In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

The high cost of experimentation and product development in the field of microelectromechanical systems (MEMS) has led to a greater emphasis on simulation-based design for increasing first-pass design success and reliability. The use of compliant or flexible mechanisms can help eliminate friction, wear, and backlash, but compliant MEMS are sensitive to variations in material properties and geometry. This dissertation proposes approaches for design stage uncertainty analysis, model validation, and robust optimization of nonlinear compliant MEMS to account for critical process uncertainties including residual stress, layer thicknesses, edge bias, and material stiffness. Methods for simulating and mitigating the effects of non-idealities such joint clearances, semi-rigid supports, non-ideal loading, and asymmetry are also presented. Approaches are demonstrated and experimentally validated using bistable micromechanisms and thermal microactuators as examples.

Randomized clinical trials (RCTs) are considered to be the "gold standard" in order to demonstrate a causal relationship between a treatment and an outcome because complete randomization ensures that the only difference between the two units being compared is the treatment. The intention-to-treat (ITT) comparison has long been regarded as the preferred analytic approach for RCTs. However, if there exists an “intermediate” variable between the treatment and outcome, and the analysis conditions on this intermediate, randomization will break down, and the ITT approach does not account properly for the intermediate. In this dissertation, we explore the principal stratification approach for dealing with intermediate variables, illustrate its applications in two different clinical trial settings, and extend the existing analytic approaches with respect to specific challenges in these settings. The first part of our work focuses on clinical endpoint bioequivalence (BE) studies with noncompliance and missing data. In clinical endpoint BE studies, the primary analysis for assessing equivalence between a generic and an innovator product is usually based on the observed per-protocol (PP) population (usually completers and compliers). The FDA Missing Data Working Group recently recommended using “causal estimands of primary interest.” This PP analysis, however, is not generally causal because the observed PP is post-treatment, and conditioning on it may introduce selection bias. To date, no causal estimand has been proposed for equivalence assessment. We propose co-primary causal estimands to test equivalence by applying the principal stratification approach. We discuss and verify by simulation the causal assumptions under which the current PP estimator is unbiased for the primary principal stratum causal estimand – the "Survivor Average Causal Effect" (SACE). We also propose tipping point sensitivity analysis methods to assess the robustness of the current PP estimator from the SACE estimand when these causal assumptions are not met. Data from a clinical endpoint BE study is used to illustrate the proposed co-primary causal estimands and sensitivity analysis methods. Our work introduces a causal framework for equivalence assessment in clinical endpoint BE studies with noncompliance and missing data. The second part of this dissertation targets the use of principal stratification analysis approaches in a pragmatic randomized clinical trial -- the Patient Activation after DXA Result Notification (PAADRN) study. PAADRN is a multi-center, pragmatic randomized clinical trial that was designed to improve bone health. Participants were randomly assigned to either intervention group with usual care augmented by a tailored patient-activation Dual-energy X-ray absorptiometry (DXA) results letter accompanied by an educational brochure, or control group with usual care only. The primary analyses followed the standard ITT principle, which provided a valid estimate for the intervention assignment. However, findings might underestimate the effect of intervention because PAADRN might not have an effect if the patient did not read, remember and act on the letter. We apply principal stratification to evaluate the effectiveness of PAADRN for subgroups, defined by patient's recall of having received a DXA result letter, which is an intermediate outcome that's post-treatment. We perform simulation studies to compare the principal score weighting methods with the instrumental variable (IV) methods. We examine principal strata causal effects on three outcome measures regarding pharmacological treatment and bone health behaviors. Finally, we conduct sensitivity analyses to assess the effect of potential violations of relevant causal assumptions. Our work is an important addition to the primary findings based on ITT. It provides a profound understanding of why the PAADRN intervention does (or does not) work for patients with different letter recall statuses, and sheds light on the improvement of the intervention.

The modeling of freight travel demand has gained increasing attention in the recent past due to the importance of efficient and safe freight transportation to regional economic growth. Despite the attention paid to the modeling of freight travel demand, advances in modeling methods and the development of practical tools for forecasting freight flows have been limited. The development of freight demand models that incorporate the behavioral aspects of freight demand face significant hurdles, partially due to the data requirements, which are a consequence of the inherent complexity of the mechanisms driving freight demand. This research attempts to make a contribution in this context by proposing a relatively data simple, but behaviorally robust statewide modeling framework for the state of Florida, in the spirit of an aggregate level four-step planning process. The modeling framework that is developed in this research can be applied to the modeling of freight travel demand using data contained in readily available commercial databases such as the Reebie TRANSEARCH database and the InfoUSA employer database. The modeling methodology consists of a structural equations modeling framework that can accommodate multiple dependent variables simultaneously. This framework predicts freight flows on various modes between two zipcodes based on the socio-economic characteristics and the modal level of service characteristics. Separate models have been developed for various commodity groups. The estimated models for various commodity groups are found to offer statistically valid indications and plausible interpretations suggesting that these models may be suitable for application in freight transportation demand forecasting applications. The sensitivity analysis conducted on these models clearly added evidence to the fact that employment is the key factor influencing freight flows between two regions.

Cette thèse porte sur l'analyse de sensibilité dans le contexte des études de fiabilité des structures. On considère un modèle numérique déterministe permettant de représenter des phénomènes physiques complexes.L'étude de fiabilité a pour objectif d'estimer la probabilité de défaillance du matériel à partir du modèle numérique et des incertitudes inhérentes aux variables d'entrée de ce modèle. Dans ce type d'étude, il est intéressant de hiérarchiser l'influence des variables d'entrée et de déterminer celles qui influencent le plus la sortie, ce qu'on appelle l'analyse de sensibilité. Ce sujet fait l'objet de nombreux travaux scientifiques mais dans des domaines d'application différents de celui de la fiabilité. Ce travail de thèse a pour but de tester la pertinence des méthodes existantes d'analyse de sensibilité et, le cas échéant, de proposer des solutions originales plus performantes. Plus précisément, une étape bibliographique sur l'analyse de sensibilité puis sur l'estimation de faibles probabilités de défaillance est proposée. Cette étape soulève le besoin de développer des techniques adaptées. Deux méthodes de hiérarchisation de sources d'incertitudes sont explorées. La première est basée sur la construction de modèle de type classifieurs binaires (forêts aléatoires). La seconde est basée sur la distance, à chaque étape d'une méthode de type subset, entre les fonctions de répartition originelle et modifiée. Une méthodologie originale plus globale, basée sur la quantification de l'impact de perturbations des lois d'entrée sur la probabilité de défaillance est ensuite explorée. Les méthodes proposées sont ensuite appliquées sur le cas industriel CWNR, qui motive cette thèse. / This thesis' subject is sensitivity analysis in a structural reliability context. The general framework is the study of a deterministic numerical model that allows to reproduce a complex physical phenomenon. The aim of a reliability study is to estimate the failure probability of the system from the numerical model and the uncertainties of the inputs. In this context, the quantification of the impact of the uncertainty of each input parameter on the output might be of interest. This step is called sensitivity analysis. Many scientific works deal with this topic but not in the reliability scope. This thesis' aim is to test existing sensitivity analysis methods, and to propose more efficient original methods. A bibliographical step on sensitivity analysis on one hand and on the estimation of small failure probabilities on the other hand is first proposed. This step raises the need to develop appropriate techniques. Two variables ranking methods are then explored. The first one proposes to make use of binary classifiers (random forests). The second one measures the departure, at each step of a subset method, between each input original density and the density given the subset reached. A more general and original methodology reflecting the impact of the input density modification on the failure probability is then explored.The proposed methods are then applied on the CWNR case, which motivates this thesis.

