Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can replace the state matrix in a state-space model with the sparse matrix of the shift encoder.

This work describes a framework for simultaneous estimation and modeling (SEAM) of dynamic systems using non-Gaussian belief fusion by first presenting the relevant fundamental formulations, then building upon these formulations incrementally towards a more general and ubiquitous framework. Multi-Gaussian belief fusion (MBF) is introduced as a natural and effective method of fusing non-Gaussian probability distribution functions (PDFs) in arbitrary dimensions efficiently and with no loss of accuracy. Construction of some multi-Gaussian structures for potential use in MBF is addressed. Furthermore, recursive Bayesian estimation (RBE) is developed for linearized systems with uncertainty in model parameters, and a rudimentary motion model correction stage is introduced. A subsequent improvement to motion model correction for arbitrarily non-Gaussian belief is developed, followed by application to observation models. Finally, SEAM is generalized to fully nonlinear and non-Gaussian systems. Several parametric studies were performed on simulated experiments in order to assess the various dependencies of the SEAM framework and validate its effectiveness in both estimation and modeling. The results of these studies show that SEAM is capable of improving estimation when uncertainty is present in motion and observation models as compared to existing methods. Furthermore, uncertainty in model parameters is consistently reduced as these parameters are updated throughout the estimation process. SEAM and its constituents have potential uses in robotics, target tracking and localization, state estimation, and more. / Doctor of Philosophy / The simultaneous estimation and modeling (SEAM) framework and its constituents described in this dissertation aim to improve estimation of signals where significant uncertainty would normally introduce error. Such signals could be electrical (e.g. voltages, currents, etc.), mechanical (e.g. accelerations, forces, etc.), or the like. Estimation is accomplished by addressing the problem probabilistically through information fusion. The proposed techniques not only improve state estimation, but also effectively "learn" about the system of interest in order to further refine estimation. Potential uses of such methods could be found in search-and-rescue robotics, robust control algorithms, and the like. The proposed framework is well-suited for any context where traditional estimation methods have difficulty handling heightened uncertainty.

The power requirements imposed on an active vibration isolation system are quite important to the overall system design. In order to improve the efficiency of an active isolation system we analyze different feedback control strategies which will provide electrical energy regeneration. The active isolation system is modeled in a state-space form for two different types of actuators: a piezoelectric stack actuator and a linear electromagnetic (EM) actuator. During regenerative operation, the power is flowing from the mechanical disturbance through the electromechanical actuator and its switching drive into the electrical storage device (batteries or capacitors). We demonstrate that regeneration occurs when controlling one or both of the flow states (velocity and/or current). This regenerative control strategy affects the closed loop dynamics of the isolator which sees its damping reduced. / Master of Science

Distributed generation for consumer applications is a relatively new field and it is difficult to satisfy both cost and performance targets. High expectations coupled with extreme cost cutting to compete with traditional technologies make converter design difficult. As power electronics mature more opportunities arise for entry into this lucrative area. An excellent understanding of converter dynamics is crucial in producing a well performing and cost competitive system. The six-switch single-phase inverter proposed in this thesis is a prime candidate for use in single households and small businesses. Its compact size and compatibility with existing electrical standards make its integration easy. However, little work is available on characterizing the system from a controls point of view. In particular balancing the two outputs with an uneven load is a concern. This thesis uses nodal and loop analysis to formulate a mathematical model of the six-switch single-phase inverter. A non-linear time invariant model is constructed for circuit simulation; details found in real circuits are added. A hardware-in-the-loop (HIL) configuration is used for more accurate simulation. In fact, its use makes for an almost seamless transition between simulation and hardware experimentation. A detailed explanation of the HIL system developed is presented. The system is simulated under various load conditions. Uneven loads and lightly loaded conditions are thoroughly examined. Controllers are verified in simulation and then are tested on real hardware using the HIL system. DC bus disturbance rejection and non-linear loads are also investigated. Acceptable inverter performance is demonstrated without expensive current sensors or high sampling frequency. / Master of Science

No / This paper presents the details of a methodology for predicting the thermoelastic properties degradation in general symmetric laminates with uniform ply cracks in some or all of the 90° layers. First, a stress transfer method is derived by using the concept of state space equation. The laminate can be subjected to any combination of in-plane biaxial and shear loading, and the uniform thermal loading is also taken into account. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. By this method, a laminate may be composed of an arbitrary number of monoclinic layers and each layer may have different material property and thickness. Second, the concept of the effective thermoelastic properties of a cracked laminate is introduced. Based on the numerical solutions of specially designed loading cases, the effective thermoelastic constants of a cracked laminate can be obtained. Finally, the applications of the methodology are shown by numerical examples and compared with numerical results from other models and experiment data in the literature. It is found that the theory provides good predictions of the thermoelastic properties degradation in general symmetric laminates.

Avian populations have undergone global declines that have profound implications for biodiversity. The prognosis of avian decline risks has been hindered by a lack of understanding of the endogenous and exogenous determinants of avian fauna declines. I investigated the spatiotemporal population dynamics of 428 North American breeding birds using the Breeding Bird Survey data from 1970 to 2018. I hypothesized life history strategies would determine avian population trends by mediating population regulation and responses to global climate changes (H1). I also hypothesized birds with increasing or stable population trends would have greater within-species spatial variability in their population responses to local climate changes and abundances than species with decreasing trends (H2). Machine learning methods classified 225 species (53%) to a decreasing group and 203 species (47%) to an increasing group. The effects of North Atlantic Oscillation (NAO) and Southern Oscillation (SO) on continentally aggregated populations were significantly greater in the increasing group than the decreasing group. However, neither direct nor delayed density dependence differed between the two groups. Bayesian phylogenetic logistic regression demonstrated that increased fledging age significantly reduced avian population decline risks, suggesting that increased investments of parental care mitigate avian population decline risks. Birds living in open areas had about 50% higher risks of population declines than those associated with densely vegetated ecosystems, signaling alarming avian faunal decline risks caused by converting grasslands and shrublands to agriculture or other land use. Structural equation models demonstrated that life history strategy was a direct causal factor of density dependence and population responses to NAO and SO and an indirect cause of avian population decline via mediating avian responses to SO, supporting H1. In metapopulations of 159 breeding birds from 1985 to 2018, density dependence did not differ significantly between the decreasing and increasing groups; however, bird species in the increasing group had greater within-species spatial variance in population responses to temperature and precipitation than declining species, partially supporting H2. Global changes may homogenize avian life history traits and population responses to climate changes, which in turn increase avian fauna decline risks.

Program analysis techniques play a crucial role in modern software development by helping developers find bugs and verify code behavior. These techniques rely heavily on systematic reasoning about program execution paths. Symbolic execution has emerged as a powerful method for systematic program analysis. However, symbolic execution faces a fundamental challenge known as state-space explosion, where the number of potential execution paths grows exponentially. While backwards symbolic execution (BSE) offers some advantages over forward approaches in managing this explosion, it still struggles with path explosion when handling complex program elements such as loops, pointers, and function calls. This dissertation advances backwards reasoning through several key contributions. We introduce BROIL, an approach that enables handling of loops in backwards reasoning without requiring complete loop unrolling. By developing parameterized loop summaries that capture loop behavior, BROIL significantly reduces the state-space explosion problem common in symbolic execution. We demonstrate BROIL's effectiveness by applying it with incorrectness logic for targeted assertions. Our empirical evaluation then investigates the question of which alias analysis technique best complements BSE. Through experimentation comparing different alias analysis approaches, we demonstrate that demand-driven analysis substantially outperforms whole-program approaches, achieving a 7.29× geometric mean speedup in symbolic execution. Finally, we develop CAMS, a compositional approach for function summarization in backwards analysis. CAMS introduces context-agnostic function summaries that capture pointer and global variable effects while supporting modular composition. By enabling the reuse of summaries across different program units, CAMS achieves significant performance improvements compared to non-compositional approach. / Doctor of Philosophy / Modern software has become increasingly complex, making it challenging for developers to ensure their code works correctly. To help with this, developers use program analysis tools that systematically check code for bugs. One promising approach is symbolic execution, which explores how a program behaves in different program paths. However, this approach struggles because the number of possible program states it needs to check grows too quickly. An approach, backwards symbolic execution, helps manage this problem by working backwards from potential bugs, but it still faces state-space explosion when analyzing common programming constructs like loops and function calls. This dissertation presents three solutions to make program analysis more practical. First, we introduce BROIL, a new approach that efficiently handles program loops by creating summaries of their behavior instead of analyzing them completely. We show how BROIL can be used effectively to find bugs in programs. Second, we investigate how different alias analysis techniques perform when integrated with backwards symbolic execution. Our experiments show that demand-driven alias analysis significantly outperforms traditional whole-program analysis approaches, achieving more than seven times speedup. Finally, we develop CAMS, a technique that creates reusable summaries of program functions. These summaries can be used across different parts of the program, making the analysis significantly faster than traditional approaches. Together, these contributions make program analysis tools more practical for analyzing real-world programs.

State-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides new ecological insights. I extend the state-space framework to create multi-species models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures and models with many parameters to limited data; often the case in ecological studies. I have taken a Bayesian model fitting approach in this thesis. The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s capabilities. The harrier data are believed to be known without error, while missing data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including one species as a covariate in the other’s model. Finally, models are included for the harriers’ alternate prey. The single- and multi-species state-space models for the predator-prey interactions provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.

This thesis studies bubbles in the U.S. stock market and how they are influenced by monetary policy pursued by the FED. Using Kalman filtering, the log-real price of S&P 500 is decomposed into a market-fundamentals component and a bubble component. The market-fundamentals component depends on the expected future dividends and the required rate of return, while the bubble component is treated as an unobserved state vector in the state-space model. The results suggest that, mainly in recent decades, the bubble has accounted for a substantial portion of S&P 500 price dynamics and might have played a significant role during major bull and bear markets. The innovation of this thesis is that it goes one step further and investigates the effects of monetary policy on both estimated components of S&P 500. For this purpose, the block- restriction VAR model is employed. The findings indicate that the decreasing interest rates have a significant short-term positive effect on the market-fundamentals component but not on the bubble. On the other hand, quantitative easing seems to have a positive effect on the bubble but not on the market-fundamentals component. Finally, the results suggest that the FED has not been successful at distinguishing between stock price movements due to fundamentals or the price misalignment.

Regression testing of an evolving software system may involve significant challenges. While, there would be a requirement of maximising the probability of finding out if the latest changes to the system has broken some existing feature, it needs to be done as economically as possible. A particularly important class of software systems are API libraries. Such libraries would typically constitute a very important component of many software systems. High quality requirements make it imperative to continually optimise the internal implementation of such libraries without affecting the external interface. Therefore, it is preferred to guide the regression testing by some kind of formal specification of the library. The testing problem comprises of three parts: computation of test data, execution of test, and analysis of test results. Current research mostly focuses on the first part. The objective of test data computation is to maximise the probability of uncovering bugs, and to do it with as few test cases as possible. The problem of test data computation for regression testing is to select a subset of the original test suite running which would suffice to test for bugs probably inserted in the modifications done after the last round of testing. A variant of this problem is that of regression testing of API libraries. The regression testing of an API is usually done by making function calls in such a way that the sequence of function calls thus made suffices a test specification. The test specification in turn embodies some concept of completeness. In this thesis, we focus on the problem of test sequence computation for the regression testing of API libraries. At the heart of this method lies the creation of a state space model of the API library by reverse engineering it by executing the system, with guidance from an formal API specification. Once the state space graph is obtained, it is used to compute test sequences for satisfying some test specification. We analyse the theoretical complexity of the problem of test sequence computation and provide various heuristic algorithms for the same. State space explosion is a classical problem encountered whenever there is an attempt of creating a finite state model of a program. Our method also faces this limitation. We explore a simple and intuitive method of ameliorating this problem – by simply reducing the size of the state vector. We develop the theoretical insights into this method. Also, we present experimental results indicating the practical effectiveness of this method. Finally, we bring all this together into the design and implementation of a tool called Modest.