基於第一模態振形與其導數之連續過濾式組合損傷診斷方法: 於建築結構之應用

Sequential Filtering Damage Detection Method Using First Mode Shape Derivatives: Applications to Building Structures

莊智豪(Chih-Hau Chuang)

指導教授 ： 張家銘

國立臺灣大學/工學院/土木工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101816

摘要

結構健康監測在近年來越來越受到重視，尤其台灣位於板塊交界地帶，在大地震過後，結構物輕則產生裂縫，嚴重則發生倒榻的意外；台灣也因地屬於亞熱帶氣候的國家，全年較為濕熱的氣候使得結構物之耐久性受到很大的挑戰。以上原因都會造成結構物的損壞，基於防患未然的原則，結構損傷診斷就變得非常的重要，尤其結構物存在內部損壞時，很難透過外觀去判斷其損傷位置或是損傷程度，並且結構物的材料與高度的不同，並沒有一個廣義的方法可針對不同類型的結構物進行損傷診斷。
現今多數的結構健康監測方法都是利用結構振動反應進行分析，並藉由結構動力特徵、訊號特徵、模型預測反應等變化，進而決定損傷之位置。利用結構動力特徵，可以觀察相關參數變化，建立相應之損傷指標，方法如模態應變能法、柔度矩陣法、頻率響應函數變化法。應用訊號處理方法，提取訊號特徵，在損傷前後判斷相關係數與特徵之變化，方法如小波轉換、希爾伯特-黃轉換、建立自回歸模型。應用模型預測中，主要比較實際量測與預測反應之間差別，進而判斷損傷位置，可利用卡氏濾波器組、機器學習等方法進行。上述之方法由過去文獻得知，皆存在一共同缺點，即在判斷單一建築結構具有多損傷之情況時，容易造成損傷位置判斷錯誤之情形。因此，本研究主要利用結構振動反應獲取結構動力特徵，如第一模態振形，進而分離撓曲與剪切模態振形，藉由不同力學行為造成之模態振形與其導數，建立損傷指標，可應用於多損傷位置之建築結構中。
本研究主要研發連續過濾式損傷診斷方法，將建築結構第一模態振形分離成撓曲與剪切部分，並將模態擴展至結構構件上（如樓層柱），估計構件之空間連續模態撓曲與剪切振形與其導數。然後，透過模態應變能法，計算相應的基於模態曲率與模態斜率損傷指標，將此兩種指標相互結合，並藉由逐步篩選法，一步一步地將損傷位置找出，其效果優於傳統基於模態曲率之模態應變能法。最後，本研究利用數值模擬之方式，應用一八層樓構架，展示九種不同之損傷情況；另外，亦透過實驗方式，建立六層樓全鋁材質之縮尺構架，透過隨機遞減法之系統識別獲取第一模態振形，其中包含位移模態振形與轉角模態振形，考慮九種損傷案例，驗證本研究所提出之連續過濾式損傷診斷方法。由實驗結果顯示，本研究之損傷診斷方法不僅可成功判斷複雜損傷情況之損傷位置，並能提供合理之殘餘性能指標，驗證該方法於建築結構之可應用性。

關鍵字

結構健康監測 ； 模態振型及其導數 ； 模態振形斜率 ； 模態振形曲率 ； 模態應變能方法 ； 連續過濾式方法 ； 組合的損傷診斷指標

並列摘要

Structural health monitoring has drawn a lot of attention in recent years, in particular for Taiwan due to the geographically location in one of actively seismic zones. After small-level earthquakes, structures may be subjected to minor damage with visible cracks; if the magnitudes of earthquakes are sufficiently large, then structures would highly likely collapse. Moreover, Taiwan is a country in a subtropical climate, and humidity continuously challenge the durability of structures. To prevent foreseeable damage in seismically excited structures, structural health monitoring becomes an important strategy. For example, most damage in structures is not observable in terms of damage locations and levels. Additionally, different structures are comprised by various materials and geometric properties. Therefore, diagnosing all sorts of structures by a generalized damage detection method is indeed crucial.
Most recent structural health monitoring strategies are developed to perform damage detection in accordance with vibrational responses of structures. These structural responses can inform damage locations from the changes of dynamic characteristics, measured signal characteristics, and model-based estimated responses. The differentiated dynamic characteristics (e.g., natural frequencies and mode shapes) can vary derived damage indices that can inform damage locations, and this type of damage detection methods include the modal strain energy, flexibility matrix, and frequency response function changes. The measured signals of structures exhibit distinct patterns (i.e., changes in coefficients or derived responses after transformation) between the intact and damaged structures through the wavelet transform, Hilbert-Huang transform, or autoaggressive model. The damage locations can also be obtained by the deviations between the measured and model-based estimated responses, and these estimated responses can be generated from predetermined Kalman filter banks or machine learning models. However, most abovementioned methods are only applicable for a building with a single damage location in literature. When multiple damage locations exist, these methods will yield wrong damage locations to be informed. Therefore, this research intends to develop a damage detection method that can concurrently identify multiple damage locations in a building from the most identifiable mode shape (i.e., the first mode shape). In this method, two types of damage indices are generated from separated flexure- and shear-induced mode shapes and mode shape derivatives over members (i.e., building columns).
In this research, the sequential filtering damage detection method is developed and experimentally verified to locate damaged columns in a building structure. First, the proposed method establish an approach to divide the first mode shapes, including the translations and rotations, into the flexure- and shear-induced portions. These flexure- and shear-induced mode shapes are extended to building columns and to construct spatially continuous flexure- and shear-induced mode shapes and mode shape derivatives over building columns. Then, the slope- and curvature-based damage indices are generated through the modal strain energy method. By integrating these two types of damage indices, damage locations can be step-by-step identified using the proposed sequential filtering damage detection method. This sequential filtering procedure can improve the incapability of detecting multiple damage locations in the conventional methods. Finally, a numerical example is demonstrated using an 8-story steel-frame building model with 9 damage scenarios (i.e., various damage locations and levels). In addition, this research carries out experimental verification using a 6-story, aluminum-frame, small-scale building. In this experimental verification, the random decrement method is employed to identify first translational and rotational mode shapes of this building, and this identification method is applied to the intact building and 9 damage scenarios. The proposed sequential filtering method is eventually verified through this experiment. As seen in the experimental results, the proposed damage detection method not only successfully diagnoses complicated damage scenarios (i.e., multiple damage locations with different damage levels) but also provides decent residual performance estimation. To sum up, both numerical and experimental results verify the applicability of the proposed sequential filtering damage detection method for building structures.

並列關鍵字

structure health monitoring ； first mode shape derivatives ； mode shape slope ； mode shape curvature ； modal strain energy method ； sequential filtering approach ； combined damage indices

參考文獻

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