The linkage between barrier island morphologies and dune topographies, vegetation, and biogeomorphic feedbacks, has been examined. The two-fold stability domain (i.e., overwash-resisting and overwash-reinforcing stability domains) model from case studies in a couple of islands along the Georgia Bight and Virginia coast has been proposed to examine the resilience properties in the barrier dune systems. Thus, there is a need to examine geographic variations in the dune topography among and within islands. Meanwhile, previous studies just analyzed and compared dune topographies based on transect-based point elevations or dune crest elevations; therefore, it is necessary to further examine dune topography in terms of multiple patterns and processes across scales. In this dissertation, I develop and deploy a cross-scale data model developed from resilience theory to represent and compare dune topographies across twelve islands over approximately 2,050 kilometers of the US southeastern Atlantic coast. Three sets of topographic variables were employed to summarize the cross-scale structure of topography (elevational statistics, patch indices, and the continuous surface properties). These metrics differed in their degree of spatial explicitness, their level of measurement, and association with patch or gradient paradigms. Topographic metrics were derived from digital elevation models (DEMs) of dune topographies constructed from airborne Light Detection and Ranging (LiDAR). These topographic metrics were used to construct dune topographic state space to investigate and visualize the cross-scale structure of dune topography. This study investigated (1) dune topography and landscape similarity among barrier islands in different barrier island morphologic contexts, (2) the differences in barrier island dune topographies and their resilience properties across large geographic extents, and (3) how geomorphic and biogeomorphic processes are related to resilience prosperities. The findings are summarized below. First, dune topography varies according to island morphologies of the Virginia coast; however, local controls (such as human modification of the shore or shoreline accretion and erosion) also play an important role in shaping dune topographies. Compared with tide-dominated islands, wave-dominated islands exhibited more convergence in dune topographies. Second, the dune landscapes of the Virginia Barrier Islands have a poorly consistent spatial structure, along with strong collinearity among elevational variables and landscape indices, which reflects the rapid retreat and erosion along the coast. The dune landscapes of the Georgia Bight have a more consistent spatial structure and a greater dimensionality in state space. Thus, the weaker multicollinearity and higher dimensionality in the dataset reflect their potential for resilience. Last, islands of different elevations may have similar dune topography characteristics due to the difference in resistance and resilience. Notwithstanding the geographic variability in geomorphic and biogeomorphic processes, convergence in dune topography exists, which is evidenced by the response curves of the topographic metrics that are correlated with both axes. This work demonstrates the usefulness of different representations of dune topography by cross-scale data modeling. Also, the two existing models of barrier island dune states were integrated to form a conceptual model that illuminates different, but complementary, resilience properties in the barrier dune system. The differences in dune topographies and resilience properties were detected in state space, and this information offers guidance for future study’s field site selections.

This manuscript consists of two papers that formulate novel methodologies pertaining to time series analysis in the state-space framework. In Chapter 1, we introduce an innovative time series forecasting procedure that relies on model-based clustering and model averaging. The clustering algorithm employs a state-space model comprised of three latent structures: a long-term trend component; a seasonal component, to capture recurring global patterns; and an anomaly component, to reflect local perturbations. A two-step clustering algorithm is applied to identify series that are both globally and locally correlated, based on the corresponding smoothed latent structures. For each series in a particular cluster, a set of forecasting models is fit, using covariate series from the same cluster. To fully utilize the cluster information and to improve forecasting for a series of interest, multi-model averaging is employed. We illustrate the proposed technique in an application that involves a collection of monthly disease incidence series. In Chapter 2, to effectively characterize a count time series that arises from a zero-inflated binomial (ZIB) distribution, we propose two classes of statistical models: a class of observation-driven ZIB (ODZIB) models, and a class of parameter-driven ZIB (PDZIB) models. The ODZIB model is formulated in the partial likelihood framework. Common iterative algorithms (Newton-Raphson, Fisher Scoring, and Expectation Maximization) can be used to obtain the maximum partial likelihood estimators (MPLEs). The PDZIB model is formulated in the state-space framework. For parameter estimation, we devise a Monte Carlo Expectation Maximization (MCEM) algorithm, using particle methods to approximate the intractable conditional expectations in the E-step of the algorithm. We investigate the efficacy of the proposed methodology in a simulation study, and illustrate its utility in a practical application pertaining to disease coding.

