Abstract: To solve the problem of the low accuracy of Laplacian Eigenmaps and Isomap algorithm in identifying weak nonlinear feature modals,a new method of operational modal parameter identification using neighborhood preserving projection algorithm was proposed.The local linear feature was used to find the low-dimensional embedding of structural displacement response data,which was corresponded to the modal coordinate response matrix.The modal natural frequencies of the structure were identified from the modal response matrix by single degree of freedom identification technology.The transformation matrix was estimated by the Moore-Penrose matrix inverse,and the transformation matrix corresponded to the modal shapes matrix.The proposed method could preserve the local linear characteristics of the data and identify the weak nonlinear modals.The identification results of three-dimensional cylindrical shells simulation dataset showed that the neighborhood preserving projection algorithm was more effective and had higher identification accuracy in identifying parameters of weak nonlinear feature modals than Laplacian Eigenmaps and Isomap.

Key words: operating modal parameters identification, neighborhood preserving projection, low dimensional embedding, moore-penrose matrix inverse

摘要： 针对拉普拉斯特征映射和等距离映射算法识别弱非线性特征模态精度低的缺点,提出一种利用邻域保留投影算法的工作模态参数识别方法。该方法利用局部线性特征寻找结构位移响应数据的低维嵌入数据,低维嵌入数据与模态坐标响应矩阵相对应;利用单自由度识别技术从模态响应矩阵中识别出结构的模态固有频率;再用最小二乘广义逆估计变换矩阵,变换矩阵与模态振型矩阵相对应。该方法能够保留数据的局部线性特征,从而识别弱非线性模态。通过三维圆柱壳仿真数据集的识别结果表明,相比拉普拉斯特征映射和等距离映射算法,邻域保留投影算法能够更有效地识别出弱非线性特征模态的参数,平均识别精度更高。

关键词: 工作模态参数识别, 邻域保留投影, 低维嵌入, 最小二乘广义逆