Standard Configural Frequency Analysis (CFA) is a one-step procedure that determines which cells of a cross-classification contradict a base model. Selecting these cells out does not guarantee that the base model fits. Therefore, the role played by these cells for the base model is unclear, and interpretation of types and antitypes can be problematic. In this paper, functional CFA is proposed. This model of CFA pursues two goals simultaneously. First, cells are selected out that constitute types and antitypes. Second, the base model is fit to the data. This is done using an iterative procedure that blanks out individual cells one at a time, until the base model fits or until there are no more cells that can be blanked out. In comparison to standard CFA, functional CFA is shown to be more parsimonious, that is, fewer types and antitypes need to be selected out. In comparison to Kieser and Victor's CFA which focuses exclusively on optimizing the fit of the base model, functional CFA needs, in most cases, more iteration steps, but the overall goodness-of-fit for the base model is better. The methods are illustrated and compared using data examples from the literature. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

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A scaling model based on an effective Gol'dberg number is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jets. Two acoustic length scales, the shock formation distance and the absorption length are expressed in terms of jet exit parameters. This approach allows one to compute the degree of cumulative nonlinear distortion in a full-scale scenario, from laboratory-scale observations, or vice versa. Surveys of the acoustic pressure waveforms emitted by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support the findings of the model. These acoustic waveforms are acquired on a planar grid in an acoustically treated and range-restricted environment. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes skewness, kurtosis, the number of zero crossings in the waveform, a wave steepening factor, the Morfey-Howell nonlinearity indicator and an application of the generalized Burgers equation. It is advocated that in order for the Morfey-Howell indicator to be used as an investigative tool for the presence of cumulative nonlinear waveform distortion, that it be applied as a multi-point indicator. Based on findings of the model and the spatial topography of the metrics, it is concluded that cumulative nonlinear steepening effects are absent in the current data set. This implies that acoustic shock-structures in the waveforms are generated by local mechanisms in, or in close vicinity to, the jet's hydrodynamic region. Furthermore, these shock-structures induce the crackle noise component. The research aims to quantify crackle in a temporal and spectral fashion, and is motivated by the fact that (1) it is perceived as the most annoying component of jet noise, (2) no unique measures of crackle exist, and (3) significant reductions in jet noise will be achieved when crackle can be controlled. A unique detection algorithm is introduced which isolates the shock-structures in the temporal waveform that are responsible for crackle. Ensemble-averages of the identified waveform sections are employed to gain an in-depth understanding of the crackling structures. Moreover, PDF's of the temporal intermittence of these shocks reveal modal trends and show evidence that crackling shock-structures are present in groups of multiple shocks. A spectral measure of crackle is considered by using wavelet-based time-frequency analyses. The increase in sound energy is computed by considering the global pressure spectra of the waveforms and the ones that represent the spectral behavior during instances of crackle. This energy-based metric is postulated to be an appropriate metric for the level of crackle. / text

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition really helps in both simulated data analysis and real world application.

Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonormal Stockwell transform is a more efficient, less redundant transform with the same properties. There has been little work on mathematical properties of the Stockwell transform, particularly how it behaves under operations such as translation and modulation. Previous results do discuss a resolution of the identity, as well as some of the function spaces that may be associated with it [2]. We extend the resolution of the identity results, and behaviour under translation, modulation, convolution and differentiation. boundedness and continuity properties are also developed, but the function spaces associated with the transform are unrelated to the focus of this thesis. There has been some work on image processing using the Stockwell transform and discrete orthonormal Stockwell transform. The tests were quite preliminary. In this thesis, we explore some of the mathematics of the Stockwell transform, examining properties, and applying it to various continuous examples. The discrete orthonormal Stockwell transform is compared directly with Newland’s harmonic wavelet transform, and we extend the definition to include varitions, as well as develop the discrete cosine based Stockwell transform. All of these discrete transforms are tested against current methods for image compression.

Orientador: Josmar Mazucheli / Resumo: Na análise de séries climatológicas, a metodologia conhecida como “análise de frequências” inicia-se, após a verificação da validade de algumas suposições, pela escolha e ajuste de uma distribuição de probabilidade. A etapa mais importante desta análise é a escolha ou seleção da distribuição de probabilidade que melhor descreva o verdadeiro comportamento da variável em estudo. Uma vez adotada uma distribuição de probabilidade que esteja bem ajustada, segundo um ou vários critérios, é de interesse, por exemplo, estimar a probabilidade de que eventos de certa magnitude sejam igualados ou excedidos em T anos. O inverso desta probabilidade é chamado de período de retorno, sendo esta uma medida de extrema importância na avaliação de riscos associados a fenômenos climatológicos. Em princípio, qualquer distribuição de probabilidade com suporte nos números reais positivos pode ser utilizada na descrição do comportamento de séries fluviométricas, pluviométricas, eólicas, entre outras. Em se tratando de séries pluviométricas, formadas, por exemplo, pelas pluviosidades diárias, decendiais, mensais, trimestrais e anuais, as distribuições Gama e Weibull são as mais utilizadas. Nos últimos anos, a partir de métodos específicos, uma infinidade de novas distribuições vêm sendo propostas para a análise de observações contínuas e estritamente positivas, cujas aplicações, em sua grande maioria, restringem-se a dados de sobrevivência e confiabilidade. Nesta dissertação de Mestrado, foram avaliad... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In the climatological series analysis, a methodology known as “frequency analysis” begins, after the validity of some assumptions, by choice and adjustment of a probability distribution. The most important step of this analysis is the choice or selection of probability distribution that best describes the true behavior of the variable under study. Once a probability distribution, that is well adjusted according to one or several criteria, is adopted, it is of interest, for example, to estimate a probability of events of a certain magnitude that are matched or exceeded in T years. The opposite of this probability is called a return period, which is a measure of extreme importance in the evaluation of risks associated with climatological phenomena. In principle, any probability distribution supported by positive real numbers can be used to describe the behavior of fluviometric, pluviometric and wind series, among others. When it comes to the case of rainfall series, formed, for example, by daily, decendial, monthly, quarterly and annual rainfall, the Gamma and Weibull Distributions are more used. In recent years, from specific methods, a plethora of new distributions are being proposed for an analysis of continuous and strictly positive observations, which applications, for the most part, are restricted to survival and reliability data. In this Master’s dissertation, the performances of the Odd Weibull, Marshall-Olkin Weibull, Exponentiated Weibull and Transmutated Weibull Dist... (Complete abstract click electronic access below) / Mestre

Time-frequency methods are widely used tools to diagnose planetary gearbox fault under non-stationary conditions. However, the existing time-frequency methods still have some problems, such as smearing effect and cross-term interference, and these problems limit the effectiveness of the existing time-frequency methods in planetary gearbox fault diagnosis under non-stationary conditions. To address the aforementioned problems, four time-frequency methods are proposed in this thesis. As nowadays a large portion of the industrial equipment is equipped with tachometers, the first three methods are for the cases that the shaft rotational speed is easily accessible and the last method is for the cases of shaft rotational speed is not easily accessible. The proposed methods are itemized as follows: (1) The velocity synchronous short-time Fourier transform (VSSTFT), which is a type of linear transform based on the domain mappings and short-time Fourier transform to address the smear effect of the existing linear transforms under known time-varying speed conditions; (2) The velocity synchrosqueezing transform (VST), which is a type of remapping method based on the domain mapping and synchrosqueezing transform to address the smear effect of existing remapping methods under known time-varying speed conditions; (3) The velocity synchronous bilinear distribution (VSBD), which is a type of bilinear distribution based on the generalized demodulation and Cohen’s class bilinear distribution to address the smear effect and cross-term interference of existing bilinear distributions under known time-varying speed conditions and (4) The velocity synchronous linear chirplet transform (VSLCT), which is a non-parametric combined approach of linear transform and concentration-index-guided parameter determination to provide a smear-free and cross-term-free TFR under unknown time-varying speed conditions. In this work, simple algorithms are developed to avoid the signal resampling process required by the domain mappings or demodulations of the first three methods (i.e., the VSSTFT, VST and VSBD). They are designed to have different resolutions, readabilities, noise tolerances and computational efficiencies. Therefore, they are capable to adapt different application conditions. The VSLCT, as a kind of linear transform, is designed for unknown rotational speed conditions. It utilizes a set of shaft-rotational-speed-synchronous bases to address the smear problem and it is capable to dynamically determine the signal processing parameters (i.e., window length and normalized angle) to provide a clear TFR with desirable time-frequency resolution in response to condition variations. All of the proposed methods in this work are smear-free and cross-term-free, the TFRs generated by the methods are clearer and more precise compared with the existing time-frequency methods. The faults of planetary gearboxes, if any, can be diagnosed by identifying the fault-induced components from the obtained TFRs. The four methods are all newly applied to fault diagnosis. The effectiveness of them has been validated using both simulated and experimental vibration signals of planetary gearboxes collected under non-stationary conditions.

This thesis presents results on the description of plasma waves in terms of wavepackets. The wave field is decomposed into a distribution of wavepackets in a space of position, wavevector, time, and frequency. A complex structure joining each pair of Fourier conjugate variables into a single complex coordinate allows the efficient derivation of equations of motion for the phase space distribution by exploiting its analytic properties. The Wick symbol calculus, a mathematical tool generalizing many convenient properties of the Fourier transform to a local setting, is used to derive new exact phase space equations which maintain full information on the phase of the waves and include effects nonlocal in phase space such as harmonic generation. A general purpose asymptotic expansion of the Wick symbol product formula is used to treat dispersion, refraction, photon acceleration, and ponderomotive forces. Examples studied include the nonlinear Schrödinger equation, mode conversion, and the Vlasov equation. The structure of partially coherent wave fields is understood in terms of zeros in the phase space distribution caused by dislocations in its complex phase which are shown to be correlated with the field entropy. Simulations of plasma heating by crossing electron beams are understood by representing the resulting plasma waves in phase space. The local coherence properties of the beam driven Langmuir waves are studied numerically.

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Made available in DSpace on 2014-10-09T12:43:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:10:10Z (GMT). No. of bitstreams: 1 06767.pdf: 4710608 bytes, checksum: 0df801946c2e3b5907a9d77d5ff698e5 (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP