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Journal articles on the topic 'Proper Orthogonal Decomposition'

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Published: 4 June 2021

Last updated: 7 September 2023

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1

Sieber, Moritz, C. Oliver Paschereit, and Kilian Oberleithner. "Spectral proper orthogonal decomposition." Journal of Fluid Mechanics 792 (March 4, 2016): 798–828. http://dx.doi.org/10.1017/jfm.2016.103.

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The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

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2

Himpe, Christian, Tobias Leibner, and Stephan Rave. "Hierarchical Approximate Proper Orthogonal Decomposition." SIAM Journal on Scientific Computing 40, no. 5 (January 2018): A3267—A3292. http://dx.doi.org/10.1137/16m1085413.

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3

Borggaard, Jeff, Traian Iliescu, and Zhu Wang. "Artificial viscosity proper orthogonal decomposition." Mathematical and Computer Modelling 53, no. 1-2 (January 2011): 269–79. http://dx.doi.org/10.1016/j.mcm.2010.08.015.

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4

Narasimha, Roddam. "Kosambi and proper orthogonal decomposition." Resonance 16, no. 6 (June 2011): 574–81. http://dx.doi.org/10.1007/s12045-011-0062-8.

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5

Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

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6

Schmidt, Oliver T., and Tim Colonius. "Guide to Spectral Proper Orthogonal Decomposition." AIAA Journal 58, no. 3 (March 2020): 1023–33. http://dx.doi.org/10.2514/1.j058809.

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7

Pironneau, Olivier. "Proper orthogonal decomposition for pricing options." Journal of Computational Finance 16, no. 1 (September 2012): 33–46. http://dx.doi.org/10.21314/jcf.2012.246.

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8

Kunisch, Karl, and Stefan Volkwein. "Proper orthogonal decomposition for optimality systems." ESAIM: Mathematical Modelling and Numerical Analysis 42, no. 1 (January 2008): 1–23. http://dx.doi.org/10.1051/m2an:2007054.

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9

Bienkiewicz, B., H. J. Ham, and Y. Sun. "Proper orthogonal decomposition of roof pressure." Journal of Wind Engineering and Industrial Aerodynamics 50 (December 1993): 193–202. http://dx.doi.org/10.1016/0167-6105(93)90074-x.

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10

Carlson, Henry A., Rolf Verberg, and Charles A. Harris. "Aeroservoelastic modeling with proper orthogonal decomposition." Physics of Fluids 29, no. 2 (February 2017): 020711. http://dx.doi.org/10.1063/1.4975673.

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11

Elezgaray, J., and F. Tallet. "Proper orthogonal decomposition of DLA clusters." Europhysics Letters (EPL) 36, no. 7 (December 1, 1996): 521–26. http://dx.doi.org/10.1209/epl/i1996-00263-9.

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12

Sanghi, Sanjeev, and Nadeem Hasan. "Proper orthogonal decomposition and its applications." Asia-Pacific Journal of Chemical Engineering 6, no. 1 (January 2011): 120–28. http://dx.doi.org/10.1002/apj.481.

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13

TAMURA, Yukio. "Proper Orthogonal Decomposition of fluctuating pressure fields." Wind Engineers, JAWE 1996, no. 68 (1996): 60–66. http://dx.doi.org/10.5359/jawe.1996.68_60.

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14

Rathinam, Muruhan, and Linda R. Petzold. "A New Look at Proper Orthogonal Decomposition." SIAM Journal on Numerical Analysis 41, no. 5 (January 2003): 1893–925. http://dx.doi.org/10.1137/s0036142901389049.

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15

ISHIKAWA, Hitoshi. "WS002 Wavelet Analysis and Proper Orthogonal Decomposition." Proceedings of the Fluids engineering conference 2013 (2013): _WS002–01_—_WS002–02_. http://dx.doi.org/10.1299/jsmefed.2013._ws002-01_.

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16

Aubry, Nadine, Wen-Yu Lian, and Edriss S. Titi. "Preserving Symmetries in the Proper Orthogonal Decomposition." SIAM Journal on Scientific Computing 14, no. 2 (March 1993): 483–505. http://dx.doi.org/10.1137/0914030.

