|摘要: || 本論文首度將田口最佳化方法(Taguchi’s Method)應用於二維介質柱體的逆散射問題。在正散射的分析部分，本研究以時域有限差分法為基礎，至於逆散射則被轉換為最佳化問題以進行求解，並和使用差異型演化法(Differential Evolution, DE)、自我適應之動態差異型演化法(Self-Adaptive Dynamic Differential Evolution, SADDE)求解的結果進行比較。|
為了描述與重建柱體的形狀，在正散射部分，本研究採用傅立葉函數展開(Fourier series expansion)，但在逆散射部分則使用仿樣函數展開(cubic spline)，如此可確保柱體形狀建構的合理性。最後將時域有限差分法結合田口最佳化法以重建均勻介質柱體，並探討田口最佳化法之特性參數對重建結果的影響。
田口最佳化法和目前常用的演算法(Algorithm)有很大的不同，後者透過機率(Probability)的概念來完成全域的搜尋；相對的，田口最佳化法則排除機率，而以直交表(Orthogonal Arrays)展現的均勻分布特性，並結合將搜尋範圍不斷地遞減(Range Reduction) 的迭代方式，來執行全域的搜尋以找出最佳解。
This thesis is the first to apply Taguchi optimization method to inverse scattering problem, for which a two-dimensional dielectric object is considered. The analysis of forward scattering part is based on the finite difference time domain (FDTD) method, while the inverse scattering part is tackled by transforming the problem into an optimization one, of which the Taguchi optimization method is chosen. The reconstructed results are compared with those obtained by Differential Evolution (DE), and Self-Adaptive Dynamic Differential Evolution (SADDE).
To described and reconstructed the shape of the dielectric cylinder, Fourier series expansion is used for the forward scattering part, while the cubic splines are employed for the inverse scattering part. In this way, the objective of shape reconstruction of this study is maintained reasonable. At the end, the FDTD method combined with Taguchi optimization method is applied to reconstruct the cylinder of the homogeneous medium. In addition, the parameter effects of Taguchi optimization method upon the reconstruction results are studied.
Taguchi optimization method is quite different from those statistic methods commonly used for global optimization. The latter utilize the random characteristic to achieve the global searching, while the former, on the contrast, exclude the concept of probability. Taguchi optimization method actually utilize the uniform characteristic of the OA table, and combine with the mechanism of range reduction to achieve the iterative searching in a global way.
In this thesis, the Taguchi optimization method, DE and SADDE are applied to test nine different benchmarked functions, at first. The performances are examined for those with dimensions of 50, 100 and 250, respectively. It is found that Taguchi optimization method, and SADDE exhibit superior performance in the test. Then, when applied to the inverse scattering problem of dielectric cylinders. Taguchi optimization method still exhibit good reconstruction results, while SADDE doesn’t. It is thus conclude that Taguchi optimization method is especially suited for the proposed inverse scattering problem.