Made available in DSpace on 2014-12-17T14:55:19Z (GMT). No. of bitstreams: 1 JoseMAJ_TESE.pdf: 3560157 bytes, checksum: 2f20316c7b980a74bdb7b82e97e3bb43 (MD5) Previous issue date: 2014-03-24 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In last decades, neural networks have been established as a major tool for the identification of nonlinear systems. Among the various types of networks used in identification, one that can be highlighted is the wavelet neural network (WNN). This network combines the characteristics of wavelet multiresolution theory with learning ability and generalization of neural networks usually, providing more accurate models than those ones obtained by traditional networks. An extension of WNN networks is to combine the neuro-fuzzy ANFIS (Adaptive Network Based Fuzzy Inference System) structure with wavelets, leading to generate the Fuzzy Wavelet Neural Network - FWNN structure. This network is very similar to ANFIS networks, with the difference that traditional polynomials present in consequent of this network are replaced by WNN networks. This paper proposes the identification of nonlinear dynamical systems from a network FWNN modified. In the proposed structure, functions only wavelets are used in the consequent. Thus, it is possible to obtain a simplification of the structure, reducing the number of adjustable parameters of the network. To evaluate the performance of network FWNN with this modification, an analysis of network performance is made, verifying advantages, disadvantages and cost effectiveness when compared to other existing FWNN structures in literature. The evaluations are carried out via the identification of two simulated systems traditionally found in the literature and a real nonlinear system, consisting of a nonlinear multi section tank. Finally, the network is used to infer values of temperature and humidity inside of a neonatal incubator. The execution of such analyzes is based on various criteria, like: mean squared error, number of training epochs, number of adjustable parameters, the variation of the mean square error, among others. The results found show the generalization ability of the modified structure, despite the simplification performed / Nas ?ltimas d?cadas, as redes neurais t?m se estabelecido como uma das principais ferramentas para a identifica??o de sistemas n?o lineares. Entre os diversos tipos de redes utilizadas em identifica??o, uma que se pode destacar ? a rede neural wavelet (ou Wavelet Neural Network - WNN). Esta rede combina as caracter?sticas de multirresolu??o da teoria wavelet com a capacidade de aprendizado e generaliza??o das redes neurais, podendo fornecer modelos mais exatos do que os obtidos pelas redes tradicionais. Uma evolu??o das redes WNN consiste em combinar a estrutura neuro-fuzzyANFIS (Adaptive Network Based Fuzzy Inference System) com estas redes, gerando-se a estrutura Fuzzy Wavelet Neural Network - FWNN. Essa rede ? muito similar ?s redes ANFIS, com a diferen?a de que os tradicionais polin?mios presentes nos consequentes desta rede s?o substitu?dos por redes WNN. O presente trabalho prop?e uma rede FWNN modificada para a identifica??o de sistemas din?micos n?o lineares. Nessa estrutura, somente fun??es waveletss?o utilizadas nos consequentes. Desta forma, ? poss?vel obter uma simplifica??o da estrutura com rela??o a outras estruturas descritas na literatura, diminuindo o n?mero de par?metros ajust?veis da rede. Para avaliar o desempenho da rede FWNN com essa modifica??o, ? realizada uma an?lise das caracter?sticas da rede, verificando-se as vantagens, desvantagens e o custo-benef?cio quando comparada com outras estruturas FWNNs. As avalia??es s?o realizadas a partir da identifica??o de dois sistemas simulados tradicionalmente encontrados na literatura e um sistema real n?o linear, consistindo de um tanque de multisse??es e n?o linear. Por fim, a rede foi utilizada para inferir valores de temperatura e umidade no interior de uma incubadora neonatal. A execu??o dessa an?lise baseia-se em v?rios crit?rios, tais como: erro m?dio quadr?tico, n?mero de ?pocas de treinamento, n?mero de par?metros ajust?veis, vari?ncia do erro m?dio quadr?tico, entre outros. Os resultados encontrados evidenciam a capacidade de generaliza??o da estrutura modificada, apesar da simplifica??o realizada

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Nesta tese consideramos um modelo de regressão não paramétrica, quando a variável explicativa e um processo estritamente estacionário e alpha-mixing. São estudadas as condições sobre o processo Xt e sua estrutura de dependência, assim como do domínio da função f a ser estimada. Também são feitas as adaptações necessárias aos procedimentos para obter as taxas de convergência do risco para a norma Lp, no caso de ondaletas deformadas. Em relação às ondaletas adaptativas de Haar, obtêm-se as taxas de convergência do risco do estimador proposto. Mediante estudos de simulação, e avaliado o desempenho dos procedimentos propostos quando aplicados a amostras finitas sob diferentes níveis de perturbação do sinal e diferentes tamanhos da amostra. Também são feitas aplicações a dados reais. / In this thesis we consider a nonparametric regression model, when the exploratory variables are alpha-mixing stationary processes. We obtain convergence rates for risk for Lp norm, via warped wavelets, under suitable regularity conditions. For estimation using design adapted Haar wavelets we obtain convergence rates for the risk of the proposed estimator. The performance of the estimators are assessed via simulation studies with dierent sample sizes and dierent signal-to-noise ratios. Applications to real data are also given.

