基于秩分析的结构损伤识别研究

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (15) : 126-130.

论文

基于秩分析的结构损伤识别研究

杨秋伟1 周卫东2 梁超锋1

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Damage detection by the rank analysis of structural system matrix

Yang Qiuwei1, Zhou Weidong2, Liang Chaofeng1

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文章历史 +

摘要

研究了结构损伤与系统矩阵秩变化之间的对应关系，以此为基础提出一种损伤识别方法。首先分析了结构损伤所引起的系统矩阵秩的变化，然后利用结构损伤前后的静力响应方程，推导了柔度扰动量的限定秩解计算公式，再结合柔度扰动新方法计算结构各单元损伤参数，据此确定损伤位置及损伤程度。本文的研究表明，损伤前后结构静力位移差向量之间必然存在着线性相关性，因此，施加静力荷载的组数并非越多越好，而是只要大于柔度扰动矩阵的秩即可。由本文方法所获得的柔度扰动量的限定秩解，是一种理论上的精确解，以它为基础可以获得很高精度的损伤识别结果。以桁架结构为例对所提方法进行了验证，结果表明了本文方法的可行性。

Abstract

The static-based damage identification methods have attracted much attention in the civil engineering field in recent years. A static rank analysis method is presented in the study for structural damage identification, which makes use of the static response data and the matrix rank analysis theory. First, the rank of the static displacement change due to damage is analyzed and then a limited rank solution of structural flexibility change is developed. With the flexibility change determined, the elemental damage parameters can be readily calculated by using the new flexibility perturbation method. As distinct from the existing detection techniques, the presented method can directly compute the damage parameters using the incomplete measured static data. The main advantage of using the static data rather than dynamic data is that the static equilibrium equation is solely related to the structural stiffness, and accurate static response data can be obtained rapidly and cheaply. Moreover, the proposed technique provides an insight to the appropriate number of the applied static loads for structural damage detection. The efficiency of the proposed method is demonstrated by a numerical example. The effect of measurement noise on damage detection performance of the proposed method is also investigated. The results show the good efficiency and stability of the proposed method on the identification of damage on more than one element. For the error-free case, the predicted results agree with the true solutions exactly. For the case with 3% and 10% noise, the prediction obtained is also reasonable.

导出引用

杨秋伟周卫东梁超锋. 基于秩分析的结构损伤识别研究[J]. 振动与冲击, 2014, 33(15): 126-130

Yang Qiuwei;Zhou Weidong;Liang Chaofeng. Damage detection by the rank analysis of structural system matrix[J]. Journal of Vibration and Shock, 2014, 33(15): 126-130