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17

Khalil, Mohammad, Sondipon Adhikari, and Abhijit Sarkar. "Linear system identification using proper orthogonal decomposition." Mechanical Systems and Signal Processing 21, no. 8 (November 2007): 3123–45. http://dx.doi.org/10.1016/j.ymssp.2007.03.007.

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18

Grinberg, L. "Proper orthogonal decomposition of atomistic flow simulations." Journal of Computational Physics 231, no. 16 (June 2012): 5542–56. http://dx.doi.org/10.1016/j.jcp.2012.05.007.

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19

Yu, Dan, and Suman Chakravorty. "A randomized balanced proper orthogonal decomposition technique." Journal of Computational and Applied Mathematics 368 (April 2020): 112540. http://dx.doi.org/10.1016/j.cam.2019.112540.

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20

Vendl, Alexander, and Heike Faßbender. "Proper Orthogonal Decomposition for steady aerodynamic applications." PAMM 10, no. 1 (November 16, 2010): 635–36. http://dx.doi.org/10.1002/pamm.201010310.

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21

Pinnau, René, and Alexander Schulze. "Radiation, Frequency Averaging and Proper Orthogonal Decomposition." PAMM 6, no. 1 (December 2006): 791–94. http://dx.doi.org/10.1002/pamm.200610376.

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22

Park, Kyung-Hyun, Sang-Ook Jun, Maeng-Hyo Cho, and Dong-Ho Lee. "Design Optimization of Transonic Wing/Fuselage System Using Proper Orthogona1 Decomposition." Journal of the Korean Society for Aeronautical Space Science 38, no. 5 (May 1, 2010): 414–20. http://dx.doi.org/10.5139/jksas.2010.38.5.414.

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23

Hou, Tianfeng, Staf Roels, and Hans Janssen. "The use of proper orthogonal decomposition for the simulation of highly nonlinear hygrothermal performance." MATEC Web of Conferences 282 (2019): 02018. http://dx.doi.org/10.1051/matecconf/201928202018.

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In this paper, the use of proper orthogonal decomposition for simulating nonlinear heat, air and moisture transfer is investigated via two applications: HAMSTAD benchmarks 2 and 3. Moreover, the potential of the reduced models constructed by proper orthogonal decomposition for simulating new problems with longer simulation periods is assessed. To illustrate the feasibilities of proper orthogonal decomposition method in the field of building physics, the accuracies of the reduced models are compared with the standard finite element method. The outcomes show that with a sufficient number of construction modes and a relatively large amount of snapshots, proper orthogonal decomposition method can deliver accurate results. In addition, guidelines on selecting an appropriate amount of simulation snapshot and construction modes are provided.

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24

Rulli, Federico, Stefano Fontanesi, Alessandro d’Adamo, and Fabio Berni. "A critical review of flow field analysis methods involving proper orthogonal decomposition and quadruple proper orthogonal decomposition for internal combustion engines." International Journal of Engine Research 22, no. 1 (April 3, 2019): 222–42. http://dx.doi.org/10.1177/1468087419836178.

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Experimental techniques like particle image velocimetry provide a powerful technical support for the analysis of the spatial and temporal evolution of the flow field in internal combustion engines. Such techniques can be used to investigate both ensemble-averaged flow structures and their cyclic variations. These last are among the major causes of cycle-to-cycle variability of the engine processes (mixture formation, combustion, heat transfer, emission formation), the reduction of which has become a paradigm recently in engine development. Proper orthogonal decomposition has been largely used in conjunction with particle image velocimetry to analyze flow field characteristics. Several methods involving proper orthogonal decomposition have been proposed in the recent years to analyze engine cycle-to-cycle variability. In this work, phase-invariant proper orthogonal decomposition analysis, conditional averaging and triple and quadruple proper orthogonal decomposition methods are first introduced and applied to a large database of particle image velocimetry data from a well-known research engine. Results are discussed with particular emphasis on the capability of the methods to perform both quantitative and qualitative evaluations on cycle-to-cycle variability. Second, a new quadruple proper orthogonal decomposition methodology is proposed and compared to those available in the literature. All the methods are found to be helpful to identify the turbulent structures responsible for cycle-to-cycle variability. They can be equally applied to both experimental and numerical datasets to analyze turbulent fields in detail and to make comparisons.

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25

Li, Richen. "Isogeometric Analysis with Proper Orthogonal Decomposition for Elastodynamics." Communications in Computational Physics 30, no. 2 (June 2021): 396–422. http://dx.doi.org/10.4208/cicp.oa-2020-0018.

