Wind and Structures

  • 제10권2호
  • /
  • Pages.153-176
  • /
  • 2007
  • /
  • 1226-6116(pISSN)
  • /
  • 1598-6225(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Proper orthogonal decomposition in wind engineering - Part 1: A state-of-the-art and some prospects

  • Solari, Giovanni (DISEG, Department of Structural and Geotechnical Engineering, University of Genoa) ;
  • Carassale, Luigi (DISEG, Department of Structural and Geotechnical Engineering, University of Genoa) ;
  • Tubino, Federica (DISEG, Department of Structural and Geotechnical Engineering, University of Genoa)
  • 투고 : 2006.06.27
  • 심사 : 2007.03.19
  • 발행 : 2007.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The Proper Orthogonal Decomposition (POD) is a statistical method particularly suitable and versatile for dealing with many problems concerning wind engineering and several other scientific and humanist fields. POD represents a random process as a linear combination of deterministic functions, the POD modes, modulated by uncorrelated random coefficients, the principal components. It owes its popularity to the property that only few terms of the series are usually needed to capture the most energetic coherent structures of the process, and a link often exists between each dominant mode and the main mechanisms of the phenomenon. For this reason, POD modes are normally used to identify low-dimensional subspaces appropriate for the construction of reduced models. This paper provides a state-of-the-art and some prospects on POD, with special regard to its framework and applications in wind engineering. A wide bibliography is also reported.

키워드

참고문헌

  1. Achatz, U. and Branstator, G. (1999), "A two-layer model with empirical linear corrections and reduced order for studies of internal climate variability", J. Atmos. Sci., 56, 3140-3160. https://doi.org/10.1175/1520-0469(1999)056<3140:ATLMWE>2.0.CO;2
  2. Achatz, U. and Opsteegh, J.D. (2003), "Primitive-equation-based low-order models with seasonal cycle. Part I: model construction. Part II: application to complexity and non-linearity of large-scale atmospheric dynamics", J. Atmos. Sci., 60, 465-477, 478-490. https://doi.org/10.1175/1520-0469(2003)060<0465:PEBLOM>2.0.CO;2
  3. Adrian R.J. and Moin, P. (1988). "Stochastic estimation of organised turbulent structure: homogeneous shear flow", J. Fluid. Mech., 190, 531-559. https://doi.org/10.1017/S0022112088001442
  4. Ahmed, N. and Rao, K. R. (1975), Orthogonal Transforms for Digital Signal Processing, Springer-Verlag, New York.
  5. Alfonsi, G., Restano, C. and Primavera, L. (2003), "Coherent structures of the flow around a surface-mounted cubic obstacle in turbulent channel flow", J. Wind Eng. Ind. Aerodyn., 91, 495-511. https://doi.org/10.1016/S0167-6105(02)00429-4
  6. Amandolese, X. and Crémona, C. (2005), "Analysing fluid loadings on moving bluff bodies using proper orthogonal decomposition", J. Fluid Struct., 20, 577-587. https://doi.org/10.1016/j.jfluidstructs.2005.02.008
  7. Amari, S.-I. and Cichocki, A. (1998), "Adaptive blind signal processing-neural Network approaches", Proc. IEEE, 86, 20269-2048.
  8. Armitt, J. (1968), "Eigenvector analysis of pressure fluctuations on the West Burton instrumented cooling tower", Internal Report RD/L/M 114/68, Central Electricity Research Laboratories, UK.
  9. Aubry, N., Guyonnet, R. and Lima, R. (1991), "Spatiotemporal analysis of complex signals: theory and applications", J. Stat. Phys., 64, 683-739. https://doi.org/10.1007/BF01048312
  10. Aubry, N., Lian, W. Y. and Titi, E. S. (1993), "Preserving symmetries in the proper orthogonal decomposition", SIAM J. Sci. Comput., 14, 483-505. https://doi.org/10.1137/0914030
  11. Autonne, L. (1915), "Sur les matrices hypohermitiennes et sur les matrices unitaires", Ann Univ. Lyon, 38, 1-77.
  12. Bagrov, N. A. (1959), "The analytic representation of a sequence of meteorological fields in terms of natural orthogonal components", Trans. Central Weather Bureau, 74.
  13. Baker, C. J. (2000), "Aspects of the use of proper orthogonal decomposition of surface pressure fields", Wind and Struct., 3, 97-115. https://doi.org/10.12989/was.2000.3.2.097
  14. Bakewell, H. P. and Lumley, J. L. (1967), "Viscous sublayer and adjacent wall region in turbulent pipe flow", Phys. Fluids, 10, 1880-1889. https://doi.org/10.1063/1.1762382
  15. Barroso, L. R. and Rodriguez, R. (2004), "Damage detection utilizing the damage index method to a benchmark structure", J. Eng. Mech., ASCE, 130, 142-151. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(142)
  16. Basilevsky, A. and Hum, D. P. J. (1979), "Karhunen-Loeve analysis of historical time series with an application to plantation births in Jamaica", J. Amer. Statist. Assoc., 74, 284-290.
  17. Bellini, S. and Rocca, R. (1990), "Asymptotically efficient blind deconvolution", Signal Proc., 20, 193-209. https://doi.org/10.1016/0165-1684(90)90010-V
  18. Beltrami, E. (1873), "Sulle funzioni bilineari", Giornale di Mathematiche di Battaglini, 11, 98-106.
  19. Benfratello, S., Di Paola, M. and Spanos, P. D. (1998), "Stochastic response of MDOF wind-excited structures by means of Volterra series approach", J. Wind Eng. Ind. Aerodyn., 74-76, 1135-1145. https://doi.org/10.1016/S0167-6105(98)00104-4
  20. Benfratello, S. and Muscolino, G. (1999), "Filter approach to the stochastic analysis of MDOF wind-excited structures", Prob. Eng. Mech., 14, 311-321. https://doi.org/10.1016/S0266-8920(98)00041-1
  21. Beran, P. S., Lucia, D. J. and Pettit, C. L. (2004), "Reduced-order modelling of limit-cycle oscillation for aeroelastic systems", J. Fluid Struct., 19, 575-590. https://doi.org/10.1016/j.jfluidstructs.2004.04.002
  22. Berkooz, G., Holmes, P. and Lumley, J. L. (1993), "The proper orthogonal decomposition in the analysis of turbulent flows", Annu. Rev. Fluid Mech., 25, 539-575. https://doi.org/10.1146/annurev.fl.25.010193.002543
  23. Best, R. J. and Holmes, J. D. (1983), "Use of eigenvalues in the covariance integration method for determination of wind load effects", J. Wind Eng. Ind. Aerodyn., 13, 359-370. https://doi.org/10.1016/0167-6105(83)90156-3
  24. Bienkiewicz, B., Ham, H. J. and Sun, Y. (1993), "Proper orthogonal decomposition of roof pressure", J. Wind Eng. Ind. Aerodyn., 50, 193-202. https://doi.org/10.1016/0167-6105(93)90074-X
  25. Bienkiewicz, B., Tamura, Y., Ham, H. J., Ueda, H. and Hibi, K. (1995), "Proper orthogonal decomposition and reconstruction of multi-channel roof pressure", J. Wind Eng. Ind. Aerodyn., 54/55, 369-381. https://doi.org/10.1016/0167-6105(94)00066-M
  26. Blackith, R. E. and Reyment, R. A. (1971), Multivariate Morphometrics, Academic Press, London.
  27. Bonnet, J. P., Cole, D. R., Delville, J., Glauser, M. N. and Ukeiley, L. (1994), "Stochastic estimation and proper orthogonal decomposition: complementary techniques for identifying structure", Exper. Fluids, 17, 307-314. https://doi.org/10.1007/BF01874409
  28. Bouhaddou, O., Obled, C. H. and Dinh, T. P. (1987), "Principal component analysis and interpolation of stochastic processes: methods and simulation", J. Appl. Statist., 14, 251-267. https://doi.org/10.1080/02664768700000030
  29. Brillinger, D. R. (1981). Time Series: Data Analysis and Theory. Holden Day, San Francisco.
  30. Brincker, R., Zhang, L. and Andersen, P. (2001), "Modal identification of output-only systems using frequency domain decomposition", Smart Mater. Struct., 10, 441-445. https://doi.org/10.1088/0964-1726/10/3/303
  31. Burlando, M., Carassale, L., Borghesi, M. V., Tubino, F., Ratto, C. F. and Solari, G. (2005), "Numerical simulation of turbulent wind fields at airports in complex terrain", C.D. Proc., 4th European-African Conf. on Wind Engineering, Prague.
  32. Caddemi, S. and Di Paola, M. (1994), "Second order statistics of the wind-excited response of structures", Proc., 4th Italian Nat. Conf. on Wind Engineering, Rome, 151-165 (in Italian).
  33. Carassale, L. (2005), "Filter-based representation of the random loads on structures". Prob. Eng. Mech., 20(3), 263-280. https://doi.org/10.1016/j.probengmech.2005.05.008
  34. Carassale, L., Hibi, K., Pagnini, L. C., Solari, G. and Tamura, Y. (2004), "POD analysis of the dynamic wind pressure on a tall building", Proc., 5th Int. Coll. on Bluff Body Aerodynamics & Applications, Ottawa, Canada.
  35. Carassale, L. and Kareem, A. (2002), "A Volterra approach for nonlinear multi-DOF structures", Structural Dynamics, Proc., EURODYN 2002, 1, 755-760.
  36. Carassale, L. and Percivale, F. (2006), "Frequency-domain output-only identification of linear structures subject to stationary excitation", Proc., 5th Int. Conf. on Computational Stochastic Mechanics, CSM5, Rhodes, Greece, in press.
  37. Carassale, L. and Piccardo, G. (2003), "Wind-induced nonlinear oscillations of cables by Volterra approach", Proc., 5th Int. Symp. on Cable Dynamics, Santa Margherita, Italy, 149-156.
  38. Carassale, L. and Piccardo, G. (2004), "A reduced model for nonlinear response of cables in turbulent wind", C.D. Proc., 3rd Int. Conf. on Advances in Structural Engineering and Mechanics, Seoul, Korea.
  39. Carassale, L., Piccardo, G. and Solari, G. (1998), "Wind response of structures by double modal transformation", Proc., 2nd East-European Conf. on Wind Engineering, Prague.
  40. Carassale, L., Piccardo, G. and Solari, G. (1999), "Double modal transformation in continuous modelling", Proc., 10th Int. Conf. on Wind Engineering, Copenhagen.
  41. Carassale, L., Piccardo, G. and Solari, G. (2001), "Double modal transformation and wind engineering applications", J. Eng. Mech., ASCE, 127, 432-439. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(432)
  42. Carassale, L. and Solari, G. (2002), "Wind modes for structural dynamics: a continuous approach", Prob. Eng. Mech., 17, 157-166. https://doi.org/10.1016/S0266-8920(01)00036-4
  43. Carassale, L. and Solari, G. (2006), "Monte Carlo simulation of wind velocity fields on complex structures", J. Wind Eng. Ind. Aerodyn., 94, 323-339. https://doi.org/10.1016/j.jweia.2006.01.004
  44. Carassale, L., Solari, G. and Tubino, F. (2007), "Proper orthogonal decomposition in wind engineering. Part 2: Theoretical aspects and some applications", Wind and Struct., 10(2), 177-208. https://doi.org/10.12989/was.2007.10.2.177
  45. Cardoso, J. F. (1991), "Super-symmetric decomposition of the fourth-order cumulant tensor, blind identification of more sources than sensors", Proc. Int. Conf. Acoust. Speech Signal Process., Glasgow, 2109-2112.
  46. Cardoso, J. F. (1998), "Blind signal separation: Statistical principles", Proc. IEEE, 86, 2009-2025. https://doi.org/10.1109/5.720250
  47. Chaumette, E., Comon, P. and Muller, D. (1993), "ICA-based technique for radiating sources estimation: Application to airport surveillance", Proc. Inst. Elect. Eng., 140, 395-401.
  48. Chen, X. and Kareem, A. (2005), "Proper orthogonal decomposition-based modeling, analysis, and simulation of dynamic wind load effects on structures", J. Eng. Mech., ASCE, 131, 325-339. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(325)
  49. Chen, Y., Kopp, G. A. and Surry, D. (2003), "The use of linear stochastic estimation for the reduction of data in the NIST aerodynamic database", Wind and Struct., 6, 107-126. https://doi.org/10.12989/was.2003.6.2.107
  50. Cichocki, A. and Amari, S.I. (2002), Adaptive Blind Signal and Image Processing, John Wiley.
  51. Comon, P. (1994), "Independent component analysis, A new concept ?" Signal Proc., 36, 287-314. https://doi.org/10.1016/0165-1684(94)90029-9
  52. Cusumano, J. P. and Bai, B. I. (1993), "Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator", Chaos, Solitons & Fractals, 3, 515-535. https://doi.org/10.1016/0960-0779(93)90003-J
  53. De Grenet, E. T. and Ricciardelli, F. (2004), "Spectral proper transformation of wind pressure fluctuations: application to a square cylinder and a bridge deck", J. Wind Eng. Ind. Aerodyn., 92, 1281-1297. https://doi.org/10.1016/j.jweia.2004.08.005
  54. Delville, J., Ukeiley, L., Cordier, L., Bonnet, J.P. and Glauser, M. (1999), "Examination of large-scale structures in a turbulent plane mixing layer. Part. 1. Proper orthogonal decomposition", J. Fluid Mech., 391, 91-122. https://doi.org/10.1017/S0022112099005200
  55. Devijver, P. A. and Kittler, J. (1982), Pattern recognition: A statistical approach, Prentice-Hall, Englewood Cliffs, New Jersey.
  56. Di Paola, M. (1998), "Digital simulation of wind field velocity", J. Wind Eng. Ind. Aerodyn., 74-76, 91-109. https://doi.org/10.1016/S0167-6105(98)00008-7
  57. Di Paola, M. and Gullo, I. (2001), "Digital generation of multivariate wind field processes", Prob. Eng. Mech., 16, 1-10. https://doi.org/10.1016/S0266-8920(99)00032-6
  58. Di Paola, M., Muscolino, G. and Sofi, A. (2004), "Monte Carlo simulation for the response analysis of long-span suspended cables under wind loads", Wind and Struct., 7, 107-130. https://doi.org/10.12989/was.2004.7.2.107
  59. Di Paola, M. and Pisano, A. A. (1996), "Multivariate stochastic wave generation", Appl. Ocean Res., 18, 361-365. https://doi.org/10.1016/S0141-1187(97)00003-5
  60. Dodds, C. J. and Robson, J. D. (1975), "Partial coherence in multivariate random processes", J. Sound Vib., 42, 243-249. https://doi.org/10.1016/0022-460X(75)90219-9
  61. Dowell, E. H. and Hall, K. C. (2001), "Modeling of fluid-structure interaction", Annu. Rev. Fluid Mech., 33, 445-490. https://doi.org/10.1146/annurev.fluid.33.1.445
  62. Dowell, E. H., Hall, K. C. and Romanowski, M. C. (1997), "Eigenmode analysis in unsteady aerodynamics: reduced order models", Appl. Mech. Rev., 50, 371-385. https://doi.org/10.1115/1.3101718
  63. Eckart, C. (1934), "The kinetic energy of polyatomic molecules", Phys. Rev., 46, 383-387. https://doi.org/10.1103/PhysRev.46.383
  64. Eckart, C. and Young, G. (1936), "The approximation of one matrix by another of lower rank", Psychometrika, 1, 211-218. https://doi.org/10.1007/BF02288367
  65. Eckart, C. and Young, G. (1939), "A principal axis transformation for non-hermitian matrices", Bull. Am. Math. Soc., 45, 118-121. https://doi.org/10.1090/S0002-9904-1939-06910-3
  66. Elsner, J. B. and Tsonis, A. A. (1996), Singular Spectrum Analysis: A New Tool in Time Series Analysis, New York: Plenum Press.
  67. Feeny, B. F. and Kappagantu, R. (1998), "On the physical interpretation of proper orthogonal modes in vibrations", J. Sound Vib., 211, 607-616. https://doi.org/10.1006/jsvi.1997.1386
  68. Fort, J. C. (1991), "Stability of the JH sources separation algorithm", Traitement du Signal, 8, 35-42.
  69. Freiberger, W. and Grenander, U. (1967), "On the formulation of statistical meteorology", Rev. Int. Stat. Inst., 33, 59-86.
  70. Georgiou, I. T. and Schwartz, I. B. (1999), "Dynamics of large scale structural/dynamical systems: a singular perturbation/proper orthogonal decomposition approach", J. Appl. Math., SIAM, 59, 1178-1207.
  71. Ghanem, R. and Spanos, P. D. (1991), Stochastic finite elements: A spectral approach,. Springer-Verlag, New York.
  72. Ghanem, R. and Spanos, P. D. (1993), "A stochastic Galerkin expansion for nonlinear random vibration analysis", Prob. Eng. Mech., 8, 255-264. https://doi.org/10.1016/0266-8920(93)90019-R
  73. Giannakis, G., Inouye, Y. and Mendel, J. M. (1989), "Cumulant-based identification of multichannel moving average models", IEEE Automat. Control, 34, 783-787. https://doi.org/10.1109/9.29415
  74. Gilliam, X., Dunyak, J. P., Smith, D. A. and Wu, F. (2004), "Using projection pursuit and proper orthogonal decomposition to identify independent flow mechanisms", J. Wind Eng. Ind. Aerodyn., 92, 53-69. https://doi.org/10.1016/j.jweia.2003.09.041
  75. Girolami, M. (2000), Advances in Independent Component Analysis, Springer-Verlag.
  76. Girshick, M. A. (1936), "Principal components", J. Amer. Statist. Assoc., 31, 519-528. https://doi.org/10.1080/01621459.1936.10503354
  77. Graham, M. and Kevrekidis, I. (1996), "Alternative approaches to the Karhunen-Loeve decomposition for model reduction and data analysis", Comp. Chem. Eng., 20, 495-506. https://doi.org/10.1016/0098-1354(95)00040-2
  78. Grimmer, M. (1963), "The space-filtering of monthly surface temperature anomaly data in terms of pattern, using empirical orthogonal functions", Quart. J. Roy. Met. Soc., 89, 395-408. https://doi.org/10.1002/qj.49708938111
  79. Gullo, I., Di Paola, M. and Spanos, P. D. (1998), "Spectral approximation for wind induced structural vibration studies", Meccanica, 33, 291-298. https://doi.org/10.1023/A:1004303315491
  80. Gunes, H. (2002), "Low-order dynamical models of thermal convection in high-aspect ratio enclosures", Fluid Dyn. Res., 30, 1. https://doi.org/10.1016/S0169-5983(01)00038-7
  81. Gunes, H. and Rist, U. (2004), "Proper orthogonal decomposition reconstruction of a transitional boundary layer with and without control", Phys. Fluids, 16, 2763-2784. https://doi.org/10.1063/1.1758151
  82. Hall, K. C. (1994), "Eigenanalysis of unsteady flows about airfoils, cascades, and wings", AIAA J., 32, 2426-2432. https://doi.org/10.2514/3.12309
  83. Han, S. and Feeny, B. F. (2002), "Enhanced proper orthogonal decomposition for the modal analysis of homogeneous structures", J. Vib. Contr., 8, 19-40. https://doi.org/10.1177/1077546302008001518
  84. Hasselmann, K. (1988), "PIPs and POPs: The reduction of complex dynamical systems using principal interaction and oscillation patterns", J. Geophys. Res., 93, 11,015-11,021.
