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姓名	范丙林(Ping-Lin Fan)  查詢紙本館藏	畢業系所	光電科學與工程學系
論文名稱	光電實驗曲線係數擬合之研究 (Study of Optoelectronic Experiments Coefficients Fitting)
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摘要(中)	中文摘要 在本論文中，吾人嘗試利用如最小方差法(least squares method)，離散式傅立葉轉換(discrete Fourier transform), 二元小波轉換(dyadic wavelet transform)和小波轉換(wavelet transform)等數學工具，將其應用在光學元件分析及電力系統傳輸線故障偵測的設計上。 首先，成長在砷化鎵上不同厚度大小的自我組成砷化銦量子點的應力影響被有系統的研究。藉由螢光光譜，各量子點的能階訊息可被觀察出來。在研究不同厚度大小砷化銦量子點的應力影響時，活化能和載子動態特性也是一個值得觀察的現象。藉由波長積分強度可定性出這些量子點試片的熱熄行為(thermal quench behavior)。而利用最小方差法和將小波轉換運用在係數估測上則可求出活化能係數，並將兩方法所得結果做一比較。 兩種不同的傳輸線保護機制同時被提出，並做比較。首先，一個以可適應式的相量測量單元為基礎的傳輸線保護方法被提出。在此一架構在雙端式演算法上的保護機制中，即時的電流和電壓資料首先被取得。藉由取樣方法可得到離散的電流和電壓資料，根據最小方差法則可得到不同寬度的離散式傅立葉轉換，藉由離散式傅立葉轉換方法，基頻的穩態相量可以很容易被估測而得。根據這些大小和相位資料，一個組合式故障偵測指標便可以被推導出來。另外一個以二元小波轉換為基礎的傳輸線故障偵測機制也被提出。藉由選取適當的離散近似係數當做故障偵測指標，根據此一簡易指標，可以在傳輸線的故障偵測，故障分類和故障方向辨別上有極佳的表現。最後並將兩方法所得結果做一比較，結果顯示架構在二元小波轉換上的方法較為簡易方便。 最後，吾人將小波轉換運用在像差係數的估測上。球差和失焦係數項同時被估測，並與最小方差法方法所得結果做一比較。當雜訊被考慮時，由於小波轉換方法在空間域和頻率域上同時具有局部化的特性，因此對雜訊較有免疫力。結果顯示小波轉換方法較最小方差法為優越。利用信號雜訊比作為一評估指標時，隨著高斯雜訊的引入，當其變異數增加時，小波轉換方法的優越性則更為明顯。
摘要(英)	Abstract In this dissertation, the authors apply the numerical methods such as the least square method (LSM), the discrete Fourier transform (DFT), dyadic wavelet transform and the wavelet transform (WT) for applications in optical device and in fault detection for transmission line of power system. The thickness-dependent renormalization of strain effects on self-organized InAs quantum dots has been systematically investigated. By means of observing the photoluminescence spectra, the related information of energy band of device microstructure can be obtained. The activation energy and the carrier dynamics of the quantum dots with various thickness are interesting phenomena for investing strain effects of InAs quantum dots grown on GaAs. We can utilize the plot of energy-integrated intensity to characterize their thermal quench behavior. With the LSM and the WT method to coefficients estimating, the activation energy of the quantum dots can be fitted. The results are also compared. Two different approaches for transmission lines protection are proposed. First, an adaptive phasor measurement unit (PMU) based protection scheme is proposed. In this algorithm based on two-ends method which the authors proposed, real-time voltage and current measurements are obtained firstly and discrete data can be obtained by sampling. With the aid of the LSM, the phasors can be solved. By using DFT of different window size, the phasors are easily estimated. Based on the amplitude and phase information, a fault detection index is then derived. Second, a dyadic wavelet transform based fault detection scheme is also proposed. The coefficient of discrete approximation of the dyadic wavelet transform is used to be an index for transmission lines fault detection, fault classification, and fault direction discrimination. The results reveal the dyadic wavelet transform based approach is a simple and effective one. The authors utilize the WT method to estimate the aberration coefficients for a simulated wave-front. The spherical aberration coefficient and defocus are both estimated, and the numerical results are compared with those obtained by the LSM. With noise added, the results reveal the excellency of the WT method. The wave-fronts are also reconstructed by two methods simultaneously. The signal-to-noise ratio is also used as a performance index for evaluation between two methods with Gaussian white noise added. As the variance of Gaussian white noise increases, the superiority of the WT method is obvious.
關鍵字(中)	★ 係數擬合	關鍵字(英)	★ Coefficients fitting
論文目次	Contents Abstract I List of Tables IV List of Figures V Acronym VIII Chapter 1 Introduction 1 1-1 Background 1 1-2 Motivation 5 1-2-1 Strain Effects on Self-Organized Quantum Dots 5 1-2-2 Transmission Lines Protection Scheme for Power System 6 1-2-3 Aberration Coefficients Fitting 8 1-3 Chapter Outlines 9 Chapter 2 Numerical Methods 12 2-1 Least Squares Methods 12 2-2 Discrete Fourier Transform 14 2-3 Wavelet Transform 17 2-4 Dyadic Wavelet Transform 18 Chapter 3 Thickness-Dependent Renormalization of Strain Effects on Self-Organized InAs Quantum Dots grown on GaAs 21 3-1 Experiments 22 3-2 Results and Discussion 23 3-3 Conclusion 26 Chapter 4 Fault Detection with PMU Based Approach and Dyadic Wavelet Transform for Transmission lines of Power System 28 4-1 Part I: PMU Based Approach 29 4-1-1 Basic Principles 29 4-1-2 The Adaptive Protection Scheme 32 4-1-3 Performance Evaluation 33 4-2 Part II: Dyadic Wavelet Transform Based Approach 36 4-2-1 Basic Ideas 36 4-2-2 Experiments with Simulated Waveforms 37 4-3 Conclusion 40 Chapter 5 Aberration Coefficients Fitting by Using the Least Squares Method and the Wavelet Transform method 41 5-1 Computing Aberration Coefficients by the Least-Squares Method 42 5-2 Computing Aberration Coefficients by the Wavelet Transform 44 5-3 Simulation Results 47 5-4 Conclusion 49 Chapter 6 Summary and Future Works 51 6-1 Summary 51 6-2 Future Works 53 References 54 Tables 67 Figures 76 Appendix A 102 Appendix B 105
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指導教授	張榮森(Rong-Seng Chang)	審核日期	2002-7-11
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