| In this dissertation,the fast optimization methods of electromagnetic structures are studied,especially the structural design methodologies applying topological optimization methods which rely purely on algorithms while little prior knowledge is needed.The difficulty for this kind of optimization problems lies in that the number of optimization variables is very large and the full-wave simulation for the objective function evaluation is very time-consuming.Hence,if a direct optimization algorithm,e.g.,Genetic Algorithm(GA),is used,desirable result usually cannot be reached in an acceptable period of time when the variable number is large,which render necessary the using of a gradient-based optimization algorithm to accelerate the convergence speed of electromagnetic optimization process.The work in this dissertation is carried out following this idea.The fast gradient derivation method for electromagnetic optimization problems,i.e.adjoint sensitivity analysis method,is studied first.Then an improved hybrid topology optimization method is proposed based on the existing methods.Besides,the sensitivity analysis method for antenna radiation characteristics is realized which make the optimization of corresponding objectives possible.Various antenna optimization examples are demonstrated to verify the efficiency and accuracy of the proposed optimization method.The main contents of this dissertation are listed as below:1.The adjoint sensitivity analysis method for complex objective functions in electromagnetic optimization problems is realized based on a full-wave simulation method,i.e.,finite element method(FEM).In electromagnetic optimization problems,the derivation of gradient by adjoint sensitivity analysis method relies directly on the intermediate data in simulation which means the study of a full-wave simulation method is the foundation of the successive work.In this dissertation,FEM applying high order vector basis functions is realized first.Then the adjoint sensitivity analysis methods for various objective functions in electromagnetic optimization problems are studied.2.A hybrid topology optimization method that is able to produce structures that are fit for fabricating and modeling is proposed.By comparing the two mostly used topology optimization methods,i.e.,material distribution method and level set method,it is discovered that the material distribution method has more powerful topology searching ability,but generate structures with coarse boundaries that are difficult to be fabricated and modeled accurately,meanwhile the level set method produces more desirable structures with smooth boundaries.In this work,a hybrid two-stage method is proposed,that is the successive applying of the material distribution method and the level set method.In this way,the powerful topology searching ability is preserved and final structures with better quality are derived.3.By the proposed hybrid topology optimization method,high gain directional microstrip antennas with different polarization and beam direction combinations are optimized.The previous study in topology optimization of microstrip antennas put emphasis on the impedance matching while radiation characteristics are ignored.In this work,antenna radiation characteristics are optimized for the first time by the topology optimization methods.Different directional antenna design examples verify that antenna characteristics,e.g.gain,polarization or beam direction,can be optimized with various combinations.4.By the proposed hybrid topology optimization method,a more difficult design case,that is the optimization of single-layer-substrate wideband circularly polarized microstrip antenna,is realized.Traditional single-layer-substrate microstrip antennas commonly have a bandwidth of merely 3%~5% which means that the design of a wideband one is very difficult.In this work,a single-layer-substrate circularly polarized microstrip antenna is derived by optimization with an impedance matching and a 3 dB axial ratio bandwidth all above 30%.This design case shows the potential of the optimization method in this dissertation for solving complex design problems.5.By the combination of the topology optimization of patches,optimization of the vias,and a fast simulation method that exploiting the model symmetry,two conical-beam antennas are optimized.By introducing the optimization of vias into the topology optimization scheme,the degree of freedoms for optimization is further increased which is beneficial for designing better performance circuits.The applying of the fast simulation method for rotational symmetric model accelerates the objective function evaluation and the optimization process considerably.The conical antenna design examples verify that the optimization method in this work is able to solve complex antenna beam-shaping design problems.6.Microstrip antennas with pixel layers are optimized by a gradient-based algorithm combining adjoint sensitivity analysis method.Pixel antennas belong to another kind of antennas purely determined by algorithms.By arranging the combination of the connection states between small metallic patches in the pixel layer,different circuit performances can be derived.To some extent,pixel structure optimization can be seen as a constrained and simplified topology optimization method.In previous studies,the pixel antennas are all optimized by direct optimization methods like GA,while the optimization process usually converges very slowly and utilizes a very limited number of variables.In this work,the adjoint sensitivity analysis method for pixel structure optimization problem is derived and used for the optimization of high gain pixel antennas with a large number of viable connections,which accelerate the optimization process considerably comparing with previous methods in corresponding literature.Besides,periodic pixel structures are also optimized,including the wideband absorber loaded with lump resistors and multifunctional wide-angle impedance matching layer,which enlarge the application of pixel type circuits. |
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