Due to its generality and flexibility, the state-space model has become one of the most popular models in modern time domain analysis for the description and prediction of time series data. The model is often used to characterize processes that can be conceptualized as "signal plus noise," where the realized series is viewed as the manifestation of a latent signal that has been corrupted by observation noise. In the state-space framework, parameter estimation is generally accomplished by maximizing the innovations Gaussian log-likelihood. The maximum likelihood estimator (MLE) is efficient when the normality assumption is satisfied. However, in the presence of contamination, the MLE suffers from a lack of robustness. Basu, Harris, Hjort, and Jones (1998) introduced a discrepancy measure (BHHJ) with a non-negative tuning parameter that regulates the trade-off between robustness and efficiency. In this manuscript, we propose a new parameter estimation procedure based on the BHHJ discrepancy for fitting state-space models. As the tuning parameter is increased, the estimation procedure becomes more robust but less efficient. We investigate the performance of the procedure in an illustrative simulation study. In addition, we propose a numerical method to approximate the asymptotic variance of the estimator, and we provide an approach for choosing an appropriate tuning parameter in practice. We justify these procedures theoretically and investigate their efficacy in simulation studies. Based on the proposed parameter estimation procedure, we then develop a new model selection criterion in the state-space framework. The traditional Akaike information criterion (AIC), where the goodness-of-fit is assessed by the empirical log-likelihood, is not robust to outliers. Our new criterion is comprised of a goodness-of-fit term based on the empirical BHHJ discrepancy, and a penalty term based on both the tuning parameter and the dimension of the candidate model. We present a comprehensive simulation study to investigate the performance of the new criterion. In instances where the time series data is contaminated, our proposed model selection criterion is shown to perform favorably relative to AIC. Lastly, using the BHHJ discrepancy based on the chosen tuning parameter, we propose two versions of an influence diagnostic in the state-space framework. Specifically, our diagnostics help to identify cases that influence the recovery of the latent signal, thereby providing initial guidance and insight for further exploration. We illustrate the behavior of these measures in a simulation study.

<p>This thesis deals with the problem of detecting faults in an environment where the measurements are affected by additive noise. To do this, a residual sensitive to faults is derived and statistical methods are used to distinguish faults from noise. Standard methods for fault detection compare a batch of data with a model of the system using the generalized likelihood ratio. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. One method to handle this is the parity-space method which solves the problem by removing the influence of the initial state using a projection.</p><p>In this thesis, the case where prior knowledge about the initial state is available is treated. This can be obtained for example from a Kalman filter. Combining the prior estimate with a minimum variance estimate from the data batch results in a smoothed estimate. The influence of the estimated initial state is then removed. It is also shown that removing the influence of the initial state by an estimate from the data batch will result in the parity-space method. To model slowly changing faults, an efficient parameterization using Chebyshev polynomials is given.</p><p>The methods described above have been applied to an Inertial Measurement Unit, IMU. The IMU usually consists of accelerometers and gyroscopes, but has in this work been extended with a magnetometer. Traditionally, the IMU has been used to estimate position and orientation of airplanes, missiles etc. Recently, the size and cost has decreased making it possible to use IMU:s for applications such as augmented reality and body motion analysis. Since a magnetometer is very sensitive to disturbances from metal, such disturbances have to be detected. Detection of the disturbances makes compensation possible. Another topic covered is the fundamental question of observability for fault inputs. Given a fixed or linearly growing fault, conditions for observability are given.</p><p>The measurements from the IMU show that the noise distribution of the sensors can be well approximated with white Gaussian noise. This gives good correspondence between practical and theoretical results when the sensor is kept at rest. The disturbances for the IMU can be approximated using smooth functions with respect to time. Low rank parameterizations can therefore be used to describe the disturbances. The results show that the use of smoothing to obtain the initial state estimate and parameterization of the disturbances improves the detection performance drastically.</p>

