利用模態擴展及模型更新法:進行結構損壞識別

Damage Detection Using Mode Shape Expansion and Finite Element Model Updating

吳宜錚(Yi-Cheng Wu)

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(2010年)

https://doi.org/10.6342/NTU.2010.01118

摘要

本文主要目的為在有限量測條件下，利用模型更新法進行結構物損壞識別。全文可分為三大部份：第一，利用模態擴展法重建未量測自由度之振態。第二，利用模型更新法修正已建立之有限元素模型。第三，引入一個具有物理意義之損壞指標，使得損壞位置及損壞程度能夠同時成功識別。
藉由一個考慮不同量測及不同破壞位置之線性八自由度系統，可驗證當選用合適的權重係數(weighting coefficient)時，模態擴展法可有效重建未量測自由度之振態。
此外，利用此數值模擬模型，本文亦比較了五種基於模型更新原理的損壞識別法。模擬結果顯示，使用完全正確的模態時，各方法皆能成功識別損壞。但當使用擴展後之模態時，有效模型修正法(EMCM)則具有較佳之表現。
最後，本文透過一個在台灣國家地震中心(NCREE)的六層樓鋼構架之振動台實驗，驗證提出的損壞識別法。實驗結果顯示有效模型修正法的確適用於實際應用上。
本文透過數值模擬及實驗皆驗證在有限量測條件下，利用模態擴展和模型更新法並配合損壞指標，可有效識別損壞位置及損壞程度。

關鍵字

有限量測 ； 模態擴展 ； 系統識別 ； 模型更新 ； 損壞識別 ； 損壞指標

並列摘要

The purpose of this research is to employ the model updating technique to conduct the structural damage detection with insufficient measurements. In this study, a three stage damage detection algorithm is investigated. First, a mode shape expansion (MSE) technique is implemented to compensate the deficiency of insufficient measurements. Second, the model updating approach is introduced to correct the parameters of the FE model by using the measurement data. Third, a physical meaning damage index is adopted to locate and quantify damage simultaneously.
To investigate the effectiveness of the proposed MSE technique and model updating approaches, numerical studies with three types of sensor distributions and five damage scenarios were investigated. It can be seen that when the weighting coefficient of the proposed MSE technique is properly selected, the ability of reconstructing the mode shape is appreciated.
In cooperated with the MSE, five damage detection techniques based on the concept of model updating are investigated in this study: (1) Improved Damage Ritz Vector Method (IDRVM), (2) Minimum Rank Perturbation Theory (MRPT), (3) Modified Quadratic Compression Method (MQCM), (4) Efficient Model Correction Method (EMCM), and (5) Ratios of Stiffness to Mass Approach (RSMA). Numerical studies were investigated on all damage detection techniques. It can be observed that if the exact mode shapes can be reconstructed, then damage detection methods can performance well. Through these studies, EMCM has the best performance to damage detection by adopting the expanded mode shapes.
Data collected from the shaking table test of a six-story steel frame structure at National Center for Research on Earthquake Engineering in Taiwan (NCREE) were used to verify the applicability of the EMCM damage detection technique.
The study concludes that damage detection through mode shape expansion is possible if the expanded mode shapes are consistent with the exact mode shapes. Among all the damage detection methods, the Efficient Model Correction Method can provide good results of damage detection.

並列關鍵字

insufficient measurement ； mode shape expansion ； system identification ； model updating ； damage detection ； damage index

參考文獻

[1] A.K. Chopra, “Dynamics of structures: Theory and applications to earthquake engineering,” 3rd edition, Prentice Hall, Upper Saddle River, New Jersey, 2007.

[2] Andrea Brasiliano , Graciela N. Doz and Jose' Luis V. de Brito, “Damage identification in continuous beams and frame structures using the residual error method in the movement equation , ” Nuclear Engineering and Design, Vol. 227, No. 1 , pp. 1-17, January 2004.

[4] C.C. Chu and M.H. Milman, “Eigenvalue error analysis of viscously damped structures using a Ritz reduction method,” Journal of AIAA, Vol. 30, No. 12, pp. 2935-2944, December 1992.

[5] C. H. Loh and J. H. Weng, “ Damage detection using stochastic subspace identification with partial measurements,” Proceedings of 7th international workshop on structural health monitoring, Stanford, California, 2009.

[6] D. C. Zimmerman and M. Kaouk, “Structural damage detection using a minimum rank update theory,” Journal of Vibration and Acoustics, Vol. 116, No. 2, pp. 222-231, April 1994.