|Abstract: ||本計劃擬研究週期性物體之微波成像問題。我們將討論週期性物體分別埋藏於半空 間與三層複雜空間中，再利用全域最佳化演算法如自我適應之動態差異演化策略法、群 聚式粒子群聚最佳化法、田口法應用於逆散射上的問題，並進行實際儀器量測最後比較 模擬與量測之差異。 第一年擬研究掩埋週期性金屬導體物體的電磁影像重建問題。吾人擬將探討於在頻 域上利用等效源法(Equivalent Source)、格林函數(Green’s Function)配合動差法(Method of Moment)求解半空間中的二維週期性金屬導體之散射場，並分別以 TM 波與TE 波入 射，將以上所使用之電磁散射理論配合自我適應之動態差異演化策略法與群聚式粒子群 聚最佳化法進行逆推散射物體形狀與電磁特性探討。 第二年擬研究週期性非均勻介質物體的電磁影像重建問題。吾人擬考慮模擬物體為 一週期出現之非均勻介質物體埋藏於三層複雜結構中，以 TM 極化波入射，利用在不 同介質的邊界條件，可以導出兩個積分方程式組，利用差分化可以化為矩陣形式，再經 由簡單的矩陣運算，就可以克服積分運算上的困擾，進而重建掩埋物體物理特性。再利 用田口法（Taguchi Method），重建出物體介電常數，此外，此年度將對田口最佳化法的 收斂速度與收斂性進行改良，包括引進多重階段田口最佳化法與多段式的範圍縮減技 巧... 等等。 第三年擬研究在三維週期性非均勻介電物體的微波成像問題上並且進行儀器實 測。吾人於非均勻介電物體周圍適當安排不同位置的天線發射極短脈衝波與極化波並分 別量測物體周圍之頻域散射場，經由適當的處理以反求物體的物理特性。吾人將利用接 收到的散射場及適當的邊界條件，導出一組非線性微分方程式，將電磁成像問題化為一 求極小值的最佳化問題，然後再利用全域搜尋法將逆散射問題轉化為求解最佳化的問 題。藉以重建物體的位置、形狀和介電常數分佈。此外，吾人也將利用無反射實驗室進 行實測，將此一結果與模擬作一比較。最後將電磁成像所得結果與原先假設者比較，藉 以驗證並改進電磁成像理論，進而做出針對三維週期性非均勻介質物體，利用不同演算 法的重建效果何者為佳的嘗試性結論。|
This three-year project will explore the image reconstructions of two-dimensional periodic objects by three different global optimal algorithms. Self-adaptive dynamic differential evolution, gregarious particle swarm optimization algorithm and Taguchi’s optimization method are investigated for microwave imaging problems. For the first year of this project, the inverse scattering problems of two-dimensional periodic perfectly conducting cylinders are investigated. Scattered fields of objects are calculated in frequency domain by the method of moment (MoM). Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived. Then, the measured EM fields are used for inverse scattering part, in which are employed to transform the inverse scattering problem is transform into optimization problem and solve by random-type global optimization algorithms . By comparing the measured scattered fields and the calculated scattered fields, the shape of two-dimensional periodic perfectly conducting cylinders are reconstructed. For the second year of this project, the inverse scattering problems of two-dimensional periodic non-uniform dielectric cylinders are investigated in the complex structure. Based on the boundary condition and the incident field, a set of nonlinear surface integral equation is derived. Moment methods and Taguchi’s optimization method are used to solve a set of linear integral equations. By using received scattered fields, the dielectric constants of non-uniform dielectric cylinders are reconstructed. Taguchi’s optimization method is proposed to solve global numerical optimization problems in inverse scattering problems. Taguchi’s optimization method uses continuous orthogonal arrays, combined with gradual range reduction techniques to solve the optimization problems. Especially for those with a large number of unknown parameters, Taguchi optimization method can efficiently and quickly search the global optimization solution. Some techniques to improve the convergence and convergence speed of Taguchi optimization method, including the multiple-phase method and multiple stages for the range reduction ... and so on will also investigate. For the third year of this project, random-type global optimization algorithms, Taguchi’s optimization method and local optimal algorithms for solving the microwave imaging problems of the three-dimensional periodic non-uniform dielectric cylinders are investigated. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The random-type global optimization algorithms, Taguchi’s optimization method and local optimal algorithms are employed to find out the global extreme solution of the objective function in three-dimensional problems. Different algorithms are used to reconstruct the images of different objects. The reconstructed images are compared for different algorithms and the best algorithm is chosen. Moreover, the topic of measurement by frequency domain equipment, which is another key point of this project, will be investigated. Finally, we would like to make some experimental conclusions for inverse problems and we will also focus on how to increase convergence speed of the different global optimal algorithms.