This thesis deals with the problem of detecting faults in an environment where the measurements are affected by additive noise. To do this, a residual sensitive to faults is derived and statistical methods are used to distinguish faults from noise. Standard methods for fault detection compare a batch of data with a model of the system using the generalized likelihood ratio. Careful treatment of the initial state of the model is quite important, in particular for short batch sizes. One method to handle this is the parity-space method which solves the problem by removing the influence of the initial state using a projection. In this thesis, the case where prior knowledge about the initial state is available is treated. This can be obtained for example from a Kalman filter. Combining the prior estimate with a minimum variance estimate from the data batch results in a smoothed estimate. The influence of the estimated initial state is then removed. It is also shown that removing the influence of the initial state by an estimate from the data batch will result in the parity-space method. To model slowly changing faults, an efficient parameterization using Chebyshev polynomials is given. The methods described above have been applied to an Inertial Measurement Unit, IMU. The IMU usually consists of accelerometers and gyroscopes, but has in this work been extended with a magnetometer. Traditionally, the IMU has been used to estimate position and orientation of airplanes, missiles etc. Recently, the size and cost has decreased making it possible to use IMU:s for applications such as augmented reality and body motion analysis. Since a magnetometer is very sensitive to disturbances from metal, such disturbances have to be detected. Detection of the disturbances makes compensation possible. Another topic covered is the fundamental question of observability for fault inputs. Given a fixed or linearly growing fault, conditions for observability are given. The measurements from the IMU show that the noise distribution of the sensors can be well approximated with white Gaussian noise. This gives good correspondence between practical and theoretical results when the sensor is kept at rest. The disturbances for the IMU can be approximated using smooth functions with respect to time. Low rank parameterizations can therefore be used to describe the disturbances. The results show that the use of smoothing to obtain the initial state estimate and parameterization of the disturbances improves the detection performance drastically.

In this work, the operating modes and characteristics of a Z-source full-bridge dc/dc converter are investigated. The mathematical analysis of the converter in continuous conduction mode, CCM and discontinuous conduction mode-2, DCM-2 operations is conducted. The transfer functions are derived for CCM and DCM-2 operation and validated by the simulation. The current mode controller of the converter is designed and its performance is checked in the simulation. The component waveforms in CCM and DCM-2 modes of operation are verified by operating the prototype converter in open-loop mode. The designed controller performance is tested with the closed-loop control implementation of the prototype converter. The theoretical efficiency analysis of the converter is made and compared with the measured efficiency of converter.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

The behaviour of a large nuclear reactor can be described with sufficient accuracy using a nodal model, like the spatial model of a 540 MWe large Pressurized Heavy Water Reactor (PHWR). This model divides the reactor into divisions or nodes to create a spatial model in order to control the xenon induced oscillations that occur in PHWRs. However, being such a large scale system, a 72nd-order model, it makes controller design challenging. Therefore, a reduced order model is much more manageable. A convenient method of model reduction while maintaining the important dynamics characteristics of the process can be done by decoupling. Also, due to the nature of the system, decentralized controllers could serve as a better option because it allows each controller to be localized. This way, any control input to a zone only affects the desired zone and the zones most coupled with, thus not causing a respective change in neutron flux in the other zones. In this thesis, three decentralized controllers were designed using the spatial model of a 540 MWe large PHWR. A decoupling algorithm was designed to divide the system into three partitions containing 20, 27, and 25 states each. Reduced order sub-systems were thus created to produce optimal decentralized controllers. An optimal centralized controller was created to compare both approaches. The decentralized versus centralized controllers’ system responses were analyzed after a reactivity disturbance. A fail-safe study was done to highlight one of the advantages of decentralized controllers. / UOIT

How can we evaluate and design integrated photonic circuit performance systematically? Can active photonic circuits be controlled for optimized performance? This work uses control theory to analyze, design, and optimize photonic integrated circuits based on versatile semiconductor optical amplifiers (SOAs). Control theory provides a mathematically robust set of tools for system analysis, design, and control. Although control theory is a rich and well-developed field, its application to the analysis and design of photonic circuits is not widespread. Following control theoretic methods already used for fibreline systems we derive three interrelated state-space models: a core photonic model, a photonic model with gain compression, and a equivalent circuit optoelectronic model. We validate each model and calibrate the gain compression model by pump/probe experiments. We then linearize the state-space models to design and analyze SOA controllers. We apply each linearized model to proof-of-concept SOA control applications such as suppressing interchannel crosstalk and regulating output power. We demonstrate the power of linearized state-space models in controller design and stability analysis. To illustrate the importance of using the complete equivalent circuit model in controller design, we demonstrate an intuitive bias-current controller that fails due to the dynamics of the intervening parasitic circuitry of the SOA. We use the linearized state-space models to map a relationship between feedback delay and controller strength for stable operation, and demonstrate that SOAs pose unusual control difficulties due to their ultrafast dynamics. Finally, we leverage the linearized models to design a novel and successful hybrid controller that uses one SOA to control another via feedback (for reliability) and feedforward (for speed) control. The feedback controller takes full advantage of the equivalent circuit modelling by sampling the voltage of the controlled SOA and using the error to drive the bias current of the controller SOA. Filtering in the feedback path is specified by transfer function analysis. The feedforward design uses a novel application of the linearized models to set the controller bias points correctly. The modelling and design framework we develop is entirely general and opens the way to the robust optoelectronic control of integrated photonic circuits.

Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning. Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow. Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.