The reconstruction of a function and its derivative from a set of measured samples is a fundamental operation in visualisation. Multiresolution techniques, such as wavelet signal processing, are instrumental in improving the performance and algorithm design for data analysis, filtering and processing. This dissertation explores the possibilities of combining traditional multiresolution analysis and processing features of wavelets with the design of appropriate filters for reconstruction of sampled data. On the one hand, a multiresolution system allows data feature detection, analysis and filtering. Wavelets have already been proven successful in these tasks. On the other hand, a choice of discrete filter which converges to a continuous basis function under iteration permits efficient and accurate function representation by providing a “bridge” from the discrete to the continuous. A function representation method capable of both multiresolution analysis and accurate reconstruction of the underlying measured function would make a valuable tool for scientific visualisation. The aim of this dissertation is not to try to outperform existing filters designed specifically for reconstruction of sampled functions. The goal is to design a wavelet filter family which, while retaining properties necessary to preform multiresolution analysis, possesses features to enable the wavelets to be used as efficient and accurate “building blocks” for function representation. The application to visualisation is used as a means of practical demonstration of the results. Wavelet and visualisation filter design is analysed in the first part of this dissertation and a list of wavelet filter design criteria for visualisation is collated. Candidate wavelet filters are constructed based on a parameter space search of the BC-spline family and direct solution of equations describing filter properties. Further, a biorthogonal wavelet filter family is constructed based on point and average interpolating subdivision and using the lifting scheme. The main feature of these filters is their ability to reconstruct arbitrary degree piecewise polynomial functions and their derivatives using measured samples as direct input into a wavelet transform. The lifting scheme provides an intuitive, interval-adapted, time-domain filter and transform construction method. A generalised factorisation for arbitrary primal and dual order point and average interpolating filters is a result of the lifting construction. The proposed visualisation filter family is analysed quantitatively and qualitatively in the final part of the dissertation. Results from wavelet theory are used in the analysis which allow comparisons among wavelet filter families and between wavelets and filters designed specifically for reconstruction for visualisation. Lastly, the performance of the constructed wavelet filters is demonstrated in the visualisation context. One-dimensional signals are used to illustrate reconstruction performance of the wavelet filter family from noiseless and noisy samples in comparison to other wavelet filters and dedicated visualisation filters. The proposed wavelet filters converge to basis functions capable of reproducing functions that can be represented locally by arbitrary order piecewise polynomials. They are interpolating, smooth and provide asymptotically optimal reconstruction in the case when samples are used directly as wavelet coefficients. The reconstruction performance of the proposed wavelet filter family approaches that of continuous spatial domain filters designed specifically for reconstruction for visualisation. This is achieved in addition to retaining multiresolution analysis and processing properties of wavelets.

Orientador: Osvaldir Pereira Taranto / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-27T00:40:14Z (GMT). No. of bitstreams: 1 Silva_CarlosAlexandreMoreirada_D.pdf: 33350422 bytes, checksum: 046e0a2c090474593621166c81042136 (MD5) Previous issue date: 2015 / Resumo: As indústrias química, alimentícia e farmacêutica têm empregado extensivamente a operação de fluidização em inúmeros processos, devido às suas características bastante atrativas, que possibilitam um contato efetivo entre a fase sólida e fluida, o que reflete na geração de altas taxas de transferência de calor e de massa. No entanto, o regime de fluidização borbulhante, o qual é condição de partida dos processos que envolvem esta operação, frequentemente é afetado pelas condições operacionais. As temperaturas elevadas, o conteúdo de umidade excessivo das partículas e a introdução de líquidos no leito fluidizado podem conduzir a instabilidades no regime fluidodinâmico e provocar o colapso parcial ou total do leito, reduzindo a eficiência do processo. A manutenção de condições estáveis do regime de fluidização durante processos de recobrimento de partículas em leitos fluidizados é de fundamental importância para garantir uma eficiência de recobrimento favorável e evitar a formação de zonas sem movimentação e aglomeração das partículas no leito, pois estes fatores indesejáveis comprometem a mistura entre as fases e conseqüentemente a qualidade do produto final. Dentro deste contexto, a utilização de um sistema de monitoramento e controle em tempo real de processos de recobrimento de partículas é extremamente desejável para permitir a operação de regimes de fluidização estáveis e garantir um filme de recobrimento uniforme e boas condições de escoabilidade dos sólidos. A presente proposta de tese de doutorado tem por objetivo aplicar a metodologia de análise espectral Gaussiana dos sinais de flutuação de pressão (Parise et al. (2008)), para o desenvolvimento de sistemas de controle baseados em inteligência artificial (Lógica Fuzzy), visando monitorar a estabilidade do regime de fluidização em processo de recobrimento de partículas. Comparações entre as condições fluidodinâmicas dos processos com e sem controle foram analisadas para operações em leito fluidizado em escala de laboratorio. Para avaliar a qualidade das partículas foi utilizada uma sonda de monitoramento in-line (Parsum IPP70), onde se pôde verificar os instantes iniciais da aglomeração indesejada. Com a aplicação desde sistema automatizado foi possível associar a estabilidade da fluidização em função do elevado grau de aglomeração. O ponto de parada do processo pôde ser definido em 420 µm (inicial em 360 µm) e a partir deste o mecanismo de recobrimento acontece simultaneamente com o de aglomeração. Os parâmetros de monitoramento do regime conseguiram não somente identificar a fase inicial da defluidização, como também foi possível a partir deles, controlar o processo por Lógica Fuzzy-PI e estabilizar a operação para altas taxas de suspensão atomizadas / Abstract: The chemical, food and pharmaceutical industries have extensively used fluidization operation in many cases, due to its very attractive features that enable effective contact between the solid and fluid phase, which reflects the generation of high heat and mass transfer rates. However, the bubbling fluidization regime, which is the starting condition of the processes involved in this operation is often affected by operating conditions. Elevated temperatures, excessive moisture content of the particles and introduction of liquid into the fluidized bed may lead to instabilities in the fluid-dynamic regime and cause partial or total collapse of the bed, reducing the process efficiency. The maintenance of stable conditions of the fluidization regime for particle coating processes in fluidized beds is of fundamental importance to ensure a favorable coating efficiency and to avoid zones without movement and agglomeration of particles in the bed, because these undesirable factors compromise the mixing between the phases and therefore the quality of the final product. Within this context, the use of a monitoring system and real-time control of particle coating processes is highly desirable to allow operation in stable fluidization regimes and to ensure a uniform coating film and good condition of flowability of the solids. This doctoral thesis aims to apply the Gaussian spectral analysis methodology of the pressure fluctuation signals (Parise et al. (2008)) , for the development of control systems based on artificial intelligence (Fuzzy Logic), to monitor the stability of fluidization regime particle coating process. Comparisons between the fluid dynamic conditions of the processes with and without control were analyzed for operations in fluidized bed laboratory scale. To assess early stages of unwanted agglomeration, a monitoring in-line probe (Parsum IPP70) was used. With the application of this automated system, it was possible to associate the stability of fluidization with a high degree of agglomeration. The process stopping point could be set at 420 µm (initial in 360 µm) and after, the coating mechanism takes place simultaneously with the agglomeration one. The monitoring parameters of the system were able to identify the initial phase of defluidization, as well as it was possible to control the process by using Fuzzy Logic and to stabilize the operation for high rates of the coating suspension atomized onto the bed / Doutorado / Engenharia de Processos / Doutor em Engenharia Química