Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: p. 252-256. / Ph.D.

Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies. Further, most structural systems are likely to exhibit nonlinear and time-varying behavior when subjected to extreme events such as severe earthquake, wind and sea wave excitations. In such cases, a reliable identification approach is behavior and for assessing its reliability. Current work addresses two research themes in the field of stochastic engineering dynamics related to the above challenges. In the first part of the dissertation, the recently developedWiener Path Integral (WPI) technique for determining the joint response probability density function (PDF) of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output of a filter equation with Gaussian white noise as its input, it is possible to define an augmented response vector process to be considered in the WPI solution technique. A significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms. In such cases, it is shown that the use of a filter approximation facilitates the implementation of the WPI technique in a straightforward manner, without compromising its accuracy necessarily. Further, in addition to dynamical systems subject to stochastic excitation, the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as non-Gaussian and non-homogeneous stochastic fields. Several numerical examples pertaining to both single- and multi-degree-of freedom systems are considered, including a marine structural system exposed to flow-induced non-white excitation, as well as a beam with a non-Gaussian and non-homogeneous Young’s modulus. Comparisons with MCS data demonstrate the accuracy of the technique. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear time-variant multi-degree-of-freedom oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear subsystems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sampling theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. A nonlinear time-variant system with fractional derivative elements is used as a numerical example to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

Choy Man Wah Minnie. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 83). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Analysis of APT using SEM --- p.3 / Chapter 2.1 --- The APT model --- p.3 / Chapter 2.2 --- The structural equation model approach --- p.5 / Chapter 3 --- Incorporating stochastic constraints into the SEM analysis of APT --- p.8 / Chapter 3.1 --- Introduction --- p.8 / Chapter 3.2 --- Bayesian analysis of stochastic constraints --- p.9 / Chapter 3.3 --- Three types of structures for T I --- p.10 / Chapter 3.3.1 --- Case 1: T = (σ2Imxm --- p.10 / Chapter 3.3.2 --- "Case 2: r is a diagonal matrix with diagonal elements σ2j for = 1， …,m" --- p.13 / Chapter 3.3.3 --- Case 3: Γ is a general positive definite matrix --- p.14 / Chapter 3.4 --- Estimation of parameters using the Mx program --- p.16 / Chapter 4 --- Empirical study on Hong Kong stock market --- p.17 / Chapter 4.1 --- Information of data --- p.17 / Chapter 4.2 --- Source of data --- p.17 / Chapter 4.3 --- Lisrel model with exact constraints --- p.19 / Chapter 4.3.1 --- The resultant model --- p.20 / Chapter 4.4 --- Lisrel model with stochastic constraints --- p.21 / Chapter 4.4.1 --- Result --- p.22 / Chapter 5 --- Simulation study --- p.35 / Chapter 5.1 --- Simulation design --- p.35 / Chapter 5.2 --- Simulation procedure --- p.40 / Chapter 5.3 --- Simulation result --- p.41 / Chapter 5.3.1 --- Sample size --- p.41 / Chapter 5.3.2 --- Analysis methods (constraints) --- p.42 / Chapter 5.3.3 --- Factor loadings --- p.43 / Chapter 5.3.4 --- Factor correlation matrix --- p.43 / Chapter 5.3.5 --- Risk premia --- p.43 / Chapter 5.3.6 --- Overall result --- p.44 / Chapter 6 --- Conclusion and discussion --- p.45 / Appendices --- p.46 / Chapter A --- Simulation result - Mean --- p.47 / Chapter B --- Simulation result - Bias --- p.56 / Chapter C --- Simulation result - RMSE --- p.65 / Chapter D --- Mx input script --- p.74 / Chapter D.l --- Stochastic constraints Case 1 --- p.74 / Chapter D.2 --- Stochastic constraints Case 2 --- p.77 / Chapter D.3 --- Stochastic constraints Case 3 --- p.80 / Bibliography --- p.83

