Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2007. / Jiangang Dai, Committee Co-Chair ; Amy Ward, Committee Co-Chair ; Anton Kleywegt, Committee Member ; Ron Billings, Committee Member ; Mor Armony, Committee Member.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion. / Science, Faculty of / Computer Science, Department of / Graduate

The matrix cracking transverse to loading direction is usually one of the most common observations of damages in composite laminates. The initiation and propagation of transverse cracks have been a longstanding issue in the last few decades. In this paper, a three-dimensional stress analysis method based on the state space approach is used to compute the stresses, including the inter-laminar stresses near transverse cracks in laminated composites. The stress field is then used to estimate the energy release rate, from which the initiation and propagation of transverse cracking are predicted. The proposed method is illustrated by numerical solutions and is validated by available experimental results. To the best knowledge of the authors, the predictions of crack behaviour for non-symmetrical laminates and laminates subject to in-plane shearing are presented for the first time in the literature.

<p>Latent variable models are widely used in modern data science for both statistic and dynamic data. This thesis focuses on large-scale latent variable models formulated for time series data and static network data. The former refers to the state space model for dynamic systems, which models the evolution of latent state variables and the relationship between the latent state variables and observations. The latter refers to a network decoder model, which map a large network into a low-dimensional space of latent embedding vectors. Both problems can be solved by adaptive stochastic gradient Markov chain Monte Carlo (MCMC), which allows us to simulate the latent variables and estimate the model parameters in a simultaneous manner and thus facilitates the down-stream statistical inference from the data. </p> <p><br></p> <p>For the state space model, its challenge is on inference for high-dimensional, large scale and long series data. The existing algorithms, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the dataset, and often suffers from the sample degeneracy issue for long series data. To address the issue, the thesis proposes the stochastic approximation Langevinized ensemble Kalman filter (SA-LEnKF) for jointly estimating the states and unknown parameters of the dynamic system, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation MCMC. Under mild conditions, we prove its consistency in parameter estimation and ergodicity in state variable simulations. The proposed algorithm can be used in uncertainty quantification for long series, large scale, and high-dimensional dynamic systems. Numerical results on simulated datasets and large real-world datasets indicate its superiority over the existing algorithms, and its great potential in statistical analysis of complex dynamic systems encountered in modern data science. </p> <p><br></p> <p>For the network embedding problem, an appropriate embedding dimension is hard to determine under the theoretical framework of the existing methods, where the embedding dimension is often considered as a tunable hyperparameter or a choice of common practice. The thesis proposes a novel network embedding method with a built-in mechanism for embedding dimension selection. The basic idea is to treat the embedding vectors as the latent inputs for a deep neural network (DNN) model. Then by an adaptive stochastic gradient MCMC algorithm, we can simulate of the embedding vectors and estimate the parameters of the DNN model in a simultaneous manner. By the theory of sparse deep learning, the embedding dimension can be determined via imposing an appropriate sparsity penalty on the DNN model. Experiments on real-world networks show that our method can perform dimension selection in network embedding and meanwhile preserve network structures. </p> <p><br></p>

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Linking the structure of a system with its dynamics is an important problem in the theory of finite dynamical systems. For monomial dynamical systems, that is, a system that can be described by monomials, information about the limit cycles can be obtained from the monomials themselves. In particular, this work contains sufficient and necessary conditions for a monomial dynamical system to have only fixed points as limit cycles. / Ph. D.

A typical approach to the synthesis/design optimization of energy systems is to only use steady state operation and high efficiency (or low total life cycle cost) at full load as the basis for the synthesis/design. Transient operation is a secondary task to be solved by system and control engineers once the synthesis/design is fixed. This thesis considers the system dynamics in the process of developing the system using a set of transient thermodynamic, kinetic, and geometric as well as physical and cost models developed and implemented for the components of a 5 kW PEMFC (Proton Exchange Membrane Fuel Cell) system. The system is composed of three subsystems: a stack subsystem (SS), a fuel processing subsystem (FPS), and a work recovery and air supply subsystem (WRAS). To study the effect of control to the optimization, State Space control design is used in a looped set of optimizations. These results are compared to those resulting from a more direct optimization of the controller designs in which the gains for the controllers are part of the decision variable set for the overall optimization. Then, dynamic optimization results are obtained and compared with steady-state optimization results to illustrate the advantages of dynamic optimization. Also, a multi-level optimization technique, dynamic iterative local-global optimization (DILGO), is utilized for the optimization of the PEMFC system by separating the system into three subsystems and the results are compared with the single level optimization results, in which the whole system is optimized together. / Ph. D.

This thesis aims towards devising a non-destructive testing methodology for ICs fabricated by a third party manufacturer to ensure the integrity of the chip. With the growing trend of outsourcing, the sanity of the final product has emerged to be a prime concern for the end user. This is especially so if the components are to be used in mission-critical applications such as space-exploration, medical diagnosis and treatment, defense equipment such as missiles etc., where a single failure can lead to a disaster. Thus, any extraneous parts (Trojans) that might have been implanted by the third party manufacturer with a malicious intent during the fabrication process must be diagnosed before the component is put to use. The inherent stealthy nature of Trojans makes it difficult to detect them at normal IC outputs. More so, with the restriction that one cannot visually inspect the internals of an IC after it has been manufactured. This obviates the use of side-channel signal(s) that acts like a signature of the IC as a means to assess its internal behavior under operational conditions. In this work, we have selected power as the side-channel signal to characterize the internal behavior of the ICs. We have used two circuit partitioning based approaches for isolating and enhancing the behavioral difference between parts of a genuine IC and one with a sequence detector Trojan in it. Experimental results reveal that these approaches are effective in exposing anomalous behavior between the targeted ICs. This is reflected as difference in power-profiles of the genuine and maligned ICs that is magnified above the process variation ensuring that the discrepancies are observable. / Master of Science