A study of fractional electrical engineering problems via the Shehu transform

Electrical energy is generated by the consumption of other energy sources. It is an indispensable energy source in people's lives and has a wide range of uses in industrial production. However, there are still some problems in electrical engineering that need to be improved and improved, such as excessive energy consumption, quality problems, lack of integration and network structure, need to solve these problems, reduce the loss of electrical energy, ensure safe and reliable operation of electrical, and make electrical Engineering and industry can be better combined to increase efficiency.

Purpose – The purpose of this paper is to present a simple approach for calculation of the sensitivities in the free-form inverse design problems. The approach is based on the analogy with the similar tasks used in the signal-processing analysis. In the proposed case it is not required to solve an adjoint problem as in the most of the similar optimization tasks. The simulation engine used in the background is a Fast Boundary Element Method. The approach is validated on some known benchmark problems. Design/methodology/approach – Inverse design is recognized nowadays as a crucial scientific grand challenge. Contrary to the conventional approach (“Given the structure, find the properties”) it purses a new paradigm (“Given the desired property, find the structure”). Inverse class of problems has a broad application area, from the material-, medical-, bio- to the engineering-class of problems. When dealing with the inverse design in free-form optimization of the engineering problems the typical approach is to calculate the adjoint problem. Calculation of the adjoint problem mostly requires the costly calculation of the gradients, which makes the whole optimization procedure rather expensive due to the high computational burden required for their solution. Findings – In this paper it is proposed a novel Simple Sensitivity Approach to get in a fast way the response (sensitivity) function of the analyzed structure. The simulation engine used in the background is the Fast Boundary Element Method. Originality/value – Novel approach for inverse design when performing the free-form optimization of engineering problems.

Singularities appear in many problems in electrical engineering. They may be geometric (for example peaks, corners or ridges in Electrostatics) or physical (for example, changes in electromagnetic properties on thin depths). Classical numerical methods like finite elements technique are badly adapted to the simulation of these singularities. The authors present the techniques that they have developed to take these singularities into account. It consists of crack elements in eddy current non destructive testing, and of bilinear elements to control insulating materials. The particularity of these techniques is the association of a numerical resolution using finite elements technique, with an analytical resolution using singular elements. The authors recall, moreover, the techniques introduced in their Boundary Integral Equations package, in order to take into account geometrical singularities in electrostatic problems.

The present paper gives an overview of different versions of Evolution Strategies, namely the (1+1) Evolution Strategy, the Higher Order (?/?,?) Evolution Strategy and the Niching [? (?/?,?)] Evolution Strategy, and how these methods can be applied to problems in Electrical Engineering. Significant features of the algorithms implemented by the authors are presented. Finally, results are discussed on three electromagnetic optimization problems. .

More often than not, the non-linear problems of electrical engineering arise from discrete physical systems and are usually reducible mathematically to the solution of systems of non-linear total differential equations or to systems of non-linear integral equations. Six independent methods of solving discrete non-linear problems are given in this paper. Each method is illustrated by means of an electrical engineering problem. The illustrative examples employed pertain to a-c and d-c non-linear circuits, reluctance-induction motors, hunting of and dynamic braking of synchronous machines. References to additional methods are given in the bibliography. The 88 given references listed represent approximately ten per cent of the field, but many of the entries contain a bibliography on their respective fields. The accelerated growth of research in the field of non-linearity is due to different causes. The general advancement of science requires increasingly more precise expressions for the laws of science. Accurate non-linear equations frequently depart from the linearized or postulated linear equations which have been previously used for approximate results. The quest for perfection and generalization and the love of difficult investigations by professional mathematicians play a large part in this growth. A recent incentive is the increasingly exacting requirements of modern manufacturing. These requirements are born of the competitive necessity of producing ever improved machines and equipment in the most economical manner.

Electric tree aging due to the action of long-term partial discharge stress of epoxy resin casting insulation is a major problem in electrical engineering. On the discharge experimental platform, initiation and culture experiments of the electric trees were carried out at a power frequency voltage of 20 kV. The mass fractions of the spherical glass fibers were 0, 0.5, 1, 2 and 3 %. The results showed that the electrical dendritic process of epoxy resin experienced initiation, growth, lag and burst periods, the phase maps of the corresponding partial discharges in the four periods were all “mountain-like”. The electric tree of pure epoxy resin showed a typical dendritic structure, after the glass fiber was properly added, the electric tree became lighter in color with a more complicated shape, the damage also became more serious, however, the growth of the electric branch was suppressed. The electric tree aging channel of the epoxy resin appeared black and under microscopy the micro-branched channel wall appeared white. When the amount of glass fiber was 2 %, the initiation time of the electric trees was prolonged, the growth rate of the electric trees decreased and suppressing development of the electric tree branches was optimal.

This paper presents an engineering-oriented method to approach the hysteresis loss problems in electrical engineering and validates it through the updated TEAM Problem 21. The TEAM Problem 21 is an engineering-oriented loss model, a 3-D nonlinear eddy current problem which was approved by the international TEAM board in 1993. (2 pages)

In this paper, we investigate the application of the adaptive higher-order Finite Element Method (hp-FEM) to heat transfer problems in electrical engineering. The proposed method is developed based on the combination of the Delaunay mesh and higher-order interpolation functions. In which the Delaunay algorithm based on the distance function is used for creating the adaptive mesh in the whole solution domain and the higher-order polynomials (up to 9th order) are applied for increasing the accuracy of solution. To evaluate the applicability and effectiveness of this new approach, we applied the proposed method to solve a benchmark heat problem and to calculate the temperature distribution of some typical models of buried double- and single -circuit power cables in the homogenous and multi-layer soils, respectively.

Heavy Traction Problems in Electrical Engineering

Many problems in electrical engineering, such as the synthesis of linear n ports and the detection and filtration of multivariable systems corrupted by stationary additive noise, depend for their successful solution upon the factorization of a matrix-valued function of a complex variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> . This paper presents several algorithms for affecting such decompositions for the class of rational matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G(p)</tex> , i.e., matrices whose entries are ratios of polynomials in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> . The methods employed are elementary in nature and center around the Smith canonic form of a polynomial matrix. Several nontrivial examples are worked out in detail to illustrate the theory.

An algorithm for matrix approximation, when only some of its entries are taken into consideration, is described. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank approximations, this type of algorithms appears recently in the literature under different names, where it usually uses the Expectation-Maximization algorithm that maximizes the likelihood for the missing entries. In this paper, the algorithm is extended to different cases other than low rank approximations under Frobenius norm, such as minimizing the Frobenius norm under nuclear norm constraint, spectral norm constraint, orthogonality constraint and more. The geometric interpretation of the proposed approximation process along with its op- timality for convex constraints is also discussed. In addition, it is shown how the approximation algorithm can be used for matrix completion as well, under a variety of spectral regularizations. Its applications to physics, electrical engineering and data interpolation problems are also described.

Investigating positivity of polynomials over the complex unit disc is a relevant problem in electrical and computer engineering. This paper provides two sufficient and necessary conditions for solving this problem via linear matrix inequalities (LMIs). These conditions are obtained by exploiting trigonometric transformations, a key tool for the representation of polynomials, and results from the theory of positive polynomials. Some numerical examples illustrate the proposed conditions.

Chapter 2 - Review of Signal-Processing Basics

Improving the quality and reliability of electrical machines is one of the most urgent problems of modern electrical engineering. Practical data show that the increase of service life and reliability of machines gives better results than the improvement of other technical and economic indicators: efficiency, power factor, utilization factor. The quantitative indicators of reliability can be best determined by the results of statistical processing of the information obtained when using the products. An algorithm of the load balancing based on the actual performance of pumping equipment and temporary changes in the connected load via the emergency shutdown of the pumps has been developed to improve the reliability operation and reduce inefficient energy losses. The main advantage of the proposed method is the analytical design models of optimization, which does not require numerical methods and iterative procedures. Such principles as active-preventative service and increasing personal responsibility for its quality and timeliness should be the basis for the organization of workposts service. Progressive forms of service are the technical re-equipment, modernization of equipment and improvement of production organization, as well as complex methods of the electric drive maintenance and application of the system of standardized tasks.

CURVES OF impedance and admittance in the complex plane for various combinations of 2-terminal 3-element linear dissipative networks are extremely useful in the solution of many electrical engineering problems because of the direct, straightforward manner in which they show graphically the resistive and reactive components of complex impedance and admittance, the magnitude of impedance and admittance, and the phase shift at all frequencies between zero and infinity. The curves also reveal that the 16 possible combinations of 2-terminal 3-element networks fall into four main groups of four networks each.