Nesta tese consideramos um modelo de regressão não paramétrica, quando a variável explicativa e um processo estritamente estacionário e alpha-mixing. São estudadas as condições sobre o processo Xt e sua estrutura de dependência, assim como do domínio da função f a ser estimada. Também são feitas as adaptações necessárias aos procedimentos para obter as taxas de convergência do risco para a norma Lp, no caso de ondaletas deformadas. Em relação às ondaletas adaptativas de Haar, obtêm-se as taxas de convergência do risco do estimador proposto. Mediante estudos de simulação, e avaliado o desempenho dos procedimentos propostos quando aplicados a amostras finitas sob diferentes níveis de perturbação do sinal e diferentes tamanhos da amostra. Também são feitas aplicações a dados reais. / In this thesis we consider a nonparametric regression model, when the exploratory variables are alpha-mixing stationary processes. We obtain convergence rates for risk for Lp norm, via warped wavelets, under suitable regularity conditions. For estimation using design adapted Haar wavelets we obtain convergence rates for the risk of the proposed estimator. The performance of the estimators are assessed via simulation studies with dierent sample sizes and dierent signal-to-noise ratios. Applications to real data are also given.

The aim of speech scrambling algorithms is to transform clear speech into an unintelligible signal so that it is difficult to decrypt it in the absence of the key. Most of the existing speech scrambling algorithms tend to retain considerable residual intelligibility in the scrambled speech and are easy to break. Typically, a speech scrambling algorithm involves permutation of speech segments in time, frequency or time-frequency domain or permutation of transform coefficients of each speech block. The time-frequency algorithms have given very low residual intelligibility and have attracted much attention. We first study the uniform filter bank based time-frequency scrambling algorithm with respect to the block length and number of channels. We use objective distance measures to estimate the departure of the scrambled speech from the clear speech. Simulations indicate that the distance measures increase as we increase the block length and the number of chan­nels. This algorithm derives its security only from the time-frequency segment permutation and it has been estimated that the effective number of permutations which give a low residual intelligibility is much less than the total number of possible permutations. In order to increase the effective number of permutations, we propose a time-frequency scrambling algorithm based on wavelet packets. By using different wavelet packet filter banks at the analysis and synthesis end, we add an extra level of security since the eavesdropper has to choose the correct analysis filter bank, correctly rearrange the time-frequency segments, and choose the correct synthesis bank to get back the original speech signal. Simulations performed with this algorithm give distance measures comparable to those obtained for the uniform filter bank based algorithm. Finally, we introduce the 2-channel perfect reconstruction circular convolution filter bank and give a simple method for its design. The filters designed using this method satisfy the paraunitary properties on a discrete equispaced set of points in the frequency domain.

The radar transmitter identification problem involves the identification of a specific radar transmitter based on a received pulse. The radar transmitters are of identical make and model. This makes the problem challenging since the differences between radars of identical make and model will be solely due to component tolerances and variation. Radar pulses also vary in time and frequency which means that the problem is non-stationary. Because of this fact, time-frequency representations such as shift-invariant quadratic time-frequency representations (Cohen’s class) and wavelets were used. A model for a radar transmitter was developed. This consisted of an analytical solution to a pulse-forming network and a linear model of an oscillator. Three signal classification algorithms were developed. A signal classifier was developed that used a radially Gaussian Cohen’s class transform. This time-frequency representation was refined to increase the classification accuracy. The classification was performed with a support vector machine classifier. The second signal classifier used a wavelet packet transform to calculate the feature values. The classification was performed using a support vector machine. The third signal classifier also used the wavelet packet transform to calculate the feature values but used a Universum type classifier for classification. This classifier uses signals from the same domain to increase the classification accuracy. The classifiers were compared against each other on a cubic and exponential chirp test problem and the radar transmitter model. The classifier based on the Cohen’s class transform achieved the best classification accuracy. The classifier based on the wavelet packet transform achieved excellent results on an Electroencephalography (EEG) test dataset. The complexity of the wavelet packet classifier is significantly lower than the Cohen’s class classifier. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

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The land–atmosphere interactions and the coupling between climate and land surface hydrological processes are gaining interest in the recent past. The increased knowledge in hydro climatology and the global hydrological cycle, with terrestrial and atmospheric feedbacks, led to the utilization of the climate variables and atmospheric tele-connections in modeling the hydrological processes like rainfall and runoff. Numerous statistical and dynamical models employing different combinations of predictor variables and mathematical equations have been developed on this aspect. The relevance of predictor variables is usually measured through the observed linear correlation between the predictor and the predictand. However, many predictor climatic variables are found to have been switching the relationships over time, which demands a replacement of these variables. The unsatisfactory performance of both the statistical and dynamical models demands a more authentic method for assessing the dependency between the climatic variables and hydrologic processes by taking into account the nonlinear causal relationships and the instability due to these nonlinear interactions. The most obvious cause for limited predictability in even a perfect model with high resolution observations is the nonlinearity of the hydrological systems [Bloschl and Zehe, 2005]. This is mainly due to the chaotic nature of the weather and its sensitiveness to initial conditions [Lorenz, 1963], which restricts the predictability of day-to-day weather to only a few days or weeks. The present thesis deals with developing association rules to extract the causal relationships between the climatic variables and rainfall and to unearth the frequent predictor patterns that precede the extreme episodes of rainfall using a time series data mining algorithm. The inherent nonlinearity and uncertainty due to the chaotic nature of hydrologic processes (rainfall and runoff) is modeled through a nonlinear prediction method. Methodologies are developed to increase the predictability and reduce the predictive uncertainty of chaotic hydrologic series. A data mining algorithm making use of the concepts of minimal occurrences with constraints and time lags is used to discover association rules between extreme rainfall events and climatic indices. The algorithm considers only the extreme events as the target episodes (consequents) by separating these from the normal episodes, which are quite frequent and finds the time-lagged relationships with the climatic indices, which are treated as the antecedents. Association rules are generated for all the five homogenous regions of India (as defined by Indian Institute of Tropical Meteorology) and also for All India by making use of the data from 1960-1982. The analysis of the rules shows that strong relationships exist between the extreme rainfall events and the climatic indices chosen, i.e., Darwin Sea Level Pressure (DSLP), North Atlantic Oscillation (NAO), Nino 3.4 and Sea Surface Temperature (SST) values. Validation of the rules using data for the period 1983-2005, clearly shows that most of the rules are repeating and for some rules, even if they are not exactly the same, the combinations of the indices mentioned in these rules are the same during validation period with slight variations in the representative classes taken by the indices. The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. In the present study, an attempt is made to identify chaos using various techniques and the behaviour of daily rainfall series in different regions. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha river basin, Mahanadi river basin and All India for the period 1955 to 2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series considered. Correlation dimension method is repeated on the phase randomized and first derivative of the data series to check the existence of any pseudo low-dimensional chaos [Osborne and Provenzale, 1989]. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A limit in predictability in chaotic system arises mainly due to its sensitivity to the infinitesimal changes in its initial conditions and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a nonlinear ensemble prediction. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996 to 2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are made from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. The predictability of the chaotic daily rainfall series is improved by utilizing information from various climatic indices and adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha river basin, India for the period 1955 to 2000 is used for the study. A multivariate phase space is generated, considering a climate data set of 16 variables. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to 8 principal components (PCs). This multivariate series (rainfall along with 8 PCs) are found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is reduced or in other words, the predictability is improved by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be reduced by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. Even though, the sensitivity to initial conditions limit the predictability in chaotic systems, a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent. All the traditional chaotic prediction methods are based on local models since these methods model the sudden divergence of the trajectories with different local functions. Conceptually, global models are ineffective in modeling the highly unstable structure of the chaotic attractor [Sivakumar et al., 2002a]. This study focuses on combining a local learning wavelet analysis (decomposition) model with a global feedforward neural network model and its implementation on phase space prediction of chaotic streamflow series. The daily streamflow series at Basantpur station in Mahanadi basin, India is found to exhibit a chaotic nature with dimension varying from 5-7. Quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimension and delay time. Compared with traditional local approximation approach, the total predictive uncertainty in the streamflow is reduced when modeled with wavelet networks for different lead times. Localization property of wavelets, utilizing different dilation and translation parameters, helps in capturing most of the statistical properties of the observed data. The need for bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor is clearly demonstrated.

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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