Inverse problems in electric circuits and electromagnetics

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.

Preface	p. ix
Chapter 1 Inverse Problems in Electrical Circuits and Electromagnetic Field Theory	p. 1
1.1 Features of inverse problems in electrical engineering	p. 1
1.1.1 Properties of inverse problems	p. 6
1.1.2 Solution methods	p. 12
1.2 Inverse problems in electric circuits theory	p. 18
1.2.1 Formulation of synthesis problems	p. 18
1.2.2 The problem of constructing macromodels (macromodeling) of devices	p. 26
1.2.3 Identifying electrical circuit parameters	p. 29
1.3 Inverse problems in electromagnetic field theory	p. 33
1.3.1 Synthesis problems	p. 35
1.3.2 Identification problems	p. 43
References	p. 45
Chapter 2 The Methods of Optimization of Problems and Their Solution	p. 47
2.1 Multicriterion inverse problems	p. 47
2.2 Search of local minima	p. 59
2.3 Search of objective functional minimum in the presence of constraints	p. 68
2.4 Application of neural networks	p. 85
2.5 Application of Volterra polynomials for macromodeling	p. 98
2.6 Search of global minima	p. 105
2.6.1 The multistart method and cluster algorithm	p. 107
2.6.2 "Soft" methods	p. 109
References	p. 119
Chapter 3 The Methods of Solution of Stiff Inverse Problems	p. 121
3.1 Stiff inverse problems	p. 121
3.2 The principle of quasistationarity of derivatives and integrals	p. 136
3.3 Using linear relationships for solving stiff inverse problems	p. 151
3.4 The problems of diagnostics and the identification of inverse problems in circuit theory	p. 156
3.4.1 Methods of identification of linear circuits	p. 159
3.4.2 Error of identification problem solution	p. 161
3.5 The method of stiff diagnostics and identification problems solutions	p. 168
3.5.1 Application of the principle of repeated measurements for solution of electric circuits' identification problem	p. 168
3.5.2 Definition of linear connections between parameters of circuit mathematical models	p. 169
3.5.3 Algorithm and results of electric circuits' identification problem solution using repeated measurements	p. 172
3.6 Inverse problems of localization of disturbance sources in electrical circuits by measurement of voltages in the circuit's nodes	p. 181
References	p. 191
Chapter 4 Solving Inverse Electromagnetic Problems by the Lagrange Method	p. 193
4.1 Reduction of an optimization problem in a stationary field to boundary-value problems	p. 193
4.2 Calculation of adjoint variable sources	p. 202
4.3 Optimization of the shape and structure of bodies in various classes of media	p. 213
4.4 Properties and numerical examples of the Lagrange method	p. 220
4.4.1 Focusing of magnetic flux	p. 221
4.4.2 Redistribution of magnetic flux	p. 223
4.4.3 The extremum of electromagnetic force	p. 229
4.4.4 Identification of substance distribution	p. 231
4.4.5 Creation of a homogeneous magnetic field	p. 234
4.5 Features of numerical optimization by the Lagrange method	p. 239
4.6 Optimizing the medium and source distribution in non-stationary electromagnetic fields	p. 242
References	p. 249
Chapter 5 Solving Practical Inverse Problems	p. 251
5.1 Search for lumped parameters of equivalent circuits in transmission lines	p. 251
5.2 Optimization of forming lines	p. 262
5.3 The problems of synthesis of equivalent electric parameters in the frequency domain	p. 275
5.4 Optimization of current distribution over the conductors of 3-phase cables	p. 285
5.5 Search of the shape of a deflecting magnet polar tip for producing homogeneous magnetic field	p. 296
5.6 Search of the shape of magnetic quadrupole lens polar tip for accelerating a particle	p. 301
5.7 Optimum distribution of specific electric resistance of a conductor in a magnetic field pulse	p. 306
References	p. 315
Appendices
Appendix A A Method of Reduction of an Eddy Magnetic Field to a Potential One	p. 317
Appendix B The Variation of a Functional	p. 323
Index	p. 325

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