使用隨機式最佳化法於二維散射體之逆散射研究

Application of Stochastic Optimization Methods to the Inverse Scattering of 2-D scatterers

孫積賢(Chi-Hsien Sun)

指導教授 ： 丘建青

淡江大學/工學院/電機工程學系博士班/博士(2012年)

https://doi.org/10.6846/TKU.2012.00695

摘要

本論文提出一種新型隨機式最佳化演算法應用於高維度測試函數與二維逆散射問題。本論文的貢獻有兩點，第一點將隨機式最佳化演算法在九種不同特性之測試函數進行測試，結果發現，將”最佳”概念引進隨機式最佳化演算法容易陷入區域極値，而加入”自我適應”的概念之後，參數可以選取到較佳的數值，可以大幅度改善動態差異形演化法的搜尋能力與提升演算法的強健性。
第二個貢獻在研究埋藏於自由空間、半空間與三層空間二維散射體的電磁影像重建。此研究分別以有限時域差分法 (FDTD) 與動差法(MoM)為基礎，利用最佳化方法於時域重建埋藏於不同空間中二維散射體之特性參數。。
為了探究埋藏於不同空間中未知形狀的二維散射體，概念上吾人可向散射體發射電磁脈波/平面波，並量測其周圍的散射場，再針對此散射場分別以粒子群聚法（PSO）、非同步粒子群聚法(APSO)、動態差異形演化法（DDE）與自我適應之動態差異形演化法（SADDE）將逆散射問題轉化為求解最佳化問題。藉由量測而得的散射場以及計算而得的散射場數值互相比較，進而重建散射體的形狀函數。
本論文探討上述多種最佳化方法對於不同環境下的二維散射體之逆散射問題，並且引用統計的數據來分析判斷各種演算法的好壞。模擬結果顯示，即使最初的猜測值與實際散射體位置相距甚遠，此四種最佳化方法幾乎可以成功地重建出柱體的形狀，其中以自我適應之動態差異形演化法（SADDE）在執行三十次程式後，透過統計數據所得到之平均錯誤率、標準差值與收斂速度上，皆優於其他種隨機式全域演算法。

關鍵字

逆散射 ； 微波成像 ； 時域有限差分法 ； 演化計算

並列摘要

This dissertation presents a new stochastic optimization algorithm for high dimensional test functions and two-dimensional inverse scattering problem. There are two contributions of this dissertation, the first point of the stochastic optimization algorithms are tested in nine different benchmark functions and found that the idea of approaching the “Best” during the course of optimization procedure are easy to fail into local optimal solution. However, the algorithm of SADDE is a self-adaptive version of DDE, which is processed of self-adaptibility and the ability of approaching the “Best”. Based on the self-adaptive concept, it can improve the robustness of the algorithm.
The second point is presented the studies of some stochastic optimization methods for the shape reconstruction and permittivity distribution of two-dimensional scatterers. The scatterers are located in free space, or embedded in a three-layered material medium, respectively. In time domain, Finite-difference time-domain (FDTD) technique is employed for electromagnetic analyses for both the forward and inverse scattering problems, while the reconstruction problem is transformed into optimization one during the course of inverse scattering.
The idea is to perform the image reconstruction by utilization of some optimization scheme to minimize the discrepancy between the measured and calculated scattered field data. Four optimization schemes are tested and employed to search the parameter space to determine the shape, location and permittivity of the two-dimensional scatterers. They are asynchronous particle swarm optimization (APSO), particle swarm optimization (PSO), dynamic differential evolution (DDE) and self-adaptive dynamic differential evolution (SADDE).
The suitability and efficiency of applying the above methods for microwave imaging of two-dimensional scatterers are examined in this dissertation. The statistical performances of these algorithms are compared. The results show that SADDE outperforms PSO, APSO and DDE in terms of the ability of exploring the optima. However, these results are considered to be indicative and do not generally apply to all optimization problems in electromagnetics.

並列關鍵字

Inverse Scattering ； Finite Difference Time Domain (FDTD) ； Moment Method (MoM) ； Green’s Function ； Dynamic Differential Evolution (DDE) ； Self-Adaptive Dynamic Differential Evolution (SADDE) ； Particle Swarm Optimization (PSO) ； Asynchronous Particle Swarm Optimization (APSO)

參考文獻

[57] C. C. Chiu, C. H. Sun and W. L. Chang “Comparison of Particle Swarm Optimization and Asynchronous Particle Swarm Optimization for Inverse Scattering of a Two- Dimensional Perfectly Conducting Cylinder.”, International Journal of Applied Electromagnetics and Mechanics Vol. 35, No.4, pp. 249-261,Apr. 2011.

[1] E. Wolf, “Three-dimensional structure determination of semi-transparentobjects from holographic data,” Opt. Commun., vol. 1, pp.153–164, Sep.-Oct. 1969.

[2] W. Imbriale, R. Mittra, “The Two-Dimensional Inverse Scattering Problem,” IEEE Transactions on Antennas and Propagation, Vol. 18, No. 5, pp. 633- 642, Sep. 1970.

[3] A. Massa, M.Pastorino, A. Rosani and M. Benedetti “A Microwave Imaging Method for NDE/NDT Based on the SMW Technique for the Electromagnetic Field Prediction,” IEEE Transactions on Instrumentation and Measurement, Vol. 55, No. 1, pp. 240 - 247, Feb. 2006.

[4] O. Mudanyalı, S. Yıldız, O. Semerci, A. Yapar, and I. Akduman, “A Microwave Tomographic Approach for Nondestructive Testing of Dielectric Coated Metallic Surfaces.”, IEEE Geoscience and Remote Sensing Letters, Vol. 5, No. 2, pp. 180 - 184, Apr. 2008.