The High Resolution Electrocardiogram (HRECG) is used to detect Ventricular Late Potentials (VLPs) in post-myocardial infarction patients. VLPs are low-amplitude, high-frequency signals that are usually found within the terminal part of the QRS complex. The aim of this research was to develop possible alternative methods and improve existing methods of detecting VLP activity. There are two main topics in this work: applications of the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT) to the HRECG. For the CWT application, a Fractionation Factor (FF) method proposed by previous work was further investigated and improved by combining the CWT and DWT for distinction between patients with and those without VLPs. A Differential Fractionation Factor was proposed as an alternative approach to the FF with better results. Observation in the time-scale plot showed a difference in the energy distribution. A 2-dimensional Fractionation Factor was proposed to quantify this difference. A new concept of local intermittency was investigated to exhibit energy nonuniformity and then a Local Intermittency Factor was developed to quantify the degree of nonuniformity. The energy computed with the CWT was also used for patient distinction. Patients with VLPs may be also characterised by a slow rate of energy decay. The CWT can reveal a difference in ECG irregularity between the patients. A new approach of approximate entropy was implemented to quantify this irregularity. For the DWT application, the DWT can reveal irregularity of VLP activity and it was quantified by the approximate entropy to identify patients with VLPs. The wavelet entropy was utilised as an alternative method to the FF. The energy computed with the DWT was used for patient classification. The potentially promising results of both the CWT and DWT applications were obtained from the methods of computing the energy and approximate entropy

The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.

The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.

The safety of pipelines distributed in the infrastructure of many industries has become very important since the industrial revolution. The guided ultrasonic wave technique can provide the possibility for rapid screening in long pipelines with corrosion. Especially the torsional mode T(0,1) of guided waves has been used in the cases of the pipe in the hidden region substantially. The ability of evaluating the inaccessible areas of the pipe makes the guided ultrasonic wave technique sit high on the roster of non-destructive testing tool for pipe inspection. However, the problem arises when attempting to detect the corrosions at the welded support bracket or under the bitumen coating on the pipe. The signal reflected from the corrosion will be covered by a large signal induced by the welded support or attenuated by the bitumen coating seriously. Therefore, the effects of welded support and bitumen coating on the T(0,1) mode are investigated by the experimental and the simulative methods. The continuous wavelet transform analysis is the signal processing method to extract the hidden signal of corrosion in this dissertation. There are five test pipes in the experiments. The response of the normal welded support is studied on the #1 test pipe. The #2 test pipe is used for attenuation investigation. The reflected signals of the features on the #3, #4, and #5 test pipes are measured and processed by continuous wavelet transform during defect detection process. In addition, the linear hexahedron elements are used to build the finite element models of the 6-inch steel pipe with support bracket and the pipe with bitumen coating. It is found that the effects of support bracket on the reflection comprise mode conversion, delayed appearance, trailing echoes, and frequency dependent behavior. When the T(0,1) mode impinges on to the support bracket, it will convert into the A0 mode inside the support due to the circumferential disturbance on the pipe surface. The reflection of the support bracket is identified as three parts formed by the direct echo, delayed echo and the trailing echo. The constructive interference of the A0 mode reflecting from the boundaries inside the support causes that the reflection spectrum shows two maxima peak at around 20-22 kHz (frequency regime of 0.0) and 32-34 kHz (frequency regime of 4.0) from both the experimental and simulated results. For the bitumen coating, the data collected from the welds and defects under the bitumen coating on the #2 test pipe show the attenuation effect on guided wave propagation and the difficulty of minor corrosion detection. In the finite element model of coated pipe, the results of predicted attenuation curves of T(0,1) mode indicate that the attenuation effect on guided wave propagation is aggravated with the increased value of the thickness, density or damping factor of the coated layer. Especially, in the case of 5-mm, the predicted attenuation curve shows a maximum point. Before this point, the attenuation increases with the operating frequency. For long range pipe inspection, it is the best way to avoid choosing the operating frequency around the corresponding frequency of the point. The measured data of corrosion affected by the welded support or the coated bitumen layer was processed by continuous wavelet transform to form a time-frequency analysis. The corrosion signals were identified in the contour map of the wavelet coefficient successfully. The understanding of the guided wave propagation on the pipe welded with support or pipe coated with bitumen is helpful to interpret the reflected signals. The use of continuous wavelet transform on signal processing techniques can improve the ability of defect detection on pipe with complex geometries.