  85. Hayden, B. P. and Smith, W. (1982), "Season-to-season cyclone frequency prediction", Mon. Weather Rev., 110, 239-253. https://doi.org/10.1175/1520-0493(1982)110<0239:STSCFP>2.0.CO;2
  86. Haykin, S. (1994), Blind Deconvolution, Prentice-Hall, Englewood Cliffs.
  87. Hemon, P. and Santi, F. (2002), "On the aeroelastic behaviour of rectangular cylinders in cross-flow", J. Fluid. Struct., 16, 855-889. https://doi.org/10.1006/jfls.2002.0452
  88. Hemon, P. and Santi, F. (2003), "Applications of biorthogonal decompositions in fluid-structure interactions", J. Fluid Struct., 17, 1123-1143. https://doi.org/10.1016/S0889-9746(03)00057-4
  89. Herzog, S. (1986), "The large scale structure in the near wall region of a turbulent pipe flow", Ph.D. Thesis, Cornell University.
  90. Holmes, J. D. (1990), "Analysis and synthesis of pressure fluctuations on bluff bodies using eigenvectors", J. Wind Eng. Ind. Aerodyn., 33, 219-230. https://doi.org/10.1016/0167-6105(90)90037-D
  91. Holmes, J. D., Sankaran, R., Kwok, K. C. S. and Syme, M. J. (1997), "Eigenvector modes of fluctuating pressures on low-rise building models", J. Wind Eng. Ind. Aerodyn., 69-71, 697-707. https://doi.org/10.1016/S0167-6105(97)00198-0
  92. Holmes, P., Lumley, J. L. and Berkooz, G. (1996), Turbulence: Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Great Britain.
  93. Holmstrom, E. I. (1963), "On a method for a parametric representation of the state of the atmosphere", Tellus, 15, 127-149. https://doi.org/10.1111/j.2153-3490.1963.tb01372.x
  94. Hotelling, H. (1933), "Analysis of a complex of statistical variables into principal components", J. Educ. Psychol., 24, 417-441, 498-520. https://doi.org/10.1037/h0070888
  95. Hotelling, H. (1936), "Simplified calculation of principal components", Psychometrika, 1, 27-35. https://doi.org/10.1007/BF02287921
  96. Huang, S. P., Quek, S. T. and Phoon, K. K. (2001), "Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes", Int. J. Num. Meth. Eng., 52, 1029-1043. https://doi.org/10.1002/nme.255
  97. Hyvarinen, A., Karhunen, J. and Oja, E. (2001), Independent Component Analysis, John Wiley.
  98. Jolliffe, I. T. (2002), Principal Component Analysis, Springer-Verlag, New York.
  99. Jordan, M. C. (1874), "Memorie sur les Formes Bilineaires", J. Math. Pures Appl., 19, 35-54.
  100. Jutten, C. and Herault, J. (1991), "Blind separation of sources, Part I: An adaptive algorithm based on neuromimatic architecture", Signal Proc., 24, 1-10. https://doi.org/10.1016/0165-1684(91)90079-X
  101. Kac, M. and Siegert, A. J. F. (1947), "An eplicit representation of a stationary Gaussian process", Ann. Math. Stat., 18, 438-442. https://doi.org/10.1214/aoms/1177730391
  102. Kappagantu, R. and Feeny, B. F. (1999), "An "optimal" modal reduction of a system with frictional excitation", J. Sound Vib., 224(5), 863-877. https://doi.org/10.1006/jsvi.1999.2165
  103. Kareem, A. and Cermak, J. E. (1984), "Pressure fluctuations on a square building model in boundary-layer flows", J. Wind Eng. Ind. Aerodyn., 16, 17-41. https://doi.org/10.1016/0167-6105(84)90047-3
  104. Karhunen, K. (1946), "Zur spektraltheorie stochastischer prozess", Ann. Acad. Sci. Fennicae, 1, 34.
  105. Katsumura, A., Tamura, Y. and Nakamura O. (2004), "Universal wind load distribution reproducing maximum load effects on structural members", Proc., 5th Int. Coll. on Bluff Body Aerodynamics & Applications, Ottawa, Canada, 351-354.
  106. Kershen, G. and Golinval, J. C. (2002), "Physical interpretation of the proper orthogonal modes using the singular value decomposition", J. Sound Vib., 249, 849-865. https://doi.org/10.1006/jsvi.2001.3930
  107. Kikuchi, H., Tamura, Y., Ueda, H. and Hibi, K. (1997), "Dynamic wind pressure acting on a tall building model - Proper orthogonal decomposition", J. Wind Eng. Ind. Aerodyn., 69-71, 631-646. https://doi.org/10.1016/S0167-6105(97)00193-1
  108. Koprova, L. I. and Malkewich, M. S. (1965), "On the empirical orthogonal functions for the optimal parameterization of the temperature and humidity profiles", Izv. Acad. Sci. USSR, Geophys. Ser., I, 15-18 (English translation).
