基于频响函数的结构健康监测主成分分析法

A PCA-based algorithm for structural health monitoring using frequency response functions

基于测试频响函数,提出一种简单而有效的结构健康监测主成分分析(PCA)新方法。以结构的频响函数作为基本数据,首先将结构健康状态下的频响函数数据作为基本训练样本,通过PCA技术提取结构健康状态特征,并获得结构健康特征变换矩阵,即协方差的特征向量矩阵;然后再对损伤结构的测试频响函数数据进行转换以提取结构相应损伤状态特征;最后在二维PCA空间比较两次提取的结构状态特征分布图即可判断结构是否发生损伤并评估其损伤程度。两个数值算例表明基于频响函数的结构健康监测主成分分析新方法正确有效。该方法基于结构振动响应,与模型无关且诊断前无需大量的训练样本、计算量小、抗噪性能好,具有良好的应用前景。

Based on measured frequency response functions（FRFs）,an easier and more efficient method for structural health monitoring was proposed by using principle component analysis（PCA） here.The FRFs of a healthy structure were used as the initial data.With this method a PCA transformation technique was used to obtain the features of the intact structure,i.e.,its principle components（PCs） with which an orthogonal transformation matrix packed using the first few eigenvectors of the covariance matrix was found.Further,the orthogonal transformation matrix was used to transform the FRFs of a damaged structure so as to find the corresponding damage state features of the structure.Both structural damage detection and structural health monitoring could be achieved by comparing the two-dimensional PCA distribution charts corresponding to the damaged state and the healthy one of the structure.Two numerical simulation examples showed that the proposed method is correct,effective and feasible.