This thesis proposes a bearing condition monitoring system using acceleration and acoustic emission (AE) signals. Bearings are perhaps the most omnipresent machine elements and their condition is often critical to the success of an operation or process. Consequently, there is a great need for a timely knowledge of the health status of bearings. Generally, bearing monitoring is the prediction of the component's health or status based on signal detection, processing and classification in order to identify the causes of the problem. As the monitoring system uses both acceleration and acoustic emission signals, it is considered a multi-sensor system. This has the advantage that not only do the two sensors provide increased reliability they also permit a larger range of rotating speeds to be monitored successfully. When more than one sensor is used, if one fails to work properly the other is still able to provide adequate monitoring. Vibration techniques are suitable for higher rotating speeds whilst acoustic emission techniques for low rotating speeds. Vibration techniques investigated in this research concern the use of the continuous wavelet transform (CWT), a joint time- and frequency domain method, This gives a more accurate representation of the vibration phenomenon than either time-domain analysis or frequency- domain analysis. The image processing technique, called binarising, is performed to produce binary image from the CWT transformed image in order to reduce computational time for classification. The back-propagation neural network (BPNN) is used for classification. The AE monitoring techniques investigated can be categorised, based on the features used, into: 1) the traditional AE parameters of energy, event duration and peak amplitude and 2) the statistical parameters estimated from the Weibull distribution of the inter-arrival times of AE events in what is called the STL method. Traditional AE parameters of peak amplitude, energy and event duration are extracted from individual AE events. These events are then ordered, selected and normalised before the selected events are displayed in a three-dimensional Cartesian feature space in terms of the three AE parameters as axes. The fuzzy C-mean clustering technique is used to establish the cluster centres as signatures for different machine conditions. A minimum distance classifier is then used to classify incoming AE events into the different machine conditions. The novel STL method is based on the detection of inter-arrival times of successive AE events. These inter-arrival times follow a Weibull distribution. The method provides two parameters: STL and L63 that are derived from the estimated Weibull parameters of the distribution's shape (y), characteristic life (0) and guaranteed life (to). It is found that STL and 43 are related hyperbolically. In addition, the STL value is found to be sensitive to bearing wear, the load applied to the bearing and the bearing rotating speed. Of the three influencing factors, bearing wear has the strongest influence on STL and L63. For the proposed bearing condition monitoring system to work, the effects of load and speed on STL need to be compensated. These issues are resolved satisfactorily in the project.

This thesis focused on developing a new wavelet for use with the continuous wavelet transform, a new detection method and two de-noising algorithms for rolling element bearing fault signals. The work is based on the continuous wavelet transform and implements a unique Fourier Series estimation algorithm that allows for least squares estimation of arbitrary frequency components of a signal. The final results of the research also included use of the developed detection algorithm for a novel method of estimating the center frequency and bandwidth for use with the industry standard detection algorithm, envelope demodulation, based on actual fault data. Finally, the algorithms and wavelets developed in this paper were tested against seven other wavelet based de-noising algorithms and shown to be superior for the de-noising and detection of inner and outer rolling element race faults.

