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Robustness and parameter selection in Stochastic Subspace Identification
|關鍵字:||隨機子空間辨識操作模態分析;正交投影;預測濾波器;強健性;蒙地卡羅法;Stochastic subspace identification operational modal analysis;Projection;Predictive filter;Robustness;Monte Carlo simulation||引用:|| J.-W. Huang, Apply MEMS acceleromter in operational modal analysis of machine tools, Taichung: Master Thesis, Department of Mechanical Engineering, National Chung Hsing University, 2016.  D. Ewins, Modal testing, theory, practice and application. 2nd edition, Research Studies Rress Ltd, 2000.  L. Zhang, R. Brincker and P. Andersen, 'An overview of operational modal analysis: Major development and issues,' in Proceedings of the 1st International Operational Modal Analysis Conference, 2005.  R. Brincker and C. Ventura, Introduction to operational modal analysis, Wiley, 2015.  P. V. Overschee and B. De Moor, Subspace identification for linear system, theory, implementation, applications, Kluwer Academic Publishers, 1996.  R. Brincker, P. Andersen and N.-J. Jacobsen, 'Automated frequency domain decomposition for operational modal analysis,' in IMAC-XXV : A Conference & Exposition on Structural Dynamics, 2007.  G. Zhang, B. Tang and G. Tang, 'An improved stochastic subspace identification for operational modal analysis,' Measurement, vol. 45, pp. 1246-1256, 2012.  I. Zaghbani and V. Songmene, 'Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis,' International Journal of Machine Tools and Manufacture, vol. 49, p. 947–957, 2009.  L. Ramos, L. Marques, P. Lourenço, G. De Roeck, A. Campos-Costa and J. Roque, 'Monitoring historical masonry structures with operational modal analysis: Two case studies,' Mechanical Systems and Signal Processing, vol. 24, pp. 1291-1305, 2010.  E. Reynders, J. Houbrechts and . G. D. Roeck, 'Fully automated (operational) modal analysis,' Mechanical Systems and Signal Processing, vol. 29, pp. 228-250, 2012.  Z. Zhang, Identify dynamic characteristics and application of spindle-tool system and Machine footing for machine tool, Chiayi: Master Thesis, Department of Mechanical Engineering, National Chung Cheng University, 2017.  H.-H. Cheng, Identification of Dynamic Characteristics of Machine Tools Using Operational Modal Analysis, Chiayi: Master Thesis, Department of Mechanical Engineering, National Chung Cheng University, 2015.  P. V. Overschee and B. De Moor, 'Subspace algorithm for the stochastic identification problem,' Automatica, vol. 29, pp. 649-660, 5 1993.  B. Peeters, G. De Roeck, T. Pollet and L. Schueremans, 'Stochastic subspace techniques applied to parameter identification of civil engineering structures,' in Proceedings of the international conference MV2 on New Advances in modal synthesis of large structures: non-linear, damped and non-deterministic cases, France, 1995.  B. Peeters, System identification and damage detection in civil engineering, Leuven: Ph,D thesis, Faculteit Toegepaste Wetenschappen, Katholieke Universiteir (in Dutch), 2000.  M. Döhler, X.-B. Lam and L. Mevel, 'Uncertainty quantification for modal parameters from stochastic subspace identification on multi-setup measurements,' Mechanical Systems and Signal Processing, vol. 36, no. 2, pp. 562-581, 2013.  V. Kuts, S. Nikolaev and S. Voronov, 'The procedure for subspace identification optimal parameters selection in application to the turbine blade modal analysis,' Procedia Engineering, vol. 176, pp. 56-65, 2017.  C. Priori, M. De Angelis and R. Betti, 'On the selection of user-defined parameters in data-driven stochastic subspace identification,' Mechanical Systems and Signal Processing, vol. 100, pp. 501-523, 2018.  E. Reynders and G. De Roeck, 'Reference-based combined deterministic–stochastic subspace identification for experimental and operational modal analysis,' Mechanical Systems and Signal Processing, vol. 22, pp. 617-637, 2008.  Y. J. Chan, Variability of blade vibration in mistuned bladed discs, London: PH,D thesis, Department of Mechanical Engineering, Imperial College London, 2009.  L. Andolfatto, J. Mayer and S. Lavernhe, 'Adaptive Monte Carlo applied to uncertainty estimation in five axis machine tool link errors identification with thermal disturbance,' International Journal of Machine Tools and Manufacture, vol. 51, pp. 618-627, 2011.  C.-Y. Tai, High-Order Finite Element Model for Rotating Shafts with Uncertain Parameters, Taichung: Master Thesis, Department of Mechanical Engineering, National Chung Hsing University, 2015.  S. Haykin, Adaptive filter theory. 4th edition, Pearson Education Inc., 2011.  E. Oran Brigham, The fast Fourier transform and its applications, Prentice-Hall Inc., 1988.  G. J. Proakis and G. D. Manolakis, Digital signal processing principles, algorithms,and applications, second edition, Macmillan Publishing Company, 1992.  K. Worden and G. Tomlinson, Nonlinearity in structural dynamics: detection, identification and modelling, IOP Publishing Ltd, 2011.||摘要:||
隨機子空間辨識操作模態分析(SSI-OMA)是一種新型的模態分析方法，此方法中決定Hankel矩陣的維度(分別為I與N值)是一個重要步驟，不同Hankel 矩陣的維度下的辨識可能導致模態參數變異。為了找出在不同Hankel 矩陣維度下正交投影結果的變化，本論文透過機率與數位訊號處理理論，對隨機子空間辨識法中的正交投影進行分析。
Stochastic subspace identification operational modal analysis (SSI-OMA) is a recent method in modal testing. In this method, determining the size of the Hankel matrix, demoted I and N, is an important step. Different sizes of the Hankel matrix may lead to variations in identified modal parameters. In this thesis, the projection procedure is analyzed using probability and digital signal processing theory, and the variation of the projection result under Hankel matrix sizes is sought.
It is found that the projection can be seen as a predictive filter and the projection quality is influenced by the location of passband if I=(3/4+1/2N_SL) T_Toep, the location of passband in Bode diagram would be located at the signal frequency. Also, the optimal value of I increases with sampling frequency. Therefore, under limited computer memory, it is beneficial to use low sampling frequency and a reduced value of I. In addition, it is found when the value of N is increased, the predictive filter would converge gradually
The identified modal parameters are also influenced by variation of excitation force. Using Monte Carlo simulation, it is found that identified damping ratios are sensitive to the variation of excitation force and negative values may emerge on a system with positive damping loss factors. Finally, the SSI is applied to a multi-degrees-of-freedom test rig and the trends shown in simulations are validated.
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