基于模型缩聚的结构损伤统计识别

Statistical Damage Detection of Structures Based on Model Reduction

提出了一种基于有限元模型缩聚技术的结构损伤统计识别方法,该方法仅需要少量传感器的测量数据.首先基于模型缩聚技术建立确定性的损伤识别过程,然后利用摄动法将概率过程融入确定性的损伤识别中,从而得到了一种基于概率统计的结构损伤识别方法.该方法通过计算未知参数(如损伤构件的弹性特征)对于测量噪声的一阶与二阶偏导数,来得到这些未知参数的均值与协方差矩阵.文中不仅阐述了该方法的理论推导过程,而且通过一个门式框架的数值仿真研究,并结合MonteCarlo数值模拟技术验证了该文方法的正确性.

A statistical damage detection method based on the finite element （FE） model reduction technique that utilizes measured modal data with a limited number of sensors is proposed. A deter- ministic damage detection process was formulated based on the model reduction technique, and then the probabilistic process was integrated into the deterministic damage detection process using the perturbation technique, which results in a statistical structural damage detection method. This is achieved by deriving the first- and second-order partial derivatives of uncertain parameters, such as the elasticity of the damaged member, with respect to the measurement noise, which then allows the expectation and the covariance matrix of the uncertain parameters to be calculated. The theoretical development of the proposed method is reported. Its numerical verification is proved by using a portal frame example and Monte Carlo simulation.