Simulation of a class of non-normal random processes

Abstract

Abstract-This study addresses the simulation of a class of non-normal processes based on measured samples and sample characteristics of the system input and output. The class of nonnormal processes considered here concerns environmental loads, such as wind and wave loads, and associated structural responses. First, static transformation techniques are used to perform simulations of the underlying Gaussian time or autocorrelationsample. An optimization procedure is employed to overcome errors associated with a truncated Hermite polynomial transformation. This method is able to produce simulations which closely match the sample process histogram, power spectral density, and central moments through fourth order. However, it does not retain the specific structure of the phase relationship between frequency components, demonstrated by the inability to match higher order spectra. A Volterra series up to second order with analytical kernels is employed to demonstrate the bispectral matching made possible with memory models. A neural network system identification model is employed for simulation of output when measured system input is available, and also demonstrates the ability to match higher order spectral characteristics. Copyright c~ 1996 Elsevier Science Ltd.

The stochastic finite element method: Past, present and future

“…Those which seek to produce sample functions matching the prescribed power spectral density function (SDF) and lower-order statistics (mean, variance, skewness and kurtosis) of a target stochastic field e.g. [85,86] and those seeking to generate sample functions compatible to complete probabilistic information. The first type of methods are suitable for the simulation of wind and wave loads, for which generation of non-Gaussian sample functions according to prescribed lower-order moments will provide accurate results for the stochastic response [86].…”

Numerical simulation of wind effects: A probabilistic perspective

“…Early work based on correlation distortion has been based on an inverse mapping of the desired probability density function, a summary of which may be found in Gurley et al (1996). In Gurley and , a simulation approach, which is significantly more robust than the correlation distortion schemes, was presented.…”

“…Gurley et al (1996) utilized Neural networks to simulate non-Gaussian pressure time histories and demonstrated that due to the static nature of the approach, the simulated time history did not reflect the memory in the process as evidenced by the lack of good comparison with the target bi-spectra and the bispectra of the simulated record using Volterra kernel of Neural networks (Gurley et al 1996 and1997).…”

A Monte Carlo simulation model for stationary non-Gaussian processes

“…Let X denote the collection of stochastic processes defined by the finite dimensional distributions and densities in Eqs. (8) and (9). A member X of X is called a mixture of translation processes.…”

“…These feature of the mixtures of translation processes can be very useful in some applications. For example, if the available information on a time series consists of the marginal distribution and the first and second order correlation functions [9], translation processes can be inadequate. The samples in Fig.…”