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研究生:黃宇璋
研究生(外文):Yu-Chang, Hwang
論文名稱:含雜訊系統之參數鑑別:離散小波轉換之應用
論文名稱(外文):Parameter Identification of Noisy Systems:An Application of Discrete Wavelet Transform
指導教授:黃世宏
指導教授(外文):Shyh-Hong, Hwang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:化學工程學系
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:135
中文關鍵詞:小波小波轉換小波去雜訊離散時間系統系統識別
外文關鍵詞:waveletswavelet transformwavelet de-noisingdiscrete time systemsystem identification
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本論文首先針對小波函數、小波轉換函數、小波去雜訊合成訊號、遞迴最小平方法、傳統的有益變數法和所提出的小波去雜訊有益變數法,作一概略性的介紹。另外,闡述小波兼具時頻特性的原因。
對於含雜訊的二階開環穩定系統,由閉環路和開環路方式,利用遞迴最小平方法、傳統的有益變數法和小波去雜訊有益變數法,分別辨識出系統參數值並與真實參數作比較。其中,閉環路方式以替續器來產生輸入訊號,開環路方式則以偽隨機二進制序列為輸入訊號。結果顯示:(1)使用小波去雜訊有益變數法優於遞迴最小平方法和傳統的有益變數法; (2)小波去雜訊有益變數法使用於開環路系統又優於閉環路系統。
對於含雜訊的三階開環穩定系統,以偽隨機二進制序列為輸入訊號的開環路方式進行模擬研究,利用遞迴最小平方法、傳統的有益變數法和小波去雜訊有益變數法分別求得系統參數值並與真實參數和賴氏圖作比較。無論由數據比較的結果或由賴氏圖近似的情況來看,小波去雜訊有益變數法皆優於遞迴最小平方法和傳統的有益變數法。
以上結果指出,以偽隨機二進制序列為輸入訊號的開環路方法配合小波去雜訊有益變數法為鑑別含雜訊的開環穩定系統參數最好的方式之一。
This thesis first discusses the concept of wavelet functions, wavelet transforms, wavelet de-noising, the recursive least-squares method, the conventional instrumental variable method, and the proposed instrumental variable method with wavelet de-noising. In addition, the time-frequency character of wavelet functions is elucidated.
A simulation study is conducted on open-loop stable, second-order systems in a closed-loop and an open-loop manner. The system parameters identified by the three methods are compared with their actual values for each system. In the closed-loop operation, the relay is employed to produce the input signal, while in the open-loop operation, the input signal is generated by the pseudo random binary sequence. The simulation results reveal that:
(1) The instrumental variable method with wavelet de-noising is superior to the other two methods.
(2) The open-loop manner is better than the closed-loop manner.
A simulation study is also carried out on third-order systems in open-loop operation where the input signal is generated by the pseudo random binary sequence. The system parameters identified by the three methods are compared by virtue of their actual values and Nyquist plots. The results show that the proposed method is superior to the other two methods.
It can be concluded that one of the best methods for parameter identification of open-loop stable systems is the proposed instrumental variable method with wavelet de-noising employed in the open-loop manner.
中文摘要………………………………………………………………… i
英文摘要……………………………………………………………… iii
表目錄……………………………………………………………………v
圖目錄………………………………………………………………… vii
第一章 緒論………………………………………………. ………..1
1.1 研究動機與目的………………………………………………...1
1.2 文獻回顧………………………………………………………...2
1.3 章節與組織……………………………………………………...5
第二章 小波函數和多層解析度分析……………………………... 6
2.1 多層解析度分析………………………………………….….. 6
2.1.1 多層解析度的近似空間…………………………………..6
2.1.2 多層解析度的細節空間…………………………………..7
2.1.3 多層解析度的特性………………………………………..8
2.2 小波函數………………………………………………….…..10
2.2.1 小波函數和尺度函數…………………………………...10
2.2.2 小波函數的種類………………………………………….11
第三章 小波轉換和去雜訊的合成訊號…………………………......14
3.1 小波轉換……………………………………………………...15
3.1.1 小波轉換之種類和離散小波逆轉換…………………….15
3.1.2 小波轉換在時間頻率定位的能力……………………….16
3.2 去雜訊的合成訊號…………………………………………...20
3.2.1 近似係數和細節係數…………………………………….20
3.2.2 快速離散一維小波分解與合成演算法………………….21
3.2.3 小波去雜訊合成訊號…………………………………….24
第四章 二階離散系統之模擬研究………………………………...26
4.1 含雜訊的二階系統模擬的模式……………………………...26
4.2 線性參數模式鑑別的方法…………………………………...29
4.2.1 遞迴最小平方法求解系統參數………………………….29
4.2.2 傳統有益變數法求解系統參數……………………. ….34
4.2.3 小波去雜訊有益變數法求解系統參數………………….36
4.3 模擬流程……………………………………………………...36
4.3.1 遞迴最小平方法求解系統參數的模擬過程…………….37
4.3.2 傳統有益變數法求解系統參數的模擬過程…………….39
4.3.3 小波去雜訊有益變數法求解系統參數的模擬過程…….41
4.4 結果與討論…………………………………………………...45
4.4.1 二階含雜訊的閉環路系統模擬的結果………………….45
4.4.2 二階含雜訊的開環路系統模擬的結果………………….48
4.4.3 比較二階含雜訊的閉環路與開環路系統模擬的結果….50
第五章 三階離散系統之模擬研究………………………………...88
5.1 含雜訊的三階系統模擬的模式……………………………...88
5.2 模擬步驟……………………………………………………...89
5.3 結果與討論…………………………………………………...92
第六章 結論與未來展望…………………………………………..107
參考文獻………………………………………………………………..109
附錄一 函數的正交………………………………………………..114
附錄二 裡的正交補集合…………………….................115
附錄三 快速一維小波分解與合成理論(簡述) ………………….118
附錄四 模擬程式及Simulink之方塊圖…………………………..123
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