A New wavelet tool to quantify non-periodicity of non-stationary economic time series

We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy

Condition Monitoring of Gas Turbines using Acoustic Emissions

Acoustic emission (AE) technology has recently found its way in condition monitoring of rotary equipment due to its advantage of earlier detection of defects and anoma- lies in comparison to vibration analysis. However, there has been very little industrial application of AE signals for condition monitoring of safety-critical equipment if any, partly due to the diffculty in processing, interpreting and classifying the acquired data in a highly reliable fashion. The motivation in this thesis was to develop a methodol- ogy for inferring health related information in a gas turbine without intruding the engine. Our work has targeted a broad class of rotary equipment known as cyclostationary processes, therefore, instead of analyzing particular AE samples of gas turbines we have tried to build a mathematical framework that would suit any arbitrary machine comply- ing certain conditions. The result of our work mainly encompasses a feature extraction technique that eliminates the random e↵ects associated with a gas turbine AE signal, and a hypothetical testing method for classification of AE signals with any desirable level of certainty, subject to a set of assumptions and conditions. We have validated our methodologies and derivations using actual real-life gas turbine AE signals, and compared our solutions with some of the techniques published in the literature

KurSL: a model of coupled oscillators based on Kuramoto's coupling and Sturm-Liouville theory

Methods commonly used to analyse oscillatory systems, such as short-time Fourier or wavelet transforms, require predefined oscillatory structures or ne-tuning of method's parameters. These limitations may be detrimental for an adequate component description and can introduce bias to the interpretation. This thesis addresses the challenge of identifying interacting components in a signal by introducing a model of coupled oscillators. The proposed model consists of two parts: Sturm-Liouville self-adjoint ordinary differential equation (ODE) and Kuramoto's coupling model. The resulting model, KurSL, is described by a set of coupled ODEs producing general amplitude- and frequency-modulated mutually interacting oscillations. The complexity of these equations depends on the definition of the coupling function, the number of oscillators and the initial state of each oscillator. Thus, the performance of the KurSL decomposition can be characterised in terms of the model parameters optimisation. After introducing the model, the thesis provides analysis and discussion of the KurSL with examples of its usage. The method is firstly tested on various synthetic data that were generated from simulated stationary and dynamical processes. Such testing allows capturing various characteristics that are desirable in coupled oscillatory components such as phase and amplitude dynamics. Subsequently, experiments were performed on empirical EEG signals recorded from patients with epilepsy. Validation of these experiments is through comparisons to different orders of the KurSL and to other time-frequency methods. Overall results indicate that the KurSL method provides a more detailed description of oscillatory processes than the Huang-Hilbert transform and it provides insights comparable to manually tuned short-time Fourier transform and Morlet-based wavelet time-frequency representations. However, the advantage of the KurSL is that the similar results can be achieved with a finite number of components. Moreover, in contrast to the mentioned representations which, due to finite resolution, are unable to localise time-frequency events precisely, the KurSL provides an instantaneous description. This exactness allows to identify any modulations in both time and frequency domains and thus better describe the behaviour of the analysed system

Computational Intelligence in Electromyography Analysis

Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles. EMG may be used clinically for the diagnosis of neuromuscular problems and for assessing biomechanical and motor control deficits and other functional disorders. Furthermore, it can be used as a control signal for interfacing with orthotic and/or prosthetic devices or other rehabilitation assists. This book presents an updated overview of signal processing applications and recent developments in EMG from a number of diverse aspects and various applications in clinical and experimental research. It will provide readers with a detailed introduction to EMG signal processing techniques and applications, while presenting several new results and explanation of existing algorithms. This book is organized into 18 chapters, covering the current theoretical and practical approaches of EMG research

Hilbert-Huang Transform: biosignal analysis and practical implementation

Any system, however trivial, is subjected to data analysis on the signals it produces. Over the last 50 years the influx of new techniques and expansions of older ones have allowed a number of new applications, in a variety of fields, to be analysed and to some degree understood. One of the industries that is benefiting from this growth is the medical field and has been further progressed with the growth of interdisciplinary collaboration. From a signal processing perspective, the challenge comes from the complex and sometimes chaotic nature of the signals that we measure from the body, such as those from the brain and to some degree the heart. In this work we will make a contribution to dealing with such systems, in the form of a recent time-frequency data analysis method, the Hilbert-Huang Transform (HHT), and extensions to it. This thesis presents an analysis of the state of the art in seizure and heart arrhythmia detection and prediction methods. We then present a novel real-time implementation of the algorithm both in software and hardware and the motivations for doing so. First, we present our software implementation, encompassing realtime capabilities and identifying elements that need to be considered for practical use. We then translated this software into hardware to aid real-time implementation and integration. With these implementations in place we apply the HHT method to the topic of epilepsy (seizures) and additionally make contributions to heart arrhythmias and neonate brain dynamics. We use the HHT and some additional algorithms to quantify features associated with each application for detection and prediction. We also quantify significance of activity in such a way as to merge prediction and detection into one framework. Finally, we assess the real-time capabilities of our methods for practical use as a biosignal analysis tool

Guided Matching Pursuit and its Application to Sound Source Separation

In the last couple of decades there has been an increasing interest in the application of source separation technologies to musical signal processing. Given a signal that consists of a mixture of musical sources, source separation aims at extracting and/or isolating the signals that correspond to the original sources. A system capable of high quality source separation could be an invaluable tool for the sound engineer as well as the end user. Applications of source separation include, but are not limited to, remixing, up-mixing, spatial re-configuration, individual source modification such as filtering, pitch detection/correction and time stretching, music transcription, voice recognition and source-specific audio coding to name a few. Of particular interest is the problem of separating sources from a mixture comprising two channels (2.0 format) since this is still the most commonly used format in the music industry and most domestic listening environments. When the number of sources is greater than the number of mixtures (which is usually the case with stereophonic recordings) then the problem of source separation becomes under-determined and traditional source separation techniques, such as “Independent Component Analysis” (ICA) cannot be successfully applied. In such cases a family of techniques known as “Sparse Component Analysis” (SCA) are better suited. In short a mixture signal is decomposed into a new domain were the individual sources are sparsely represented which implies that their corresponding coefficients will have disjoint (or almost) disjoint supports. Taking advantage of this property along with the spatial information within the mixture and other prior information that could be available, it is possible to identify the sources in the new domain and separate them by going back to the time domain. It is a fact that sparse representations lead to higher quality separation. Regardless, the most commonly used front-end for a SCA system is the ubiquitous short-time Fourier transform (STFT) which although is a sparsifying transform it is not the best choice for this job. A better alternative is the matching pursuit (MP) decomposition. MP is an iterative algorithm that decomposes a signal into a set of elementary waveforms called atoms chosen from an over-complete dictionary in such a way so that they represent the inherent signal structures. A crucial part of MP is the creation of the dictionary which directly affects the results of the decomposition and subsequently the quality of source separation. Selecting an appropriate dictionary could prove a difficult task and an adaptive approach would be appropriate. This work proposes a new MP variant termed guided matching pursuit (GMP) which adds a new pre-processing step into the main sequence of the MP algorithm. The purpose of this step is to perform an analysis of the signal and extract important features, termed guide maps, that are used to create dynamic mini-dictionaries comprising atoms which are expected to correlate well with the underlying signal structures thus leading to focused and more efficient searches around particular supports of the signal. This algorithm is accompanied by a modular and highly flexible MATLAB implementation which is suited to the processing of long duration audio signals. Finally the new algorithm is applied to the source separation of two-channel linear instantaneous mixtures and preliminary testing demonstrates that the performance of GMP is on par with the performance of state of the art systems