Opis: Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. Ključne besede:analytical modeling, anhysteretic curve, applied mathematics, Bézier curve, curve fitting, first magnetization curve, major loop, mathematical modeling, non-oriented electrical steel Objavljeno v DKUM: 01.02.2024; Ogledov: 382; Prenosov: 25 Celotno besedilo (4,90 MB)

Opis: This paper proposes new approach for modeling of various processes in metal-forming industry. As an example, we demonstrate the use of genetic programming (GP) for modeling of forming efficiency. The forming efficiency is a basis for determination of yield stress which is the fundamental characteristic of metallic materials. Several different genetically evolved models for forming efficiency on the basis of experimental data for learning were discovered. The obtained models (equations) differ in size, shape, complexity and precision of solutions. In one run out of many runs of our GP system the well-known equation of Siebel was obtained. This fact leads us to opinion that GP is a very powerful evolutionary optimization method appropriate not only for modeling of forming efficiency but also for modeling of many other processes in metal-forming industry. Ključne besede:metal forming, yield stress, forming efficiency, mathematical modeling, adaptation, genetic methods, genetic algorithm, genetic programming, artificial intelligence, process optimisation Objavljeno v DKUM: 01.06.2012; Ogledov: 2212; Prenosov: 121 Povezava na celotno besedilo

Opis: This work describes the statistical analysis of three mathematical models, modified for describing the kefir grain biomass growth curve. Experimental data of time-dependent kefir grain mass increase were used. The propagation was performed in RC1 batch reaction system under optimal bioprocess parameters (temperature, rotational frequency of stirrer, glucose mass concentration) using traditional cultivation in fresh, high-temperature, pasteurized whole fat cow's milk. We compared values of biological parameters obtained by applying the nonlinear regression of experimental data in logistic, Gompertz and Richards models. The most statistically appropriate model was determined using the seven statistical indicators. We established that the kefir grain biomass growth curve during batch propagation under optimal bioprocess conditions can be most successfully described using the Gompertz growth model. Ključne besede:chemical processing, milk products, kefir grain growth, process parameters, design of experiments, modeling, mathematical models, Gompertz growth model, RC1 Objavljeno v DKUM: 31.05.2012; Ogledov: 2990; Prenosov: 134 Povezava na celotno besedilo