This thesis examines the ability of the wavelet transform to form features which may be used successfully in a discriminant analysis. We apply our methods to two different data sets and consider the problem of selecting the 'best' features for discrimination. In the first data set, our interest is in automatically recognising the variety of a carrot from an image. After necessary image preprocessing we examine the usefulness of shape descriptors and texture features for discrimination. We show that it is better to use the different 'types' of features separately, and that the wavelet coefficients of the outline coordinates are more useful. In the second data set we consider the task of automatically identifying individual haddock from the sounds they produce. We use the smoothing property of wavelets to automatically isolate individual haddock sounds, and use the stationary wavelet transform to overcome the shift dependence of the standard wavelet transform. Again we calculate different 'types' of wavelet features and compare their usefulness in classification and show that including information on the source of the previous sound can substantially increase the correct classification rate. We also apply our techniques to recognise different species of fish which is also highly successful. In each analysis, we explore different allocation rules via regularised discriminant analysis and show that the highest classification rates obtained are only slightly better than linear discriminant analysis. We also consider the problem of selecting the best subset of features for discrimination. We propose two new measures for selecting good subsets and using a genetic algorithm we search for the 'best' subsets. We investigate the relationship between out measures and classification rates showing that our method is better than selection based on F-ratios and we also discover that our two measures are closely related.

Στο πείραμα των μικροσυστοιχιών, η απόκτηση εικόνας συνοδεύεται πάντα από θόρυβο, ο οποίος είναι έμφυτος σε τέτοιου είδους διεργασίες. Είναι λοιπόν επιτακτική ανάγκη να χρησιμοποιηθούν τεχνικές προς καταστολή αυτού. Στην παρούσα εργασία αναλύονται μέθοδοι και παρουσιάζονται τα αποτελέσματά τους σε 5 επιλεγμένα παραδείγματα. Ιδιαίτερη έμφαση δίνεται στο wavelet denoising και συγκεκριμένα στους αλγορίθμους soft thresholding, hard thresholding και stationary wavelet transform. / The subject of this diploma thesis is the manufacturing of a driver assistance system. Robust and reliable vehicle detection from images acquired by a moving vehicle (i.e., on road vehicle detection) is an important problem with applications to driver assistance systems and autonomous, self-guided vehicles. The focus of this diploma is on the issues of feature extraction and classification for rear-view vehicle detection. Specifically, by treating the problem of vehicle detection as a two-class classification problem, we have investigated several different feature extraction methods such as wavelets and Gabor filters. To evaluate the extracted features, we have experimented with two popular classifiers, neural networks and support vector machines (SVMs).

Leakage and blockage of oil and gas pipeline systems, water pipelines, pipe-work of process plants and other pipe networks can cause serious environmental, health and economic problems. There are a number of non-destructive testing (NDT) methods for detecting these defects in pipeline systems such as radiographic, ultrasonic, magnetic particle inspection, pressure transient and acoustic wave methods. In this study, the acoustic wave method and a modal frequency technique, which based on a roving mass method, are used. The aim of the thesis is to employ acoustic wave propagation based methods in conjunction with stationary wavelet transform (SWT) to identify leakage and blockage in pipe systems. Moreover, the research is also aimed at using the difference of modal frequencies of fluid-filled pipes with and without defects and a roving mass, and consequently, to develop a roving mass-based defect detection method for pipelines. In the study, the acoustic finite-element analysis (AFEA) method is employed to simulate acoustic wave propagation in small and large air-filled water-filled straight pipe and pipe networks with leakage and blockage but without flow. Computational fluid dynamics (CFD) analysis was also employed to simulate acoustic wave propagation in air-and water-filled pipes with flow, leakage and blockage. In addition, AFEA was used to predict the modal frequencies of air- and water-filled pipes with leakage and blockage in the presence of a roving mass that was traversed along the axis of the pipes. Experimental testing was conducted to validate some of the numerical results. Two major experiments were performed. The first set of experiments consisted of the measurement of acoustic wave propagation in a straight air-filled pipe with leakage and blockage. The second set of experiments concerned the measurement of acoustic wave propagation in an air-filled pipe network comprising straight pipe, elbows and T-piece and flange. The AFEA and CFD analysis of fluid-filled pipe can be used to simulate the acoustic wave propagation and acoustic wave reflectometry of a fluid-filled pipe with leakage and blockage of different sizes down to a small leakage size of 1mm diameter and a blockage depth of 1.2mm in a pipe. Similarly, the AFEA method of a static fluid-filled pipe can be used to simulate acoustic wave modal frequency analysis of a fluid-filled pipe with leakage and blockage of different sizes down to a leakage of 1mm diameter and a blockage depth of 1.2mm. Moreover, the measured signal of acoustic wave propagation in an air-filled can be successfully decomposed and de-noised using the SWT method to identify and locate leakages of different sizes down to 5mm diameter, and small blockage depth of 1.2mm. Also, the SWT approximation coefficient, detail and de-noised detail coefficient curves of an air-filled pipe with leakage and blockage and a roving mass give leakage and blockage indications that can be used to identify, locate and estimate the size of leakage and blockage in a pipe.