  109. Kosambi, D. D. (1943), "Statistics in function space", J. Indian Math. Soc., 7, 76-88.
  110. Kostas, J., Soria, J. and Chong, M. S. (2005), "A comparison between snapshot POD analysis of PIV velocity and vorticity data", Exp. Fluids, 38, 146-160. https://doi.org/10.1007/s00348-004-0873-4
  111. Kreuzer, E. and Kust, O. (1996), "Analysis of long torsional strings by proper orthogonal decomposition", Arch. Appl. Mech., 67, 68-80. https://doi.org/10.1007/BF00787141
  112. Lee, B. E. (1975), "The effect of turbulence on the surface pressure field of a square prism", J. Fluid Mech., 69, 263-282. https://doi.org/10.1017/S0022112075001437
  113. Lenaerts, V., Kerschen, G. and Golinval, J. C. (2003), "ECL Benchmark: application of the proper orthogonal decomposition", Mech. Syst. & Sign. Proc., 17, 237-242. https://doi.org/10.1006/mssp.2002.1565
  114. Letchford, C. W. and Mehta, K. C. (1993), "The distribution and correlation of fluctuating pressure on the Texas Tech Building", J. Wind Eng. Ind. Aerodyn., 50, 225-234. https://doi.org/10.1016/0167-6105(93)90077-2
  115. Li, Y. and Kareem, A. (1989), "On stochastic decomposition and its applications in probabilistic dynamics", Proc. 5th Int. Conf. On Structural Safety and Reliability, San Francisco, 1311-1318.
  116. Li, Y. and Kareem, A. (1993), "Simulation of multivariate random processes: Hybrid DFT and digital filtering approach", J. Eng. Mech., ASCE, 119, 1078-1098. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:5(1078)
  117. Li, Y. and Kareem, A. (1995), "Stochastic decomposition and application to probabilistic dynamics", J. Eng. Mech., ASCE, 121, 162-174. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:1(162)
  118. Li, Y. and Kareem, A. (1997), "Simulation of multivariate nonstationary random processes: Hybrid DFT and digital filtering approach", J. Eng. Mech., ASCE, 123, 1302-1310. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:12(1302)
  119. Loeve, M. (1945), "Fonctions aleatoire de second ordre", Compte Red. Acad. Sci. Paris, 220.
  120. Loeve, M. (1955), Probability theory, Van Nostrand, New York.
  121. Lorenz, E. N. (1956), "Empirical orthogonal functions and statistical weather prediction", Sci. Rep. No. 1, Dept. Meteor., MIT.
  122. Lorenz, E. N. (1959), "Prospects for statistical whether forecasting", Final Report, Statistical Forecasting Project, MIT, Cambridge, Massachusetts.
  123. Lucia, D. J., Beran, P. S. and Silva, W. A. (2005), "Aeroelastic system development using proper orthogonal decomposition and volterra theory", J. Aircraft, 42, 509-518. https://doi.org/10.2514/1.2176
  124. Lumley, J. L. (1967), "The structure of inhomogeneous turbulent flows", Proc., Int. Coll. on the Fine Scale Structure of the Atmosphere and its Influence on Radio Wave Propagation, Doklady Akademia Nauk SSSR, Moscow, 166-176.
  125. Lumley, J. L. (1970), Stochastic Tools in Turbulence, Academic Press, New York.
  126. Lumley, J. L. (1981). "Coherent structures in turbulence", Transition and Turbulence, Meyer, R.E. (Ed.), Academic Press, New York, 215-241.
  127. Lumley, J. and Blossey, P. (1998), "Control of turbulence", Annu. Rev. Fluid Mech., 30, 311. https://doi.org/10.1146/annurev.fluid.30.1.311
  128. MacDonald, P. A., Holmes, J. D. and Kwok, K. C. S. (1990), "Wind loads on circular storage bins, silos and tanks. III: Fluctuating and peak pressure distributions", J. Wind Eng. Ind. Aerodyn., 34, 319-337. https://doi.org/10.1016/0167-6105(90)90160-E
  129. Masri, S. F., Miller, R. K. and Traina, M. I. (1990), "Probabilistic representation and transmission of earthquake ground motion records", Earthq. Eng. Struct. Dyn., 19, 1025-1040. https://doi.org/10.1002/eqe.4290190707
  130. Masri, S. F., Smyth, A. W. and Traina, M. I. (1998), "Probabilistic representation and transmission of nonstationary processes in multi-degree-of-freedom systems", J. Appl. Mech., ASME, 65, 398-409. https://doi.org/10.1115/1.2789068
  131. Moin, P. (1984), "Probing turbulence via large-eddy simulation", AIAA Paper 84-0174.
  132. Moin, P. and Moser, R. D. (1989), "Characteristic-eddy decomposition of turbulence in a channel", J. Fluid. Mech., 200, 471-509. https://doi.org/10.1017/S0022112089000741
  133. Mokhasi, P. and Rempfer, D. (2004), "Optimized sensor placement for urban flow measurement", Phys. Fluids, 16, 1758-1764. https://doi.org/10.1063/1.1689351
  134. Mulaik, S. A. (1972), The Foundations of Factor Analysis, McGraw-Hill, N.Y.
  135. Obled, C. and Creutin, J. D. (1986), "Some developments in the use of empirical orthogonal functions for mapping meteorological fields", J. Clim. Appl. Meteor., 25, 1189-1204. https://doi.org/10.1175/1520-0450(1986)025<1189:SDITUO>2.0.CO;2
  136. Obukhov, A. M. (1947), "Statistically homogeneous fields on a sphere", Usp. Mat. Nauk, 2, 196-198.
  137. Obukhov, A. M. (1954), "Statistical description of continuous fields", Tr. Geophys. Int. Akad. Nauk. SSSR, 24, 3-42.
  138. Obukhov, A. M. (1960), "The statistically orthogonal expansion of empirical functions", Izv. Geophys. Ser. Atmos. Oceanic Phys., 60, 280-291.
  139. Panofsky, H. A. and Dutton, J. A. (1984), Atmospheric Turbulence: Models and Methods for Engineering Applications, John Wiley and Sons, New York.
  140. Papoulis, A. (1965), Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York.
  141. Payne, F. R. and Lumley, J. L. (1967), "Large eddy structure of the turbulent wake behind a circular cylinder", Phys. Fluids, S194-S196.
