On multi-degree splines

Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree splines that can be derived by existing approaches. We then propose a new alternative method for constructing and evaluating the B-spline basis, based on the use of so-called transition functions. Using the transition functions we develop general algorithms for knot-insertion, degree elevation and conversion to B\'ezier form, essential tools for applications in geometric modeling. We present numerical examples and briefly discuss how the same idea can be used in order to construct geometrically continuous multi-degree splines

Digital measurement of lightning impulse parameters using curving fitting algorithms

This paper describes the application of curve fitting algorithms to aid the evaluation of lightning impulse parameters. A number of popular curve fitting algorithms have been evaluated and compared. Investigations using the genetic algorithm and other optimisation methods for the purpose of curve fitting have also been carried out and will be described

Evolutionary structural pptimisation based on boundary element representation of b-spline geometry

Evolutionary Structural Optimisation (ESO) has become a well-established technique for determining the optimum shape and topology of a structure given a set of loads and constraints. The basic ESO concept that the optimum topology design evolves by slow removal and addition of material has matured over the last ten years. Nevertheless, the development of the method has almost exclusively considered finite elements (FE) as the approach for providing stress solutions. This thesis presents an ESO approach based on the boundary element method. Non-uniform rational B-splines (NURBS) are used to define the geometry of the component and, since the shape of these splines is governed by a set of control points, use can be made of the locations of these control points as design variables. The developed algorithm creates internal cavities to accomplish topology changes. Cavities are also described by NURBS and so they have similar behaviour to the outside boundary. Therefore, both outside and inside are optimised at the same time. The optimum topologies evolve allowing cavities to merge between each other and to their closest outer boundary. Two-dimensional structural optimisation is investigated in detail exploring multi-load case and multi-criteria optimisation. The algorithm is also extended to three-dimensional optimisation, in which promising preliminary results are obtained. It is shown that this approach overcomes some of the drawbacks inherent in traditional FE-based approaches, and naturally provides accurate stress solutions on smooth boundary representations at each iteration

Matrix representations for multi-degree B-splines

The paper is concerned with computing the B-spline basis of a multi-degree spline space, namely a space of piecewise functions comprised of polynomial segments of different degrees. To this aim, we provide a general method to work out a matrix representation relating the sought basis with another one easier to compute. This will allow us, for example, to calculate a multi degree B-spline basis starting from local Bernstein bases of different degrees or from the B-spline basis of a spline space where all sections have the same degree. This change of basis can be translated into a conceptually simple and computationally efficient algorithm for the evaluation of multi-degree B-splines

Constructing an overall dynamical model for a system with changing design parameter properties

This study considers the identification problem for a class of non-linear parameter-varying systems associated with the following scenario: the system behaviour depends on some specifically prescribed parameter properties, which are adjustable. To understand the effect of the varying parameters, several different experiments, corresponding to different parameter properties, are carried out and different data sets are collected. The objective is to find, from the available data sets, a common parameter-dependent model structure that best fits the adjustable parameter properties for the underlying system. An efficient Common Model Structure Selection (CMSS) algorithm, called the Extended Forward Orthogonal Regression (EFOR) algorithm, is proposed to select such a common model structure. Two examples are presented to illustrate the application and the effectiveness of the new identification approach

Determination of suitable values for parameters governing B-spline based evolutionary structural optimisation using the boundary element method

The basic evolutionary structural optimisation concept (ESO) has been developed for several years. Recently, the first ESO algorithm based on the boundary element method (BEM) has been presented. In this thesis, this algorithm is used for the 2D shape optimisation. The aim is to develop a greater understanding of the role of certain governing parameters that drive the optimisation using this algorithm, and to make recommendations as to appropriate values of these parameters that give rise to good optimal solutions most efficiently. Two problems, a short cantilever beam and a fillet, are selected as test cases in this work. By using a wide range of numerical tests, the performance of the optimisation has been evaluated using a variety of methods including mean performance analysis and multi-objective optimisation approaches using Pareto curves and weighted sums. Recommendations are made as to appropriate values of these parameters that give rise to good optimal solutions most efficiently. Sensitivity analysis is another important method in engineering design. In this work a new algorithm to undertake a sensitivity analysis has been developed and used in a small number of investigations for boundary element structural optimisation process. ESO is selected when computational efficiency is thought the most important consideration, since it can reach the optimum in fewer iterations and lower run-time compared with sensitivity analysis in structural optimisation

A modern vision of simulation modelling in mining and near mining activity

The paper represents the creation of the software simulation system, which reproduce the basic processes of mining and near production. It presents the consideration of such systems for both traditional and non-traditional mineral extraction systems. The principles of using computer recognition of processes are also presented in other processes of carbon-containing raw materials transition, as well as power production and waste utilization of mining production. These systems considerably expand the manageability of a rather complicated mining enterprise. The main purpose of such research is the simulation reproduction of all technological processors associated with the activity of mining enterprises on the display of the dispatch center. For this purpose, is used so-called UML-diagrams, which allows to simulate mining and near mining processes. Results of this investigation were included to the Roman Dychkovskyi thesis of the scientific degree of the Doctor of the Technique Sciences “Scientific Principles of Technologies Combination for Coal Mining in Weakly Metamorphoses Rockmass”