Increased pressure on high voltage power distribution components has been created in recent years by a demand to lower costs and extend equipment lifetimes. This has led to a need for condition based maintenance, which requires a continuous knowledge of equipment health. Power transformers are a vital component in a power distribution network. However, there are currently no established techniques to accurately monitor and diagnose faults in real-time while the transformer is on-line. A major factor in the degradation of power transformer insulation is partial discharging. Left unattended, partial discharges (PDs) will eventually cause complete insulation failure. PDs generate a variety of signals, including electrical pulses that travel through the windings of the transformer to the terminals. A difficulty with detecting these pulses in an on-line environment is that they can be masked by external electrical interference. This thesis develops a method for identifying PD pulses and determining the number of PD sources while the transformer is on-line and subject to external interference. The partial discharge detection system (PDDS) acquires electrical signals with current and voltage transducers that are placed on the transformer bushings, making it unnecessary to disconnect or open the transformer. These signals are filtered to prevent aliasing and to attenuate the power frequency, and then digitised and analysed in Matlab, a numerical processing software package. Arbitrary narrowband interference is removed with an automated Fourier domain threshold filter. Internal PD pulses are separated from stochastic wideband pulse interference using directional coupling, which is a technique that simultaneously analyses the current and voltage signals from a bushing. To improve performance of this stage, the continuous wavelet transform is used to discriminate time and frequency information. This provides the additional advantage of preserving the waveshapes of the PD pulses for later analysis. PD pulses originating within the transformer have their waveshapes distorted when travelling though the windings. The differentiation of waveshape distortion of pulses from multiple physical sources is used as an input to a neural network to group pulses from the same source. This allows phase resolved PD analysis to be presented for each PD source, for instance, as phase/magnitude/count plots. The neural network requires no prior knowledge of the transformer or pulse waveshapes. The thesis begins with a review of current techniques and trends for power transformer monitoring and diagnosis. The description of transducers and filters is followed by an explanation of each of the signal processing steps. Two transformers were used to conduct testing of the PDDS. The first transformer was opened and modified so that internal PDs could be simulated by injecting artificial pulses. Two test scenarios were created and the performance of the PDDS was recorded. The PDDS identified and extracted a high rate of simulated PDs and correctly allocated the pulses into PD source groups. A second identically constructed transformer was energised and analysed for any natural PDs while external interference was present. It was found to have a significant natural PD source.

This thesis deals with analysis of dynamic forces and vibrations created during cutting with saw. The analysis is done on both simulation and experimental level. Acquired signals are evaluated with signal tools as STFT, CWT and DWT.

The use of ultra-wideband (UWB) signals holds great promise for remote monitoring of vital-signs which has applications in the medical, for first responder and in security. Previous research has shown the feasibility of a UWB-based radar system for respiratory and heartbeat rate estimation. Some simulation and real experimental results are presented to demonstrate the capability of the respiration rate detection. However, past analysis are mostly based upon the assumption of an ideal experiment environment. The accuracy of the estimation and interference factors of this technology has not been investigated. This thesis establishes an analytical framework for the FFT-based signal processing algorithms to detect periodic bio-signals from a single target. Based on both simulation and experimental data, three basic challenges are identified: (1) Small body movement during the measurement interval results in slow variations in the consecutive received waveforms which mask the signals of interest. (2) The relatively strong respiratory signal with its harmonics greatly impact the detection of heartbeat rate. (3) The non-stationary nature of bio-signals creates challenges for spectral analysis. Having identified these problems, adaptive signal processing techniques have been developed which effectively mitigate these problems. Specifically, an ellipse-fitting algorithm is adopted to track and compensate the aperiodic large-scale body motion, and a wavelet-based filter is applied for attenuating the interference caused by respiratory harmonics to accurately estimate the heartbeat frequency. Additionally, the spectrum estimation of non-stationary signals is examined using a different transform method. Results from simulation and experiments show that substantial improvement is obtained by the use of these techniques. Further, this thesis examines the possibility of multi-target detection based on the same measurement setup. Array processing techniques with subspace-based algorithms are applied to estimate multiple respiration rates from different targets. The combination of array processing and single- target detection techniques are developed to extract the heartbeat rates. The performance is examined via simulation and experimental results and the limitation of the current measurement setup is discussed. / Master of Science

