Simulation of wind velocities on long span structures: A novel stochastic wave based model

Abstract A methodology is presented for efficient and accurate modeling of correlated wind velocities along long span structures at a virtually infinite number of points. Currently, the standard approach is to model wind velocities as discrete components of a multivariate stochastic vector process, characterized by a Cross-Spectral Density Matrix. To simulate sample realizations of the vector process, the Spectral Representation Method is one of the most commonly used, which involves a Cholesky decomposition of the Cross-Spectral Density Matrix. However, it is a well-known issue that as the length of the structure, and consequently the size of the vector process, increases, this Cholesky decomposition breaks down numerically. Alternatively, this paper introduces the use of the frequency–wavenumber spectrum to model the wind velocities as a stochastic “wave”, continuous in both space and time. This allows the wind velocities to be modeled at a virtually infinite number of points along the length of the structure. In this paper, the relationship between the Cross Spectral Density Matrix and the frequency–wavenumber spectrum is first examined. The frequency–wavenumber spectrum is then derived for wind velocities. Numerical examples are carried out demonstrating that the simulated wave samples exhibit the desired spectral and coherence characteristics. The efficiency of this method, specifically through the use of the Fast Fourier Transform, is also demonstrated.

[1]  Haifan Xiang,et al.  An efficient ergodic simulation of multivariate stochastic processes with spectral representation , 2011 .

[2]  Masanobu Shinozuka,et al.  Stochastic Methods in Wind Engineering , 1989 .

[3]  G. Solari,et al.  Probabilistic 3-D turbulence modeling for gust buffeting of structures , 2001 .

[4]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[5]  Emil Simiu,et al.  Wind Effects on Structures: An Introduction to Wind Engineering , 1980 .

[6]  Steen Krenk,et al.  Wind Field Coherence And Dynamic Wind Forces , 1996 .

[7]  Haifan Xiang,et al.  SIMULATION OF STOCHASTIC WIND VELOCITY FIELD ON LONG-SPAN BRIDGES , 2001 .

[8]  M. Shinozuka,et al.  Simulation of Seismic Ground Motion Using Stochastic Waves , 1989 .

[9]  A. Davenport.  The spectrum of horizontal gustiness near the ground in high winds , 1961 .

[10]  Alan G. Davenport.  THE APPLICATION OF STATISTICAL CONCEPTS TO THE WIND LOADING OF STRUCTURES. , 1961 .

[11]  T. Kármán.  Progress in the Statistical Theory of Turbulence , 1948 .

[12]  A. Kareem,et al.  AERODYNAMIC COUPLING EFFECTS ON FLUTTER AND BUFFETING OF BRIDGES , 2000 .

[13]  Richard Haberman,et al.  Applied Partial Differential Equations with Fourier Series and Boundary Value Problems , 2012 .

[14]  George Deodatis,et al.  Non-stationary stochastic vector processes: seismic ground motion applications , 1996 .

[15]  Hitoshi Yamada,et al.  Numerical simulation of wind turbulence and buffeting analysis of long-span bridges , 1999 .

[16]  J. Mann.  Wind field simulation , 1998 .

[17]  George Deodatis,et al.  A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic vector process by a translation process with applications in wind velocity simulation , 2013 .

[18]  G. Deodatis.  Simulation of Ergodic Multivariate Stochastic Processes , 1996 .

[19]  Hanlong Liu,et al.  An improved approximation for the spectral representation method in the simulation of spatially varying ground motions , 2012 .

[20]  Einar N. Strømmen.  Theory of Bridge Aerodynamics , 2010 .

[21]  N. Wiener.  Generalized harmonic analysis , 1930 .

[22]  M. D. Paola,et al.  Digital simulation of wind field velocity , 1998 .

[23]  Nicholas P. Jones,et al.  Wind Cross-Spectrum Effects on Long-Span Bridges , 1992 .

[24]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[25]  Aspasia Zerva,et al.  Spatial Variation of Seismic Ground Motions: Modeling and Engineering Applications , 2009 .

[26]  Shizhong Qiang,et al.  Simplifying the simulation of stochastic wind velocity fields for long cable-stayed bridges , 2004 .

[27]  J. Kaimal,et al.  Spectral Characteristics of Surface-Layer Turbulence , 1972 .

[28]  Giovanni Solari,et al.  Gust buffeting of long span bridges: Double Modal Transformation and effective turbulence , 2007 .

[29]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

[30]  A. Khintchine.  Korrelationstheorie der stationären stochastischen Prozesse , 1934 .

[31]  Ragnar Sigbjörnsson,et al.  Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study , 2010 .

[32]  R. Scanlan,et al.  Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks , 1991 .

[33]  M. Di Paola,et al.  Digital generation of multivariate wind field processes , 2001 .

[34]  Chih-Chen Chang,et al.  An efficient wind field simulation technique for bridges , 1997 .

[35]  R. I. Harris.  Some further thoughts on the spectrum of gustiness in strong winds , 1990 .

[36]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[37]  N. Jensen,et al.  Lateral coherence in isotropic turbulence and in the natural wind , 1979 .

[38]  K. Aas-Jakobsen,et al.  Time domain buffeting response calculations of slender structures , 2001 .

[39]  Aspasia Zerva,et al.  Seismic ground motion simulations from a class of spatial variability models , 1992 .

[40]  Ragnar Sigbjörnsson,et al.  Effects of co-spectral densities of atmospheric turbulence on the dynamic response of cable-supported bridges: A case study , 2013 .

[41]  Masanobu Shinozuka,et al.  Stochastic wave models for stationary and homogeneous seismic ground motion , 1991 .