Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2009 / Traditional high voltage power transformers feature sensors measuring basic parameters from oil and gas and are limited to on-site monitoring. Unforeseen failures and breakdowns on these transformers have led to extensive financial losses even with planned maintenance schedules in place. A distinct need has arisen to actively monitor and identify causes of such failures. However, no or little infrastructure exists for effective remote condition monitoring. Wireless sensor networks can be introduced to actively monitor and identify causes of such failures. Sensor motes in the network are battery operated and therefore constrained by limited energy in these batteries. An alternative to battery-powered sensor motes is the conversion of available energy harvested from the surrounding environment into useable electrical energy powering the sensor motes. The primary objective of this research was to examine methods to harvest energy from both the environment and high voltage power transformer. A low cost and feasibly sized hybrid energy harvesting power management prototype was successfully developed that enabled sustained sensor mote operation for prolonged condition monitoring of high voltage transformers. The sensor mote utilised a piezoelectric cantilever to generate usable electrical energy from the transformer tank vibration. Together with solar energy harvesting, the system allowed for a battery-less self-sustained wireless sensor mote capable of autonomously monitoring its surroundings. The power management system's modular architecture provided for the inclusion of additional energy harvesting techniques. This allowed condition monitoring solutions not exclusively for power transformers but proposed an extensible condition monitoring solution for various applications.

A hybrid dynamical system is a mathematical model for a part of the real world where discrete and continuous parts interact with each other. Typically such systems are complex, and it is difficult to know how they will behave for general parameters and initial conditions. However, the method of formal verification gives us the ability to prove automatically that certain behaviour does or does not happen for a range of parameters in a system. The challenge is then to define suitable methods for proving properties on hybrid systems.This thesis looks at using formal verification for proving liveness properties on hybrid systems: a liveness property says that something good eventually happens in the system. This work presents the theoretical background and practical application of various methods for proving and disproving inevitability properties (a type of liveness) in different classes of hybrid systems. The methods combine knowledge of dynamical behaviour of a system with the brute-force approach of model checking, in order to make the most of the benefits of both sides. The work on proving liveness properties is based on abstraction of dynamical systems to timed automata. This thesis explores the limits of a pre-defined abstraction method, adds some dynamical knowledge to the method, and shows that this improvement makes liveness properties provable in certain continuous dynamical systems. The limits are then pushed further to see how this method can be used for piecewise-continuous dynamical systems. The resulting algorithms are implemented for both classes of systems.In order to disprove liveness properties in hybrid systems a novel framework is proposed, using a new property called deadness. Deadness is a dynamically-aware property of the hybrid system which, if true, disproves the liveness property by means of a finite execution: we usually require an infinite execution to disprove a liveness property. An algorithm is proposed which uses dynamical properties of hybrid systems to derive deadness properties automatically, and the implementation of this algorithm is discussed and applied to a simplified model of an oilwell drillstring.

This dissertation provides a complete mathematical framework to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Differential Equation (ODE) and rank 1 and 3 Differential Algebraic Equation (DAE) systems. The hybrid system is characterized by discontinuities in the velocity state variables due to an impulsive forces at the time of event. At the time of event, such system may also exhibit a change in the equations of motion or in the kinematic constraints. The analytical methodology that solves the sensitivities for hybrid systems is structured based on jumping conditions for both, the velocity state variables and the sensitivities matrix. The proposed analytical approach is then benchmarked against a known numerical method. The mathematical framework is extended to compute sensitivities of the states of the model and of the general cost functionals with respect to model parameters for both, unconstrained and constrained, hybrid mechanical systems. This dissertation emphasizes the penalty formulation for modeling constrained mechanical systems since this formalism has the advantage that it incorporates the kinematic constraints inside the equation of motion, thus easing the numerical integration, works well with redundant constraints, and avoids kinematic bifurcations. In addition, this dissertation provides a unified mathematical framework for performing the direct and the adjoint sensitivity analysis for general hybrid systems associated with general cost functions. The mathematical framework computes the jump sensitivity matrix of the direct sensitivities which is found by computing the Jacobian of the jump conditions with respect to sensitivities right before the event. The main idea is then to obtain the transpose of the jump sensitivity matrix to compute the jump conditions for the adjoint sensitivities. Finally, the methodology developed obtains the sensitivity matrix of cost functions with respect to parameters for general hybrid ODE systems. Such matrix is a key result for design analysis as it provides the parameters that affect the given cost functions the most. Such results could be applied to gradient based algorithms, control optimization, implicit time integration methods, deep learning, etc. / Ph. D.

Following results over recent years, this thesis enhances the problem of minimizing a cost functional defined on a state trajectory of an autonomous switched dynamical system. The cost functional traditionally used, is augmented with explicit costs on the switching times and the final time is set by a constraint as opposed to being given. An equation for the gradient of the cost functional is derived and an algorithm is proposed for computing local minima. The algorithm is based on existing steepest descent methods including the Armijo procedure and gradient projection. A matlab implementation of the algorithm is developed in order to solve optimal problems that can be modelled with costs on or between the switching times. An existing problem, the motivation for this research, where repairs on a bridge is to be optimized, is provided and solved.

