In order to identify the modal parameters of time invariant three-dimensional engineering structures with damping and small nonlinearity, a novel isometric feature mapping (Isomap)-based three-dimensional operational modal analysis (OMA) method is proposed to extract nonlinear features in this paper. Using this Isomap-based OMA method, a low-dimensional embedding matrix is multiplied by a transformation matrix to obtain the original matrix. We find correspondence relationships between the low-dimensional embedding matrix and the modal coordinate response and between the transformation matrix and the modal shapes. From the low-dimensional embedding matrix, the natural frequencies can be determined using a Fourier transform and the damping ratios can be identified by the random decrement technique or natural excitation technique. The modal shapes can be estimated from the Moore–Penrose matrix inverse of the low-dimensional embedding matrix. We also discuss the effects of different parameters (i.e., number of neighbors and matrix assembly) on the results of modal parameter identification. The modal identification results from numerical simulations of the vibration response signals of a cylindrical shell under white noise excitation demonstrate that the proposed method can identify the modal shapes, natural frequencies, and ratios of three-dimensional structures in operational conditions only from the vibration response signals.

中文翻译：

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基于等值线图的三维操作模态分析

为识别具有阻尼和小非线性的时不变三维工程结构的模态参数，本文提出了一种基于等距特征映射（Isomap）的三维操作模态分析（OMA）方法提取非线性特征。 . 使用这种基于 Isomap 的 OMA 方法，将一个低维嵌入矩阵乘以一个变换矩阵，得到原始矩阵。我们找到了低维嵌入矩阵和模态坐标响应之间以及变换矩阵和模态形状之间的对应关系。从低维嵌入矩阵中，可以使用傅立叶变换确定固有频率，并且可以通过随机递减技术或自然激励技术识别阻尼比。模态形状可以通过低维嵌入矩阵的 Moore-Penrose 矩阵逆来估计。我们还讨论了不同参数（即邻居数和矩阵集合）对模态参数识别结果的影响。白噪声激励下圆柱壳振动响应信号的模态识别结果表明，该方法仅从振动响应信号即可识别运行工况下三维结构的模态形状、固有频率和比值.