Gravitational Search Algorithm for NURBS Curve Fitting

By providing great flexibility non-uniform rational B-spline (NURBS) curves and surfaces are reason of preferability on areas like computer aided design, medical imaging and computer graphics. Knots, control points and weights provide this flexibility. Computation of these parameters makes the problem as a non-linear combinational optimization problem on a process of reverse engineering. The ability of solving these problems using meta-heuristics instead of conventional methods attracts researchers. In this paper, NURBS curve estimation is carried out by a novel optimization method namely gravitational search algorithm. Both knots and knots together weights simultaneous optimization process is implemented by using research agents. The high performance of the proposed method on NURBS curve fitting is showed by obtained results.Keywords: Non-uniform rational B-spline, gravitational search algorithm, meta-heuristi

Evalutionary algorithms for ship hull skinning approximation

Traditionally, the design process of a hull involves simulation using clay models. This must be done cautiously, accurately and efficiently in order to sustain the performance of ship. Presently, the current technology of Computer Aided Design, Manufacturing, Engineering and Computational Fluid Dynamic has enabled a 3D design and simulation of a hull be done at a lower cost and within a shorter period of time. Besides that, automated design tools allow the transformation of offset data in designing the hull be done automatically. One of the most common methods in constructing a hull from the offset data is the skinning method. Generally, the skinning method comprised of skinning interpolation and skinning approximation. Skinning interpolation constructs the surface perfectly but improper selection of parameterization methods may cause bumps, wiggles, or uneven surfaces on the generated surface. On the other hand, using the skinning surface approximation would mean that the surface can only be constructed closer to data points. Thus, the error between the generated surface and the data points must be minimized to increase the accuracy. Therefore, this study aims to solve the error minimization problem in order to produce a smoother and fairer surface by proposing Non Uniform Rational B-Spline surface using various evolutionary optimization algorithms, namely, Gravitational Search Algorithm, Particle Swarm Optimization and Genetic Algorithm. The proposed methods involve four procedures: extraction of offset data from line drawing plan; generation of control points; optimization of a surface; and validations of hull surfaces. Validation is done by analyzing the surface curvature and errors between the generated surface and the given data points. The experiments were implemented on both ship hull and free form models. The findings from the experiments are compared with interpolated skinning surface and conventional skinning surface approximation. The results show that the optimized skinning surfaces using the proposed methods yield a smaller error, less control points generation and feasible surfaces while maintaining the shape of the hull

Structural topology optimisation based on the Boundary Element and Level Set methods

The research work presented in this thesis is related to the development of structural optimisation algorithms based on the boundary element and level set methods for two and three-dimensional linear elastic problems. In the initial implementation, a stress based evolutionary structural optimisation (ESO) approach has been used to add and remove material simultaneously for the solution of two-dimensional optimisation problems. The level set method (LSM) is used to provide an implicit description of the structural geometry, which is also capable of automatically handling topological changes, i.e. holes merging with each other or with the boundary. The classical level set based optimisation methods are dependent on initial designs with pre-existing holes. However, the proposed method automatically introduces internal cavities utilising a stress based hole insertion criteria, and thereby eliminates the use of initial designs with pre-existing holes. A detailed study has also been carried out to investigate the relationship between a stress and topological derivative based hole insertion criteria within a boundary element method (BEM) and LSM framework. The evolving structural geometry (i.e. the zero level set contours) is represented by non-uniform rational b-splines (NURBS), providing a smooth geometry throughout the optimisation process and completely eliminating jagged edges. The BEM and LSM are further combined with a shape sensitivity approach for the solution of minimum compliance problems in two-dimensions. The proposed sensitivity based method is capable of automatically inserting holes during the optimisation process using a topological derivative approach. In order to investigate the associated advantages and disadvantages of the evolutionary and sensitivity based optimisation methods a comparative study has also been carried out. There are two advantages associated with the use of LSM in three-dimensional topology optimisation. Firstly, the LSM may readily be applied to three-dimensional space, and it is shown how this can be linked to a 3D BEM solver. Secondly, the holes appear automatically through the intersection of two surfaces moving towards each other. Therefore, the use of LSM eliminates the need for an additional hole insertion mechanism as both shape and topology optimisation can be performed at the same time. A complete algorithm is proposed and tested for BEM and LSM based topology optimisation in three-dimensions. Optimal geometries compare well against those in the literature for a range of benchmark examples

Intelligent Freeform Deformation for LED Illumination Optics

In freeform optics, the optimization is limited due to large number of parameters present in it. This limitation was overcome by a technique known as optimization using freeform deformation (OFFD). Though this technique proved to work well, it has left many challenges to the optical designer. These challenges are solved by providing mathematical design techniques. This implementation transformed the OFFD into an intelligent tool replacing the optical designer\u27s efforts during the design process

Micro-EDM numerical simulation and experimental validation

This paper introduces a new method for simulating the micro-EDM process in order to predict tool wear. The tool and workpiece are defined by NURBS surfaces whose shapes result from an iterative crater-by-crater deformation technique driven by physical parameters. The simulation method is validated through a comparison with experimental data. Different simulations are presented with an increase in computation accuracy in order to study its influence on the results and their deviation from expected values

