Simulation Of Non-Gaussian Stochastic Process Based On Spectral Representation Method

Stochastic process theory is an indispensable theory to study physical quantities such as wind velocity,ocean wave and ground motion time histories in civil engineering.In order to carry out the computational analysis and simulation of these stochastic processes,it is very important to identify and generate the sample function of the stochastic process.In this paper,some non-Gaussian phenomena in nature are identified and simulated,and a new method for simulating non-Gaussian stochastic processes in one-dimensional and two-dimensional space is proposed based on Spectral Representation Method(SRM).The main elements are as follows:First of all,in Chapter 2,established the models for the probabilistic characteristics of the stochastic variation of the residual radius of corroded steel reinforcing bars along their axis.The stationary property is analyzed,and its autocorrelation function and power spectral density function are calculated.It is found that its power spectral density function is close to white noise,and its corrosion is a random probability problem of time-empty field.Finally,the marginal probability distribution function of the stochastic field was found to be non-Gaussian and the beta distribution provided the best fit.Finally,a methodology for efficient and accurate modeling and simulation of correlated one and two spatial dimensions non-Gaussian wind velocity time histories for space structures at an arbitrarily large number of points is proposed in chapter 4 and chapter 5.The Spectral Representation Method is a widely used method for simulating pulsating wind speed.To solve the computational challenges of the Cholesky decomposition involved in the SRM,a Frequency-Wavenumber Spectrum(FKS)based on SRM was proposed recently.The method was used for the simulation of Gaussian wind fields.In this paper,it is extended to simulate non-Gaussian wind velocities as a non-Gaussian stochastic wave in one/two spatial dimensions.The non-Gaussian stochastic wave is characterized by its FKS and marginal Probability Density Function(PDF).The compatibility of the FKS and marginal PDF according to translation process theory is secured using an extension of the Iterative Translation Approximation Method.This method does not need to generate any sample functions in the iterative process,and improves the iterations efficiency significantly.To enhance the computational efficiency,the Fast Fourier Transform(FFT)is used.Numerical examples show the simulated 3D nonGaussian stochastic wave wind velocity samples exhibit the desired spectral and marginal PDF characteristics.