Digital Signal Processing has been dominated by the Fourier transform since the Fast Fourier Transform (FFT) was developed in 1965 by Cooley and Tukey. In the 1980's a new transform was developed called the wavelet transform, even though the first wavelet goes back to 1910. With the Fourier transform, all information about localized changes in signal features are spread out across the entire signal space, making local features global in scope. Wavelets are able to retain localized information about the signal by applying a function of a limited duration, also called a wavelet, to the signal. As with the Fourier transform, the discrete wavelet transform has an inverse transform, which allows us to make changes in a signal in the wavelet domain and then transform it back in the time domain. In this thesis, we have investigated the filtering properties of this technique and analyzed its performance under various settings. Another popular application of wavelet transform is data compression, such as described in the JPEG 2000 standard and compressed digital storage of fingerprints developed by the FBI. Previous work on filtering has focused on the discrete wavelet transform. Here, we extended that method to the stationary wavelet transform and found that it gives a performance boost of as much as 9 dB over that of the discrete wavelet transform. We also found that the SNR of noise filtering decreases as a frequency of the base signal increases up to the Nyquist limit for both the discrete and stationary wavelet transforms. Besides filtering the signal, the discrete wavelet transform can also be used to estimate the standard deviation of the white noise present in the signal. We extended the developed estimator for the discrete wavelet transform to the stationary wavelet transform. As with filtering, it is found that the quality of the estimate decreases as the frequency of the base signal increases. Many interesting signals are self-similar, which means that one of their properties is invariant on many different scales. One popular example is strict self-similarity, where an exact copy of a signal is replicated on many scales, but the most common property is statistical self-similarity, where a random segment of a signal is replicated on many different scales. In this work, we investigated wavelet-based methods to detect statistical self-similarities in a signal and their performance on various types of self-similar signals. Specifically, we found that the quality of the estimate depends on the type of the units of the signal being investigated for low Hurst exponent and on the type of edge padding being used for high Hurst exponent. / Master of Science

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.

Este trabalho apresenta o estudo e o desenvolvimento de um algoritmo híbrido para detecção, classificação e localização de faltas em sistemas com três terminais utilizando como principal ferramenta a transformada wavelet (TW) em suas versões discreta (TWD) e estacionária (TWE). O algoritmo é dito híbrido, pois alia duas metodologias para localizar a falta. A primeira baseada na análise de componentes de alta freqüência (ondas viajantes) e a segunda, baseada na extração dos componentes fundamentais para o cálculo da impedância aparente. A metodologia proposta foi concebida de maneira a trabalhar com dados sincronizados dos três terminais ou apenas dados locais para estimar a localização da falta. O localizador híbrido escolhe automaticamente qual a melhor técnica de localização ser utilizada para alcançar uma localização confiável e precisa. Deste modo, um método pode suprir as dificuldades do outro, ou, no mínimo, fornecer mais informações para que, junto ao conhecimento do operador, uma localização próxima da ótima possa ser alcançada. Com o objetivo de testar e validar a aplicabilidade do algoritmo de localização de faltas híbrido para linhas com três terminais, utilizou-se de dados de sinais faltosos obtidos através de simulações do software ATP (Altenative Transients Program), levando-se em conta a variação de diversos parâmetros que poderiam influenciar o desempenho do algoritmo proposto. Os resultados alcançados pelo algoritmo frente às situações avaliadas são bastante animadores, apontando a uma promissora aplicabilidade do mesmo. / This work presents a study and development of a hybrid algorithm for fault detection, classification and location in tree terminal lines based on wavelet transform (WT). It will be presented in two versions: discrete wavelet transform (DWT) and stationary wavelet transform (SWT). The algorithm is called hybrid because it uses two fault location methodologies: one based on fundamental components and other based on traveling waves. The proposed methodology works either with synchronized tree terminal data or only local data. The hybrid fault locator chooses automatically which location technique to be used in order to reach a reliable and accurate fault location. In this manner, this technique can avoid some difficulties present in other techniques, aiming to reach an optimized fault location. The proposed hybrid fault location was evaluated by simulated fault signals obtained by alternative transient program (ATP). In the tests, several parameters, which would influence the performance of the hybrid algorithm, were varied, such as: fault inception angle, fault resistance, fault type, etc. The results obtained by the proposed methodology are very encouraging and it points out to a very promising application.

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