Abstract
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.
Highlights
Operational modal analysis (OMA) has received widespread attention because it enables the identification of the modal parameters of a structure in its working condition using only the vibration response [1]
Embedding dimension of 6 and number of neighbors K 40, when the modal response matrix Q(t) is obtained by isometric feature mapping (Isomap), we apply a fast Fourier transform (FFT) to each of its columns and take the X-coordinate corresponding to the highest amplitude to be the modal natural frequencies of each order
We have described the application of the Isomap algorithm to OMA to identify modal shapes, modal natural frequencies, and modal ratios of three-dimensional structures
Summary
Operational modal analysis (OMA) has received widespread attention because it enables the identification of the modal parameters of a structure in its working condition using only the vibration response [1]. Based on Isomap algorithm, this paper proposes a threedimensional OMA method for complex three-dimensional continuum structures. (1) An Isomap-based OMA method is proposed for the identification of modal shapes, modal natural frequencies, and modal ratios of three-dimensional structures (2) We identify the correspondence between the lowdimensional embedding matrix and the modal response matrix and between the transformation matrix and the modal shapes (3) We conduct a theoretical analysis of the characteristics of the Isomap-based OMA method (4) We analyze the effects of different parameters (e.g., matrix assembly method, number of neighbors, and dimensionality reduction method) on the algorithm (5) We design numerical simulations of the vibration response signals of a cylindrical shell to verify the effectiveness of our algorithm e remainder of this paper is organized as follows.
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