Abstract: To identify the operational modal parameters of linear time-invariant three- dimensional structures only from the stationary vibration response signals,a method based on Laplacian Eigenmaps was proposed.The vibration response data was regarded as the data set in the high-dimensional space,and the low-dimensional embedded data was found by using Laplacian Eigenmaps.Then,the natural frequency of the modal was identified from the modal response matrix corresponding to the low dimensional embedded matrix by using the single degree of freedom recognition technique.The modal shapes could be calculated from the Moore-Penrose matrix inverse of the low-dimensional embedding matrix.The simulation results of three-dimensional cylindrical shell showed that compared with equidistant mapping,Laplacian Eigenmaps was effectively identify the modal shape and natural frequency of the structure with lower time consumption and higher recognition accuracy.Compared with principal component analysis,Laplacian Eigenmaps had higher recognition accuracy.

Key words: operating modal parameters, Laplacian Eigenmaps, three-dimensional structure, the moore-penrose matrix inverse, low dimensional embedding

摘要： 为了仅从平稳振动响应信号中识别线性时不变三维结构的工作模态参数,提出一种基于拉普拉斯特征映射的三维结构模态分析方法。该方法首先将复杂三维结构的振动响应数据视作处于高维空间的数据集,利用拉普拉斯特征映射寻找该数据集的低维嵌入数据。低维嵌入数据对应模态响应矩阵,利用单自由度识别技术从模态响应矩阵中识别出模态固有频率。最后,利用最小二乘广义逆,将求解的模态响应矩阵代入振动响应数据分解公式求得模态振型矩阵。三维圆柱壳仿真实验结果表明：相较于等距离映射,拉普拉斯特征映射能有效地识别出系统的模态振型与固有频率,且识别速度更快,精度更高;相较于主成分分析,拉普拉斯特征映射识别精度更高。

关键词: 工作模态参数, 拉普拉斯特征映射, 三维结构, 最小二乘广义逆, 低维嵌入