應用破壞定位向量法於土木結構之探討

Abstract

結構損傷診斷是一重要之研究課題，以結構系統損傷前後動態特性變化做為依據，為一常用之方法。但由於自然頻率對損傷不夠敏感或高階模態不易識別，皆使得其無法準確地用於損傷診斷分析。而藉由柔度矩陣進行損傷診斷，其具有較自然頻率及模態更為敏感，且受高階模態影響較小之優點。 破壞定位向量法(Damage Locating Vectors Method, 簡稱DLV)，是以損傷前後之柔度矩陣差異，經由奇異值分解(singular value decomposition, SVD)求得破壞定位向量，再將其加載於損傷前之有限元素模型進行內力分析，以內力之正規化累計應力指標做為破壞位置判斷之參考。 本研究即為探討DLV法用於土木結構損傷診斷分析之可行性及實用性。本研究考慮幾種實際常見因素：雜訊之影響、僅以少數模態進行分析、不完全量測、有限元素模型與實際結構有所差異之情況。使用小波轉換配合ARX模式識別結構模態參數，透過桁架數值模擬分析驗證DLV法之可行性及探討各參數之影響，再進一步用於八層樓鋼構振動台實驗分析，並評估此法之實用性。

Structural health monitoring has become an important issue in academia and practical engineering. One of the most popular means to assess damage of a structure is based on its vibration characteristics. However, this approach often encounters the difficulties that lower mode frequencies and mode shapes may not be sensitive to the existence of damages, and higher mode frequencies and mode shapes are not easy to estimate accurately. The advantage of using the flexibility matrix of a structure for damage assessment over using the structural vibration characteristics is that the flexibility matrix is not significantly influenced by the higher mode characteristics of the structure and it is sensitive to the existence of damages. The damage locating vectors method determines a set of load vectors from the change of the flexibility matrix due to damages, and applies these load vectors as static loads to the finite element model of the undamaged structure for static analyses. The damaged locations are found from the so-called normalized cumulative stress index determined from the static analyses. This work investigates the applicability of damage locating vectors method in civil engineering structures including truss and frame systems. To simulate the situations often encountered in real applications, we study the effects of noise, number of modes used in constructing a flexibility matrix, incomplete measurements, and incorrectness of a finite element model on accurately locating the damages. A continuous wavelet transform along with the ARX model is employed to process dynamic responses of a structure to estimate the needed accurate dynamic characteristics of the structure. Numerical simulation responses are carried out for truss systems, while measured dynamic responses of eight-storey frames in shaking table tests are used in the work.