published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Thesis (Ph. D.)--University of Sydney, 2008. / Title from title screen (viewed February 12, 2009). Includes graphs and tables. Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Geosciences, Faculty of Science. Includes bibliographical references. Also available in print form.

Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 129-141).

Thesis (M.S. in Operations Research)--Naval Postgraduate School, December 2005. / Thesis Advisor(s): Patricia A. Jacobs, Donald P. Gaver. Includes bibliographical references (p.117-119). Also available online.

Ph.D.

by Tung-lok Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 57-59. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Full Maximum Likelihood Estimation of the General Model --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Model --- p.4 / Chapter 2.3 --- Identification of the model --- p.5 / Chapter 2.4 --- Maximum likelihood estimation --- p.7 / Chapter 2.5 --- Computational Procedure --- p.12 / Chapter 2.6 --- Tests of Hypothesis --- p.13 / Chapter 2.7 --- Example --- p.14 / Chapter Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Bayesian Analysis of the general model --- p.18 / Chapter 3.3 --- Computational Procedure --- p.22 / Chapter 3.4 --- Test the Compatibility of the Prior Information --- p.24 / Chapter 3.5 --- Example --- p.25 / Chapter Chapter 4 --- Simulation Study --- p.27 / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.2 --- Simulation1 --- p.27 / Chapter 4.3 --- Simulation2 --- p.30 / Chapter 4.4 --- Summary and Discussion --- p.31 / Chapter Chapter 5 --- Concluding Remarks --- p.33 / Tables / References --- p.57

Bibliography: leaves 127-128.

Response behavior of a nonlinear structural system subject to environmental loadings is investigated in this study. The system contains a nonlinear restoring force due to large geometric displacement. The external excitation is modeled as a narrowband stochastic process possessing dynamic characteristics of typical environmental loadings. A semi-analytical method is developed to predict the stochastic nonlinear response behavior under narrowband excitations in both the primary and the subharmonic resonance regions. Preservation of deterministic response characteristics under the narrowband random field is assumed. The stochastic system response induced by variations in the narrowband excitations is considered as a sequence of successive transient states. Due to the system nonlinearity, under a combination of excitation conditions, several response attraction domains may co-exist. Presence of co-existence of attraction domains and variations in the excitation amplitude often induce complex response inter-domain transitions. The response characteristics are found to be attraction domain dependent. Among different response attraction domains, their corresponding response amplitude domains overlap. In addition, within an individual attraction domain, response amplitude domains corresponding to different excitation amplitudes also overlap. Overlapping of response amplitude domains and the time-dependent variations in the excitation parameters induce response intra-domain transitions. Stationary Markovian assumption is employed to characterize the stochastic behavior of the response amplitude process and the excitation parameter processes. Based on the stochastic excitation properties and the deterministic response characteristics, governing equations of the response amplitude probability inter- and intra-domain transitions are formulated. Numerical techniques and an iteration procedure are employed to evaluate the stationary response amplitude probability distribution. The proposed semi-analytical method is validated by extensive numerical simulations. The capability of the method is demonstrated by good agreements among the predicted response amplitude distributions and the simulation results in both the primary and the subharmonic resonance regions. Variations in the stochastic response behavior under varying excitation bandwidth and variance are also predicted accurately. Repeated occurrences of various subharmonic responses observed in the numerical simulations are taken into account in the proposed analysis. Comparisons of prediction results with those obtained by existing analytical methods and simulation histograms show that a significant improvement in the prediction accuracy is achieved. / Graduation date: 1999

Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from a probabilistic perspective. A multi-point-moored ocean structural system under regular and irregular wave excitations is analytically examined via a generalized stochastic Melnikov function and Markov process approach. Time domain simulations and associated experimental observations are employed to assist in the interpretation of the analytical predictions. Taking into account the presence of random noise, a generalized stochastic Melnikov function associated with the corresponding averaged system, where a homoclinic connection exists near the primary resonance, is derived. The effects of random noise on the boundary of regions of possible existence of chaotic response is demonstrated via a mean-squared Melnikov criterion. The random wave field is approximated as random perturbations on regular and nearly regular (with very narrow-band spectrum) waves by adding a white noise component, or using a filtered white noise process to fit the JONSWAP spectrum. A Markov process approach is then applied explicitly to analyze the response. The evolution of the probability density function (PDF) of nonlinear stochastic response under the Markov process approach is characterized by a deterministic partial differential equation called the Fokker-Planck equation, which in this study is solved by a path integral solution procedure. Numerical evaluation of the path integral solution is based on path sum, and the short-time propagator is discretized accordingly. Short-time propagation is performed by using a fourth order Runge-Kutta scheme to calculate the most probable (i.e. mean) position in the phase space and to establish the fact that discrete contributions to the random response are locally Gaussian. Transient and steady-state PDF's can be obtained by repeat application of the short-time propagation. Based on depictions of the joint probability density functions and time domain simulations, it is observed that the presence of random noise may expedite the occurrence of "noisy" chaotic response. The noise intensity governs the transition among various types of stochastic nonlinear responses and the relative strengths of coexisting response attractors. Experimental observations confirm the general behavior depicted by the analytical predictions. / Graduation date: 1995

Thesis (Ph. D.)--Ohio State University, 1983. / Includes vita. Includes bibliographical references (leaves 80-81). Available online via OhioLINK's ETD Center.