Elastically restrained Bernoulli-Euler beams applied to rotary machinery modelling

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh's quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

Modelling a Rotating Shaft as an Elastically Restrained Bernoulli-Euler Beam

Industrial rotating machines may be exposed to severe dynamic excitations due to resonant working regimes. Dealing with the bending vibration, problem of a machine rotor, the shaft - and attached discs - can be simply modelled using the Bernoulli-Euler beam theory, as a continuous beam subjected to a specific set of boundary conditions. In this study, the authors recall Rayleigh's method to propose an iterative strategy, which allows for the determination of natural frequencies and mode shapes of continuous beams taking into account the effect of attached concentrated masses and rotational inertias, including different stiffness coefficients at the right and the left end sides. The algorithm starts with the exact solutions from Bernoulli-Euler's beam theory, which are then updated through Rayleigh's quotient parameters. Several loading cases are examined in comparison with the experimental data and examples are presented to illustrate the validity of the model and the accuracy of the obtained values.

Incremental filter and wrapper approaches for feature discretization

Discrete data representations are necessary, or at least convenient, in many machine learning problems. While feature selection (FS) techniques aim at finding relevant subsets of features, the goal of feature discretization (FD) is to find concise (quantized) data representations, adequate for the learning task at hand. In this paper, we propose two incremental methods for FD. The first method belongs to the filter family, in which the quality of the discretization is assessed by a (supervised or unsupervised) relevance criterion. The second method is a wrapper, where discretized features are assessed using a classifier. Both methods can be coupled with any static (unsupervised or supervised) discretization procedure and can be used to perform FS as pre-processing or post-processing stages. The proposed methods attain efficient representations suitable for binary and multi-class problems with different types of data, being competitive with existing methods. Moreover, using well-known FS methods with the features discretized by our techniques leads to better accuracy than with the features discretized by other methods or with the original features. (C) 2013 Elsevier B.V. All rights reserved.

An unsupervised approach to feature discretization and selection

Many learning problems require handling high dimensional datasets with a relatively small number of instances. Learning algorithms are thus confronted with the curse of dimensionality, and need to address it in order to be effective. Examples of these types of data include the bag-of-words representation in text classification problems and gene expression data for tumor detection/classification. Usually, among the high number of features characterizing the instances, many may be irrelevant (or even detrimental) for the learning tasks. It is thus clear that there is a need for adequate techniques for feature representation, reduction, and selection, to improve both the classification accuracy and the memory requirements. In this paper, we propose combined unsupervised feature discretization and feature selection techniques, suitable for medium and high-dimensional datasets. The experimental results on several standard datasets, with both sparse and dense features, show the efficiency of the proposed techniques as well as improvements over previous related techniques.

Feature Discretization with Relevance and Mutual Information Criteria

Feature discretization (FD) techniques often yield adequate and compact representations of the data, suitable for machine learning and pattern recognition problems. These representations usually decrease the training time, yielding higher classification accuracy while allowing for humans to better understand and visualize the data, as compared to the use of the original features. This paper proposes two new FD techniques. The first one is based on the well-known Linde-Buzo-Gray quantization algorithm, coupled with a relevance criterion, being able perform unsupervised, supervised, or semi-supervised discretization. The second technique works in supervised mode, being based on the maximization of the mutual information between each discrete feature and the class label. Our experimental results on standard benchmark datasets show that these techniques scale up to high-dimensional data, attaining in many cases better accuracy than existing unsupervised and supervised FD approaches, while using fewer discretization intervals.

Análise dinâmica de um equipamento industrial

Equipamentos rotativos podem ser encarados como vigas em apoios elásticos suportando um número finito de elementos concentrados ao longo do seu comprimento. Em operação, este tipo de equipamento pode ser exposto a solicitações dinâmicas severas. Com a finalidade de evitar regimes críticos, os autores propõem um algoritmo baseado no Quociente de Rayleigh, utilizando ateoria das vigas de Bernoulli-Euler. Este algoritmo permite a determinação das soluções próprias de vigas contínuas, considerando diversas condições de fronteira e o efeito da massa concentrada e inércia de rotação dos elementos suportados. Tentando reproduzir as configurações de sistemasreais são usadas diferentes condições de fronteira na formulação da teoria das vigas de Bernoulli- Euler. Salienta-se o facto dos dados analíticos serem experimentalmente verificados através de ensaios de impacto, sendo por sua vez utilizados como entradas do algoritmo de modelação, para a identificação da rigidez torsional dos apoios. Os resultados são discutidos e comparados,sempre que apropriado, com resultados já publicados. Finalmente, o trabalho futuro é delineado.

Simulação numérica do comportamento dinâmico de uma laje

Nesta dissertação pretende-se simular o comportamento dinâmico de uma laje de betão armado aplicando o Método de Elementos Finitos através da sua implementação no programa FreeFEM++. Este programa permite-nos a análise do modelo matemático tridimensional da Teoria da Elasticidade Linear, englobando a Equação de Equilíbrio, Equação de Compatibilidade e Relações Constitutivas. Tratando-se de um problema dinâmico é necessário recorrer a métodos numéricos de Integração Directa de modo a obter a resposta em termos de deslocamento ao longo do tempo. Para este trabalho escolhemos o Método de Newmark e o Método de Euler para a discretização temporal, um pela sua popularidade e o outro pela sua simplicidade de implementação. Os resultados obtidos pelo FreeFEM++ são validados através da comparação com resultados adquiridos a partir do SAP2000 e de Soluções Teóricas, quando possível.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Análise e implementação de filtros e controladores num sistema de processamento digital de sinal

Dissertação para obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Automação e Electrónica Industrial

Integração de reacção e deliberação em agentes inteligentes

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Redes de Comunicação e Multimédia

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Exploiting the bin-class histograms for feature selection on discrete data

In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio.