Inverse Problems in Electric Circuits And Electromagnetics By Korovkin Chechurin Hayakawa
The design and development of electrical devices involves choosing from many possible variants that which is the best or optimum according to one or several criteria. These optimization criteria are usually already clear to the designer at the statement of the design problem. The methods of optimization considered in this book, allow us to sort out variants of the realization of a design on the basis of these criteria and to create the best device in the sense of the set criteria.
Optimization of devices is one of the major problems in electrical engineering that is related to an extensive class of inverse problems including synthesis, diagnostics, fault detection, identification, and some others with common mathematical properties. When designing a device, the engineer actually solves inverse problems by defining the device structure and its parameters, and then proceeds to deal with the technical specifications followed by the incorporation of his own notions of the best device. Frequently the solutions obtained are based on intuition and previous experience. New methods and approaches discussed in this book will add mathematical rigor to these intuitive notions.
By virtue of their urgency inverse problems have been investigated for more than a century. However, general methods for their solution have been developed only recently. An analysis of the scientific literature indicates a steadily growing interest among scientists and engineers in these problems. As a result, there has been an increase in the number of publications of new methods of solution of inverse problems as well as their active application in practice. It is essential that methods of solution of inverse problems find application not only for the development of new devices, but also for the modernization of existing equipment with the purpose of improving its characteristics or the extension of its operational life. I
nverse problems that are significant for practical purposes are, as a rule, solved numerically. The increase in efficiency of computers has allowed us to put into practice many new and effective methods of solution of inverse problems. Therefore we have focused the book on an account of methods oriented towards numerical solutions. We have not included analytical methods because they are not so effective for optimization of designs of real devices or physical properties of materials. Furthermore, an exposition of analytical methods would substantially expand the volume of this book and would result in excessive complication.
Inverse problems in the theory of electric circuits and in electromagnetic field theory have some particular features. We, however, notice numerous common features of these problems that allow their exposition to be combined within the limits of one book. In particular, the solution of inverse problems in the theory of circuits and in field theory is based on the same mathematical apparatus, namely, methods of solution of incorrect problems and methods of optimization. This material is presented throughout the book from a general point of view.
Together with well-known methods of solution of inverse problems that have been widely used in practice, we have described some methods based on ideas borrowed from various areas of science. Generic methods of minimization of functionals, or methods based on the application of neural networks can be treated among them. The method of Lagrange multipliers explicitly considered in the book was found to be very effective for the solution of optimization problems in electromagnetic field theory.
In the first chapter a classification of inverse problems is given with an analysis of their properties, and we describe the basic methods for the numerical solution of inverse problems in electrical engineering. In the second chapter methods of searching for local and global minima of functionals are discussed, as well as methods of searching for the minima of functionals in the presence of constraints on the parameters to be optimized. In the third chapter we discuss methods of solution of inverse problems in the theory of electric circuits. Special attention is given to the solution of stiff inverse problems, in particular problems of identification that are characterized by the presence of measurement errors. The fourth chapter is concerned with a systematic account of the Lagrange Method of continuous multipliers, which is applied to optimization in an electromagnetic field characterized by quite a large number of parameters. The fifth chapter presents examples that demonstrate the solution of practical inverse problems in the theory of electric circuits and in electromagnetic field theory, thus illustrating the effectiveness of methods considered in this book.
Alongside the classical methods of solution of inverse problems in electrical engineering, up-to-date methods have also been investigated by the authors themselves within the limits of their scientific activities, as well as by their colleagues: A.Adalev, A.Potienko, T.Minevich, A.Plaks, M.Eidmiller and others. The authors have also used the results of scientific studies of research workers of the faculty of Fundaments of Theoretical Electrical Engineering in the State Polytechnic University, St.-Petersburg (Russia) concerned with the solution of problems involving the analysis of electric circuits and electromagnetic fields. These include using the method of the scalar magnetic potential for the analysis of direct current magnetic fields (K.S.Demirchian). The authors are very grateful to professor K.S.Demirchian and professor P.A.Butyrin for useful discussions and valuable advice that helped improve the book and the understanding of distinctive features of the solution of inverse problems in electrical engineering.
The authors express their appreciation to Mr. R.Hogg, Mr. D.Bailey, and Mr. M.Repetto for helpful discussion of optimization problems in electromagnetics, as well as to Mr. Kh.Partamyan and Mr. B.DeCarlo for their help during the writing of the book.
The authors thank professors I.G.Chernorutski and E.B.Soloviova, whose scientific ideas have helped us with the preparation of this work.
The authors believe that this book will be useful for engineers, scientific researchers, postgraduate students and students major in electrotechnology, electrical power systems, and other specialties.
it is hoped that this book will promote further interest in inverse problems in electrical engineering among university students, lecturers and research workers.
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