運用適應性卡氏過濾理論即時系統損壞識別

On-line Damage Identification of Structural System Based on Adaptive Extended Kalman Filter

黃謝恭(Shieh-Kung Huang)

指導教授 ： 羅俊雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.02858

摘要

結構健康度檢測（Structural Health Monitoring）在土木工程領域裡頭一直非常受到重視，為了實現這個理念，系統識別（System Identification）與傷害檢測（Damage Detection）變成近十或十五年裡最重要的技術。在一個強大的動力事件中，結構系統也許遭受了某種程度的損害，而此結構系統的損壞將會反應在參數數值的變動上，且被包含在振動反應的量測中。因此系統識別的技術，尤其是即時識別的技術（On-line Identification Technique）近年來大量的被採用。
在即時識別的技術上，時間域的分析（Time Domain Analysis）以迭代運算（iterative computation）的形式被應用，例如卡氏過濾理論（Kalman Filter Technique）。然而此種迭代運算非常地倚賴過去的資料且無法識別系統參數瞬間的改變，為了克服這個缺點，適應性卡氏過濾理論（Adaptive Kalman Filter）使用了適應性尋跡的技術（Adaptive Tracking Technique）而被提出。
在這篇論文中將提出一個適應性尋跡的技術，此技術運用卡氏過濾理論為基礎，並著眼於誤差共變數矩陣（error covariance matrix）的發展。首先，每一個時間點的殘餘誤差（residual error）將被算出，而適應性矩陣（adaptation matrix）根據殘餘誤差產生，最後透過推薦的誤差指數（error index）使得系統參數可以即時的被識別。此方法能夠在嚴重的動力事件中識別系統參數瞬間的改變，此外也可以應用於識別非線性系統之恢復力（restoring force）的背脊線（backbone curve）。為了驗證這方法，結構系統的反應將以數值模擬與實驗量測兩種方法產生，而用以識別結構系統參數。最後，識別結果會有所比較與討論。

關鍵字

卡氏過濾理論 ； 結構健康度檢測 ； 系統識別 ； 傷害檢測 ； 即時識別

並列摘要

Structural health monitoring (SHM) received considerable attention in civil engineering. To realize this, system identification and damage detection becomes the most important technique in the last ten or fifteen years. During a severe dynamic event, the structural system may suffer certain degree of damage. The damage of the structural system will be reflected by the variations of parametric value, and contained in the response measurements. Therefore, system identification techniques, especially on-line identification techniques, are commonly used recently.
For the on-line identification techniques, time domain analysis has been applied with iterative computation, such as Kalman filter technique. However, the iterative analyses rely highly on the past data, and can not detect the abrupt change of system parameters. To overcome this drawback, adaptive Kalman filter are proposed using adaptive tracking techniques.
In this thesis, an adaptive tracking technique based on the Kalman filter will be proposed. This proposed method is focus on the development of error covariance matrix. Firstly, the residual error of each time step is calculated, and then the adaptation matrix is generated in accordance with the residual error. Through the proposed error index the on-line adaptive tracking of system parameter can be identified. The proposed method is capable of tracking the abrupt change of parameters from a severe dynamic event. Moreover, it is also applied to identity the backbone curve of the inelastic restoring force of the nonlinear system. To verify the adaptive tracking technique, the responses of the structural system will be simulated numerically and measured experimentally, then, used to identify the parameters in structural system. Finally, the identification results are compared and discussed.

並列關鍵字

Kalman filter ； structural health monitoring ； system identification ； damage detection ； on-line identification

參考文獻

[1] U. Lee and J. Shin, “A Frequency-domain Method of Structural Damage Identification Formulated from the Dynamic Stiffness Equation of Motion,” Journal of Sound and Vibration (2002) 257(4), 615-634

[2] Douglas E. Adams and Charles R. Farrar, “Application of Frequency Domain ARX Features for Linear and Nonlinear Structural Damage Identification,” Proceedings of SPIE - The International Society for Optical Engineering, v 4702, 2002, 134-147

[3] R. Ghanem and M. Shinozuka, “Structural System Identification I,” Journal of Engineering Mechanics, February 1995, 255-264

[4] M. Shinozuka, H. Member, and R. Ghanem, “Structural System Identification II,” Journal of Engineering Mechanics, February 1995, 265-273

[5] H. Lus, R. Betti, and R. W. Longman, “Identification of Linear Structural Systems using Earthquake-induced Vibration Data,” Earthquake Engineering and Structural Dynamics, 1999, 28:1449-1467