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26

Wang, Chao-Fu. "EFFICIENT PROPER ORTHOGONAL DECOMPOSITION FOR BACKSCATTER PATTERN RECONSTRUCTION." Progress In Electromagnetics Research 118 (2011): 243–51. http://dx.doi.org/10.2528/pier11060102.

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27

Lee, Sang Bong, Bum Woo, Dong Woo Park, You Won Ahn, Seok Cheon Go, and Heung Won Seo. "Proper Orthogonal Decomposition of Pressure Fluctuations in Moonpool." Journal of the Society of Naval Architects of Korea 49, no. 6 (December 20, 2012): 484–90. http://dx.doi.org/10.3744/snak.2012.49.6.484.

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28

Yao, Weigang, Min Xu, and Xiaojuan Wang. "Aerodynamic System Modeling based on Proper Orthogonal Decomposition." International Journal of Information Technology and Computer Science 3, no. 5 (November 18, 2011): 25–31. http://dx.doi.org/10.5815/ijitcs.2011.05.04.

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29

Behzad, Fariduddin, Brian T. Helenbrook, and Goodarz Ahmadi. "Multilevel Algorithm for Obtaining the Proper Orthogonal Decomposition." AIAA Journal 56, no. 11 (November 2018): 4423–36. http://dx.doi.org/10.2514/1.j056807.

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30

Willcox, K., and J. Peraire. "Balanced Model Reduction via the Proper Orthogonal Decomposition." AIAA Journal 40, no. 11 (November 2002): 2323–30. http://dx.doi.org/10.2514/2.1570.

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31

Ahmed, Shady E., Omer San, Adil Rasheed, and Traian Iliescu. "Nonlinear proper orthogonal decomposition for convection-dominated flows." Physics of Fluids 33, no. 12 (December 2021): 121702. http://dx.doi.org/10.1063/5.0074310.

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32

Camphouse, R. Chris. "Boundary Feedback Control Using Proper Orthogonal Decomposition Models." Journal of Guidance, Control, and Dynamics 28, no. 5 (September 2005): 931–38. http://dx.doi.org/10.2514/1.10523.

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33

Cizmas, Paul G. A., and Antonio Palacios. "Proper Orthogonal Decomposition of Turbine Rotor-Stator Interaction." Journal of Propulsion and Power 19, no. 2 (March 2003): 268–81. http://dx.doi.org/10.2514/2.6108.

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34

Allison, Timothy C., A. Keith Miller, and Daniel J. Inman. "Free-Response Simulation via the Proper Orthogonal Decomposition." AIAA Journal 45, no. 10 (October 2007): 2538–43. http://dx.doi.org/10.2514/1.28516.

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35

TERASHIMA, Osamu, Toru WATANABE, Kiyoshi MORITA, Yukinobu ABE, Yasuhiko SAKAI, Kouji NAGATA, and Kazuhiro ONISHI. "Aeroacoustic Measurement with Combined Proper Orthogonal Decomposition Analysis." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B 79, no. 808 (2013): 2764–68. http://dx.doi.org/10.1299/kikaib.79.2764.

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36

Brevis, Wernher, and Manuel García-Villalba. "Shallow-flow visualization analysis by proper orthogonal decomposition." Journal of Hydraulic Research 49, no. 5 (September 26, 2011): 586–94. http://dx.doi.org/10.1080/00221686.2011.585012.

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37

Graham, Michael D., Samuel L. Lane, and D. Luss. "Proper orthogonal decomposition analysis of spatiotemporal temperature patterns." Journal of Physical Chemistry 97, no. 4 (January 1993): 889–94. http://dx.doi.org/10.1021/j100106a014.

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38

Fareed, Hiba, John R. Singler, Yangwen Zhang, and Jiguang Shen. "Incremental proper orthogonal decomposition for PDE simulation data." Computers & Mathematics with Applications 75, no. 6 (March 2018): 1942–60. http://dx.doi.org/10.1016/j.camwa.2017.09.012.

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39

Arifin, N. M., M. S. M. Noorani, and A. Kiliçman. "Modelling of Marangoni convection using proper orthogonal decomposition." Nonlinear Dynamics 48, no. 3 (January 16, 2007): 331–37. http://dx.doi.org/10.1007/s11071-006-9052-x.

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40

Liberge, Erwan, Mustapha Benaouicha, and Aziz Hamdouni. "Proper orthogonal decomposition investigation in fluid structure interaction." European Journal of Computational Mechanics 16, no. 3-4 (January 2007): 401–18. http://dx.doi.org/10.3166/remn.16.401-418.

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41

Willcox, K., and J. Peraire. "Balanced model reduction via the proper orthogonal decomposition." AIAA Journal 40 (January 2002): 2323–30. http://dx.doi.org/10.2514/3.15326.

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42

Kramer, Boris. "Solving Algebraic Riccati Equations via Proper Orthogonal Decomposition." IFAC Proceedings Volumes 47, no. 3 (2014): 7767–72. http://dx.doi.org/10.3182/20140824-6-za-1003.02477.

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43

Mangold, Michael, and Mykhaylo Krasnyk. "Application of Proper Orthogonal Decomposition to Particulate Processes." IFAC Proceedings Volumes 45, no. 2 (2012): 728–33. http://dx.doi.org/10.3182/20120215-3-at-3016.00129.

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44

Kunisch, K., and S. Volkwein. "Galerkin proper orthogonal decomposition methods for parabolic problems." Numerische Mathematik 90, no. 1 (November 1, 2001): 117–48. http://dx.doi.org/10.1007/s002110100282.

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45

TAMURA, Y., S. SUGANUMA, H. KIKUCHI, and K. HIBI. "PROPER ORTHOGONAL DECOMPOSITION OF RANDOM WIND PRESSURE FIELD." Journal of Fluids and Structures 13, no. 7-8 (October 1999): 1069–95. http://dx.doi.org/10.1006/jfls.1999.0242.

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46

LENAERTS, V., G. KERSCHEN, and J. C. GOLINVAL. "ECL BENCHMARK: APPLICATION OF THE PROPER ORTHOGONAL DECOMPOSITION." Mechanical Systems and Signal Processing 17, no. 1 (January 2003): 237–42. http://dx.doi.org/10.1006/mssp.2002.1565.

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47

Aquino, W., J. C. Brigham, C. J. Earls, and N. Sukumar. "Generalized finite element method using proper orthogonal decomposition." International Journal for Numerical Methods in Engineering 79, no. 7 (August 13, 2009): 887–906. http://dx.doi.org/10.1002/nme.2604.

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48

Iliescu, Traian, and Zhu Wang. "Variational multiscale proper orthogonal decomposition: Navier-stokes equations." Numerical Methods for Partial Differential Equations 30, no. 2 (December 6, 2013): 641–63. http://dx.doi.org/10.1002/num.21835.

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49

Heizer, B., and T. Kalmar-Nagy. "Proper Orthogonal Decomposition and Dynamic Mode Decomposition of Delay-Differential Equations." IFAC-PapersOnLine 51, no. 14 (2018): 254–58. http://dx.doi.org/10.1016/j.ifacol.2018.07.232.

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50

Hu, Shufan, Chen Zhang, Hong Liu, and Fuxin Wang. "Study on vortex shedding mode on the wake of horn/ridge ice contamination under high-Reynolds conditions." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 13 (March 19, 2019): 5045–56. http://dx.doi.org/10.1177/0954410019835971.

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This paper studied the unsteadiness of vortex motion produced by a three-dimensional wing section with horn/ridge ice contamination. Using improved delayed detached eddy simulation method, multi-scale vortex and their associated flow structures were successfully captured. Results have shown a diversity of unsteadiness scales at different time series, including shear layer instability, vortex pairing, co-rotating and breaking up. Proper orthogonal decomposition was then introduced to extract the characteristic vortex shedding modes with scheduling the eigenvalues λi from large to small. The dominate and secondary proper orthogonal decomposition modes under horn ice condition were displayed, which could be illustrated as fluctuations near recirculation zone, and large-scale vortex shedding/reattaching motion, respectively. The proper orthogonal decomposition modal characteristics for ridge ice showed that vortex scales varied from large to small. The trajectory of large-scale vortex reattaching and co-rotating exist simultaneously with the pressure peak and recover, which also verified the association of proper orthogonal decomposition modes with different scales of vortices. Future works would be presented on demonstration of the complex structures and the dynamic features in such flow.

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