This thesis primarily addresses the problem of automatic measurement of ore textures by image analysis in a way that is relevant to mineral processing. Specifically, it addresses the following major hypotheses: • Automatic logging of drill core by image analysis provides a feasible alternative to manual logging by geologists. • Image analysis can quantify process mineralogy by physically meaningful parameters. • Multi-scale image analysis, over a wide range of size scales, provides potential benefits to process mineralogy that are additional to those available from small-scale analysis alone, and also better retains the information content of manual logging. • Image analysis can provide physically meaningful, ore-texture-related, additive regionalised variables that can be input to geostatistical models and the definition of domains. The central focus of the thesis is the development of an automatic, multi-scale method to identify and measure objects in an image, using a specially-developed skeleton termed the morphological CWT skeleton. This skeleton is a multi-scale extension of the morphological skeleton commonly used in image analysis, and is derived from the continuous wavelet transform (CWT). Objects take the form of hierarchical segments from image segmentation based on the CWT. Only the Mexican hat, also known as the Laplacian-of-Gaussian, wavelet is used, although other wavelet shapes are possible. The natural scale of each object is defined to be the size scale at which its CWT signal (the contrast between the interior and exterior of the object) is strongest. In addition to the natural scale, the analysis automatically records the mineral composition of both the interior and exterior of each object, and shape descriptors of the object. The measurements of natural scale, mineral composition and shape are designed to relate to: • The size to which ore must be broken in order to liberate objects. • Minerals that need to be separated by physical or chemical means once objects have been liberated. • Capability to distinguish qualitatively different ore-texture types that may have different geological origins and for which different processing regimes may provide an economic benefit. Measurements are taken over size scales from three pixels to hundreds of pixels. For the major case study the pixel size is about 50 µm, but the methodology is equally applicable to photomicrographs in which the pixel size is about 4 µm. The methodology for identifying objects in images contributes to the field of scale-space image segmentation, and has advantages in performing the following actions automatically: • Finding optimal size scales in hierarchical image segmentation (natural scale). • Merging segments that are similar and spatially close together (although not necessarily touching), using the structure of the morphological CWT skeleton, thus aiding recognition of complex structures in an image. • Defining the contrast between each segment and its surrounding segments appropriately for the size scale of the segment, in a way that extends well beyond the segment boundary. For process mineralogy this contrast quantifies mineral associations at different size scales. The notion of natural scale defined in this thesis may have applications to other fields of image processing, such as mammography and cell measurements in biological microscopy. The objects identified in images are input to cluster analysis, using a finite mixture model to group the objects into object populations according to their size, composition and shape descriptors. Each image is then characterised by the abundances of different object populations that occur in it. These abundances form additive, regionalised variables that can be input into geostatistical block models. The images are themselves input to higher-level cluster analysis based on a hidden Markov model. A collection of images is divided into different ore texture types, based on differences in the abundances of the textural object populations. The ore texture types help to define geostatistical domains in an ore body. Input images for the methodology take the form of mineral maps, in which a particular mineral has been assigned to each pixel in the image prior to analysis. A method of analysing unmapped, raw colour images of ore is also outlined, as is a new model for fracture of ore. The major case study in the thesis is an analysis of approximately 1000 metres of continuously-imaged drill core from four drill holes in the Ernest Henry iron-oxide-copper-gold ore deposit (Queensland, Australia). Thirty-one texture-related variables are used to summarise the individual half-metres of drill core, and ten major ore texture types are identified. Good agreement is obtained between locations of major changes in ore type found by automatic image analysis, and those identified from manual core logging carried out by geologists. The texture-related variables are found to explain a significant amount of the variation in comminution hardness of ore within the deposit, over and above that explained by changes in abundances of the component minerals. The thesis also contributes new algorithms with wide applicability in image processing: • A fast algorithm for computing the continuous wavelet transform of a signal or image: The new algorithm is simpler in form and several times faster than the best previously-published algorithms. It consists of a single finite impulse response (FIR) filter. • A fast algorithm for computing Euclidean geodesic distance. This algorithm runs in O(1) arithmetic operations per pixel processed, which has not been achieved by any previously published algorithm. Geodesic distance is widely used in image processing, for segmentation and shape characterisation.