Analysis Methodology for Vortex-Induced Motion (VIM) of a Monocolumn Platform Applying the Hilbert-Huang Transform Method

Vortex-induced motion (VIM) is a highly nonlinear dynamic phenomenon. Usual spectral analysis methods, using the Fourier transform, rely on the hypotheses of linear and stationary dynamics. A method to treat nonstationary signals that emerge from nonlinear systems is denoted Hilbert-Huang transform (HHT) method. The development of an analysis methodology to study the VIM of a monocolumn production, storage, and offloading system using HHT is presented. The purposes of the present methodology are to improve the statistics analysis of VIM. The results showed to be comparable to results obtained from a traditional analysis (mean of the 10% highest peaks) particularly for the motions in the transverse direction, although the difference between the results from the traditional analysis for the motions in the in-line direction showed a difference of around 25%. The results from the HHT analysis are more reliable than the traditional ones, owing to the larger number of points to calculate the statistics characteristics. These results may be used to design risers and mooring lines, as well as to obtain VIM parameters to calibrate numerical predictions. [DOI: 10.1115/1.4003493]

Evaluación de la condición de salud del transformador mediante análisis de vibraciones usando la transformada hilbert-huang.

Tesis (Maestro en Ingeniería Eléctrica con Orientación en Potencia) UANL, 2011.

Identification of cause of impairment in spiral drawings, using non-stationary feature extraction approach

Parkinson’s disease is a clinical syndrome manifesting with slowness and instability. As it is a progressive disease with varying symptoms, repeated assessments are necessary to determine the outcome of treatment changes in the patient. In the recent past, a computer-based method was developed to rate impairment in spiral drawings. The downside of this method is that it cannot separate the bradykinetic and dyskinetic spiral drawings. This work intends to construct the computer method which can overcome this weakness by using the Hilbert-Huang Transform (HHT) of tangential velocity. The work is done under supervised learning, so a target class is used which is acquired from a neurologist using a web interface. After reducing the dimension of HHT features by using PCA, classification is performed. C4.5 classifier is used to perform the classification. Results of the classification are close to random guessing which shows that the computer method is unsuccessful in assessing the cause of drawing impairment in spirals when evaluated against human ratings. One promising reason is that there is no difference between the two classes of spiral drawings. Displaying patients self ratings along with the spirals in the web application is another possible reason for this, as the neurologist may have relied too much on this in his own ratings.

Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms. [DOI: 10.1115/1.4006755]

Caraterização funcional cardíaca por fonocardiografia

Atualmente o uso da tecnologia como auxílio ao diagnóstico médico faz parte da rotina de atendimento diário na prestação de cuidados de saúde nos hospitais. O recurso à tecnologia na assistência à saúde tem aumentado, e até mesmo nos casos em que uma examinação clínica detalhada fornece informações confiáveis o suficiente para o diagnóstico correto, os exames de diagnóstico têm assumido um papel central na prática clínica, o que aumentou, por consequência, os custos em saúde. A ausculta cardíaca clássica é uma poderosa ferramenta clínica que, apesar de ter algumas limitações, pode ser reforçada com a aquisição, armazenamento e processamento do sinal fonocardiograma (FCG) e com a sua caraterização funcional pelo uso de sons cardíacos e caraterísticas de forma quantitativa. Neste trabalho é apresentada a caraterização de FCGs normais através do uso da Transformada de Hilbert-Huang, permitindo a identificação de caraterísticas quantitativas que possam ser usadas como marcadores na análise da disfunção cardíaca através do FCG. Essa caraterização vai estabelecer marcadores normais de função cardíaca, cuja comparação com sons patológicos, irá contribuir para estabelecer uma avaliação de baixo custo na medicina cardiovascular.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Hilbert transform

The Hilbert transform is an important tool in both pure and applied mathematics. It is largely used in the field of signal processing. Lately has been used in mathematical finance as the fast Hilbert transform method is an efficient and accurate algorithm for pricing discretely monitored barrier and Bermudan style options. The purpose of this report is to show the basic properties of the Hilbert transform and to check the domain of definition of this operator.

A simple but efficient voice activity detection algorithm through Hilbert transform and dynamic threshold for speech pathologies

A simple but efficient voice activity detector based on the Hilbert transform and a dynamic threshold is presented to be used on the pre-processing of audio signals -- The algorithm to define the dynamic threshold is a modification of a convex combination found in literature -- This scheme allows the detection of prosodic and silence segments on a speech in presence of non-ideal conditions like a spectral overlapped noise -- The present work shows preliminary results over a database built with some political speech -- The tests were performed adding artificial noise to natural noises over the audio signals, and some algorithms are compared -- Results will be extrapolated to the field of adaptive filtering on monophonic signals and the analysis of speech pathologies on futures works

Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform

Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form $T_*f\lesssim M(Tf)$ or $T_*f\lesssim M^2(Tf)$ for certain singular integral operators $T$, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve.

The application of the Hilbert spectrum to the analysis of electromyographic signals

This paper investigates the application of the Hilbert spectrum (HS), which is a recent tool for the analysis of nonlinear and nonstationary time-series, to the study of electromyographic (EMG) signals. The HS allows for the visualization of the energy of signals through a joint time-frequency representation. In this work we illustrate the use of the HS in two distinct applications. The first is for feature extraction from EMG signals. Our results showed that the instantaneous mean frequency (IMNF) estimated from the HS is a relevant feature to clinical practice. We found that the median of the IMNF reduces when the force level of the muscle contraction increases. In the second application we investigated the use of the HS for detection of motor unit action potentials (MUAPs). The detection of MUAPs is a basic step in EMG decomposition tools, which provide relevant information about the neuromuscular system through the morphology and firing time of MUAPs. We compared, visually, how MUAP activity is perceived on the HS with visualizations provided by some traditional (e.g. scalogram, spectrogram, Wigner-Ville) time-frequency distributions. Furthermore, an alternative visualization to the HS, for detection of MUAPs, is proposed and compared to a similar approach based on the continuous wavelet transform (CWT). Our results showed that both the proposed technique and the CWT allowed for a clear visualization of MUAP activity on the time-frequency distributions, whereas results obtained with the HS were the most difficult to interpret as they were extremely affected by spurious energy activity. (c) 2008 Elsevier Inc. All rights reserved.

Microcalcification enhancement and classification on mammograms using the wavelet transform

This paper presents a method to enhance microcalcifications and classify their borders by applying the wavelet transform. Decomposing an image and removing its low frequency sub-band the microcalcifications are enhanced. Analyzing the effects of perturbations on high frequency subband it's possible to classify its borders as smooth, rugged or undefined. Results show a false positive reduction of 69.27% using a region growing algorithm. © 2008 IEEE.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.