| 摘要: | 本計畫將研究埋藏於半空間中之二維不均勻介質柱體的時域電磁逆散射問題。概念上，當在空氣側的不同適當位置，安排發射一脈衝波來照射該掩埋柱體，並量測在此柱體周圍之散射場，便可經由適當的後續處理以反求散射柱體的位置、大小與內部電磁特性。針對此一逆散射問題，本計劃提出幾種創新的後續處理方法，使其面對高維度問題的「維度詛咒」時，能展現強健性與極佳的搜尋效率；它們奠基於田口最佳化法，並將充分利用直交表的均勻分佈特性。本計畫提出將田口最佳化法與隨機搜尋法結合的創新概念，並依序探討三種創新的結合技巧以提升搜尋效率，這包括「串聯」與「並聯」的結合方式；「串聯」指的是結合田口最佳化法與隨機搜尋法以交叉迭代方式進行搜尋，「並聯」則是指結合田口最佳化法與隨機搜尋法「同時」進行最佳化，但各具有不同權重的族群大小，兩種技巧皆要求不同演算法間彼此傳遞各自的全域最佳解訊息。 此創新概念源自於同時保留直交表的均勻分佈特點與隨機搜尋法向global best趨近的優點，使其不只維持面對「維度詛咒」時的強健性，並且能大幅提升其搜尋效率，後者在計算負荷量相當大的電磁逆散射問題上具有相當關鍵的價值。另外，本計畫將進一步使用spline技巧以減少此一問題未知數，並探究時域逆散射課題之物理與計算限制。針對此一計算量龐大的問題，吾人將藉用CUDA技術，希望可以將計算時間大幅減少，以利本計畫的順利進行。
This project will investigate the electromagnetic inverse scattering of time domain problem for a two-dimensional inhomogeneous dielectric cylinder buried in the half space. Conceptually, if in different locations of the air side, it is arranged to transmit a pulse irradiation upon a buried cylinder, and measure the scattered field around the cylinder, then it is possible to retrieve the location, size and internal electromagnetic properties of the cylinder by appropriate procedure. For this specific inverse scattering problem, this project proposes several innovative and robust ( without "dimension curse") procedures enen when a high-dimensional problem is concerned. They are based on Taguchi's Optimization Method, and would fully utilized the features of orthogonal array. This project proposes the innovative concept to combine the Taguchi optimization method and some random search method, and in turn three innovative techniques will be developed to improve search efficiency, which include the "series" and "parallel" combination; "series" combination means that the Taguchi optimization method and random search method are employed to work together in a interleaved way, while "parallel" combination refers to the co-work in a simultaneous way by the two kinds of methods. Note that each method with associated with different weights for population size. In addition, both methods are required to pass each other the message of their respective global optimum. This innovative concept comes from the orthogonal array of uniformly distributed random search features and global best method to combine the advantages of closer to not only maintain the face of "dimension curse" when the robustness, and can significantly improve its search efficiency, the latter a large load in the calculation of the electromagnetic inverse scattering problem on the real key to a considerable value. In addition, this project will be further reduced by spline techniques to this problem is unknown, and explore issues of time-domain inverse scattering and the calculation of physical limitations. Excessive for the calculation of the problem, I will borrow GPU technology, hope to significantly reduce the computation time, in order to facilitate the smooth progress of this project. This innovative concept comes from the motivation of retaining the uniform distribution property of orthogonal array and the merit of approaching the global best of random search method. It is expected to significantly improve its search efficiency, in addition to maintain the robustness with respect to the "dimension curse". The search efficiency actually is a considerable value when a problem with large computataion load, such as the electromagnetic inverse scattering problem, is considered. In addition, this project will be further employs the spline interpolation technique to reduce the unknown number, and also explore the issues of physical and/or computation limitation of the time-domain inverse scattering problem. For this problem with excessive need for computer calculation, we will borrow the CUDA technology with the hope to significantly reduce the computation time, in order to facilitate the progress of this project smoothly. |