Design of neuro-fuzzy models by evolutionary and gradient-based algorithms

All systems found in nature exhibit, with different degrees, a nonlinear behavior. To emulate this behavior, classical systems identification techniques use, typically, linear models, for mathematical simplicity. Models inspired by biological principles (artificial neural networks) and linguistically motivated (fuzzy systems), due to their universal approximation property, are becoming alternatives to classical mathematical models. In systems identification, the design of this type of models is an iterative process, requiring, among other steps, the need to identify the model structure, as well as the estimation of the model parameters. This thesis addresses the applicability of gradient-basis algorithms for the parameter estimation phase, and the use of evolutionary algorithms for model structure selection, for the design of neuro-fuzzy systems, i.e., models that offer the transparency property found in fuzzy systems, but use, for their design, algorithms introduced in the context of neural networks. A new methodology, based on the minimization of the integral of the error, and exploiting the parameter separability property typically found in neuro-fuzzy systems, is proposed for parameter estimation. A recent evolutionary technique (bacterial algorithms), based on the natural phenomenon of microbial evolution, is combined with genetic programming, and the resulting algorithm, bacterial programming, advocated for structure determination. Different versions of this evolutionary technique are combined with gradient-based algorithms, solving problems found in fuzzy and neuro-fuzzy design, namely incorporation of a-priori knowledge, gradient algorithms initialization and model complexity reduction.Todos os sistemas encontrados na natureza exibem, com maior ou menor grau, um comportamento linear. De modo a emular esse comportamento, as técnicas de identificação clássicas usam, tipicamente e por simplicidade matemática, modelos lineares. Devido à sua propriedade de aproximação universal, modelos inspirados por princípios biológicos (redes neuronais artificiais) e motivados linguisticamente (sistemas difusos) tem sido cada vez mais usados como alternativos aos modelos matemáticos clássicos. Num contexto de identificação de sistemas, o projeto de modelos como os acima descritos é um processo iterativo, constituído por vários passos. Dentro destes, encontra-se a necessidade de identificar a estrutura do modelo a usar, e a estimação dos seus parâmetros. Esta Tese discutirá a aplicação de algoritmos baseados em derivadas para a fase de estimação de parâmetros, e o uso de algoritmos baseados na teoria da evolução de espécies, algoritmos evolutivos, para a seleção de estrutura do modelo. Isto será realizado no contexto do projeto de modelos neuro-difusos, isto é, modelos que simultaneamente exibem a propriedade de transparência normalmente associada a sistemas difusos mas que utilizam, para o seu projeto algoritmos introduzidos no contexto de redes neuronais. Os modelos utilizados neste trabalho são redes B-Spline, de Função de Base Radial, e sistemas difusos dos tipos Mamdani e Takagi-Sugeno. Neste trabalho começa-se por explorar, para desenho de redes B-Spline, a introdução de conhecimento à-priori existente sobre um processo. Neste sentido, aplica-se uma nova abordagem na qual a técnica para a estimação dos parâmetros é alterada a fim de assegurar restrições de igualdade da função e das suas derivadas. Mostra-se ainda que estratégias de determinação de estrutura do modelo, baseadas em computação evolutiva ou em heurísticas determinísticas podem ser facilmente adaptadas a este tipo de modelos restringidos. É proposta uma nova técnica evolutiva, resultante da combinação de algoritmos recentemente introduzidos (algoritmos bacterianos, baseados no fenómeno natural de evolução microbiana) e programação genética. Nesta nova abordagem, designada por programação bacteriana, os operadores genéticos são substituídos pelos operadores bacterianos. Deste modo, enquanto a mutação bacteriana trabalha num indivíduo, e tenta otimizar a bactéria que o codifica, a transferência de gene é aplicada a toda a população de bactérias, evitando-se soluções de mínimos locais. Esta heurística foi aplicada para o desenho de redes B-Spline. O desempenho desta abordagem é ilustrada e comparada com alternativas existentes. Para a determinação dos parâmetros de um modelo são normalmente usadas técnicas de otimização locais, baseadas em derivadas. Como o modelo em questão é não-linear, o desempenho deste género de técnicas é influenciado pelos pontos de partida. Para resolver este problema, é proposto um novo método no qual é usado o algoritmo evolutivo referido anteriormente para determinar pontos de partida mais apropriados para o algoritmo baseado em derivadas. Deste modo, é aumentada a possibilidade de se encontrar um mínimo global. A complexidade dos modelos neuro-difusos (e difusos) aumenta exponencialmente com a dimensão do problema. De modo a minorar este problema, é proposta uma nova abordagem de particionamento do espaço de entrada, que é uma extensão das estratégias de decomposição de entrada normalmente usadas para este tipo de modelos. Simulações mostram que, usando esta abordagem, se pode manter a capacidade de generalização com modelos de menor complexidade. Os modelos B-Spline são funcionalmente equivalentes a modelos difusos, desde que certas condições sejam satisfeitas. Para os casos em que tal não acontece (modelos difusos Mamdani genéricos), procedeu-se à adaptação das técnicas anteriormente empregues para as redes B-Spline. Por um lado, o algoritmo Levenberg-Marquardt é adaptado e a fim de poder ser aplicado ao particionamento do espaço de entrada de sistema difuso. Por outro lado, os algoritmos evolutivos de base bacteriana são adaptados para sistemas difusos, e combinados com o algoritmo de Levenberg-Marquardt, onde se explora a fusão das características de cada metodologia. Esta hibridização dos dois algoritmos, denominada de algoritmo bacteriano memético, demonstrou, em vários problemas de teste, apresentar melhores resultados que alternativas conhecidas. Os parâmetros dos modelos neuronais utilizados e dos difusos acima descritos (satisfazendo no entanto alguns critérios) podem ser separados, de acordo com a sua influência na saída, em parâmetros lineares e não-lineares. Utilizando as consequências desta propriedade nos algoritmos de estimação de parâmetros, esta Tese propõe também uma nova metodologia para estimação de parâmetros, baseada na minimização do integral do erro, em alternativa à normalmente utilizada minimização da soma do quadrado dos erros. Esta técnica, além de possibilitar (em certos casos) um projeto totalmente analítico, obtém melhores resultados de generalização, dado usar uma superfície de desempenho mais similar aquela que se obteria se se utilizasse a função geradora dos dados

Enhancing 3D Autonomous Navigation Through Obstacle Fields: Homogeneous Localisation and Mapping, with Obstacle-Aware Trajectory Optimisation

Small flying robots have numerous potential applications, from quadrotors for search and rescue, infrastructure inspection and package delivery to free-flying satellites for assistance activities inside a space station. To enable these applications, a key challenge is autonomous navigation in 3D, near obstacles on a power, mass and computation constrained platform. This challenge requires a robot to perform localisation, mapping, dynamics-aware trajectory planning and control. The current state-of-the-art uses separate algorithms for each component. Here, the aim is for a more homogeneous approach in the search for improved efficiencies and capabilities. First, an algorithm is described to perform Simultaneous Localisation And Mapping (SLAM) with physical, 3D map representation that can also be used to represent obstacles for trajectory planning: Non-Uniform Rational B-Spline (NURBS) surfaces. Termed NURBSLAM, this algorithm is shown to combine the typically separate tasks of localisation and obstacle mapping. Second, a trajectory optimisation algorithm is presented that produces dynamically-optimal trajectories with direct consideration of obstacles, providing a middle ground between path planners and trajectory smoothers. Called the Admissible Subspace TRajectory Optimiser (ASTRO), the algorithm can produce trajectories that are easier to track than the state-of-the-art for flight near obstacles, as shown in flight tests with quadrotors. For quadrotors to track trajectories, a critical component is the differential flatness transformation that links position and attitude controllers. Existing singularities in this transformation are analysed, solutions are proposed and are then demonstrated in flight tests. Finally, a combined system of NURBSLAM and ASTRO are brought together and tested against the state-of-the-art in a novel simulation environment to prove the concept that a single 3D representation can be used for localisation, mapping, and planning

A radial basis function method for solving optimal control problems.

This work presents two direct methods based on the radial basis function (RBF) interpolation and arbitrary discretization for solving continuous-time optimal control problems: RBF Collocation Method and RBF-Galerkin Method. Both methods take advantage of choosing any global RBF as the interpolant function and any arbitrary points (meshless or on a mesh) as the discretization points. The first approach is called the RBF collocation method, in which states and controls are parameterized using a global RBF, and constraints are satisfied at arbitrary discrete nodes (collocation points) to convert the continuous-time optimal control problem to a nonlinear programming (NLP) problem. The resulted NLP is quite sparse and can be efficiently solved by well-developed sparse solvers. The second proposed method is a hybrid approach combining RBF interpolation with Galerkin error projection for solving optimal control problems. The proposed solution, called the RBF-Galerkin method, applies a Galerkin projection to the residuals of the optimal control problem that make them orthogonal to every member of the RBF basis functions. Also, RBF-Galerkin costate mapping theorem will be developed describing an exact equivalency between the Karush–Kuhn–Tucker (KKT) conditions of the NLP problem resulted from the RBF-Galerkin method and discretized form of the first-order necessary conditions of the optimal control problem, if a set of conditions holds. Several examples are provided to verify the feasibility and viability of the RBF method and the RBF-Galerkin approach as means of finding accurate solutions to general optimal control problems. Then, the RBF-Galerkin method is applied to a very important drug dosing application: anemia management in chronic kidney disease. A multiple receding horizon control (MRHC) approach based on the RBF-Galerkin method is developed for individualized dosing of an anemia drug for hemodialysis patients. Simulation results are compared with a population-oriented clinical protocol as well as an individual-based control method for anemia management to investigate the efficacy of the proposed method