Yeni iki global karma optimizasyon algoritması ve bu algoritmaların mikrodalga devrelerin tasarımına uygulanması
New two global hybrid optimization algorithms and their applications to the design of microweve circuits
- Tez No: 39182
- Danışmanlar: PROF.DR. BİNGÜL YAZGAN
- Tez Türü: Doktora
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Algoritmalar, Elektronik haberleşme, Mikrodalga devreleri, Tasarım, Algorithms, Electronic communication, Microwave circuits, Design
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışmada bilgisayar destekli devre ve sistem tasarımında kullanılan çeşitli optimisasyon yöntemleri incelenerek mevcut yöntemlere göre daha hisli ve as sayıda fonksiyon incelemesi gerektiren global karma optimisasyon algoritmaları geliştirilmeye çalışılmış ve geliştirilen karma algoritmalar aktif ve pasif mikrodalga devrelerinin tasarımına uygulanmıştır. Bu algoritmalar türev bilgisi gerektirmemektedirler. Türev bilgisi gerektirmeme özelliği, türev bilgisini elde etmek için ek hesaplamalar yapılması zorunluluğunu ortadan kaldırdığı gibi algoritmaların basitliği bunların her tür probleme uygulanmasını da kolaylaştırmaktadır. Oluşturulan algoritmalar global optimisasyon için test fonksiyonlarına uygulanmış ve elde edilen sonuçlar fonksiyon inceleme sayısı, standard süre ve global minimumu bulma yüzdesi bakımlarından literatürde verilen çeşitli algoritmalara ait sonuçlarla karşılaştırılmıştır. Ayrıca yeni geliştirilen karma algoritmalar geniş bandlı kararlı mikrodalga kuvvetlendiricisi, parabolik iletim hattı ve filtre tasarım örneklerine uygulanarak elde edilen sonuçlar tartışılmıştır. (v)
Özet (Çeviri)
SUMMARY NEW TWO GLOBAL HYBRID OPTIMIZATION ALGORITHMS AND THEIR APPLICATIONS TO THE DESIGN OF MICROWAVE CIRCUITS Since the 1970s, significant progress has been made in the computer aided design of microwave circuits. In the initial design stage, the configuration and the topology of the circuit are determined. The performance of the initial circuit design is evaluated by computer-aided analysis methods. In the next stage of the CAD procedure, characteristics of a designed circuit computed by circuit analysis subroutines are compared with the given specifications. If the results do not satisfy the desired specifications, the circuit design parameters must be appropriately changed. The sequence of circuit analysis, comparison of circuit characteristics with design specifica tions, and then parameter modification is performed until acceptable performance goals for the circuit are met. This kind of CAD of microwave circuits is performed by using optimisation methods. Optimisation methods may also be used for parameter estimation of passive and active devices on the basis of experimental data. Optimisation in general means to determine the extreme value (maximum or, more often, minimum) of a mathematical function. The optimisation problem is to minimise the scalar function ü-UM (D subject to the inequality constraints: c(x)<0 (2) and equality constraint: /i(*)-0 (3) (vi)Here c{x) and h(x) are, in general nonlinear vector-valued functions of x: for example C(x)= cifx) C2(x).cmcfx), h<x)= 'hi(x) 1 hzfaâ hmh(x) (4) In (1) to (4), x is a vector of n independent variables or parameters: x= XI X2 Xn (5) Thus, the vector x is an element of an n- dimensional parameter space Rn, An acceptable region Ha (or a feasible, a constrained region) is given by &Am {x \c(x)<0,h(x) = 0} (6) Any point belonging to Ra is said to be feasible. The objective function can be called a cost function or an error function Optimisation problems encountered in the CAD of microwave circuits may be divided into the folio-wing classes: Linear programming : 0, c, h, linear function of x; Quadratic programming: U quadratic, c, and h are linear. Nonlinear programming: At least one of the D, c, h is a nonlinear function of x. A very important class of problems in the CAD of microwave circuits concerns techniques for adjusting circuit parameters to minimise the deviation between the circuit performance achieved at some stage of the design and the desired specifications. Such techniques are used to refine iteratively an initial design until specifications are met. The refinement process is an optimisation process involving the minimisation of a performance criterion that measures the difference between existing and desired response characteristics of the designed circuits. In microwave (vii)circuit design, the physical system can be a network, a device, or a measured or manufacturing process. As an example, the physical system may be a bandpass wavequide filter, ÎÎESFET transistor amplifier in MIC technology, a procedure for noise parameter measurements and so on. The desired performance of a system may be expressed by s pacifications independent temperature. computed at independent independent be designed which are usually functions of some variables such as frequency, time, or Because the response functions can be a finite number of values of one or more variables, discrete set of samples of variables is to be considered. A circuit must to meet desired specifications. Very often in practice the design problem has upper specifications. to be defined by lower and The error function must arise from the difference between the actually calculated responses and the given specifications. In general for lower and upper specifica tions, the error function is defined as ©uj(p)=wuj(Fj(p)-Suj), jeJu (7a) eij(p)=wij(Fj(p)-Sij), jeJi (7b) where Fj(p) is the response function, p represents the network parameters. Suj is an upper specification, Sij is a lower specification, wuj is a nonnegative weighting factor for Suj, and wij is a nonnegative weighting factor for Si 3. The index sets Ju and Ji defined as Ju = {jl,j2,...,jk} (8) Jl={jk+l,jk+2,...,jra} (9) are not necessarily disjoint. By redefining the error function as eifp)= euj(p) j=Ji, i=l,2,..,k eij(p) j=ji, i=k+l,k+2. (10) a set of uniformly indexed error functions are obtained. A positive value of error function ei indicates a violation of Cviii)the corresponding specifications. In design problems with the single specifications, the definition of the error functions, is much simpler: ei=wi|Fi(p)-Sil. 1=1.2,.., m (11) The error functions ei, i=l,2,..,ra can be treated as the components of a vector defined as e(p)= ei(p) e2fp) em(p) (12) Many microwave circuit design problems are best formulated in terms of minimising a scalar objective function U(p) which is defined as a lp norm or a generalised lp function of ei(p). For iel and is'p^00 the lp norm of ei{p) is defined as l/p (P) (13) lp norm is a scalar measure of the deviations between the desired and actual responses of the designed circuits. The choice of the value of the parameter p to the lp norm has an essential