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

Wind and Structures, An International Journal

Volumn 10, Issue 2, 2007, Pages 153-176

  Solari, Giovanni ^a   Carassale, Luigi ^a   Tubino, Federica ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

Aerodynamics; Aeroelasticity; Digital simulation; Fluid dynamics; Meteorology; Proper orthogonal decomposition; Structural dynamics; Turbulence; Wind engineering

Indexed keywords

AERODYNAMICS; BIBLIOGRAPHIC RETRIEVAL SYSTEMS; COMPUTER SIMULATION; DECOMPOSITION; MATHEMATICAL MODELS; STATISTICAL METHODS; STRUCTURAL DYNAMICS; TURBULENCE;

ENERGETIC COHERENT STRUCTURES; PROPER ORTHOGONAL DECOMPOSITION (POD); WIND ENGINEERING;

WIND;

EID: 34247133576     PISSN: 12266116     EISSN: None     Source Type: Journal    
DOI: 10.12989/was.2007.10.2.153     Document Type: Article

References (202)

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.
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.
3. Adrian R.J. and Moin, P. (1988). "Stochastic estimation of organised turbulent structure: homogeneous shear flow", J. Fluid. Mech., 190, 531-559.
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.
6. Amandolèse, X. and Cremona, C. (2005), "Analysing fluid loadings on moving bluff bodies using proper orthogonal decomposition", J. Fluid Struct, 20, 577-587.
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/M114/68, 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.
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.
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.
14. Bakewell, H. P. and Lumley, J. L. (1967), "Viscous sublayer and adjacent wall region in turbulent pipe flow", Phys. Fluids, 10, 1880-1889.
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.
16. Basilevsky, A. and Hum, D. P. J. (1979), "Karhunen-Loève 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.
18. Beltrami, E. (1873), "Sulle funzioni bilineari", Giomale 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.
20. Benfratello, S. and Muscolino, G. (1999), "Filter approach to the stochastic analysis of MDOF wind-excited structures", Prob. Eng. Mech., 14, 311-321.
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.
22. erkooz, 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.
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.
24. Bienkiewicz, B., Ham, H. J. and Sun, Y. (1993), "Proper orthogonal decomposition of roof pressure", J. Wind Eng. Ind. Aerodyn., 50, 193-202.
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.
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.
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.
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.
31. Burlando, M., Carassale, L., Borghesi, M. V., Tubino, F., Ratio, 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.
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.
42. Carassale, L. and Solari, G. (2002), "Wind modes for structural dynamics: a continuous approach", Prob. Eng. Mech., 17, 157-166.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
57. Di Paola, M. and Gullo, I. (2001), "Digital generation of multivariate wind field processes", Prob. Eng. Mech., 16, 1-10.
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., 1, 107-130.
59. Di Paola, M. and Pisano, A. A. (1996), "Multivariate stochastic wave generation", Appl. Ocean Res., 18, 361-365.
60. Dodds, C. J. and Robson, J. D. (1975), "Partial coherence in multivariate random processes", J. Sound Vib., 42, 243-249.
61. Dowell, E. H. and Hall, K. C. (2001), "Modeling of fluid-structure interaction", Annu. Rev. Fluid Mech., 33, 445-490.
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.
63. Eckart, C. (1934), "The kinetic energy of polyatomic molecules", Phys. Rev., 46, 383-387.
64. Eckart, C. and Young, G. (1936), "The approximation of one matrix by another of lower rank", Psychometrika, 1, 211-218.
65. Eckart, C. and Young, G. (1939), "A principal axis transformation for non-hermitian matrices", Bull. Am. Math. Soc., 45, 118-121.
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.
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.
73. Giannakis, G., Inouye, Y. and Mendel, J. M. (1989), "Cumulant-based identification of multichannel moving average models", IEEE Automat. Control, 34, 783-787.
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.
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.
77. Graham, M. and Kevrekidis, I. (1996), "Alternative approaches to the Karhunen-Loève decomposition for model reduction and data analysis", Comp. Chem. Eng., 20, 495-506.
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.
79. Gullo, I., Di Paola, M. and Spanos, P. D. (1998), "Spectral approximation for wind induced structural vibration studies", Meccanica, 33, 291-298.
80. Gunes, H. (2002), "Low-order dynamical models of thermal convection in high-aspect ratio enclosures", Fluid Dyn. Res., 30, 1.
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.
82. Hall, K. C. (1994), "Eigenanalysis of unsteady flows about airfoils, cascades, and wings", AIAA J., 32, 2426-2432.
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.
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.
86. Haykin, S. (1994), Blind Deconvolution, Prentice-Hall, Englewood Cliffs.
87. Hémon, P. and Santi, F. (2002), "On the aeroelastic behaviour of rectangular cylinders in cross-flow", J. Fluid. Struct., 16, 855-889.
88. Hémon, P. and Santi, F. (2003), "Applications of biorthogonal decompositions in fluid-structure interactions", J. Fluid Struct., 17, 1123-1143.
