimensional isothermal simulation using the reduced-order model is shown to be 114 times faster than using the full-order model.In the pursue of achieving the objectives of the project and completing the tasks planned for this program, several unplanned and unforeseen results, methods and studies have been generated. These additional accomplishments are also presented and they include: (1) a study of the effect of snapshot sampling time on the computation of the POD basis functions, (2) an investigation of different strategies for generating the autocorrelation matrix used to find the POD basis functions, (3) the development and implementation of a bubble detection and tracking algorithm based on mathematical morphology, (4) a method for augmenting the proper orthogonal decomposition to better capture flows with discontinuities, such as bubbles, and (5) a mixed reduced-order/full-order model, called point-mode proper orthogonal decomposition, designed to avoid unphysical due to approximation errors.The limitations of the proper orthogonal decomposition method in simulating transient flows with moving discontinuities, such as bubbling flows, are discussed and several methods are proposed to adapt the method for future use.

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Practical Aspects of the Implementation of Proper Orthogonal Decomposition

Cited by 3 publications

References 26 publications

Proper Orthogonal Decomposition as a technique for identifying two-phase flow pattern based on electrical impedance tomography

Proper Orthogonal Decomposition as a technique for identifying two-phase flow pattern based on electrical impedance tomography

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

A Reduced-Order Model of Transport Phenomena for Power Plant Simulation

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