Simulation Of Non-stationary Non-gaussian Wind Loads

With the development of computing power, cloud computing and parallel computing technology of computer, the stochastic process based on Monte-Carlo simulation has become increasingly convenient. Most of the random phenomena in nature possess characters of non-stationary and non-Gaussian, and when the system is subjected to external excitation, their characteristics are very complex. It is assumed that the wind loads on structures is a stationary and Gaussian stochastic process, the analysis and calculation of the effect of wind load on structures may lead to erroneous results, consequently, it is necessary to modify the hypothesis. Since the analysis, design and optimization of the modern system basically depend on the computer simulation. Accordingly, it is essential to simulate the stochastic process holding non-stationary non-Gaussian characteristics. The main contents of this dissertation are summarized as follows:Firstly, in order to simulate the non-stationary non-Gaussian wind loads effectively, According to the evolutionary spectrum theory, the simulation of non-stationary stochastic process is needed to establish an effective non-uniform modulation function to modulate the power spectrum of the stationary random process. Firstly, three other non-uniform modulation functions are obtained according to the existing theories in this paper, which provide the precondition for simulating non-stationary fluctuating wind. Subsequently, make a further consideration of the time variability of the autoregressive(AR) model, a time-varying autoregressive(TAR) model is established, which provides an effectual method for non-stationary wind speed simulation. Then,it needs to establish a nonlinear translation relationship to achieve mutual conversion between non-stationary non-Gaussian and non-stationary Gaussian random processes based on TAR model and the transformation relationship between the power spectrums or correlation functions of the non-stationary non-Gaussian and non-stationary Gaussian stochastic processes after the nonlinear transformation. Accordingly, the simulation of a non-stationary non-Gaussian stochastic process can be converted into the simulation of the non-stationary Gaussian random process. Finally, taking the simulation of the fluctuating wind velocity possessing the target non-stationary non-Gaussian characteristics as a numerical example, verifies the effectiveness of the method for generating non-stationary non-Gaussian wind loads based on TAR model.Secondly, in order to simulate effectively non-stationary non-Gaussian wind loads possessing the given time-varying power spectrum and probability density function, a nonlinear translation relationship to achieve mutual conversion between non-Gaussian and Gaussian random processes is established, and the transformation relationship between the power spectrums or correlation functions of the non-Gaussian and Gaussian stochastic processes after the nonlinear transformation is further found in this paper. Then, the non-stationary non-Gaussian stochastic process can be generated through the nonlinear translation of a non-stationary Gaussian stochastic process simulated effectively by the spectral representation. In order to verify the effectiveness of this method, the simulation of fluctuating wind velocity possessing the target non-stationary non-Gaussian characteristics has been made in this paper. Therefore, the simulated random samples not only have the non-stationary features of target time-varying power spectrum, but also have the non-Gaussian features of target probability density function, verifying the effectiveness of the simulation of non-stationary non-Gaussian wind loads.