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.
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.
92. Holmes, P., Lumley, J. L. and Berkooz, G. (1996), Turbulence: Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Great Britain.
93. Holmström, E. I. (1963), "On a method for a parametric representation of the state of the atmosphere", Tellus, 15, 127-149.
94. Hotelling, H. (1933), "Analysis of a complex of statistical variables into principal components", J. Educ. Psychol., 24, 417-441, 498-520.
95. Hotelling, H. (1936), "Simplified calculation of principal components", Psychometrika, 1, 27-35.
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.
97. Hyvärinen, 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), "Mémorie sur les Formes Bilinéaires", 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.
101. Kac, M. and Siegert, A. J. F. (1947), "An eplicit representation of a stationary Gaussian process", Ann. Math. Stat., 18, 438-442.
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.
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.
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.
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.
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.
111. Kreuzer, E. and Kust, O. (1996), "Analysis of long torsional strings by proper orthogonal decomposition", Arch. Appl. Mech., 67, 68-80.
112. Lee, B. E. (1975), "The effect of turbulence on the surface pressure field of a square prism", J. Fluid Mech., 69, 263-282.
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.
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.
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.
117. Li, Y. and Kareem, A. (1995), "Stochastic decomposition and application to probabilistic dynamics", J. Eng. Mech., ASCE, 121, 162-174.
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.
119. Loeve, M. (1945), "Fonctions aléatoire 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.
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.
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.
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.
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.
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.
133. Mokhasi, P. and Rempfer, D. (2004), "Optimized sensor placement for urban flow measurement", Phys Fluids 16, 1758-1764.
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.
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.
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.
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.
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.
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.
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.
148. Podvin, B. and Le Quéré, P. (2001), "Low-order models for flow in a differentially heated cavity", Phys. Fluids, 13, 3204.
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.
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.
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.
154. Rathinam, M. and Petzold, L. R. (2003), "A new look at proper orthogonal decomposition", SIAM J. Numer. Anal., 41, 1893-1925.
155. Ravindra, B. (1999), "Comments on "On the physical interpretation of proper orthogonal modes in vibrations"", J. Sound Vib., 219, 189-192.
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.
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.
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.
159. Ricciardelli, F. (2003), "On the wind loading mechanism of long-span bridge deck box sections", J. Wind Eng. Ind. Aerodyn., 91, 1411-1430.
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.
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.
167. Schubert, S. D. (1986), "The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes", J. Atmos. Sci., 43, 1210-1237.
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.
170. Shinozuka, M., Yun, C. B. and Seya, H. (1990), "Stochastic methods in wind engineering", J. Wind Eng. Ind. Aerodyn., 36, 829-843.
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.
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.
175. Solari, G. and Carassale, L. (2000), "Modal transformation tools in structural dynamics and wind engineering", Wind and Struct., 3, 221-241.
176. Solari, G. and Tubino, F. (2002), "A new turbulence model based on principal components", Prob. Eng. Mech., 17, 327-335.
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.
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.
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.
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.
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. Themen, 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.
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.
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.
191. Tubino, F. and Solari, G. (2005), "Double POD for representing and simulating turbulence fields", J. Eng. Mech., ASCE, 131, 1302-1312.
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 large-scale 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.
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.
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, U.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.
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.
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.