{"title":"Stochastic Subspace Modelling of Turbulence","authors":"M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen","country":null,"institution":"","volume":34,"journal":"International Journal of Civil and Environmental Engineering","pagesStart":443,"pagesEnd":452,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15627","abstract":"Turbulence of the incoming wind field is of paramount\r\nimportance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and\r\nstructural safety analysis. In the paper an empirical cross spectral\r\ndensity function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially\r\ndiscretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive\r\ndefinite. Since the succeeding state space and ARMA modelling of\r\nthe turbulence rely on the positive definiteness of the cross-spectral\r\ndensity matrix, the problem with the non-positive definiteness of such\r\nmatrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density\r\nmatrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise.\r\nFinally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 34, 2009"}