Extrapolation reconstruction of wind pressure fields on the claddings of high-rise buildings

Abstract

Recent research about reconstruction methods mainly used the interpolation reconstruction of the fluctuating wind pressure field on the surface. However, to investigate wind pressure at the edge of the building, the work presented in this paper focuses on the extrapolation reconstruction of wind pressure fields. Here, we propose an improved proper orthogonal decomposition (POD) and Kriging method with a von Kármán correlation function to resolve this issue. The studies show that it works well for not only interpolation reconstruction but also extrapolation reconstruction. The proposed method does require determination of the Hurst exponent and other parameters analysed from the original data. Hence, the fluctuating wind fields have been characterized by the von Kármán correlation function, as an a priori function. Compared with the cubic spline method and different variogram, preliminary results suggest less time consumption and high efficiency in extrapolation reconstruction at the edge.

Keywords

extrapolation reconstruction / proper orthogonal decomposition / Kriging method / von Kármán function / Hurst exponent / rescaled range analysis

References

[1] Quan Y, Liang Y, Wang F, Gu M. Wind tunnel test study on the wind pressure coefficient of claddings of high-rise buildings. Frontiers of Architecture and Civil Engineering in China, 2011, 5(4): 518–524

[2] Han D J, Li J. Application of proper orthogonal decomposition method in wind field simulation for roof structures. Journal of Engineering Mechanics, 2009, 135(8): 786–795

[3] Wang Y G, Li Z N, Li Q S, Gong B. Application of POD method on the wind-induced vibration response of heliostat. Journal Vibration and Shock, 2008, 27(12): 107–111 (in Chinese)

[4] Zhou X Y, Li G. Application of POD combined with thin-plate splines in research on wind pressure. Building Structure, 2011, (06): 98–102 (in Chinese)

[5] Cammelli S, Vacca L, Li Y F. The investigation of multi-variate random pressure fields acting on a tall building through proper orthogonal decomposition. International Association for Bridge and Structural Engineering Symposium Report, 2016: 897–904

[6] Zhao Z W, Chen Z H, Wang X D, Hao X, Liu H B. Wind-induced response of large-span structures based on POD-pseudo-excitation method. Advanced Steel Construction, 2016, 12(1): 1–16

[7] Fu J Y, Li Q S, Xie Z N. Prediction of wind loads on a large flat roof using fuzzy neural networks. Engineering Structures, 2006, 28(1): 153–161

[8] Fu J Y, Liang S G, Li Q S. Prediction of wind-induced pressures on a large gymnasium roof using artificial neural networks. Computers & Structures, 2007, 85(3–4): 179–192

[9] Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535

[10] Armitt J. Eigenvector analysis of pressure fluctuations on the West Burton instrumented cooling tower. Internal Report RD/L/N 114/68, Central Electricity Research Laboratories UK, 1968

[11] Berkooz G, Holmes P, Lumley J L. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics, 1993, 25(1): 539–575

[12] Borée J. Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Experiments in Fluids, 2003, 35(2): 188–192

[13] Motlagh S Y, Taghizadeh S. POD analysis of low Reynolds turbulent porous channel flow. International Journal of Heat and Fluid Flow, 2016, 61: 665–676

[14] Kareem A, Cermak J E. Pressure fluctuations on a square building model in boundary-layer flows. Journal of Wind Engineering and Industrial Aerodynamics, 1984, 16(1): 17–41

[15] Holmes J D. Analysis and synthesis of pressure fluctuations on bluff bodies using eigenvectors. Journal of Wind Engineering and Industrial Aerodynamics, 1990, 33(1–2): 219–230 (J)

[16] Bienkiewicz B, Tamura Y, Ham H J, Ueda H, Hibi K. Proper orthogonal decomposition and reconstruction of multi-channel roof pressure. Journal of Wind Engineering and Industrial Aerodynamics, 1995, 54: 369–381

[17] Tamura Y, Suganuma S, Kikuchi H, Hibi K. Proper orthogonal decomposition of random wind pressure field. Journal of Fluids and Structures, 1999, 13(7–8): 1069–1095 (J)

[18] Uematsu Y, Kuribara O, Yamada M, Sasaki A, Hongo T. Wind-induced dynamic behavior and its load estimation of a single-layer latticed dome with a long span. Journal of Wind Engineering and Industrial Aerodynamics, 2001, 89(14-15): 1671–1687 (J)

[19] Wang Y G, Li Z N, Gong B, Li Q S. Reconstruction & prediction of wind pressure on heliostat. Acta Aerodynamica Sinica, 2009, 27(5): 586–591 (in Chinese)

