臺灣博碩士論文加值系統

本研究主要探討線性系統的識別技術，希望利用小波分析的方法解決富立葉分析方法在多自由度系統鑑別及時變系統鑑別上的缺失。我們分別探討了線性非時變與線性時變系統之脈衝響應函數的鑑別。
在非時變系統鑑別上，我們以兩個方向進行，其一為估測系統參數，主要利用脈衝響應在Morlet小波轉換後與自然頻率、阻尼之間的關係來做鑑別。模擬及實驗結果顯示，此法所鑑別出之自然頻率與阻尼優於富立葉分析方法，尤其在伴隨雜訊及多自由度之情形下。另一方向為建立系統之脈衝響應函數。此部份我們提出了小波系統描述法，亦即利用小波基底描述系統的脈衝響應函數。在時變系統部分我們將小波系統描述法加以拓展應用，利用兩組的小波基底描述系統之脈衝響應函數，藉以掌握時變特性。除了理論分析與數值模擬外，本研究也以實驗驗證理論分析，結果均令人滿意。

This thesis presents a wavelet transform-based method for linear system identification. The proposed wavelet based method is applicable to system identification of multi-degree of freedom systems and even time-varying systems, which are difficult, if not impossible, to be identified by Fourier techniques.
In the identification of LTI(linear time invarient) systems, two approaches are taken. One is to estimate the system’s parameters. This method is based on the relationship between nature frequency, damping ratio and the Morlet wavelet transform of the system’s impulse response. Both numerical and simulation results show that this method is better than those by Fourier analysis, especially for the cases with noises and for multi-degree of freedom systems. The other approach is to identify the system’s impulse response. Here we propose a method called the Wavelet Based System Characterization (WBSC) Method. This method is to use a wavelet basis to represent system’s impulse response. The WBSC method is then extended to linear time-varying systems. Two sets of wavelet bases are now needed in order to capture the time-varying property. In addition to theoretical analysis and numerical simulations, experimental results also demonstrate satisfactory agreement with the analysis.

第一章 前言…………………………………………….1
第二章 文獻回顧………………………………………4
2.1小波理論概述…………………………………………4
2.2 小波分析於系統鑑別之應用……………………….10
第三章 線性非時變系統鑑別………………………….13
3.1 前言………………………………………………….13
3.2 系統參數之估測…………………………………….13
3.2.1 單自由度系統…………………………………….19
3.2.2 多自由度系統…………………………………….25
3.2.3 小波分析與富立葉分析之比較………………….36
3.3 小波系統描述法…………………………………….41
3.3.1 問題討論………………………………………….42
3.3.2模擬結果……………………………………………43
第四章 線性時變系統鑑別…………………………….47
4.1 前言………………………………………………….47
4.2 理論架構…………………………………………….47
4.3模擬結果………………………………………………52
第五章 實驗架構與實驗結果………………………….60
5.1實驗架構………………………………………………60
5.2 非時變系統實驗結果……………………………….65
5.3 時變系統實驗結果………………………………….71
第六章 結論與未來研究方向………………………….75
6.1 結論………………………………………………….75
6.2 未來展望…………………………………………….75
附錄A………………………………………………………77
附錄B………………………………………………………80
參考文獻………………………………………………….82

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