Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Energy storage systems for wave energy converters and microgrids

The thesis initially gives an overview of the wave industry and the current state of some of the leading technologies as well as the energy storage systems that are inherently part of the power take-off mechanism. The benefits of electrical energy storage systems for wave energy converters are then outlined as well as the key parameters required from them. The options for storage systems are investigated and the reasons for examining supercapacitors and lithium-ion batteries in more detail are shown. The thesis then focusses on a particular type of offshore wave energy converter in its analysis, the backward bent duct buoy employing a Wells turbine. Variable speed strategies from the research literature which make use of the energy stored in the turbine inertia are examined for this system, and based on this analysis an appropriate scheme is selected. A supercapacitor power smoothing approach is presented in conjunction with the variable speed strategy. As long component lifetime is a requirement for offshore wave energy converters, a computer-controlled test rig has been built to validate supercapacitor lifetimes to manufacturer’s specifications. The test rig is also utilised to determine the effect of temperature on supercapacitors, and determine application lifetime. Cycle testing is carried out on individual supercapacitors at room temperature, and also at rated temperature utilising a thermal chamber and equipment programmed through the general purpose interface bus by Matlab. Application testing is carried out using time-compressed scaled-power profiles from the model to allow a comparison of lifetime degradation. Further applications of supercapacitors in offshore wave energy converters are then explored. These include start-up of the non-self-starting Wells turbine, and low-voltage ride-through examined to the limits specified in the Irish grid code for wind turbines. These applications are investigated with a more complete model of the system that includes a detailed back-to-back converter coupling a permanent magnet synchronous generator to the grid. Supercapacitors have been utilised in combination with battery systems for many applications to aid with peak power requirements and have been shown to improve the performance of these energy storage systems. The design, implementation, and construction of coupling a 5 kW h lithium-ion battery to a microgrid are described. The high voltage battery employed a continuous power rating of 10 kW and was designed for the future EV market with a controller area network interface. This build gives a general insight to some of the engineering, planning, safety, and cost requirements of implementing a high power energy storage system near or on an offshore device for interface to a microgrid or grid.

Artefact detection and removal algorithms for EEG diagnostic systems

The electroencephalogram (EEG) is a medical technology that is used in the monitoring of the brain and in the diagnosis of many neurological illnesses. Although coarse in its precision, the EEG is a non-invasive tool that requires minimal set-up times, and is suitably unobtrusive and mobile to allow continuous monitoring of the patient, either in clinical or domestic environments. Consequently, the EEG is the current tool-of-choice with which to continuously monitor the brain where temporal resolution, ease-of- use and mobility are important. Traditionally, EEG data are examined by a trained clinician who identifies neurological events of interest. However, recent advances in signal processing and machine learning techniques have allowed the automated detection of neurological events for many medical applications. In doing so, the burden of work on the clinician has been significantly reduced, improving the response time to illness, and allowing the relevant medical treatment to be administered within minutes rather than hours. However, as typical EEG signals are of the order of microvolts (μV ), contamination by signals arising from sources other than the brain is frequent. These extra-cerebral sources, known as artefacts, can significantly distort the EEG signal, making its interpretation difficult, and can dramatically disimprove automatic neurological event detection classification performance. This thesis therefore, contributes to the further improvement of auto- mated neurological event detection systems, by identifying some of the major obstacles in deploying these EEG systems in ambulatory and clinical environments so that the EEG technologies can emerge from the laboratory towards real-world settings, where they can have a real-impact on the lives of patients. In this context, the thesis tackles three major problems in EEG monitoring, namely: (i) the problem of head-movement artefacts in ambulatory EEG, (ii) the high numbers of false detections in state-of-the-art, automated, epileptiform activity detection systems and (iii) false detections in state-of-the-art, automated neonatal seizure detection systems. To accomplish this, the thesis employs a wide range of statistical, signal processing and machine learning techniques drawn from mathematics, engineering and computer science. The first body of work outlined in this thesis proposes a system to automatically detect head-movement artefacts in ambulatory EEG and utilises supervised machine learning classifiers to do so. The resulting head-movement artefact detection system is the first of its kind and offers accurate detection of head-movement artefacts in ambulatory EEG. Subsequently, addtional physiological signals, in the form of gyroscopes, are used to detect head-movements and in doing so, bring additional information to the head- movement artefact detection task. A framework for combining EEG and gyroscope signals is then developed, offering improved head-movement arte- fact detection. The artefact detection methods developed for ambulatory EEG are subsequently adapted for use in an automated epileptiform activity detection system. Information from support vector machines classifiers used to detect epileptiform activity is fused with information from artefact-specific detection classifiers in order to significantly reduce the number of false detections in the epileptiform activity detection system. By this means, epileptiform activity detection which compares favourably with other state-of-the-art systems is achieved. Finally, the problem of false detections in automated neonatal seizure detection is approached in an alternative manner; blind source separation techniques, complimented with information from additional physiological signals are used to remove respiration artefact from the EEG. In utilising these methods, some encouraging advances have been made in detecting and removing respiration artefacts from the neonatal EEG, and in doing so, the performance of the underlying diagnostic technology is improved, bringing its deployment in the real-world, clinical domain one step closer.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Achieving continuous professional development in higher education

Traditional higher education technology emphasizes knowledge transmission. In contrast, the Community platform presented in this paper follows a social approach that interleaves knowledge delivery with social and professional skills development, engaging with others, and personal growth. In this paper, we apply learning and complex adaptive systems theory to motivate and justify a continuous professional development model that improves higher education outcomes such as placement. The paper follows action design research (ADR) as the research method to propose and evaluate design principles.