  142. Pearson, K. (1901), "On lines and planes of closet fit to systems of points in space", Phil. Mag. (6), 2, 559-572. https://doi.org/10.1080/14786440109462720
  143. Pedersen, J. M. and Meyer, K. E. (2002), "POD analysis of flow structures in a scale model of a ventilated room", Exp. Fluids, 33, 940-949. https://doi.org/10.1007/s00348-002-0514-8
  144. Phoon, K. K., Huang, S. P. and Quek, S. T. (2002a), "Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme", Prob. Eng. Mech., 17, 293-303. https://doi.org/10.1016/S0266-8920(02)00013-9
  145. Phoon, K. K., Huang, S. P. and Quek, S. T. (2002b), "Simulation of second-order processes using Karhunen-Loeve expansion", Comput. Struct., 80, 1049-1060. https://doi.org/10.1016/S0045-7949(02)00064-0
  146. Phoon, K. K., Huang, S. P. and Quek, S. T. (2004a), "Comparison between Karhunen-Loeve and wavelet expansions for simulation of Gaussian processes", Comput. Struct., 82, 985-991. https://doi.org/10.1016/j.compstruc.2004.03.008
  147. Phoon, K. K., Quek, S. T. and Huang, S. P. (2004b), "Simulation of non-Gaussian processes using fractile correlation", Prob. Eng. Mech., 19, 287-292. https://doi.org/10.1016/j.probengmech.2003.09.001
  148. Podvin, B. and Le Quere, P. (2001), "Low-order models for flow in a differentially heated cavity", Phys. Fluids, 13, 3204. https://doi.org/10.1063/1.1408919
  149. Pougachev, V. S. (1953), "General theory of the correlations of random functions", Izv. Akad. Nauk. SSSR, Ser. Mat., 17, 1401-2.
  150. Prabhu, R. D., Collis, S. S. and Chang, Y. (2001), "The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows", Phys. Fluids, 13, 520-537. https://doi.org/10.1063/1.1333038
  151. Presendorfer, R. W. and Mobley, C. D. (1988), Principal Components Analysis in Meteorology and Oceanography, Elsevier, Amsterdam.
  152. Rasmusson, E. M., Arkin, P. A., Chen, W. Y. and Jalickee, J. B. (1981), "Biennial variations in surface temperature over the United States as revealed by singular decomposition", Mon. Weather Rev., 109, 587-598. https://doi.org/10.1175/1520-0493(1981)109<0587:BVISTO>2.0.CO;2
  153. Rathinam, M. and Petzold, L. R. (2002), "Dynamic iteration using reduced order models: A method for simulation of large scale modular systems", SIAM J. Numer. Anal., 40, 1446-1474. https://doi.org/10.1137/S0036142901390494
  154. Rathinam, M. and Petzold, L. R. (2003), "A new look at proper orthogonal decomposition", SIAM J. Numer. Anal., 41, 1893-1925. https://doi.org/10.1137/S0036142901389049
  155. Ravindra, B. (1999), "Comments on "On the physical interpretation of proper orthogonal modes in vibrations"", J. Sound Vib., 219, 189-192. https://doi.org/10.1006/jsvi.1998.1895
  156. Ravindran, S. S. (2000), "A reduced-order approach for optimal control of fluids using proper orthogonal decomposition", Int. J. Numer. Meth. Fl., 34, 425-448. https://doi.org/10.1002/1097-0363(20001115)34:5<425::AID-FLD67>3.0.CO;2-W
  157. Rempfer, D. and Fasel, H. (1994). "Evolution of three-dimensional coherent structures in a flat-plate boundary layer", J. Fluid. Mech., 275, 351-375. https://doi.org/10.1017/S0022112094002399
  158. Riaz, M. S. and Feeny, B. F. (2003), "Proper orthogonal modes of a beam sensed with strain gages", J. Vib. and Acoust., ASME, 125, 129-131. https://doi.org/10.1115/1.1521950
  159. Ricciardelli, F. (2003), "On the wind loading mechanism of long-span bridge deck box sections", J. Wind Eng. Ind. Aerodyn., 91, 1411-1430. https://doi.org/10.1016/j.jweia.2003.09.011
  160. Ricciardelli, F., De Grenet, E. T. and Solari, G. (2002), "Analysis of the wind loading of a bridge deck box section using proper orthogonal decomposition", Fluid Mech. Res., 29, 312-322.
  161. Rice, S. O. (1944), "Mathematical analysis of random noise", Bell System Tech. J., 23, 283-322.
  162. Rinne, J. and Karhila, V. (1975), "A spectral barotropic model in horizontal empirical orthogonal functions", Quart. J. Roy. Meteor. Soc., 101, 365-382. https://doi.org/10.1002/qj.49710142817
  163. Roberts, S. and Everson, R. (2001), Independent Component Analysis: Principles and Practice, Cambridge University Press.
  164. Rosenfeld, A. and Kak, A. C. (1982), Digital Picture Processing, Academic, New York.
  165. Roukhovets, L. V. (1963), "The optimum representation of the vertical distribution of certain meteorological elements", Izv.. Acad. Sci. USSR, Geophys. Ser., 4, 626-636 (English translation).
  166. Schmidt, E. (1907), "Zur Theorie de linearen und nichtlinearen Integralgleichungen. I Teil. Entwecklung willkurlichen Funktionen nach System vorgeschreibener", Mathematische Annalen, 63, 433-476. https://doi.org/10.1007/BF01449770
  167. Schubert, S. D. (1986), "The structure, energetics and evolution of the dominant frequency-dependent threedimensional atmospheric modes", J. Atmos. Sci., 43, 1210-1237. https://doi.org/10.1175/1520-0469(1986)043<1210:TSEAEO>2.0.CO;2
  168. Sellers, W. D. (1957), "A statistical-dynamical approach to numerical weather prediction", Sci. Report No. 2, Statistical Forecasting Project, Dept. of Meteorology, M.I..T., Cambridge, Mass., 151.
  169. Selten, F. M. (1993), "Toward an optimal description of atmospheric flow", J. Atmos. Sci., 50, 861-877. https://doi.org/10.1175/1520-0469(1993)050<0861:TAODOA>2.0.CO;2
  170. Shinozuka, M., Yun, C. B. and Seya, H. (1990), "Stochastic methods in wind engineering", J. Wind Eng. Ind. Aerodyn., 36, 829-843. https://doi.org/10.1016/0167-6105(90)90080-V
  171. Shorr, B. (1957), "Empirical orthogonal functions applied to prediction of the sea-level pressure field", Sci. Report No. 3, Statistical Forecasting Project, Dept. of Meteorology, M.I..T., Cambridge, Mass., 88.
  172. Sirovich, L. (1987), "Turbulence and the dynamics of coherent structures. Part I-III", Quart. Appl. Math., 45, 561-590. https://doi.org/10.1090/qam/910462
  173. Sirovich, L. and Park, H. (1990), "Turbulent thermal convection in a finite domain: Part I. Theory; Part II. Numerical results", Phys. Fluids A, 2, 1649, 1659.
