Simulation of Stochastic Processes: Applications in Civil Engineering.

摘要

Part I deals with simulation of response spectrum compatible ground motion time histories. This part begins with a general overview of the motivation for simulating such time histories and the advantages and disadvantages of their use in structural analysis. Chapter 3 begins with an outline of some previously devised techniques for response spectrum compatible time history simulation with an emphasis on the existing Spectral Representation Method based technique. A new Spectral Representation Method based methodology is then presented for simulation of uni-variate response spectrum compatible time histories. This methodology is generalized for simulation of multi-variate response spectrum compatible time histories in Chapter 4. The relative advantages and disadvantages of this new methodology compared with the existing Spectral Representation Method based technique are discussed for both the uni-variate and multi-variate cases.;Chapter 5 deals specifically with the simulation of stationary and non-Gaussian stochastic translation processes. Of particular interest are those processes whose prescribed marginal non-Gaussian probability density function and non-Gaussian Power Spectral Density Function are "incompatible" according to translation process/field theory [27]. The chapter starts with an outline of a family of existing Spectral Representation Method based techniques for simulating these processes. A new, and significantly simpler, methodology is then proposed which reduces computational effort significantly without any loss of accuracy. The chapter concludes with numerical examples and a direct comparison of these examples with the existing technique developed by Bocchini and Deodatis [9].;Chapters 6 and 7 deal with the simulation of stochastic processes which are both non-stationary and non-Gaussian. In fact, the work in these chapters represents the first efforts toward the simulation of processes which are both non-stationary and non-Gaussian using the Spectral Representation Method. Various other techniques have been used to simulate these processes such as modal decomposition and Karhunen-Loeve Expansion/Polynomial Chaos Decomposition with differing degrees of success. However, to date, the Spectral Representation Method has not been used. In Chapter 6, a methodology for estimating the evolutionary spectrum of non-stationary and non-Gaussian processes/fields with prescribed underlying Gaussian evolutionary spectrum (or equivalently non-stationary autocorrelation function) and marginal non-Gaussian probability density function is developed. No exact formulation exists for the direct computation of the non-Gaussian evolutionary spectrum in this case. In fact, there are significant theoretical barriers which prevent such an exact computation. Therefore estimation techniques are required. These theoretical barriers are addressed and discussed. To circumvent these barriers, the estimation technique outlined in this chapter relies on a critical assumption of "local stationarity" wherein the process is considered independently stationary at each and every time instant. The technique is shown to be very accurate for processes/fields which are strongly non-Gaussian and have a significant degree of non-stationarity (specifically frequency modulation). Its limitations are presented as well and several numerical examples are given.;In Chapter 7 the so-called "reverse" case is considered where the underlying Gaussian evolutionary spectrum of processes with prescribed non-Gaussian evolutionary spectrum (or equivalently non-stationary autocorrelation function) and marginal non-Gaussian probability density function is estimated. Once again, theoretical constraints prohibit the direct computation of the underlying Gaussian evolutionary spectrum. Therefore, a technique is developed to estimate the underlying Gaussian evolutionary spectrum of processes where the prescribed non-Gaussian evolutionary spectrum and probability density function are "incompatible" according to the extension of translation process/field theory to non-stationary processes [21]. It should be mentioned that the "compatible" case involves only a trivial inversion of the technique developed in Chapter 6. The technique developed in this chapter to estimate this underlying Gaussian evolutionary spectrum uses an iterative scheme conceptually similar to that developed in Chapter 5 for stationary processes/fields. This methodology represents the first of its kind and proves to be quite accurate. Furthermore, its applications in simulation of processes/fields with significant non-stationarity and strongly non-Gaussian distribution are important. Numerical examples are presented which demonstrate both the capabilities and limitations of this technique. (Abstract shortened by UMI.)