This thesis presents an approach for generating long synthetic sequences of single-site daily rainfall which can incorporate low-frequency features such as drought, while still accurately representing the day-to-day variations in rainfall. The approach is implemented in a two-stage process. The first stage is to generate the entire sequence of rainfall occurrence (i.e. whether each day is dry or wet). The second stage is to generate the rainfall amount on all wet days in the sequence. The models used in both stages are nonparametric (they make minimal general assumptions rather than specific assumptions about the distributional and dependence characteristics of the variables involved), and ensure an appropriate representation of the seasonal variations in rainfall. A key aspect in formulation of the models is selection of the predictor variables used to represent the historical features of the rainfall record. Methods for selection of the predictors are presented here. The approach is applied to daily rainfall from Sydney and Melbourne. The models that are developed use daily-level, seasonal-level, annual-level, and multi-year predictors for rainfall occurrence, and daily-level and annual-level predictors for rainfall amount. The resulting generated sequences provide a better representation of the variability associated with droughts and sustained wet periods than was previously possible. These sequences will be useful in catchment water management studies as a tool for exploring the potential response of catchments to possible future rainfall.

Non-uniform sampling comes natural in many applications, due to for example imperfect sensors, mismatched clocks or event-triggered phenomena. Examples can be found in automotive industry and data communication as well as medicine and astronomy. Yet, the literature on statistical signal processing to a large extent focuses on algorithms and analysis for uniformly, or regularly, sampled data. This work focuses on Fourier analysis, system identification and decimation of non-uniformly sampled data. In non-uniform sampling (NUS), signal amplitude and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this thesis, the sampling times are assumed to be generated by a stochastic process, and the main idea is to use information about the stochastic sampling process to calculate a priori properties of approximate frequency transforms. These results are also used to give insight in frequency domain system identification and help with analysis of down-sampling algorithms. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Based on this, decimation of non-uniformly sampled signals, using continuous-time anti-alias filters, is analyzed. The decimation is based on interpolation in different domains, and interpolation in the convolution integral proves particularly useful. The same idea is also used to investigate how stochastic unmeasurable sampling jitter noise affects the result of system identification. The result is a modification of known approaches to mitigate the bias and variance increase caused by the sampling jitter noise. The bottom line is that, when non-uniform sampling is present, the approximate frequency transform, identified transfer function and anti-alias filter are all biased to what is expected from classical theory on uniform sampling. This work gives tools to analyze and correct for this bias.

In this thesis, load scheduling problem for cogeneration plants is interpreted in the context of stochastic programming. Cogeneration (CHP) is an important technology in energy supply of many countries. Cogeneration plants are designed and operated to cover the requested time varying demands in heat and power. Load scheduling of cogeneration plants represents a multidimensional optimization problem, where heat and electricity demands, operational parameters and associated costs exhibit uncertain behavior. Cogeneration plants are characterized by their &lsquo / heat to power ratio&rsquo / . This ratio determines the operating conditions of the plant. However, this ratio may vary in order to adapt to the physical and economical changes in power and to the meteorological conditions. Employing reliable optimization models to enhance short term scheduling capabilities for cogeneration systems is an important research area. The optimal load plan is targeted by achieving maximum revenue for cogeneration plants. Revenue is defined for the purpose of the study as the sales revenues minus total cost associated with the plant operation. The optimization problem, which aims to maximize the revenue, is modeled by thermodynamic analyses. In this context, the study introduces two objective functions: energy based optimization, exergy-costing based optimization. A new method of stochastic programming is developed. This method combines dynamic programming and genetic algorithm techniques in order to improve computational efficiency. Probability density function estimation method is introduced to determine probability density functions of heat demand and electricity price for each time interval in the planning horizon. A neural network model is developed for this purpose to obtain the probabilistic data for effective representation of the random variables. In this study, thermal design optimization for cogeneration plants is also investigated with particular focus on the heat storage volume.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 180-190).

Thesis (Ph.D.)--University of Wyoming, 2007. / Title from PDF title page (viewed on June 17, 2009). Includes bibliographical references (p. 91-97).

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy