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Several recent engineering applications in multi-agent systems, communication networks, and machine learning deal with decision problems that can be formulated as optimization problems. For many of these problems, new constraints limit the usefulness of traditional optimization algorithms. In some cases, the problem size is much larger than what can be conveniently dealt with using standard solvers. In other cases, the problems have to be solved in a distributed manner by several decision-makers with limited computational and communication resources. By exploiting problem structure, however, it is possible to design computationally efficient algorithms that satisfy the implementation requirements of these emerging applications. In this thesis, we study a variety of techniques for improving the convergence times of optimization algorithms for large-scale systems. In the first part of the thesis, we focus on multi-step first-order methods. These methods add memory to the classical gradient method and account for past iterates when computing the next one. The result is a computationally lightweight acceleration technique that can yield significant improvements over gradient descent. In particular, we focus on the Heavy-ball method introduced by Polyak. Previous studies have quantified the performance improvements over the gradient through a local convergence analysis of twice continuously differentiable objective functions. However, the convergence properties of the method on more general convex cost functions has not been known. The first contribution of this thesis is a global convergence analysis of the Heavy- ball method for a variety of convex problems whose objective functions are strongly convex and have Lipschitz continuous gradient. The second contribution is to tailor the Heavy- ball method to network optimization problems. In such problems, a collection of decision- makers collaborate to find the decision vector that minimizes the total system cost. We derive the optimal step-sizes for the Heavy-ball method in this scenario, and show how the optimal convergence times depend on the individual cost functions and the structure of the underlying interaction graph. We present three engineering applications where our algorithm significantly outperform the tailor-made state-of-the-art algorithms. In the second part of the thesis, we consider the Alternating Direction Method of Multipliers (ADMM), an alternative powerful method for solving structured optimization problems. The method has recently attracted a large interest from several engineering communities. Despite its popularity, its optimal parameters have been unknown. The third contribution of this thesis is to derive optimal parameters for the ADMM algorithm when applied to quadratic programming problems. Our derivations quantify how the Hessian of the cost functions and constraint matrices affect the convergence times. By exploiting this information, we develop a preconditioning technique that allows to accelerate the performance even further. Numerical studies of model-predictive control problems illustrate significant performance benefits of a well-tuned ADMM algorithm. The fourth and final contribution of the thesis is to extend our results on optimal scaling and parameter tuning of the ADMM method to a distributed setting. We derive optimal algorithm parameters and suggest heuristic methods that can be executed by individual agents using local information. The resulting algorithm is applied to distributed averaging problem and shown to yield substantial performance improvements over the state-of-the-art algorithms. / <p>QC 20150327</p>

This thesis focuses on acoustic and prosodic (fundamental frequency (F0), duration, intensity) analyses of French from large-scale audio corpora portraying different speaking styles: prepared and spontaneous speech. We are interested in particularities of segmental phonetics and prosody that may characterize pronunciation. In French, many errors caused by automatic speech recognition (ASR) systems arise from frequent homophone words, for which ASR systems depend on language model weights. Automatic classification (AC) was conducted to discriminate homophones by only acoustic and prosodic properties depending on their part-of-speech function or their position within prosodic words. Results from AC of two homophone pairs, et/est (and/is) and à/a (ton/has), revealed that the et/est pair was more discriminable. A selection of prosodic and inter-phoneme attributes, that is 15 attributes, performed as good results as with 62 attributes. Then corresponding perceptual tests have been conducted to verify if humans also use acoustico-prosodic parameters for the discrimination. Results suggested that acoustic and prosodic information might help in operating the correct choice in similar ambiguous syntactic structures. From the hypothesis that pronunciation variants were due to varying prosodic constraints, we examined overall prosodic properties of French on a lexical and phrase level. The comparison between lexical and grammatical words revealed F0 rise and lengthening at the end of final syllable on lexical words, while these phenomena were not observed for grammatical words. Analyses also revealed that the mean profile of a n length noun phrase could be different from that of a n length noun with a low F0 at the beginning of a noun phrase. The prosodic profiles can be helpful to locate word boundaries. Findings in this thesis will lead to localize focus and named-entity using discriminative classifiers, and to improve word boundary locations by an ASR post-processing step.

Assimilating real time sensor into a running simulation model can improve simulation results for simulating large-scale spatial temporal systems such as wildfire, road traffic and flood. Particle filters are important methods to support data assimilation. While particle filters can work effectively with sophisticated simulation models, they have high computation cost due to the large number of particles needed in order to converge to the true system state. This is especially true for large-scale spatial temporal simulation systems that have high dimensional state space and high computation cost by themselves. To address the performance issue of particle filter-based data assimilation, this dissertation developed distributed particle filters and applied them to large-scale spatial temporal systems. We first implemented a particle filter-based data assimilation framework and carried out data assimilation to estimate system state and model parameters based on an application of wildfire spread simulation. We then developed advanced particle routing methods in distributed particle filters to route particles among the Processing Units (PUs) after resampling in effective and efficient manners. In particular, for distributed particle filters with centralized resampling, we developed two routing policies named minimal transfer particle routing policy and maximal balance particle routing policy. For distributed PF with decentralized resampling, we developed a hybrid particle routing approach that combines the global routing with the local routing to take advantage of both. The developed routing policies are evaluated from the aspects of communication cost and data assimilation accuracy based on the application of data assimilation for large-scale wildfire spread simulations. Moreover, as cloud computing is gaining more and more popularity; we developed a parallel and distributed particle filter based on Hadoop & MapReduce to support large-scale data assimilation.

This dissertation presents a stochastic framework for modeling the degradation processes of components in complex engineering systems using sensor based signals. Chapters 1 and 2 discuses the challenges and the existing literature in monitoring and predicting the performance of complex engineering systems. Chapter 3 presents the degradation model with the absorbing failure threshold for a single unit and the RLD estimation using the first-passage-time approach. Subsequently, we develop the estimate of the RLD using the first-passage-time approach for two cases: information prior distributions and non-informative prior distributions. A case study is presented using real-world data from rolling elements bearing applications. Chapter 4 presents a stochastic methodology for modeling degradation signals from components functioning under dynamically evolving environmental conditions. We utilize in-situ sensor signals related to the degradation process, as well as the environmental conditions, to predict and continuously update, in real-time, the distribution of a component’s residual lifetime. Two distinct models are presented. The first considers future environmental profiles that evolve in a deterministic manner while the second assumes the environment evolves as a continuous-time Markov chain. Chapters 5 and 6 generalize the failure-dependent models and develop a general model that examines the interactions among the degradation processes of interconnected components/subsystems. In particular, we model how the degradation level of one component affects the degradation rates of other components in the system. Hereafter, we refer to this type of component-to-component interaction caused by their stochastic dependence as degradation-rate-interaction (DRI). Chapter 5 focuses on the scenario in which these changes occur in a discrete manner, whereas, Chapter 6 focuses on the scenario, in which DRIs occur in a continuous manner. We demonstrate that incorporating the effects of component interactions significantly improves the prediction accuracy of RLDs. Finally, we outline the conclusion remarks and a future work plan in Chapter 7.