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研究生:游思齊
研究生(外文):Sih-Ci You
論文名稱:改良型多自由度模態參數辨識系統
論文名稱(外文):Improved modal parameter identification system for Multiple-degree-of-freedom systems
指導教授:陳任之
指導教授(外文):Yum-Ji CHAN
口試委員:王栢村吳天堯
口試委員(外文):Bor-Tsuen WangTian-Yau Wu
口試日期:2016-07-25
學位類別:碩士
校院名稱:國立中興大學
系所名稱:機械工程學系所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:88
中文關鍵詞:模態分析小波轉換PolyMAX限制最小平方權重函數
外文關鍵詞:Modal analysisWavelet transformPolyMAXConstrained least squaresWeighting function
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實驗模態分析在動態結構分析領域裡是一種重要技術。在分析結構特性時,我們因追求精準的自然頻率、阻尼比和模態振型。因此,前人提出了頻域的PolyMAX和時域的小波轉換兩種模態參數識別方法。本論文的主要目的在於提升PolyMAX方法的識別能力,PolyMAX方法是利用權重最小平方法配合高階多項式模型作曲線擬合,並進一步發展自動化的模態分析方法。使用越高階的多項式可能會導致PolyMAX方法的產生病態矩陣,甚至在z頻域上產生不穩定的極值。這些問題都會影響PolyMAX方法的辨識能力。因此,本論文內提出了兩種改善方法,利用權重函數方法及最佳化方法可以使PolyMAX利用較低階數多項式或是任意階數多項式來精準的辨識模態參數。為了精準的辨識阻尼比,本文利用小波轉換方法取代原本的PolyMAX方法。此外,鋁製樑、主軸頭架和工具機(部分組裝)會透過模態測試來取得量測訊號,改善之辨識方法和小波轉換方法會經由這些實驗來驗證。

Experiment Modal Analysis is one of the key technologies in structural dynamics analysis. Natural frequencies, damping ratios and mode shapes should be sought accurately when analyzing structural properties. Therefore, the frequency-domain PolyMAX method and time-domain wavelet transform method have been proposed. The study is to enhance the accuracy of PolyMAX method which is based on the weighted least squares method with the high-order polynomial model, and facilitate further automatic modal analysis method. The higher-order polynomials may generate ill-conditioned matrices and generate “unstable” poles in Z-domain system. The weighting function method and the constrained least squares method are proposed to allow PolyMAX to use lower-order polynomial to estimate modal parameters accurately. The wavelet transform method is proposed to replace the PolyMAX method in order to estimate damping ratios. In addition, an aluminum beam, machine slides and machine tool (sub-assembly) will undergo modal testing. And the improved methods of PolyMAX and wavelet transform method will be verified with the measured signals.

Acknowledgements.....................................i
摘要.................................................ii
Abstract.............................................iii
Table of Contents....................................iv
List of Tables.......................................vii
List of Figure.......................................viii
List of Symbols......................................xi
Chapter 1. Introduction..............................1
1.1. Background...................................1
1.2. Literature Review............................1
1.2.1. PolyMAX frequency-domain method..............3
1.2.2. Wavelet transform in modal analysis..........4
1.3. Objectives...................................5
1.4. Methodology and Structure of Thesis..........6
1.4.1. Methodology..................................6
1.4.2. Structure of Thesis..........................6
Chapter 2. Theoretical Background....................7
2.1. Least-squares method.........................7
2.2. Frequency-domain PolyMAX method..............9
2.3. Constrained least squares....................14
2.4. Error level..................................15
2.5. Stabilization diagram........................16
2.6. Time-domain wavelet transform method.........17
2.6.1. Wavelet function.............................17
2.6.2. Complex Morlet wavelet.......................18
2.6.3. Time-domain modal parameters identification..21
2.6.4. Application of wavelet transform.............22
Chapter 3. Improvements to PolyMAX...................25
3.1. Weighting function selection.................25
3.2. Application of constrained least squares to PolyMAX..............................................28
3.3. Process of modal analysis....................36
Chapter 4. Application of the improved methods.......37
4.1. Validation with discrete dynamic model.......37
4.2. Down-sampling and related issues.............40
4.3. Objects to be tested.........................42
4.4. Aluminum beam................................46
4.4.1. Weighting function method....................49
4.4.2. Constrained least squares method and choice of lambda...............................................51
4.4.3. Time-domain wavelet transform................57
4.5. Machine slides...............................59
4.5.1. Weighting function method....................60
4.5.2. Constrained least squares method.............63
4.5.3. Time-domain wavelet transform................66
4.6. Machine tool sub-assembly....................67
4.6.1. Weighting function method....................69
4.6.2. Constrained least squares method.............71
4.6.3. Time-domain wavelet transform................77
Chapter 5. Conclusion and Future work................78
5.1. Conclusions..................................78
5.2. Proposed Future work.........................79
References...........................................80
Appendix A: Mathematical background definition.......84
Appendix B: Properties of experimental instruments...85
Appendix C: Mode shapes of free-free beam............86
Appendix D: Mode shapes of machine slides............87


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