Nonlinear parametric response of a flexible cantilever beam is simulated. In the simulations, lateral response of the beam due to an imposed axial harmonic base displacement excitation is calculated. The response frequency is approximately half the input frequency. The transient simulations include the assumption of damping proportional to the square of the velocity along the beam. Velocity-squared damping is realistic for situations in which fluid forces resisting the structural motion are significant. The commercial finite element software, ANSYS, is used to perform the simulations. A flexible method is developed and implemented in this work, based on the ANSYS Parametric Design Language, for including the quadratic damping assumption in the analysis. Variation of steady state response amplitude is examined for a range of quadratic damping coefficients over a range of axial base excitation frequencies. Further, a definition of phase angle of the response with the respect to the input is proposed for these nonlinear cases in which the input frequency is an integer multiple of the response frequency. The response phase with respect to excitation is studied over a range of damping coefficients and excitation frequencies. In addition, numerical solutions of nonlinear dynamic systems obtained from the implicit finite element method and the explicit dynamics finite element method are compared. The nonlinear dynamic systems considered are a flexible beam subjected to axial base excitation and also lateral excitations. The studies comparing explicit and implicit method results include cases of stress-stiffening and large deflections.

Gaussian process regression (GPR) is a long-standing technique for statistical interpolation between observed data points. Having originally been applied to spatial analysis in the 1950s, GPR offers highly nonlinear predictions with uncertainty adjusting to the degree of extrapolation -- at the expense of very few model parameters to be fit. Thus GPR has gained considerable popularity in statistical applications such as machine learning and nonparametric density estimation. In this thesis, we explore the potential for GPR to improve the efficiency of parametric inference for continuous-time stochastic processes. For almost all such processes, the likelihood function based on discrete observations cannot be written in closed-form. However, it can be very well approximated if the inter-observation time is small. Therefore, a popular strategy for parametric inference is to introduce missing data between actual observations. In a Bayesian context, samples from the posterior distribution of the parameters and missing data are then typically obtained using Markov chain Monte Carlo (MCMC) methods, which can be computationally very expensive. Here, we consider the possibility of using GPR to impute the marginal distribution of the missing data directly. These imputations could then be leveraged to produce independent draws from the joint posterior by Importance Sampling, for a significant gain in computational efficiency. In order to illustrate the methodology, three continuous processes are examined. The first one is based on a neural excitation model with a non-standard periodic component. The second and third are popular financial models often used for option pricing. While preliminary inferential results are quite promising, we point out several improvements to the methodology which remain to be explored.

Two parametric models for income and financial return distributions are presented. There are the four-parameter normal Laplace (NL) and the five-parameter generalized normal Laplace (GNL) distributions. Their properties are discussed; furthermore, estimation of the parameters by the method of moments and maximum likelihood is presented. The performances of fitting the two models to nine empirical distributions of family income have been evaluated and compared against the four- and five-parameter generalized beta2 (GB2) and generalized beta (GB) distributions which had been previously claimed as best-fitting four- and five- parameter models for income distribution. The results demonstrate that the NL distribution has better performance than the GB and GB2 distributions with the GNL distribution providing an even better fit. Limited application to data on financial log returns shows that the fit of the GNL is comparable to the well-known generalized hyperbolic distribution. However, the GNL suffers from a lack of closed-form expressions for its probability density and cumulative distribution functions, and fitting the distribution numerically is slow and not always reliable. The results of this thesis suggest a strong case for considering the GNL family as parametric models for income data and possibly for financial logarithmic returns.

In this study, we examined the effect of cool roofs on commercial and residential buildings in each climate zone, by looking at monitored case studies and DOE-2 simulations from various sources of literature; and using an online tool - the Cool Roof Calculator and a simple COP ratio model to validate the results of the case studies. It was found that the Cool Roof Calculator does not take building form into account, hence a sensitivity analysis was first conducted to rank the importance of various building parameters against one another. The analysis was conducted on the EPC normative building energy model. Results indicated that roof absorptance coefficient, aspect ratio and number of floors were the three parameters that either ranked highest or were important parameters, and were chosen for further parametric analysis to evaluate the impact of these building parameters on total building loads. A simple COP ratio model was also developed to validate the results from the literature review and Cool Roof Calculator, and it was found that in terms of cost, for a prototype medium-sized commercial building, it is always beneficial to use a white roof, but cities in northern climates may have little advantage, and insulation may be a better choice.

No description available.

Thesis (M.Sc.) - Carleton University, 2008. / Includes bibliographical references (p. 114-117). Also available in electronic format on the Internet.

Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, March 2007. / Thesis Advisor(s): Andrés Larraza, Bruce C. Denardo. "March 2007." Includes bibliographical references (p. 63-64). Also available in print.

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This thesis deals with the topic of min-max formulations of robust model predictive control problems. The sets involved in guaranteeing robust feasibility of the min-max program in the presence of state constraints are of particular interest, and expanding the applicability of well understood solvers of linearly constrained quadratic min-max programs is the main focus. To this end, a generalisation for the set of uncertainty is considered: instead of fixed bounds on the uncertainty, state- and input-dependent bounds are used. To deal with state- and input dependent constraint sets a framework for a particular class of set-valued maps is utilised, namely parametrically convex set-valued maps. Relevant properties and operations are developed to accommodate parametrically convex set-valued maps in the context of robust model predictive control. A quintessential part of this work is the study of fundamental properties of piecewise polyhedral set-valued maps which are parametrically convex, we show that one particular property is that their combinatorial structure is constant. The study of polytopic maps with a rigid combinatorial structure allows the use of an optimisation based approach of robustifying constrained control problems with probabilistic constraints. Auxiliary polytopic constraint sets, used to replace probabilistic constraints by deterministic ones, can be optimised to minimise the conservatism introduced while guaranteeing constraint satisfaction of the original probabilistic constraint. We furthermore study the behaviour of the maximal robust positive invariant set for the case of scaled uncertainty and show that this set is continuously polytopic up to a critical scaling factor, which we can approximate a-priori with an arbitrary degree of accuracy. Relevant theoretical statements are developed, discussed and illustrated with examples.

The advent of new quasi phase matched materials and high spectral/spatial quality pump sources has led to a renaissance in the development of continuous-wave optical parametric oscillators for the coherent generation of broadly tunable light in the mid infrared spectral region. This thesis describes a novel technique which overcomes the threshold constraints of the singly resonant oscillator (SRO) and stability constraints of the doubly resonant oscillator (DRO) traditionally associated with these devices by placing a singly resonant optical parametric oscillator in the high circulating field found within the cavity of a laser: the intracavity optical parametric oscillator. An SRO based upon the nonlinear material periodically poled LiNb03 (PPLN) operating internal to an all solid state, 1W diode pumped Nd:YV04 mini-laser is demonstrated and characterised. This system exhibits SRO threshold at only 330mW of external diode pump power, and produced a total of 70mW of extractable idler at 1W diode pump power. Through multi-parameter tuning of the poled nonlinear material we demonstrate broad tuning of the non-resonant idler through the spectrally important range 3.1 - 4μm. Novel cavity design desensitises the system to the effects of thermal lensing in the nonlinear medium, resulting in stable spatial and mean power outputs. The short term pump field stability is characterised by intensity modulation brought about by the onset of relaxation oscillations ; a consequence of placing the SRO within the cavity of the pump laser. A comparative study of SRO's based upon PPLN and the new material periodically poled RbTi0As04 (PPRTA) pumped internal to a high power fibre coupled diode pumped Nd:YV04 laser cavity is undertaken and presented. We see that although the nonlinearity and interaction length of the PPRTA is smaller than that of PPLN, the system based upon PPRTA outperforms or is at least comparable with that based upon PPLN in every respect with the exception of idler tuning range. We attribute this to the reduced sensitivity of this material to the effect of thermal lensing. Up to 440mW of extracted idler was produced by each system. The reduction of interferometric feedback of the pump field by the signal cavity mirror was found to eliminate the onset of relaxation oscillations in the case of PPRTA but not PPLN, due to thermal air currents dominating the triggering process in iii this system. Recently published Sellmeier equations and temperature derivatives for PPRTA are compared with the experimentally observed temperature tuning behaviour. The inclusion of an optical parametric oscillator within the cavity of the pump laser impacts significantly upon the transient dynamics of the pump laser in which it resides. We show experimental evidence of this effect and outline a strategy to minimise the effects of relaxation oscillations in the context of a simple numerical model which shall be derived. Possible future avenues of research are discussed in the context of the results and conclusions obtained over the course of this research program.