臺灣博碩士論文加值系統

操作模態分析法是模態測試的一個新趨勢，利用操作模態分析法可對機械結構的動態特性進行分析。數據驅動的隨機子空間辨識法(DD-SSI)是一種時域分析方法，用於辨識機械和結構中的模態參數。雖然數據驅動的隨機子空間辨識操作模態分析的運算法已被建立，但是仍欠缺其中的I值和N值兩個參數的選擇原則。I值和N值為Hankel矩陣的維度而在不同Hankel矩陣的維度下，會導致所辨識的模態參數發生變化。其中I值會影響投影結果和模態參數的選取，此外，計算模型的維度會隨著I值的變化而有所改變。
本研究之目標為找出適用於數據驅動的隨機子空間辨識法的I值和模型階數，以識別多輸出多自由度(MO-MDOF)模型的模態參數。確定模型階數的方法是利用circulant矩陣的特性來找出投影矩陣O的奇異值和奇異矩陣。然而，此種方法會導致頻域分析的洩漏問題，解決的方法為透過選擇合適的I值以避開洩漏的發生，可是此種方法難以在實際結構中應用。對於多輸出多自由度的系統來說，提取模態參數牽涉大量計算，而利用穩態圖可以快速的估計在後處理中所需使用的模型階數，也可利用將多輸出系統(MO)分解為多個單輸出(SO)系統進行辨識。通過優化這些計算工具，本論文示範兩個MO-MDOF結構的模態參數辨識。

Operational modal analysis (OMA) is currently one of the key technologies used in mechanical dynamics analysis. The data driven stochastic subspace identification (DD-SSI) is a time-domain method used to identify modal parameters in machinery and structures. Although the DD-SSI OMA procedure has now been established, guidelines selecting the user-defined variables do not yet exist. The variables I and N, the dimensions of Hankel matrix, lead to the variation of identified modal parameters. The variable I makes an impact on the projection process and modal parameters extraction. Besides, the model (computing) order is also followed by the variable I.
In this research, the aim is to determine the suitable value of I for identification of multiple-output (MO) with multiple degree of freedom (MDOF) system and the model (computing) order in identification. The model order is sought by applying the characteristics of circulant matrix to indicate the non-zero singular values and corresponding singular values of projection matrix O. It’s found that frequency-domain issues arise in DD-SSI OMA method which could be avoided by selecting particular values of I practically unfeasible. The use of stabilization diagram can make a quick estimation of the model order of post-processing progress. For MO-MDOF system, computation for extracting modal parameters would be considerable. Under limited computer memory, it is available to resolve the MO system response into multiple SO system responses in identification. By combining these optimization techniques, modal parameters of two MO-MDOF systems are identified.

摘要 i
Abstract ii
Table of Contents iii
List of Tables iv
List of Figures v
Abbreviations vi
Nomenclature vii
Chapter 1. Introduction 1
1.1. Background 1
1.2. Literature Review 2
1.3. Objectives 7
1.4. Methodology 8
1.5. Structure of Thesis 9
Chapter 2. Theory and Methods 10
2.1. Random Variables and Signal Processing Tools 10
2.2. Data Driven SSI-OMA 14
2.3. Singular Value Decomposition 20
Chapter 3. Analysis of the Process in Data Driven SSI-OMA 22
3.1. Order Determination of Post-Processing Progress 23
3.2. Identification Performance on Parameters 32
3.3. Analysis of the MO-MDOF block Hankel matrix 36
Chapter 4. Experimental Demonstration 42
4.1. Three-Storey Frame 43
4.2. 8-sector Integral Bladed Disc 51
Chapter 5. Conclusions and Future Prospects 57
5.1. Conclusions 57
5.2. Future prospects 60
References 61
Appendix A. Derivation 65
A.1. Derivation of Matrices F_1 and F_2 Being Circulant 65
A.2. Derivation of T_pp for MO-SDOF system 67
Appendix B. Equipment 70

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