Ljubiša Kocić

Wind speed parameters sensitivity analysis based on fractals and neuro-fuzzy selection technique

Fluctuation of wind speed affects wind energy systems since the potential wind power is proportional the cube of wind speed. Hence precise prediction of wind speed is very important to improve the performances of the systems. Due to unstable behavior of the wind speed above different terrains, in this study fractal characteristics of the wind speed series were analyzed. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Afterward neuro-fuzzy technique was applied to the fractal data because of high nonlinearity of the data. The neuro-fuzzy approach was used to detect the most important variables which affect the wind speed according to the fractal dimensions. The main goal was to investigate the influence of terrain roughness length and different heights of the wind speed on the wind speed prediction.

Fractal Geometry and Properties of Doped BaTiO3 Ceramics

Taking into account that the complex grain structure is difficult to describe by using traditional analytical methods, in this study, in order to establish ceramic grain shapes of sintered BaTiO3, new approach on correlation between microstructure and properties of doped BaTiO3 ceramics based on fractal geometry has been developed. BaTiO3 ceramics doped with various dopants (MnCO3, Er2O3, Yb2O3) were prepared using conventional solid state procedure, and were sintered at 1350oC for four hours. The microstructure of sintered specimens was investigated by SEM-5300. Using method of fractal modeling a reconstruction of microstructure configurations, like grains shapes, or intergranular contacts has been successfully done. Furthermore, the area of grains surface was calculated using fractal correction that expresses the irregularity of grains surface through fractal dimension. The presented results, indicate that fractal method for ceramics structure analysis provides a new approach for describing, predicting and modeling the grain shape and relations between the BaTiO3-ceramic structure and dielectrical properties.

TRIZ Creativity Approach to the Design of an Innovative Wind Turbine System

The main aim of a conceptual design is to obtain the innovative projects or ideas to enable the products and designs with best performance, what is also including the materials especially ceramics optimal selection for the effective solutions. The theory of inventive problem solution (TRIZ) is a systematic methodology for innovation. The design of a wind turbine system as an engineering example is illuminated in this paper to show the significance and approaches of applying TRIZ in getting the creative conceptual design ideas. In recent years the use of renewable energy including wind energy has risen dramatically. Because of the increasing development of wind power production, improvement of the design and control of wind turbines is necessary. To optimize the power produced in a wind turbine, it is important to analyze the wind turbine designs and systems. To build a wind turbine model with the best features, it is desirable to analyze factors that are truly relevant to the converted wind energy. The main aim of this work is to show a systematic methodology for innovation as an effective procedure to enhance the capability of developing innovative products and to overcome the main design problems. The TRIZ method will be used in order to eliminate the technical contradictions which appear in the wind turbine systems.

Processing parameter influence on BaTiO3 ceramic fractal microstructure and dielectric characteristics

Abstract In the process of BaTiO3 ceramics consolidation, technological parameters like sintering temperature, pressing pressure and additives significantly determine the microstructure and electrical properties. Slight change of a particular sintering parameter can considerably change the microstructure as well as the electrical parameters. Structural complex grain–contact–grain is observed on Ho doped BaTiO3 ceramics, sintered from 1320 to 1380°C. The new configuration model of ceramic grain contact surfaces is presented in this paper. This model is based on Coble’s two-sphere approximation and its generalisation to ellipsoidal geometry. The integral contact surface directly influences the value of the total ceramic capacity. Fractal method is applied for intergrain contact analysis. Ceramic grains are considered to have fractal surface (as it is elsewhere in nature) and, therefore, fractal structure influences on the dielectric properties of BaTiO3 ceramics. The obtained results give better understanding of ceramic microstructure with the final aim to establish significant interrelation among processing, structural and electrical parameters.

Fractals and BaTiO3-Ceramic Microstructure Analysis

The complex grainy structure of BaTiO3 is difficult to describe by using traditional analytical or geometrical methods. Here, an attempt is made to establish new mathematical models based on both Euclidean and fractal geometrical methods. The first uses ellipsoidal approximations for barium-titanate grains describing the contact area as surface patches with an ellipsoidal boundary. The fractal method offers a better approach in describing the irregular and wavy surface of such contact zones and therefore, it defines aspects that are complementary to those defined by Euclidean methods. Electric, ferroelectric and opto-electric properties of BaTi03 are influenced strongly by the fractal dimension of the intergranular contact surfaces. This parameter is measured in a laboratory environment using SEM micrographs with different magnifications. The BaTiO3 samples examined have been sintered using different sintering pressures and temperatures. Then, the fractal dimension is calculated from a log-log diagram, and the grain contours are constructed using Iterated Function Systems connected with fractal interpolation.

Minimal Simplex for IFS Fractal Sets

Fractal sets manipulation and modeling is a difficult task due to their complexity and unpredictability. One of the basic problems is to determine bounds of a fractal set given by some recursive definitions, for example by an Iterated Function System (IFS). Here we propose a method of bounding an IFS-generated fractal set by a minimal simplex that is affinely identical to the standard simplex. First, it will be proved that for a given IFS attractor, such simplex exists and it is unique. Such simplex is then used for definition of an Affine invariant Iterated Function System (AIFS) that then can be used for affine transformation of a given fractal set and for its modeling.

Adaptive Neuro-Fuzzy Optimization of Wind Farm Project Investment Under Wake Effect

The engineering planning of a wind farm generally includes critical decision-making, regarding the layout of the turbines in the wind farm, the number of wind turbines to be installed and the types of wind turbines to be installed. Two primary objectives of optimal wind farm planning are to minimize the cost of energy and to maximize the net energy production or to maximize wind farm efficiency. The optimal wind turbine placement on a wind farm could be modified by taking economic aspects into account. The net present value (NPV) and internal rate of return (IRR) are two of the most important criteria for project investment estimating. To assess the investment risk of wind power project, this paper constructed a process which initially simulated maximal NPV with adaptive neuro-fuzzy (ANFIS) method and then evaluated the IRR based on it. Afterwards, ANFIS simulated maximal IRR and then evaluated the NPV based on it. ANFIS shows very good learning and prediction capabilities, which makes it an efficient tool to deal with encountered uncertainties in any system. The aim of this paper is to develop a model to determine economically optimal layouts for wind farms which include the aerodynamic interactions between the turbines, the various cost factors and wind regime.

A property of farey tree

The Farey tree is a binary tree containing all rational numbers from [0, 1] in ordered way. It is constructed hierarchically, level by level, using the Farey mediant sum. Some extreme properties of the Farey sum tree, i.e., the set of points {p+q} associated with Farey tree in the way that rationals {p/q} belong to k-th level of the Farey tree are investigated.

Fractals In Ceramic Structure

Using combination of Euclidean and fractal geometry, the new structural configuration model of BaTiO3-ceramic grains is presented. The stereological configuration of the position of BaTiO3-ceramic grains and the influence of grain’s displacement on contact surfaces is studied. The model of structural pattern, containing a pair of grains is used. The contact area size is of distinguished importance in grains structure. The intergrain contact area is a basis of electronic processes in BaTiO3-ceramics material1,2. Any contact area, between any two grains can be seen as a geometry of a microcapacitor. Its microimpedance contains capacitive, inductive and passive resistance components. On the other hand, any contact surface, apart of the method being used can be represented as a function of mutual position of grains and parameters of sintering process (pressure, temperature and sintering time). Therefore, experiments were made by using the electronic microscopy method, with the ceramic samples prepared under pressing pressure up to 150 MPa and sintering temperature up to 1370°C.

Exploring fractality of microcrystalline diamond films

Diamond is renowned as a material with superlative physical qualities, most of which originate from the strong covalent bonding between its atoms. The possibility to deposit polycrystalline diamond films via chemical vapor deposition (CVD) methods on large areas and on a large variety of substrates is posing numerous scientific challenges but also enables relevant industrial applications. Especially for small grain sizes, the grain’s misorientation and consequently the atomic structure of grain boundaries plays a significant role on transport properties and mechanical properties. Hence, the size and shape of the crystallites of poly- and nanocrystalline diamond films are one important key to optimize film properties for their specific applications. Fractal theory helps to find and define order in systems where disorder seems to prevail. Therefore, we apply fractal geometry analysis to characterize the grain morphology and surface topology of CVD grown diamond films.Diamond is renowned as a material with superlative physical qualities, most of which originate from the strong covalent bonding between its atoms. The possibility to deposit polycrystalline diamond films via chemical vapor deposition (CVD) methods on large areas and on a large variety of substrates is posing numerous scientific challenges but also enables relevant industrial applications. Especially for small grain sizes, the grain’s misorientation and consequently the atomic structure of grain boundaries plays a significant role on transport properties and mechanical properties. Hence, the size and shape of the crystallites of poly- and nanocrystalline diamond films are one important key to optimize film properties for their specific applications. Fractal theory helps to find and define order in systems where disorder seems to prevail. Therefore, we apply fractal geometry analysis to characterize the grain morphology and surface topology of CVD grown diamond films.