本文以一振動系統及簡易模型分別來測試卡爾曼濾波器於估測時的效能及驗證其可行性。本研究利用有限元素軟體ANSYS進行系統建模及計算模態參數，並藉由卡爾曼濾波器將可能的感測雜訊及系統不確定性濾除，進一步可以更新系統的模態參數並估測結構系統的振動響應。此外，模擬監測之加速規在失效的情況下，預測結構後續的動態行為。本研究分析結構存在不確定性及雜訊強度的估測情況，並進行反相位更新時，卡爾曼濾波器估測加速度響應之追蹤效能。研究結果發現，進行模型更新後的系統可將估測誤差降至10%以內，證實此研究能有效降低量測誤差。

In this thesis, a vibration system and a simple model were used to test the estimation efficiency of Kalman filter and to verify its feasibility. Finite element software ANSYS was used for modeling and calculation of modal parameters, and Kalman filter was used to filter out possible sensor noise and uncertainty. Further, modal parameters of system can be updated and the system response was estimated. In addition, the simulation of the accelerometer to monitor in the failure was predicted the dynamic behavior. This study analyzed the uncertainty of the structure and noise intensity estimated, and for anti-phase updating, the tracking performance of acceleration response was estimated by Kalman filter. It can be observed that when system with model updating, the error between real and estimation responses is less than 10%. This proves that the present approach can effectively reduce the measurement error.

1. R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems”, Journal of Basic Engineering 82, 35-45 (1960).
2. C.-F. Hung, W.-J. Ko and Y.-T. Peng, “Application of ARX/ERA to Identify the Equivalent State Equation of Motion”, Bulletin of the College of Engineering National Taiwan University 82, 21-31 (2001).
3. S. Deng and T.-Y. Heh, “The Study of Structural System Dynamic Problems by Recursive Estimation Method”, Int J Adv Manuf Technol 30, 195-202 (2006).
4. K.-V. Yuen, K.-I. Hoi and K.M. Mok, “Selection of Noise Parameters for Kalman Filter”, Earthquake Engineering and Engineering Vibration 6, 49-56 (2007).
5. 李勝源, 結構系統動態行為之系統建模與識別, 國立中央大學機械工程研究所碩士論文, (2000).
6. J. Yu, M. Imbimbo and R. Betti, “Identification of Linear Structural Systems with a Limited Set of Input-Output Measurements”, Journal of Applied Mechanics 76, 1-10 (2009).
7. F. Gao and Y. Lu, “A Kalman-Filter Based Time-domain Analysis for Structural Damage Diagnosis with Noisy Signals”, Journal of Sound and Vibration 297, 916-930 (2006).
8. J.-W. Sohn, H.-S. Kim and S.-B. Choi, “Dynamics Characteristics of Smart Hull Structures Featuring Piezoelectric Materials”, Key Engineering Materials 306, 1145-1150 (2006).
9. S.-J. Moon and C.-W. Lim, “Structural Vibration Control Using Linear Magnetostrictive Actuators”, Journal of Sound and Vibration 302, 875-891 (2007).
10. R. Caracciolo, A. Gasparetto and M. Giovagnoni, “Measurement of the Isotropic Dynamic Young’s Modulus in Seismically Excited Cantilever Beam Using a Laser Sensor”, Journal of Sound and Vibration 231, 1339-1353 (2000).
11. A. C. Pisoni and C. Santolini, “Displacements in a Vibrating Body by Strain Gauge Measurements”, Massachusetts Institute of Technology 13, 1-8 (1995).
12. H.F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York (1969).
13. B.-T. Wang and P.-H. Cheng., “Finite Element Modal Verification for the Use of Piezoelectric Sensor in Structural Modal Analysis”, Journal of Mechanics 22, 235-242 (2006).
14. X.-J. Dong, G. Meng and J.-C. Peng, “Vibration Control of Piezoelectric Smart Structures Based on System Identification Technique: Numerical Simulation and Experimental Study”, Journal of Sound and Vibration 297, 680-693 (2006).
15. Z. Kiral, L. Malgaca and M. Akdag, “Active Control of Residual Vibrations of a Cantilever Smart Beam”, Turkish Journal of Engineering and Environmental Sciences 32, 51-57 (2008).
16. J.-C. Yu and C.-B. Lan, “System Modeling of Microaccelerometer Using Piezoelectric Thin Films,” Sensors and Actuators 88, 178-186 (2001).
17. A. Albarbar and S. Mekid, “Suitability of MEMS Accelerometers for Condition Monitoring: An Experimental Study”, Sensors 8, 784-799 (2008).
18. 王柏村, 振動學, 全華圖書,(2000).
19. M. S. Grewal, Kalman Filtering: Theory and Practice Using MATLAB, Wiley-IEEE, (2008).
20. G. Welch and G. Bishop, “An Introduction to the Kalman Filter”, University of North Carolina Department of Computer Science, (2006).
21. R.-W. Stark, G. Schitter and M. Stark, “State-Space Model of Freely Vibrating and Surface-Coupled Cantilever Dynamics in Atomic Force Microscopy”, Physical Review 69, 085412 (2004).
22. 陳精一, ANSYS振動學實務分析, 高立圖書, 台北(2005).
23. 楊士徹,應用卡爾曼濾波理論於系統的估算與控制, 逢甲大學航太與系統工程學系碩士論文,(2006).
24. F. Gao and Y. Lu, “An Acceleration Residual Generation Approach for Structural Damage Identification”, Journal of Sound and Vibration 319, 163-181 (2009).
25. A. D. Dimarogonas, Vibration for Engineers, Simon & Schuster Company, New Jersey (1992).