Crystal Structure Algorithm (CryStAl) Based Selective Harmonic Elimination Modulation in a Cascaded H-Bridge Multilevel Inverter

This paper introduces an effective Selective Harmonic Elimination (SHE) modulation technique in a five, seven, and nine-level cascaded H-bridge (CHB) multilevel inverter (MLI). Minimization of the harmonics and device counts is the basis for the ongoing research in the area of MLI. Reduced harmonics and hence the lower Total Harmonic Distortion (THD), improve the output power quality. SHE is a low-frequency modulation scheme to achieve this goal. SHE techniques are used to eliminate the distinct lower-order harmonics by determining the optimum switching angles. These angles are evaluated by solving the non-linear transcendental equations using any optimization technique. For this purpose, the Crystal Structure Algorithm (CryStAl) has been used in this paper. It is a metaheuristic, nature-inspired, and highly efficient optimization technique. CryStAl is a simple and parameter-free algorithm that doesn’t require the determination of any internal parameter during the optimization process. It is based on the concept of crystal structure formation by joining the basis and lattice point. This natural occurrence can be realized in crystalline minerals in their symmetrically organized components: ions, atoms, and molecules. The concept has been utilized to solve non-linear transcendental equations. SIMULINK/MATLAB environment has been used for the simulation. The simulation result shows that the crystal structure algorithm is very effective and excels the other metaheuristic algorithm. Hardware results validate the performance.

Program complex for optimization of surface hardening of steel billets

The aim of the paper is to develop program complex in software MATLAB with integrated numerical 2D nonlinear FLUX model, which is used for solving optimal inductor design and control problems for heating stage of surface induction hardening. Considered program complex is based on alternance method, that allows to write systems of transcendental equations, closed with respect to all unknown design and control parameters of the process. The suggestion for implementation of obtained optimal control algorithm is presented.

A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it’s observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods.

A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables

A system of transcendental equations (SoTE) is a set of simultaneous equations containing at least a transcendental function. Solutions involving transcendental equations are often problematic, particularly in the form of a system of equations. This challenge has limited the number of equations, with inter-related multi-functions and multi-variables, often included in the mathematical modelling of physical systems during problem formulation. Here, we presented detailed steps for using a code-based modelling approach for solving SoTEs that may be encountered in science and engineering problems. A SoTE comprising six functions, including Sine-Gordon wave functions, was used to illustrate the steps. Parametric studies were performed to visualize how a change in the variables affected the superposition of the waves as the independent variable varies from x1 = 1:0.0005:100 to x1 = 1:5:100. The application of the proposed approach in modelling and simulation of photovoltaic and thermophotovoltaic systems were also highlighted. Overall, solutions to SoTEs present new opportunities for including more functions and variables in numerical models of systems, which will ultimately lead to a more robust representation of physical systems.

Buckling Resistance of Two-Segment Stepped Steel Columns

Columns of stepwise variable bending stiffness are encountered in the engineering practice quite often. Two different load cases can be distinguished: firstly, the axial force acting only at the end of the column; secondly, besides the force acting at the end, the additional force acting at the place where the section changes suddenly. Expressions for critical forces for these two cases of loading are required to correctly design such columns. Analytical formulae defining critical forces for pin-ended columns are derived and presented in the paper. Derivations were based on the Euler-Bernoulli theory of beams. The energetic criterion of Timoshenko was adopted as the buckling criterion. Both formulae were derived in the form of Rayleigh quotients using the Mathematica® system. The correctness of formulae was verified based on one the of transcendental equations derived from differential equations of stability and presented by Volmir. Comparisons to results obtained by other authors were presented, as well. The derived formulae on the critical forces can be directly used by designers in procedures leading to the column’s buckling resistance assessment. The relatively simple procedure leading to buckling resistance assessment of steel stepped columns and based on general Ayrton-Perry approach was proposed in this work. The series of experimental tests made on steel, stepped columns and numerical simulations have confirmed the correctness of the presented approach.

Methodology of Mathematics Teaching. Treatment to School Mathematics Equations

This book is aimed at pre-university students and its purpose is to contribute to the development of their knowledge related to the algebraic and transcendent equations studied at school, as well as their application to different situations that occur in practice in an innovative and creative way, using the procedures for solving them, so that it allows the consolidation of attitudes such as industriousness, responsibility and science. The system of knowledge worked on and treated didactically in this book is related to the algebraic equations and within them the linear, quadratic, fractional and radical equations, the modular equations and the transcendental equations such as, the exponential, logarithmic and trigonometric equations, providing the minimum theoretical and methodological resources, necessary to learn and to successfully face the exercises and problems proposed in each chapter.