significance. By taking a small value for p to effect we emphasise those error functions ei that have smaller values. When the parameter p has a large value, about the value of the lp norm, we emphasise those error functions ei that have larger values. Three class of the İç» no I'm, p=l, p=2, and p=<» are best known and most widely used to the circuit optimization. In general- purpose computer programs, the objective functions usually have a form:“cp)- ili i »v w( *”wcp)- s“ ”- n (14) where j= optimisation frequency band 1 to k 1= frequency points 1 to lj to a frequency band j m= circuit function being optimised wi.jW=weight for circuit function m at a frequency point i to band j (ix)FijW(p)=a value of circuit function m at a frequency point i in tend j SijW=de8irecl value of circuit function m at a frequency point i in tend j p= circuit parameters 17= norm Optimisation methods can be classified in three groups according to the information they use about the error function. fl) Direct methods (no gradient computation): rotating coordinates, conjugate directions, pattern search methods, simplex or poly tope methods etc. (2) First- order methods (computation of the gradient): steepest-descend, conjugate gradients, quasi- Newton methods etc. (3) Second-order methods (computation of the gradient and the Hessian matrix of second derivatives): Newton methods etc. Gradient methods have been successfully applied to optimisation problems for some time. The direct application of such methods can be computationally intensive and the issue of convergence must be adres s ed. However, the problem of local minima has not been directly tackled, the usual way is to try a number of initial solutions. Theoretically, the best solution of an optimisation problem exists under a certain well-defined objective function and can be guaranteed only by generating and evaluating all possible solutions. However, the sise of the solution space (ie. all possible solutions) is extremely large and it grows exponentially with the number of variables for a given problem. It is generally imposible to perform an exhaustive search to locate the best solution in a reasonable time. A typical optimisation process utilises an iterative improve ment strategy. First, an initial set of estimated parameters is generated as the starting point of a search process; small variations are then made to these parameters at each step to generate a new set of parameters, which is evaluated according to the objective function to be minimised. In order to guarantee the convergence of an optimisation process, traditional algorithms are greedy and accept only those changes that can improve the cost of the objective function. One inherent drawback of this type of search is that it can be easily trapped into the local minima of an objective function if good initial values are not available. (x)Many practical engine er log applications can be formulated as global optimisation problems in which the objective function is not convex and possesses many local minima in the region of interest. The aim of global optimisation is to find the solution in a region for which the objective function obtairies its smallest value, the global minimum. Global optimisation thus aims at determin ing not just a local minimum but the smallest local minimum in the region. The class of methods with guaranteed accuracy 'is called covering methods. The residual class of methods is divided into Direct methods utilising only local information (function evaluation) and indirect methods where local information is used to build a global model of the level set or the objective function. This gives the following classification: Methods with guaranteed accuracy Covering methods Direct Methods Random search methods Clustering methods Generalised descend methods indirect Methods Methods approximating the objective function. Chapter 1 is an introduction to optimisation problem. In section 1.3 global optimisation is defined and global optimisation methods are classified. In chapter 2 optimisation algorithms used in the new hybrid algorithms are examined. Simulated annealing, Hooke-Jeeves, controlled random search and adaptive complex algorithms are introduced in sections 2.2, 2.3, 2.4 and 2.5 respectively. Chapter 3 covers the optimisation of microwave circuits. In section 3.2 physical systems and simulation model are introduced. Design specifications and error functions are examined in section 3.3. In section 3.4, after error functions are examined, lp norms are introduced and compared with each others. Generalised lp norm and multiple objective optimisation are introduced in section 3.5 and 3.6 respectively. (xi)In chapter 4 new hybrid optimisation algorithms are explained and convergences of algorithms are examined. Optimisation results are compared with other methods in terms of the number of function evaluations and standard time to section 4.4. In chapter 5 the application of the hybrid optimisation algorithms to the design of microwave circuits are explained. Designed microwave circuits are broadband microwave amplifier, nonuniform parabolic transmission line and microwave filter. Finally, to the last section the results obtained are discussed. New global hybrid algorithms constructed in this thesis give better results than some algorithms given in the literature to terms of the number of function evaluations, standard time and proportions of total runs that converged to global optima. New algorithms don't require gradient information and very suitable to parallel processing. Using these, it is possible to increase the speed of the algorithm. They can be easily adapted to various problems and discontinuous functions. New algo rithms are applied to 6-16 GHs stable microwave amplifier, nonuniform transmission Itoe and filter design. Thus, design problems are transformed toto optimisation problems. In the design of microwave amplifier, loss effect of the matching network elements and stability factor are considered. Nonuniform transmission gives desired input impedance for a given real or complex load impedance. None of the terms is ignored to the formulation. It is also possible to take into account the loss of the nonuniform transmission line. The essence of the filter design method is to adjust a set of filter's element values until the seros, poles and the scale factor of the characteristic function of the micros trip filter match their desired values. The method requires only simple analysis, avoids complications normally associated with network synthesis of high- degree networks, and doesn't require any gradient information. It is also possible to design nonlinear microwave circuits using new global hybrid optimisation algorithms. (xii)
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