部分掩埋導體之逆散射問題研究

Imaging Reconstruction for a Partial Embedded Conductor

蕭為均(Wei-Chun Hsiao)

指導教授 ： 丘建青

淡江大學/工學院/電機工程學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00763

摘要

本論文是在研究粒子群聚法(Particle Swarm Optimization)及動態 差異演算法(Dynamic Differential Evolution)應用在二維物體之電磁成像問題。我們針對在TE (Transverse Electric)及TM (TransverseMagnetic) 極化波入射的情況下且分別於近場及遠場下於半空間中完全導體的逆散射進行探討。 對於完全導體而言，電磁波在完全導體表面之總電場的切線分量為零。因此我們利用完全導體表面電流的觀念，可導出非線性積分方 程式，繼而利用動差法求得正散射公式。利用正散射公式，我們可以得到散射場的相關資料。對於逆散射部分，我們引進了粒子群聚法及動態差異演算法。利用兩種演算法時，我們適當地選取參數形式，同時結合所求的散射公式，由此即可求出散射場的相關資料，藉以求得柱體的形狀函數。 不論初始的猜測值如何，粒子群聚法及動態差異演算法總會收歛到整體的極值(Global Extreme)，因此，在數值模擬顯示中，即使最初的猜測值與實際值相距甚遠，我們仍可求得準確的數值解，成功的重建出物體形狀函數。而且在數值模擬顯示中，量測的散射場即使加入高斯分佈的雜訊存在，依然可以得到良好的重建結果，研究證實其有良好的抗雜訊能力。 所以我選擇粒子群聚法及動態差異演算法，利用散射體形狀越 相近則其散射場越相近的關係，來重建未知的形狀。

關鍵字

部分掩埋導體 ； 動態差異演算法 ； 粒子群聚法

並列摘要

The application of two techniques for the of shape reconstruction of a perfectly two-dimensional partial embedded conducting cylinder from mimic the measurement data is studied in the present paper. After an integral formulation, the microwave imaging is recast as a nonlinear
optimization problem; an objective function is defined by the norm of a difference between the measured scattered electric fields and the calculated scattered fields for an estimated shape of a conductor. In order to solve this inverse scattering problem, transverse electric (TE) and
transverse magnetic (TM) waves are incident upon the objects and two techniques are employed to solve these problems. The first is based on a particle swarm optimization (PSO) and the second is a dynamic differential evolution (DDE). Both techniques have been tested in the case of simulated data contaminated by additive white Gaussian noise. Numerical results indicate that the DDE algorithm and the PSO have almost the same reconstructed accuracy. However, the accuracy of TM wave is better than TE wave in conducting cylinder cases and near-field is better than far-field.

並列關鍵字

Particle Swarm Optimization ； Dynamic Differential Evolution ； Partial Embedded Conductor ； Moment Method ； Imaging Reconstruction

參考文獻

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