Thesis (Ph. D.)--University of Washington, 2008. / Vita. Includes bibliographical references (leaves 126-133).

Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Title from PDF title page (viewed Feb. 4, 2010). Additional advisors: Barrett R. Bryant, Chittoor V. Ramamoorthy, Jeffrey H. Kulick, Gary J. Grimes, Gregg L. Vaughn, Murat N. Tanju. Includes bibliographical references (p. 161-183).

Simulation of large physical systems often leads to initial value problems in which some of the solution components contain high frequency oscillations and/or fast transients, while the remaining solution components are relatively slowly varying. Such a system is referred to as two-time-scale (TTS), which is a partial generalization of the concept of stiffness. When using conventional numerical techniques for integration of TTS systems, the rapidly varying components dictate the use of small stepsizes, with the result that the slowly varying components are integrated very inefficiently. This could mean that the computer time required for integration is excessive. To overcome this difficulty, the system is partitioned into "fast" and "slow" subsystems, containing the rapidly and slowly varying components of the solution respectively. Integration is then performed using small stepsizes for the fast subsystem and relatively large stepsizes for the slow subsystem. This is referred to as multirate integration, and it can lead to substantial savings in computer time required for integration of large systems having relatively few fast solution components. This study is devoted to multirate integration of TTS initial value problems which are partitioned into fast and slow subsystems. Techniques for partitioning are not considered here. Multirate integration algorithms based on explicit Runge-Kutta (RK) methods are developed. Such algorithms require a means for communication between the subsystems. Internally embedded RK methods are introduced to aid in computing interpolated values of the slow variables, which are supplied to the fast subsystem. The use of averaging in the fast subsystem is discussed in connection with communication from the fast to the slow subsystem. Theoretical support for this is presented in a special case. A proof of convergence is given for a multirate algorithm based on Euler's method. Absolute stability of this algorithm is also discussed. Four multirate integration routines are presented. Two of these are based on a fixed-step fourth order RK method, and one is based on the variable step Runge-Kutta-Merson scheme. The performance of these routines is compared to that of several other integration schemes, including Gear's method and Hindmarsh's EPISODE package. For this purpose, both linear and nonlinear examples are presented. It is found that multirate techniques show promise for linear systems having eigenvalues near the imaginary axis. Such systems are known to present difficulty for Gear's method and EPISODE. A nonlinear TTS model of an autopilot is presented. The variable step multirate routine is found to be substantially more efficient for this example than any other method tested. Preliminary results are also included for a pressurized water reactor model. Indications are that multirate techniques may prove fruitful for this model. Lastly, an investigation of the effects of the step-size ratio (between subsystems) is included. In addition, several suggestions for further work are given, including the possibility of using multistep methods for integration of the slow subsystem.

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 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.

Thesis (Ph.D.)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Haddad, Wassim; Committee Member: Feron, Eric; Committee Member: JVR, Prasad; Committee Member: Taylor, David; Committee Member: Tsiotras, Panagiotis

Thesis (Ph. D., Information and Computer Science)--University of California, Irvine, 1997. / Includes bibliographical references.

by Michael Athans. / "November 30, 1978." Caption title. / Travel support provided in part by National Science Foundation Grant NSF/ENG77-07777

Avec la complexité croissante des systèmes dynamiques qui apparaissent dans l'ingénierie et d'autres domaines de la science, l'étude des systèmes de grande taille composés d'un ensemble de sous-systèmes interconnectés est devenue un important sujet d'attention dans différents domaines, tels que la robotique, les réseaux de transports, les grandes structures spatiales (panneaux solaires, antennes, télescopes,...), les bâtiments,… et a conduit à des problèmes intéressants d'analyse d'identification paramétrique, de contrôle distribué et d'optimisation. L'absence d'une définition universelle et reconnue des systèmes qu'on appelle "grands systèmes", "systèmes complexes", "systèmes interconnectés",..., témoigne de la confusion entre ces différents concepts et la difficulté de définir des limites précises pour tels systèmes. L'analyse de l'identifiabilité et de l'identification de ces systèmes nécessite le traitement de modèles numériques de grande taille, la gestion de dynamiques diverses au sein du même système et la prise en compte de contraintes structurelles (des interconnections,...). Ceci est très compliqué et très délicat à manipuler. Ainsi, ces analyses sont rarement prises en considération globalement. La simplification du problème par décomposition du grand système en sous-problèmes de complexité réduite est souvent la seule solution possible, conduisant l'automaticien à exploiter clairement la structure du système.Cette thèse présente ainsi, une approche décentralisée d'identification des systèmes de grande taille "large scale systems" composés d'un ensemble de sous-systèmes interconnectés. Cette approche est basée sur les propriétés structurelles (commandabilité, observabilité et identifiabilité) du grand système. Cette approche à caractère méthodologique est mise en œuvre sur des applications thermiques des bâtiments. L'intérêt de cette approche est montré à travers des comparaisons avec une approche globale. / With the increasing complexity of dynamical systems that appear in engineering and other fields of science, the study of large systems consisting of a set of interconnected subsystems has become an important subject of attention in various areas such as robotics, transport networks, large spacial structures (solar panels, antennas, telescopes, \ldots), buildings, … and led to interesting problems of parametric identification analysis, distributed control and optimization. The lack of a universal definition of systems called "large systems", "complex systems", "interconnected systems", ..., demonstrates the confusion between these concepts and the difficulty of defining clear boundaries for such systems. The analysis of the identifiability and identification of these systems requires processing digital models of large scale, the management of diverse dynamics within the same system and the consideration of structural constraints (interconnections, ...) . This is very complicated and very difficult to handle. Thus, these analyzes are rarely taken into consideration globally. Simplifying the problem by decomposing the large system to sub-problems is often the only possible solution. This thesis presents a decentralized approach for the identification of "large scale systems" composed of a set of interconnected subsystems. This approach is based on the structural properties (controllability, observability and identifiability) of the global system. This methodological approach is implemented on thermal applications of buildings. The advantage of this approach is demonstrated through comparisons with a global approach.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22808号 / 情博第738号 / 新制||情||126(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 大塚 敏之, 教授 加納 学, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM