古塔结构损伤的系统识别Ⅰ:理论

在结构损伤的系统识别中，损伤是结构参数的减小来反映的。由于存在模型误差和测试误差，并不是所有的参数值减小代表损伤。本文提出的损伤区域的判别分析法将对每一个可能的损伤状态定义为一个随机总体，通过比较样品到第一个总体的距离来确定样品与哪个总体最靠近，进而对损伤区域作出判断。算例表明，这一方法可以避免确定损伤单元数时的主观测断，减小误判的风险。本文提出的条件分布下损伤程度估计方法不仅利用参数变化量的均值信息，还利用它的协差阵信息，因而具有更高的识别精度。

System Identification for Structural Damage of Ancient Tower I: Theory

In the system identification of structural damage, damage is usually expressed in terms of a reduction in the structural parameters. However, due to the errors in modeling and measurements, not all reductions in the structural parameters indicate damage. In the distinguish analysis method proposed in this paper for isolating the damage locations, every possible damage state is defined as a random collective entity. The distance between each of these collective entities and a given sample is calculated and compared, and that nearest to the sample is used for identifying the damage region. Trial examples of using this method show that subjective influences in determining the number of damage elements can be avoided and the risk of eventual misjudgment is substantially reduced. The method proposed in this paper for assessing the degree of damage under conditional distributions makes use not only the message imparted in the average value of changes in parameters, but also the message in the covariance matrix of changes in parameters, hence, it can achieve better identification accuracy.