Le but de la Nano- Opto- Mécanique et Electronic à base de graphène est d'utiliser des membranes de graphène en suspension comme blocs de construction pour aborder le couplage entre l'optique, la mécanique et l'électronique dans ce nouveau matériau. Avec un module d'Young similaire à celui du diamant (1 TPA), le graphène est une membrane extrêmement rigide, légère et mince (epaaisseur de seulement un atome) qui peut supporter son propre poids sans effondrement ou la rupture lorsqu'il est suspendu. Ces membranes, intégrées dans des dispositifs mécaniques, peuvent être actionnés à partir de DC jusqu'à des fréquences de vibration mécaniques très élevées (GHz). En outre, le graphène est un gaz d'électrons 2D exposé pour lequel une porte électrostatique tunes considérablement la densité de porteurs de charge et ses propriétés optiques. Last but not least, il offre une architecture unique pour effectuer la fonctionnalisation physico-chimiques et obtenir des matériaux hybrides combinant les propriétés particulières des espèces chimisorbées avec ceux du graphène. / The aim of the Graphene Nano- Opto- Mechanics and Electronics is to use suspended graphene membranes as building blocks to address the coupling of optics, mechanics and electronics in this novel material. With a Young modulus similar to that of diamond (1 TPa), graphene is an extremely stiff, light and atomically thin membrane that can withstand its own weight without collapsing or breaking when suspended. Such membranes, integrated as mechanical devices, can be actuated from DC up to very high mechanical vibration frequencies (GHz). Moreover, graphene is an exposed 2D electron gas for which an electrostatic gate dramatically tunes the charge carrier density and its optical properties. Last but not least, it provides a unique architecture to perform physico-chemical functionalization and obtain hybrid materials combining the peculiar properties of adsorbed and chemisorbed species with the graphene ones.

Hybrid systems for analyzing big data integrate an analytic tool and a dedicated data-management platform, storing data and operating on the data at both components. While hybrid systems have benefits over alternative architectures, in order to be effective, data movement between the two hybrid components must be minimized. Extant hybrid systems either fail to address performance problems stemming from inter-component data movement, or else require the user to explicitly reason about and manage data movement. My work presents the design, implementation, and evaluation of a hybrid analytic system for array-structured data that automatically minimizes data movement between the hybrid components. The proposed research first motivates the need for automatic data-movement minimization in hybrid systems, demonstrating that under workloads whose inputs vary in size, shape, and location, automation is the only practical way to reduce data movement. I then present a prototype hybrid system that automatically minimizes data movement. The exposition includes salient contributions to the research area, including a partial semantic mapping between hybrid components, the adaptation of rewrite-based query transformation techniques to minimize data movement in array-modeled hybrid systems, and empirical evaluation of the approach's utility. Experimental results not only illustrate the hybrid system's overall effectiveness in minimizing data movement, but also illuminate contributions made by various elements of the design.

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During the past three years the Institute for Fluid Power Drives and Controls in Aachen has developed a new hydraulic system for mobile machinery called STEAM. The system represents a new step in excavator hydraulics, as it aims to reduce both the hydraulic system losses as well as those of the internal combustion engine by using a hybrid hydraulic architecture with accumulators. Starting with initial simulation studies the development has been followed by scaled test bench measurements and has progressed to a full scale validation using an 18 t excavator. The following publication aims to summarise the results obtained thus far with the aim of making them available to industry and encouraging their implementation in future applications.

This thesis is devoted to the analysis of problems that arise when long products of matrices taken in a given set are constructed. A typical application is the stability of switched linear systems. The stability of a discrete-time linear system is a classical engineering problem that has been well understood for long: the dynamics can be expressed in terms of the eigenvalues of the matrix ruling the system. A more complicated problem arises when the dynamical system can switch, that is, if the matrix changes over time. If this matrix is taken from a given set but can be chosen arbitrarily in this set at every time, the stability problem turns to the computation of a quantity, the joint spectral radius of the set of matrices, introduced in the early sixties. While this quantity appears to be hard to compute, it has acquired more and more importance during the last decades, and new applications of the joint spectral radius in engineering or mathematics are frequently discovered. It has for instance been proved useful for the analysis of regularity of fractals, for the continuity of wavelets, or for autonomous agents detection in sensor networks. In the first part of this thesis, we present a theoretical survey of the joint spectral radius, including old and new results. The joint spectral subradius, which is its stabilizability counterpart, is also considered. In a second part, we study some applications related to long products of matrices. We first analyse in detail a problem in coding theory, that has been recently shown to involve a joint spectral radius computation. We then propose a new application of the joint spectral radius (and related quantities) to a classical problem in number theory, namely the counting of overlap-free words. We then turn to problems related with autonomous agents detection: we analyse the trackability of sensor networks, and introduce and analyse a new notion, namely the observability of sensor networks.