Probability density evolution method for vibration analysis of wind-excited tall buildings

This paper proposed a new procedure for simulation of random wind velocity field with only a few random variables. The procedure starts with decomposing the random wind velocity field into a product of a stochastic process and a random field, which represent the time property and spatial correlation property of the wind velocity fluctuation respectively. Then the stochastic process for wind velocity fluctuations is represented as a finite sum of deterministic time functions with corresponding uncorrelated random coefficients by an innovative orthogonal expansion technology. Similarly, the random field is expressed as a combination form with only a few random variables by the Karhunen-Loeve decomposition. The proposed technique provides a basis to employ the probability density evolution method which was developed in the past few years to study the stochastic responses of general linear/nonlinear structural systems. In fact, using this method, the instantaneous probability density function and its evolution of arbitrary physical quantities of interest of the linear/nonlinear stochastic systems can be captured successfully and the reliability evaluation of MDOF systems could be obtained. A numerical example, which deals with a MDOF tall building subjected to wind loads, is given for the purpose of illustrating the proposed approach.