In recent years, the popularity of wind energy has grown. It is starting to play a large role in generating renewable, clean energy around the world. In New Zealand, there is increasing recognition and awareness of global warming and the pollution caused by burning fossil fuels, as well as the increased difficulty of obtaining oil from foreign sources, and the fluctuating price of non-renewable energy products. This makes wind energy a very attractive alternative to keep New Zealand clean and green. There are many issues involved in wind farm development. These issues can be grouped into two categories - economic issues and environmental issues. Wind farm developers often use site selection process to minimise the impact of these issues. This thesis aims to develop GIS based models that provide effective decision support tool for evaluating, at a regional scale, potential wind farm locations. This thesis firstly identifies common issues involved in wind farm development. Then, by reviewing previous research on wind farm site selection, methods and models used by academic and corporate sector to solve issues are listed. Criteria for an effective decision support tool are also discussed. In this case, an effective decision support tool needs to be flexible, easy to implement and easy to use. More specifically, an effective decision support tool needs to provide users the ability to identify areas that are suitable for wind farm development based on different criteria. Having established the structure and criteria for a wind farm analysis model, a GIS based tool was implemented using AML code using a Boolean logic model approach. This method uses binary maps for the final analysis. There are a total of 3645 output maps produced based on different combination of criteria. These maps can be used to conduct sensitivity analysis. This research concludes that an effective GIS analysis tool can be developed for provide effective decision support for evaluating wind farm sites.

This thesis is aimed at analysis of sampled-data feedback systems. Our approach is in the frequency-domain, and stresses the study of sensitivity and complementary sensitivity operators. Frequency-domain methods have proven very successful in the analysis and design of linear time-invariant control systems, for which the importance and utility of sensitivity operators is well-recognized. The extension of these methods to sampled-data systems, however, is not straightforward, since they are inherently time-varying due to the intrinsic sample and hold operations. In this thesis we present a systematic frequency-domain framework to describe sampled-data systems considering full-time information. Using this framework, we develop a theory of design limitations for sampled-data systems. This theory allows us to quantify the essential constraints in design imposed by inherent open-loop characteristics of the analog plant. Our results show that: (i) sampled-data systems inherit the difficulty imposed upon analog feedback design by the plant's non-minimum phase zeros, unstable poles, and time-delays, independently of the type of hold used; (ii) sampled-data systems are subject to additional design limitations imposed by potential non-minimum phase zeros of the hold device; and (iii) sampled-data systems, unlike analog systems, are subject to limits upon the ability of high compensator gain to achieve disturbance rejection. As an application, we quantitatively analyze the sensitivity and robustness characteristics of digital control schemes that rely on the use of generalized sampled-data hold functions, whose frequency-response properties we describe in detail. In addition, we derive closed-form expressions to compute the L2-induced norms of the sampled-data sensitivity and complementary sensitivity operators. These expressions are important both in analysis and design, particularly when uncertainty in the model of the plant is considered. Our methods provide some interesting interpretations in terms of signal spaces, and admit straightforward implementation in a numerically reliable fashion. / PhD Doctorate

Appropriately constructed pollutant export models can help set management priorities for catchments, identify critical pollutant source areas, and are important tools for developing and evaluating economically viable ways of minimising surface water pollution.¶ This thesis presents a comparison, an evaluation and an integration of models for predicting the export of environmental pollutants, in particular sediment, through river systems. A review of the capabilities and limitations of current water quality modelling approaches is made. Several water quality and quantity modelling approaches are applied and evaluated in the catchment of the upper Murrumbidgee River.¶ The IHACRES rainfall-runoff model and a simple hydrologic routing model are applied with the aim of developing a capacity to predict streamflow at various catchment scales and to enable integration with other pollutant load estimation techniques. Methods for calculating pollutant loads from observed pollutant concentration and modelled streamflow data are also investigated. Sediment export is estimated using these methods over a 10-year period for two case study subcatchments. Approaches for water quality sampling are discussed and a novel monitoring program using rising stage siphon samplers is presented. Results from a refinement of the Sediment River Network model in the upper Murrumbidgee catchment (SedNet-UM) are presented. The model provides a capacity to quantify sediment source, transport and to simulate the effects of management change in the catchment. The investigation of the model includes rigorous examination of the behaviour of the model through sensitivity assessment and comparison with other sediment modelling studies. The major conclusion reached through sensitivity assessment was that the outputs of the model are most sensitive to perturbation of the hydrologic parameters of the model.¶ The SedNet-UM application demonstrates that it is possible to construct stream pollutant models that assist in prioritising management across catchment scales. It can be concluded that SedNet and similar variants have much potential to address common resource management issues requiring the identification of the source, propagation and fate of environmental pollutants. In addition, incorporating the strengths of a conceptual rainfall-runoff model and the semi-distributed SedNet model has been identified as very useful for the future prediction of environmental pollutant export.

Shape control of a structure with distributed piezoelectric actuators can be achieved through optimally selecting the loci, shapes and sizes of the piezoelectric actuators and choosing the electric fields applied to the actuators. Shape control can be categorised as either static or dynamic shape control. Whether it is a transient or gradual change, static or dynamic shape control, both aim to determine the loci, sizes, and shapes of piezoelectric actuators, and the applied voltages such that a desired structural shape is achieved effectively. This thesis is primarily concerned with establishing a finite element formulation for the general smart laminated composite plate structure, which is capable to analyse static and dynamic deformation using non-rectangular elements. The mechanical deformation of the smart composite plate is modelled using a third order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation for static and dynamics analysis is verified by comparing with available numerical results. Selected experiments have also been conducted to measure structural deformation and the experimental results are used to correlate with those of the finite element formulation for static analysis. In addition, the Linear Least Square (LLS) method is employed to study the effect of different piezoelectric actuator patch pattern on the results of error function, which is the least square error between the calculated and desired structural shapes in static structural shape control. The second issue of this thesis deals with piezoelectric actuator design optimisation (PADO) for quasi-static shape control by finding the applied voltage and the configuration of piezoelectric actuator patch to minimise error function, whereas the piezoelectric actuator configuration is defined based on the optimisation technique of altering nodal coordinates (size/shape optimisation) or eliminating inefficient elements in a structural mesh (topology optimisation). Several shape control algorithms are developed to improve the structural shape control by reducing the error function. Further development of the GA-based voltage and piezoelectric actuator design optimisation method includes the constraint handling, where the error function can be optimised subjected to energy consumption or other way around. The numerical examples are presented in order to verify that the proposed algorithms are applicable to quasi-static shape control based on voltage and piezoelectric actuator design optimisation (PADO) in terms of minimising the error function. The third issue is to use the present finite element formulation for a modal shape control and for controlling resonant vibration of smart composite plate structures. The controlled resonant vibration formulation is developed. Modal analysis and LLS methods are also employed to optimise the applied voltage to piezoelectric actuators for achieving the modal shapes. The Newmark direct time integration method is used to study harmonic excitation of smart structures. Numerical results are presented to induce harmonic vibration of structure with controlled magnitude via adjusting the damping and to verify the controlled resonant vibration formulation.

There is a need for ecological modelling to help understand the dynamics in ecological systems, and thus aid management decisions to maintain or improve the quality of the ecological systems. This research focuses on non linear statistical modelling of observations from an estuarine system, Gippsland Lakes, on the south-eastern coast of Australia. Feed forward neural networks are used to model chlorophyll time series from a fixed monitoring station at Point King. The research proposes a systematic approach to modelling in ecology using feed forward neural networks, to ensure: (a) that results are reliable, (b) to improve the understanding of dynamics in the ecological system, and (c) to obtain a prediction, if possible. An objective filtering algorithm to enable modelling is presented. Sensitivity analysis techniques are compared to select the most appropriate technique for ecological models. The research generated a chronological profile of relationships between biophysical parameters and chlorophyll level for different seasons. A sensitivity analysis of the models was used to understand how the significance of the biophysical parameters changes as the time difference between the input and predicted value changes. The results show that filtering improves modelling without introducing any noticeable bias. Partial derivative method is found to be the most appropriate technique for sensitivity analysis of ecological feed forward neural networks models. Feed forward neural networks show potential for prediction when modelled on an appropriate time series. Feed forward neural networks also show capability to increase understanding of the ecological environment. In this research, it can be seen that vertical gradient and temperature are important for chlorophyll levels at Point King at time scales from a few hours to a few days. The importance of chlorophyll level at any time to chlorophyll levels in the future reduces as the time difference between them increases.