卡爾曼濾波法於建築結構系統之參數識別

Identification Structures Parametric System using Kalman Filter

江奇融(Chi-Rung Jiang)

指導教授 ： 王安培

中原大學/工學院/土木工程學系/碩士(2007年)

https://doi.org/10.6840/cycu200700755

摘要

近年來地震災害頻傳，對於預防地震造成建築結構破壞之科技尚未成熟，目前只能按照法規進行耐震設計來防範未然，而建築結構受震時的動態行為一直是耐震設計與分析中所考量重要因素之一。在各種系統識別模型中，參數系統識別的建立，如ARX模型。利用整批處理的參數推測法，不適用於非線性與時變性系統。
而卡爾曼濾波法優點在於採用線性遞推的方法獲得系統狀態的最佳估計，適應性強，應用範圍較廣，然而它要求目標的狀態模型是已知的，但是這常常不易做到。為解決此問題本研究發展出RARX-KF模型將卡爾曼濾波法與遞迴參數推測(recursive parameter estimation)做一結合。由於所得到的量測資料往往含有雜訊，所以藉由卡爾曼濾波法降低雜訊對識別的影響，即時檢測預測值和實際值之合理值，使模擬與預測的準確性提高。最後針對台東消防分隊大樓與加裝阻尼器之鋼構架試驗作非線性識別，由識別結果可以發現建築結構破壞時，會有頻率降低而阻尼比增加的趨勢，由此現象可尋找出破壞的時間區域，往後如果可以應用到結構主動控制，相信對降低地震災害將有所幫助。

關鍵字

卡爾曼濾波法 ； 系統識別

並列摘要

The earthquake disasters occurs frequently recent years, since the science and technology of preventing the earthquakes have not been mature yet, the dynamic behavior of the building structures has been able to bear shaking the important factor considered while designing and analyzing all the time. In system identification models such as ARX, parameters are determined by using a batch of parameters estimating, but it is inappropriate for nonlinear and time-varying systems.
The advantage of Kalman filter is adopting linear recursive to obtain the optimal estimation for systematic state. Also, it has the advantage of wide adaptability and application. However, the state model which is necessary during modeling process is difficult to obtain. To solve this problem, this research developed RARX-KF model, Kalman filter which is combined with recursive parameter estimation. Kalman filter method is applied to reduce the noise from the measured data and improve the identification. The accuracy of model objective was revised by inspecting on-line estimations and observations. The fire bureau building in Taitung and a test of the steel framework with damper are taken as an example of testifying non-linear behavior. The results showed that the damping ratio will increase when the building structure is destroyed and the frequency decreases. Therefore, the range of the destroyed time can be found out. The approach in this paper can be applied to the active control of the structure and to reduce the earthquake disaster.

並列關鍵字

System Identification ； Kalman Filter

參考文獻

【15】 林昭葳，「結構加裝圓棒形加勁消能器之動力分析及試驗驗證」，碩士論文，國立台灣大學土木工程學研究所，臺北，2005。

【1】 McVerry, G. H., “Structural Identification in the Frequency Domain from Earthquake Records,” Int. J. of Earthquake Engineering and Structural Dynamics, Vol. 8, pp. 161-180(1980).

【2】 Beck, J. L. and Jennings, P. C., “Structural Identification Using Linear Models and Earthquake Records,” Int. J. of Earthquake Engineering and Structural Dynamics, Vol. 8, pp. 145-160(1980).

【3】 Udwadia, F. E. and Kuo, C. P., “Non-Parametric Identification of a Class of Nonlinear Close Coupled Dynamic Systems,” Int. J. of Earthquake Engineering and Structural Dynamics, Vol. 9, pp. 385-409 (1981).

【4】 Masri, S. F. and et al., “Non-Parametric Identification of a Class of Nonlinear Multidegree Dynamic System,” Int. J. of Earthquake Engineering and Structural Dynamics, Vol. 10, pp.1-30(1982).