TIME SERIES GENERATION USING THE AUTO-REGRESSIVE MOVING-AVERAGE MODEL.

摘要

More realistic modelling of structures and loading conditions is increasingly demanded by society at large in order to assess structural safety and integrity with greater confidence, particularly when dealing with high risk systems such as nuclear power plant structures. To this end, loads are often idealized in terms of the random functions of temporal and/or spatial variables. Indeed, much research effort has been devoted in the last three decades or so to the application of stochastic process theory in the general area of structural engineering.; Most of these applications, however, took advantage of the frequency domain analysis under the assumption that a linear relationship exists between the excitation and the response and that the excitation is of a non-parametric nature. When the relationship is severely nonlinear or highly parametric, the frequency domain analysis can no longer be used in general. Under these circumstances, the use of Monte Carlo techniques remains one of the very few approaches that can be taken for the response evaluation.; In this context, the present study develops a technique for generating sample functions of a homogeneous Gaussian vector process with the aid of the Auto-Regressive Moving-Average method. The method uses a recursive equation involving a vector process to be simulated and a Gaussian white noise vector process. Once the coefficient matrices of the recursive equation are determined in accordance with the prescribed cross-correlation matrix of the vector process, its sample function vector is digitally generated with computational ease. This is because independent sample sequences of the components of a Gaussian white noise vector can be generated routinely. Unlike the Fast Fourier Transform method of generating sample functions, which is widely used currently, there is no difficulty associated with the computer memory space in this case.