[20] Jiang Z R, Ni Z H, Xie Z N. Reconstruction and prediction of wind pressure field on roof. Chinese Journal of Applied Mechanics, 2007, 24(4): 592–598 (in Chinese)

[21] Li F H, Ni Z H, Shen S Z, Gu M. Theory of POD and its application in wind engineering of structure. Journal of Vibration and Shock, 2009, 28(4): 29–32 (in Chinese)

[22] Li F H, Gu M, Ni Z H, Shen S Z. Wind pressures on structures by proper orthogonal decomposition. Journal of Civil Engineering and Architecture, 2012, 6(2): 238–243

[23] Chen F B, Li Q S. Application investigation of predicting wind loads on large-span roof by Kriging-POD method. Engineering Mechanics, 2014, 31(1): 91–96 (in Chinese)

[24] Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, (3): 1–13

[25] Zhuang X, Huang R, Liang C, Rabczuk T. A coupled thermo-hydro-mechanical model of jointed hard rock for compressed air energy storage. Mathematical Problems in Engineering, 2014, 2014, 179169

[26] Wang Y G, Li Z N, Wu H H, Zhang L H. Predication of fluctuating wind pressure on low building roof. Journal of Vibration and Shock, 2013, 32(5): 157–162 (in Chinese)

[27] Loeve M. Probability theory, vol. ii. Vol. 46, Graduate texts in mathematics, 1978, 1–387

[28] Liang Y C, Lee H P, Lim S P, Lin W Z, Lee K H, Wu C G. Proper orthogonal decomposition and its applications—Part I: Theory. Journal of Sound and Vibration, 2002, 252(3): 527–544 (J)

[29] Matheron G. Principles of geostatistics. Economic Geology and the Bulletin of the Society of Economic Geologists, 1963, 58(8): 1246–1266

[30] Oliver M A, Webster R. Basic steps in geostatistics: the variogram and kriging. Springer International, 2015

[31] Sarma D D. Geostatistics with Applications in Earth Sciences. Springer Science & Business Media, 2009, 265–269

[32] Von Kármán T. Progress in the statistical theory of turbulence. Proceedings of the National Academy of Sciences of the United States of America, 1948, 34(11): 530–539

[33] Sidler R. Kriging and Conditional Geostatistical Simulation Based on Scale-Invariant Covariance Models. Swiss Federal Institute of Technology Zurich, 2003

[34] Müller T M, Toms-Stewart J, Wenzlau F. Velocity-saturation relation for partially saturated rocks with fractal pore fluid distribution. Geophysical Research Letters, 2008, 35(9): L09306

[35] Guatteri M, Mai P M, Beroza G C. A pseudo-dynamic approximation to dynamic rupture models for strong ground motion prediction. Bulletin of the Seismological Society of America, 2004, 94(6): 2051–2063

[36] Cody W J. An overview of software development for special functions. In: Alistair Watson G, ed. Numerical Analysis: Proceedings of the Dundee Conference on Numerical Analysis.Berlin, Heidelberg: Springer Berlin Heidelberg, 1976, 38–48

[37] Abramowitz M, Stegun I A. Handbook of Mathematical Functions. National Bureau of Standards: Applied Math. Series #55: Dover Publications, 1965

[38] Klimeš L. Correlation functions of random media. Pure and Applied Geophysics, 2002, 159(7): 1811–1831

[39] Katsev S, L’Heureux I. Are Hurst exponents estimated from short or irregular time series meaningful? Computers & Geosciences, 2003, 29(9): 1085–1089

[40] Hurst H E. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 1951, 116(1): 770–799

[41] Aue A, Horváth L, Steinebach J. Rescaled range analysis in the presence of stochastic trend. Statistics & Probability Letters, 2007, 77(12): 1165–1175

[42] Mason D M. The Hurst phenomenon and the rescaled range statistic. Stochastic Processes and Their Applications, 2016, 126(12): 3790–3807

[43] Mandelbrot B B, Wallis J R. Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence. Water Resources Research, 1969, 5(5): 967–988

[44] Pardo-Igúzquiza E. MLREML: a computer program for the inference of spatial covariance parameters by maximum likelihood and restricted maximum likelihood. Computers & Geosciences, 1997, 23(2): 153–162

[45] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

Acknowledgements

This work is supported by the National Natural Science Fundation of China (Grant No. 51469016), and its supports are gratefully acknowledged.

RIGHTS & PERMISSIONS

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature