Inverse Problems in Electric Circuits and Electromagnetics

By: N.V. Korovkin, V.L. Chechurin, M. Hayakawa

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Hardcover | 28 December 2006

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344 Pages

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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 engi- neering 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 ac- tually solves inverse problems by defining the device structure and its pa- rameters, and then proceeds to deal with the technical specifications followed by the incorporation of his own notions of the best device. Frequently the so- lutions obtained are based on intuition and previous experience. New meth- ods 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.

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Preface	p. ix
Inverse Problems in Electrical Circuits and Electromagnetic Field Theory	p. 1
Features of inverse problems in electrical engineering	p. 1
Properties of inverse problems	p. 6
Solution methods	p. 12
Inverse problems in electric circuits theory	p. 18
Formulation of synthesis problems	p. 18
The problem of constructing macromodels (macromodeling) of devices	p. 26
Identifying electrical circuit parameters	p. 29
Inverse problems in electromagnetic field theory	p. 33
Synthesis problems	p. 35
Identification problems	p. 43
References	p. 45
The Methods of Optimization of Problems and Their Solution	p. 47
Multicriterion inverse problems	p. 47
Search of local minima	p. 59
Search of objective functional minimum in the presence of constraints	p. 68
Application of neural networks	p. 85
Application of Volterra polynomials for macromodeling	p. 98
Search of global minima	p. 105
The multistart method and cluster algorithm	p. 107
"Soft" methods	p. 109
References	p. 119
The Methods of Solution of Stiff Inverse Problems	p. 121
Stiff inverse problems	p. 121
The principle of quasistationarity of derivatives and integrals	p. 136
Using linear relationships for solving stiff inverse problems	p. 151
The problems of diagnostics and the identification of inverse problems in circuit theory	p. 156
Methods of identification of linear circuits	p. 159
Error of identification problem solution	p. 161
The method of stiff diagnostics and identification problems solutions	p. 168
Application of the principle of repeated measurements for solution of electric circuits' identification problem	p. 168
Definition of linear connections between parameters of circuit mathematical models	p. 169
Algorithm and results of electric circuits' identification problem solution using repeated measurements	p. 172
Inverse problems of localization of disturbance sources in electrical circuits by measurement of voltages in the circuit's nodes	p. 181
References	p. 191
Solving Inverse Electromagnetic Problems by the Lagrange Method	p. 193
Reduction of an optimization problem in a stationary field to boundary-value problems	p. 193
Calculation of adjoint variable sources	p. 202
Optimization of the shape and structure of bodies in various classes of media	p. 213
Properties and numerical examples of the Lagrange method	p. 220
Focusing of magnetic flux	p. 221
Redistribution of magnetic flux	p. 223
The extremum of electromagnetic force	p. 229
Identification of substance distribution	p. 231
Creation of a homogeneous magnetic field	p. 234
Features of numerical optimization by the Lagrange method	p. 239
Optimizing the medium and source distribution in non-stationary electromagnetic fields	p. 242
References	p. 249
Solving Practical Inverse Problems	p. 251
Search for lumped parameters of equivalent circuits in transmission lines	p. 251
Optimization of forming lines	p. 262
The problems of synthesis of equivalent electric parameters in the frequency domain	p. 275
Optimization of current distribution over the conductors of 3-phase cables	p. 285
Search of the shape of a deflecting magnet polar tip for producing homogeneous magnetic field	p. 296
Search of the shape of magnetic quadrupole lens polar tip for accelerating a particle	p. 301
Optimum distribution of specific electric resistance of a conductor in a magnetic field pulse	p. 306
References	p. 315
Appendices
A Method of Reduction of an Eddy Magnetic Field to a Potential One	p. 317
The Variation of a Functional	p. 323
Index	p. 325
Table of Contents provided by Ingram. All Rights Reserved.

Inverse Problems in Electric Circuits and Electromagnetics

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