We describe an entirely new generation of the meshless methods for stochastic modelling of microstructure formation in this book chapter. The method is based on the discretisation based on randomly distributed nodes and not on the basis of polygons like in the classical cellular automata method. Higher discretisation flexibility and indepenedence of the results with respect to the orientation of the discretisation is achieved. An important consequence of this approach is independence of the shape of the dendritic structures as a function of the position of the crystallographic angles. We apply the method to multiple dendritic growth in steel.

COBISS.SI-ID: 1857531

A meshless solution of the recently proposed industrial benchmark test for continuous casting (Šarler et al., 2012) is displayed in the present paper. The physical model is established on a set of macroscopic equations for mass, energy, momentum, turbulent kinetic energy, and dissipation rate in two dimensions. The mixture continuum model is used to treat the solidification system. The mushy zone is modelled as a Darcy porous media with Kozeny–Karman permeability relation, where the morphology of the porous media is modeled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number (LRN) k–ε turbulence model, closed by the Abe–Kondoh–Nagano closure coefficients and damping functions. The numerical method is established on explicit time-stepping, collocation with multiquadrics radial basis functions on non-uniform five-nodded influence domains, and adaptive upwinding technique. The velocity–pressure coupling of the incompressible flow is resolved by the explicit Chorin’s fractional step method. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion. The results are carefully presented and tabulated, together with the results obtained by ANSYS-Fluent, which would in the future permit straightforward comparison with other numerical approaches as well.

COBISS.SI-ID: 3222523

The Energy Agency of the Republic of Slovenia regulates and determines the operations of the natural-gas market, charges for related gas imbalances, decides on suppliers and controls penalty provisions relating to breaches of stipulated provisions. Each supplier regulates and determines the charges for the differences between the ordered (predicted) and the actually supplied quantities. Store Steel Company is one of the major spring-steel producers in Europe. Its natural gas consumption represents approximately 1.1% of Slovenia’s national natural gas consumption. The company is contractually bound to a supplier which exacts penalties according to the differences mentioned above. A successful approach to gas consumption prediction is elaborated in this paper, with the aim of minimizing associated costs. In the attempt to model and predict the gas consumption and, accordingly, to minimize ordered and supplied gas quantity error, we used linear regression and the genetic programming approach. The genetic programming model performs approximately two times more favourably. The developed gas consumption model has been used in practice since April 2005. The results show good agreement between the model-based ordered quantities and the actually supplied quantities, with savings amounting to approximately 100,000 EUR per year.

COBISS.SI-ID: 3219707

This book covers the characterization and modeling of polycrystalline metallic material (spring steel) microstructures, with the aim to better understand the complex problem of predicting material properties based on a knowledge and representation of the microstructure. The microstructure features of the spring steel were studied on numerous samples in order to understand the basic geometrical characteristics needed to build the model. An overview of light microscopy, scanning electron microscopy, and Auger electron spectroscopy techniques is provided. Some general aspects of the methods used for the microstructure modeling are provided. The presented approach is the non-mesh based representation of the material. The core idea described in the book is to generate randomly shaped grains, where each grain represents a stand-alone object. In order to make a realistic model of the observed material, the shape of the grains represented by the neural network must come as close as possible to the observed material. The virtual grains are first generated. Separately the microstructural properties of the observed material are gathered and the process of grain-shape optimization is used to modify the shape of virtual grains to come as close as possible to the observed real sample. The modeled material is then constructed by the extremely large number of uniquely shaped virtual grains. A new approach to the grain-shape optimization with a genetic algorithm is introduced. The grain-shape similarity is determined by a grain-roughness assessment and a new method named the grain-roughness histogram is developed and evaluated. The grain-roughness histogram provides the metrics needed for the grain-shape optimization. Since the grain structure is represented by the neural network, the process of the grain-shape modification must alter the neural network weights. Therefore, a sensitivity study of the neural network weights was performed. On the basis of the weights sensitivity study, the genetic algorithm application for grain-roughness optimization was designed. Furthermore the alternate genetic algorithm optimization was used, which directly influences the grain-boundary properties without interfering with the grain representation provided by the neural network. The method using neural networks and genetic algorithms is an original breakthrough contribution and provides the foundation for a completely new approach to the modeling of metallic materials. The representation of a random grain structure (as an object) is realized using the neural networks. The manipulation and optimization of the randomly generated grain shape is achieved by the genetic algorithms. The established concept of the 2D modeling is designed and can be directly used in the 3D space.

COBISS.SI-ID: 1024170

This paper presents a systematic analysis of the existing methods for visualization of Pareto front approximations (approximation sets). Their outcomes are shown on two novel 4D benchmark approximation sets. In addition, a visualization method that uses prosection (projection of a section) to visualize 4D approximation sets is proposed. The method reproduces the shape, range and distribution of vectors in the observed approximation sets well and can handle multiple large approximation sets while being robust and computationally inexpensive. Even more importantly, for some vectors, the visualization with prosections preserves the Pareto dominance relation and relative closeness to reference points. The method is analyzed theoretically and demonstrated on several approximation sets. Comment: Paper accepted for publication in top journal IEEE Transactions on Evolutionary Computation, 2014.