  174. Smith, T. R., Moehlis, J. and Holmes, P. (2005), "Low-dimensional modelling of turbulence using the proper orthogonal decomposition: A tutorial", Nonlinear Dinam, 41, 275-307. https://doi.org/10.1007/s11071-005-2823-y
  175. Solari, G. and Carassale, L. (2000), "Modal transformation tools in structural dynamics and wind engineering", Wind and Struct., 3, 221-241. https://doi.org/10.12989/was.2000.3.4.221
  176. Solari, G. and Tubino, F. (2002), "A new turbulence model based on principal components", Prob. Eng. Mech., 17, 327-335. https://doi.org/10.1016/S0266-8920(02)00016-4
  177. Solari, G. and Tubino, F. (2005), "Gust buffeting of long span bridges by double modal transformation", Proc., 4th European & African Conf. on Wind Engineering, Prague, Czech Republic.
  178. Spanos, P. D. and Ghanem, R. (1989), "Stochastic finite element expansion for random media", J. Eng. Mech., ASCE, 115, 1035-1053. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1035)
  179. Spearman, C. (1904), "General intelligence, objectively determined and measured", Am. J. Phys., 15, 201-293.
  180. Stone, J. V. (2004), Independent Component Analysis: A Tutorial Introduction, MIT Press.
  181. Sylvester, J. J. (1889), "On the reduction of a bilinear quantic of the nth order to the form of a sum of n products by a double orthogonal substitution", Messenger of Mathematics, 19, 42-46.
  182. Tamura, Y., Suganuma, S. Kikuchi, H. and Hibi, K. (1999), "Proper orthogonal decomposition of random wind pressure field", J. Fluids Struct., 13, 1069-1095. https://doi.org/10.1006/jfls.1999.0242
  183. Tamura, Y., Ueda, H., Kikuchi, H., Hibi, K., Suganuma, S. and Bienkiewicz, B. (1997), "Proper orthogonal decomposition study of approach wind-building pressure correlation", J. Wind Eng. Ind. Aerodyn., 72, 421-432. https://doi.org/10.1016/S0167-6105(97)00270-5
  184. Tang, D., Kholodar, D., Juang, J. N. and Dowell, E. H. (2001), "System identification and proper orthogonal decomposition method applied to unsteady aerodynamics", AIAA J., 39, 1569-1576. https://doi.org/10.2514/2.1482
  185. Taniguchi, T., Taniike, Y. and Nishimura, H. (1996), "POD analysis with weighted-area and time-lag for pressures on a spherical roof", Proc., 14th Nat. Symp. on Wind Engineering, Tokyo, Japan, 323-328 (in Japanese).
  186. Therrien, C. W. (1992), Discrete Random Signals and Statistical Signal Processing, Prentice-Hall, Englewood Cliffs, New Jersey.
  187. Thomas, J. P., Dowell, E. H. and Hall, K. C. (2003), "Three-dimensional transonic aero-elasticity using proper orthogonal decomposition-based reduced-order models", J. Aircraft, 40, 544-551. https://doi.org/10.2514/2.3128
  188. Tong, L., Inouye, Y. and Liu, R.-W. (1993), "Waveform preserving blind estimation of multiple independent sources", IEEE Trans. Sign. Proc., 41, 2461-2470. https://doi.org/10.1109/78.224254
  189. Tong, L., Liu, R. W., Soon, V. C. and Huang, J. F. (1991), "Indeterminacy and identifiability of blind identification", IEEE Trans. Circuits Syst., 38, 409-509.
  190. Traina, M. I., Miller, R. K., and Masri, S. F. (1986), "Orthogonal decomposition and transmission of nonstationary random processes", Prob. Eng. Mech., 1, 136-149. https://doi.org/10.1016/0266-8920(86)90023-8
  191. Tubino, F. and Solari, G. (2005), "Double POD for representing and simulating turbulence fields", J. Eng. Mech., ASCE, 131, 1302-1312. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:12(1302)
  192. Tubino, F. and Solari, G. (2007), "Double modal transformation and effective turbulence for the gust buffeting of long span bridges", Eng. Struct., in press.
  193. Ukeiley, L., Cordier, L., Manceau, R., Delville, J., Glauser, M. and Bonnet, J. P. (2001), "Examination of largescale structures in a turbulent plane mixing layer. Part. 2. Dynamical systems model", J. Fluid Mech., 441, 67-108.
  194. Utturkar, Y., Zhang, B. and Shyy, W. (2005), "Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition", Int. J. Heat Fluid Flow., 26, 276-288. https://doi.org/10.1016/j.ijheatfluidflow.2004.08.008
  195. Van Trees, H. I. (1968), Detection, Estimation and Modulation Theory. Part 1, John Wiley and Sons, New York.
  196. Vasta, M. and Schueller, G. I. (2000), "Phase space reduction in stochastic dynamics", J. Eng. Mech., ASCE, 126, 626-632. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:6(626)
  197. Wadsworth, G. P., Bryan, J. G. and Gordon, C. H. (1948), "Short range and extended forecasting by statistical methods", U.S. Air Force, Air Weather Service Tech. Report No. 105-38, Washington, D.C., 186.
  198. Weyl, H. (1912), "Das Asymptotische Verteilungs gesetz der Eigenwert linearer partieller Differentialgleichungen (mit einer Anwendung auf der Theorie der Hohlraumstrahlung)", Mathematische Annalen, 71, 441-479. https://doi.org/10.1007/BF01456804
  199. White, R. M., Cooley, R. C. and Seaver, F. A. (1958), "The development of efficient linear statistical operators for the prediction of sea-level pressure", J. Atmos. Sci., 15, 426-434.
  200. Whitehouse, S. G., Lewis, S. R., Moroz, I. M. and Read, P. L. (2005), "A simplified model of the Martian atmosphere. Part 1: A diagnostic analysis. Part 2: A POD-Galerkin analysis", Nonlinear Proc. Geophys., submitted.
  201. Yamazaki, F. and Shinozuka, M. (1990), "Simulation of stochastic fields by statistical preconditioning", J. Eng. Mech., ASCE, 116, 268-287. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:2(268)
  202. Yoshida, A. and Tamura, Y. (2004), "System identification of structure for wind-induced response", Proc., 5th Int. Coll. on Bluff Body Aerodynamics & Applications, Ottawa, Canada, 335-338.

피인용 문헌

  1. Time–frequency analysis of the dynamics of different vorticity structures generated from a finite-length triangular prism vol.99, pp.6-7, 2011, https://doi.org/10.1016/j.jweia.2011.03.015
  2. Covariance proper transformation-based pseudo excitation algorithm and simplified SRSS method for the response of high-rise building subject to wind-induced multi-excitation vol.100, 2015, https://doi.org/10.1016/j.engstruct.2015.05.040
  3. Principal static wind loads vol.113, 2013, https://doi.org/10.1016/j.jweia.2012.12.009
  4. Error Analysis of Spatially Varying Seismic Ground Motion Simulation by Spectral Representation Method vol.143, pp.9, 2017, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001282
  5. Prediction of wind loads on high-rise building using a BP neural network combined with POD vol.170, 2017, https://doi.org/10.1016/j.jweia.2017.07.021
  6. Flow-induced actions on cylinders in statistically-symmetric cross flow vol.24, pp.3, 2009, https://doi.org/10.1016/j.probengmech.2008.07.005
  7. Error Assessment for Spectral Representation Method in Wind Velocity Field Simulation vol.136, pp.9, 2010, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000058
  8. Processing of dynamic wind pressure loads for temporal simulations vol.21, pp.4, 2015, https://doi.org/10.12989/was.2015.21.4.425
  9. A web-based GIS platform for the safe management and risk assessment of complex structural and infrastructural systems exposed to wind vol.117, 2018, https://doi.org/10.1016/j.advengsoft.2017.03.002
  10. POD analysis of crosswind forces on a tall building with square and H-shaped cross sections vol.21, pp.1, 2015, https://doi.org/10.12989/was.2015.21.1.063
  11. A study on the motion characteristics and their impact on the wind measurement post-processing of the GPS dropwindsonde Part I: effects of the wind-finding equations vol.117, pp.1-2, 2014, https://doi.org/10.1007/s00704-013-0962-5
  12. The variation of the GPS dropwindsonde drag coefficient and its impact on the wind retrieval from dropwindsonde measurements vol.114, pp.1-2, 2013, https://doi.org/10.1007/s00704-012-0792-x
  13. Effective wind actions on ideal and real structures vol.98, pp.8-9, 2010, https://doi.org/10.1016/j.jweia.2010.01.002
  14. Analysis of aerodynamic pressure measurements by dynamic coherent structures vol.28, 2012, https://doi.org/10.1016/j.probengmech.2011.08.010
  15. Tropical Storm–Induced Buffeting Response of Long-Span Bridges: Enhanced Nonstationary Buffeting Force Model vol.143, pp.6, 2017, https://doi.org/10.1061/(ASCE)ST.1943-541X.0001745
  16. Proper orthogonal decomposition in wind engineering - Part 2: Theoretical aspects and some applications vol.10, pp.2, 2007, https://doi.org/10.12989/was.2007.10.2.177
  17. Wind-tunnel tests on high-rise buildings: wind modes and structural response vol.18, pp.1, 2014, https://doi.org/10.12989/was.2014.18.1.037
  18. Mathematical explanation on the POD applications for wind pressure fields with or without mean value components vol.23, pp.4, 2016, https://doi.org/10.12989/was.2016.23.4.367
  19. Statistical analysis of wind-induced pressure fields: A methodological perspective vol.99, pp.6-7, 2011, https://doi.org/10.1016/j.jweia.2011.03.011
  20. Hybrid simulation of thunderstorm outflows and wind-excited response of structures vol.52, pp.13, 2017, https://doi.org/10.1007/s11012-017-0718-x
  21. Understanding of unsteady pressure fields on prisms based on covariance and spectral proper orthogonal decompositions vol.16, pp.5, 2013, https://doi.org/10.12989/was.2013.16.5.517
  22. Application of Snapshot POD Analysis in Extracting Flow Structures around Bridge Decks vol.18, pp.6, 2015, https://doi.org/10.1260/1369-4332.18.6.803
  23. Evaluating Wind Load and Wind-induced Response of a Twin Building using Proper Orthogonal Decomposition vol.31, pp.6, 2018, https://doi.org/10.7734/COSEIK.2018.31.6.309
  24. Energy and Entropy in Turbulence Decompositions vol.21, pp.2, 2019, https://doi.org/10.3390/e21020124
  25. Wind tunnel investigations on aerodynamics of a 2:1 rectangular section for various angles of wind incidence vol.25, pp.3, 2017, https://doi.org/10.12989/was.2017.25.3.301
  26. Turbulent wind field representation and conditional mean-field simulation vol.475, pp.2223, 2007, https://doi.org/10.1098/rspa.2018.0887
  27. 트윈 빌딩의 공력 특성이 풍응답에 미치는 영향 평가 vol.33, pp.1, 2007, https://doi.org/10.7734/coseik.2020.33.1.1
  28. Gust Buffeting and Aerodynamic Admittance of Structures with Arbitrary Mode Shapes. II: A POD-Based Interpretation vol.147, pp.1, 2007, https://doi.org/10.1061/(asce)em.1943-7889.0001873
  29. Simulation of Nonstationary and Nonhomogeneous Wind Velocity Field by Using Frequency-Wavenumber Spectrum vol.7, pp.None, 2007, https://doi.org/10.3389/fbuil.2021.636815
  30. Reduction of experimental effort in conventional engine calibration process by using reduced order model vol.235, pp.2, 2007, https://doi.org/10.1177/0954407020954595
  31. Identification of three-dimensional flow features around a square-section building model via spectral proper orthogonal decomposition vol.33, pp.3, 2007, https://doi.org/10.1063/5.0041395
  32. Effect of aerodynamic modifications on the surface pressure patterns of buildings using proper orthogonal decomposition vol.32, pp.3, 2007, https://doi.org/10.12989/was.2021.32.3.227
  33. Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies vol.147, pp.4, 2021, https://doi.org/10.1061/(asce)em.1943-7889.0001904
  34. Pressure pattern recognition in buildings using an unsupervised machine-learning algorithm vol.214, pp.None, 2021, https://doi.org/10.1016/j.jweia.2021.104629
  35. An Energy Closure Criterion for Model Reduction of a Kicked Euler-Bernoulli Beam vol.143, pp.4, 2021, https://doi.org/10.1115/1.4048663
  36. Characteristics of wind loads on Twin-Tower structure in comparison with single tower vol.251, pp.no.pa, 2022, https://doi.org/10.1016/j.engstruct.2021.112780