Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Wooden Structure; Damage Detection; Structural Health Monitoring; Instantaneous Modal Parameters; Wavelet Analysis; Time Varying Systems; Sifting Process. Includes bibliographical references (p. 77-82).

A new technique that couples modal analysis and wavelet transforms for detection of multiple damage in structures is introduced. Structural damage may cause local changes in one or more of the following parameters; stiffness, mass and damping that affect the dynamic behavior of the structure. For example, a crack reduces the stiffness of the structure in a localized sense, and thus reducing its natural frequency, and causes changes in both modal damping and mode shapes. In this research, two different structures have been analyzed: beams and plates. First, uniform beams with a single damage (notch) of different sizes at different locations were considered. Then, a beam with multiple damages was analyzed. Secondly, a uniform plate with a single square damage was considered. For all structures considered, the responses were obtained experimentally (using experimental modal analysis) and numerically (using finite element analysis), then wavelet transform was used to detect and characterize these defects. Most vibration-based methods require knowledge of the undamaged state of the structure, which is unavailable in most cases. However, using wavelet transformation has the advantage of not requiring knowledge of the undamaged state. In addition, wavelet transform has the characteristics that make the visualization of the signal discontinuities clear. Here it has been found that some wavelets were able to detect the damage location for all cases. Also it was observed that the magnitude of the wavelet coefficient increased linearly with the increase in the amount of damage.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-09-03T15:08:48Z No. of bitstreams: 1 ALDINETE BEZERRA BARRETO - TESE PPGMET 2012..pdf: 6263495 bytes, checksum: 1008afd187e39f22ffed865972093dbc (MD5) / Made available in DSpace on 2018-09-03T15:08:48Z (GMT). No. of bitstreams: 1 ALDINETE BEZERRA BARRETO - TESE PPGMET 2012..pdf: 6263495 bytes, checksum: 1008afd187e39f22ffed865972093dbc (MD5) Previous issue date: 2012-05-08 / CNPq / O objetivo deste estudo é caracterizar o regime de chuvas de Salvador em várias escalas de tempo, com foco em eventos extremos de chuva, e identificar padrões da circulação atmosférica de grande escala relacionados com tais eventos. O período de estudo é de 1964 a 2009. Métodos matemático-estatísticos (Percentil, Correlação Linear, Análise de Ondeletas, Análise de Componentes Principais (ACP) e Análise de Agrupamento) foram aplicados a dados observacionais de precipitação e dados em ponto de grade de reanálise. A técnica do percentil aplicada à série temporal dos dados diários de precipitação possibilitou classificar como eventos extremos os totais diários com valor igual ou maior do que 50 mm. O principal período chuvoso, abril a julho, detém 61% de todos os eventos da série. A análise de correlação linear mostrou uma relação direta entre a ocorrência dos eventos extremos e total mensal de chuva acima da média. A análise de ondeletas indicou que os eventos estão relacionados com, pelo menos, três tipos de oscilação na escala intrassazonal: de até 12 dias, de 12-24 dias e de 48-96 dias, o que sugere a contribuição de sistemas de escala sinótica como os distúrbios de leste e os sistemas frontais, e de circulações de escala planetária como a Oscilação de Madden-Julian. A ACP aplicada a dados de reanálise identificou padrões nos baixos níveis com configuração indicativa da presença do cavado equatorial/ZCIT, ondas de latitudes médias austrais e ZCAS, essa última relacionada com eventos dos meses de verão (dezembro-janeiro-fevereiro). O padrão do principal período chuvoso tem estrutura ondulatória no escoamento de oeste do hemisfério sul. Todos os padrões apresentam um cavado invertido no leste do Nordeste e área oceânica próxima, resultante da propagação/interação de sistemas atmosféricos da área tropical-extratropical. Nos altos níveis (200 hpa), o padrão relacionado com os eventos de verão mostra a Alta da Bolívia deslocada para nordeste, e o cavado de ar superior posicionado sobre o Atlântico tropical. A estrutura dominante nos padrões de inverno (junho-julho-agosto) é: (a) ondas de latitudes médias austrais com propagação em latitudes baixas, ou (b) uma área de difluência próxima ao equador relacionada com a ZCIT. / The objective in this study is to characterize the rainfall regime of Salvador on various time scales, with a focus on extreme rainfall events, and to identify large scale atmospheric circulation patterns related to such events. The period of study is from 1964 to 2009. Mathematical-statistical methods (Percentiles, Linear Correlation, Wavelet Analysis, Principal Component Analysis (PCA), Cluster Analysis) were applied to observational precipitation and gridpoint reanalysis data. The percentile technique applied to daily precipitation time series allowed to classify as extreme events daily rainfall totals equal to or greater than 50 mm. The main rainy period, from April to July, has 61% of all events. The linear correlation analysis identified a direct relation between the occurrence of extreme events and above-normal monthly rainfall totals. The wavelet analysis indicated that the events are related to, at least, three types of oscillations on the intraseasonal time scale: up to 12 days, 12-24 days and 48-96 days, suggesting the contribution of synoptic scale systems such as easterly disturbances and frontal systems, and planetary scale circulations as the Madden-Julian Oscillation. The PCA applied to reanalysis data identified low level patterns depicting the equatorial trough/ITCZ, southern mid-latitude waves and SACZ, the last one related to summer month events (December-January-February). The pattern of the main rainy period has a wavelike structure in the southern westerlies. All patterns show an inverted trough in eastern Northeast and the nearby oceanic area, a result of the propagation /interaction of tropical-extratropical atmospheric systems. At high levels (200 hpa), the summer pattern shows the Bolivian high displaced northeastward, and the upper level trough located over the tropical Atlantic. The dominating structure in the winter patterns (June-July-August) is: (a) southern mid-latitude waves propagating toward low latitudes, or (b) a difluence area close to the equator related to the ITCZ.

Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.