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The purpose of this dissertation is to enhance the applicability and the accuracy of the Poisson cluster stochastic rainfall generators. Firstly, the 6 parameters of the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) stochastic rainfall simulation model were regionalized across the contiguous United States. Each of the parameters of MBLRP model estimated at 3,444 National Climate Data Center (NCDC) rain gages was spatially interpolated based on the Ordinary Kriging technique to produce the parameter surface map for each of the 12 months of the year. Cross-validation was used to assess the validity of the parameter maps. The results indicate that the suggested maps reproduce well the statistics of the observed rainfall for different accumulation intervals, except for the lag-1 autocorrelation coefficient. The estimated parameter values were also used to produce the maps of storm and rain cell characteristics. Secondly, the relative importance of the rainfall statistics in the generation of watershed response characteristics was estimated based on regression analyses using the rainfall time series observed at 1099 NCDC rain gages. The result of the analyses was used to weigh the rainfall statistics differently in the parameter calibration process of MBLRP model. It was observed that synthetic rainfall time series generated weighing the precipitation statistics according to their relative importance outperformed those generated weighing all statistics equally in predicting watershed runoff depths and peak flows. When all statistics were given the same weight, runoff depths and peak flows were underestimated by 20 percent and 14 percent, respectively; while, when the statistics were weighed proportionally to their relative importance, the underestimation was reduced to 4 percent and 3 percent, which confirms the advantage of weighing the statistics differently. In general, the value of the weights depends on the hydrologic process being modeled. Lastly, a stochastic rainfall generation model that can integrate year-to-year variability of rainfall statistics is suggested. The new framework consists of two parts. The first part generates the short-term rainfall statistics based on the correlation between the observed rainfall statistics. The second part generates the rainfall time series using the modified Bartlett-Lewis rectangular pulse model based on the simulated rainfall statistics. The new approach was validated at 104 NCDC gages across the United States in its ability to reproduce rainfall and watershed response characteristics. The result indicates that the new framework outperformed the traditional approach in reproducing the distribution of monthly maximum rainfall depths, monthly runoff volumes and monthly peak flows.

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Taiwan be called ¡§Taiwan¡¦s miracle¡¨ after World War II, the important factor is the accumulation of human capital . We use the model of Lucas(1988) and the definition of human capital by Whang and Zhao(1997) to re-examine the relationship between the human capital and economic growth in Taiwan. The research not only uses the Johansen¡¦s Maximum Likelihood Estimation (MLE) to make cointegration relation numbers and cointegration vectors but also use the stochastic cointegration developed by Harris, McCabe and Leybourne ( 2002, 2003 ) to re-examine the relationship between human capital and economic growth in Taiwan. Conclusion of the research, there¡¦s one cointegration vector existed by the Johansen¡¦s cointegration test . We found the stochastic cointegration exist between the human capital and economic growth in Taiwan, but not exist the heteroscedastic cointegration. Besides we recognize the the positive relationship between the human capital and economic growth in Taiwan and estimate the contribution rate 18% of human capital.

It is often desirable to compare risky investments in the context of economic decision theory. Expected utility analyses are means by which stochastic alternatives can be ranked by re-weighting the probability mass using a decision-making agent’s utility function. By maximizing expected utility, an agent seeks to balance expected returns with the inherent risk in each investment alternative. This can be accomplished by ranking prospects based on the certainty equivalent associated with each alternative. In instances where only a small sample of observed data is available to estimate the underlying distributions of the risky options, reliable inferences are difficult to make. In this process of comparing alternatives, when estimating explicit probability forms or nonparametric densities, the variance of the estimate, in this case the certainty equivalent, is often ignored. Resampling methods allow for estimating dispersion for a statistic when no parametric assumptions are made about the underlying distribution. An objective of this dissertation is to utilize these methods to estimate confidence regions for the sample certainty equivalents of the alternatives over a subset of the parameter space of the utility function. A second goal of this research is to formalize a testing procedure when dealing with preference ranking with respect to utility. This is largely based on Meyer’s work (1977b) developing stochastic dominance with respect to a function and more specific testing procedures outlined by Eubank et. al. (1993). Within this objective, the asymptotic distribution of the test statistic associated with the hypothesis of preference of one risky outcome over another given a sub-set of the utility function parameter space is explored.

Uncertainties in both loading and structural characteristics can adversely affect the response and reliability of a structure. Parameter uncertainties in structural dynamics can arise due to several sources. These include variations due to intrinsic material property variability, measurement errors, manufacturing and assembly errors, differences in modeling and solution procedures. Problems of structural dynamics with randomly distributed spatial inhomogeneities in elastic, mass, and damping properties, have been receiving wide attention. Several mathematical and computational issues include discretization of random fields, characterization of random eigensolutions, inversion of random matrices, solutions of stochastic boundary-value problems, and description of random matrix products. Difficulties are encountered when one has to include interaction between nonlinear and stochastic system characteristics, or if one is interested in controlling the system response. The study of structural systems including the effects of system nonlinearity in the presence of parameter uncertainties presents serious challenges and difficulties to designers and reliability engineers. In the analysis of large structures, the situation for substructuring frequently arises due to the repetition of identical assemblages (substructures), within a structure, and the general need to reduce the size of the problem, particularly in the case of non-linear inelastic dynamic analysis. A small reduction in the model size can have a large effect on the storage and time requirement. A primary structural dynamic system may be coupled to subsystems such as piping systems in a nuclear reactor or in a chemical plant. Usually subsystem in itself is quite complex and its modeling with finite elements may result in a large number of degrees of freedom. The reduced subsystem model should be of low-order yet capturing the essential dynamics of the subsystem for useful integration with the primary structure. There are two major issues to be studied: one, techniques for analyzing a complex structure into component subsystems, analyzing the individual sub-system dynamics, and from thereon determining the dynamics of the structure after assembling the subsystems. The nonlinearity due to support gap effects such as supports for piping system in nuclear reactors further complicates the problem. The second is the issue of reviewing the methods for reducing the model-order of the component subsystems such that the order of the global dynamics, after assembly, is within some predefined limits. In the reliability analysis of complex engineering structures, a very large number of the system parameters have to be considered as random variables. The parameter uncertainties are modeled as random variables and are assumed to be time independent. Here the problem would be to reduce the number of random variables without sacrificing the accuracy of the reliability analysis. The procedure involves the reduction of the size of the vector of random variables before the calculation of failure probability. The objectives of this thesis are: 1.To use the available model reduction techniques in order to effectively reduce the size of the finite element model, and hence, compare the dynamic responses from such models. 2.Study of propagation of uncertainties in the reduced order/coupled stochastic finite element dynamic models. 3.Addressing the localized nonlinearities due to support gap effects in the built up structures, and also in cases of sudden change in soil behaviour under the footings. The irregularity in soil behaviour due to lateral escape of soil due to failure of quay walls/retaining walls/excavation in neighbouring site, etc. 4.To evolve a procedure for the reduction of size of the vector containing the random variables before the calculation of failure probability. In the reliability analysis of complex engineering structures, a very large number of the system parameters are considered to be random variables. Here the problem would be to reduce the number of random variables without sacrificing the accuracy of the reliability analysis. 5.To analyze the reduced nonlinear stochastic dynamic system (with phase space reduction), and effectively using the network pruning technique for the solution, and also to use filter theory (wavelet theory) for reducing the input earthquake record to save computational time and cost. It is believed that the techniques described provide highly useful insights into the manner structural uncertainties propagate. The cross-sectional area, length, modulus of elasticity and mass density of the structural components are assumed as random variables. Since both the random and design variables are expressed in a discretized parameter space, the stochastic sensitivity function can be modeled in a parallel way. The response of the structures in frequency domain is considered. This thesis is organized into seven chapters. This thesis deals with the reduced order models of the stochastic structural systems under deterministic/random loads. The Chapter 1 consists of a brief introduction to the field of study. In Chapter 2, an extensive literature survey based on the previous works on model order reduction and the response variability of the structural dynamic systems is presented. The discussion on parameter uncertainties, stochastic finite element method, and reliability analysis of structures is covered. The importance of reducing mechanical models for dynamic response variability, the systems with high-dimensional variables and reduction in random variables space, nonlinearity issues are discussed. The next few chapters from Chapter 3 to Chapter 6 are the main contributions in this thesis, on model reduction under various situations for both linear and nonlinear systems. After forming a framework for model reduction, local nonlinearities like support gaps in structural elements are considered. Next, the effect of reduction in number of random variables is tackled. Finally influence of network pruning and decomposition of input signals into low and high frequency parts are investigated. The details are as under. In Chapter 3, the issue of finite element model reduction is looked into. The generalized finite element analysis of the full model of a randomly parametered structure is carried out under a harmonic input. Different well accepted finite element model reduction techniques are used for FE model reduction in the stochastic dynamic system. The structural parameters like, mass density and modulus of elasticity of the structural elements are considered to be non-Gaussian random variables. Since the variables considered here are strictly positive, the probabilistic distribution of the random variables is assumed to be lognormal. The sensitivities in the eigen solutions are compared. The response statistics based on response of models in frequency domain are compared. The dynamic responses of the full FE model, separated into real and imaginary parts, are statistically compared with those from reduced FE models. Monte Carlo simulation is done to validate the analysis results from SFEM. In Chapter 4, the problem of coupling of substructures in a large and complex structure, and FE model reduction, e.g., component mode synthesis (CMS) is studied in the stochastic environment. Here again, the statistics of the response from full model and reduced models are compared. The issues of non-proportional damping, support gap effects and/local nonlinearity are considered in the stochastic sense. Monte Carlo simulation is done to validate the analysis results from SFEM. In Chapter 5, the reduction in size of the vector of random variables in the reliability analysis is attempted. Here, the relative entropy/ K-L divergence/mutual information, between the random variables is considered as a measure for ranking of random variables to study the influence of each random variable on the response/reliability of the structure. The probabilistic distribution of the random variables is considered to be lognormal. The reliability analysis is carried out with the well known Bucher and Bourgund algorithm (1990), along with the probabilistic model reduction of the stochastic structural dynamic systems, within the framework of response surface method. The reduction in number of random variables reduces the computational effort required to construct an approximate closed form expression in response surface approach. In Chapter 6, issues regarding the nonlinearity effects in the reduced stochastic structural dynamic systems (with phase space reduction), along with network pruning are attempted. The network pruning is also adopted for reduction in computational effort. The earthquake accelerogram is decomposed using Fast Mallat Algorithm (Wavelet theory) into smaller number of points and the dynamic analysis of structures is carried out against these reduced points, effectively reducing the computational time and cost. Chapter 7 outlines the contributions made in this thesis, together with a few suggestions made for further research. All the finite element codes were developed using MATLAB5.3. Final pages of the thesis contain the references made in the preparation of this thesis.

Ce document présente plusieurs méthodes de renormalisation utilisées dans l'étude des réseaux stochastiques. En premier lieu il s'agit d'analyser les limites de processus markoviens de sauts renormalisés en temps et en espace suivant une échelle d'Euler (type loi fonctionnelle des grands nombres). Plusieurs aspects sont détaillés: la question des limites non déterministe et ses conséquences, ainsi que le cas de la dimension infinie intervenant pour les processus de Markov à valeurs dans<br />les chaînes de caractères. L'étude des réseaux avec un grand nombre de noeuds (limite thermodynamique) ou avec des liens de capacité très grandes (Régime limite de Kelly) est discuté ainsi que les perspectives de ce type d'étude.<br />L'étude mathématique de plusieurs algorithmes distribués gérant des réseaux stochastiques est présentée. L'accent est mis sur les méthodes probabilistes utilisées dans un contexte qui n'est pas nécessairement probabiliste, elles permettent notamment d'étendre et de simplifier une partie des résultats connus dans ce domaine.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 140-150).

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 167-180). Available also in a digital version from Dissertation Abstracts.