# Low-Rank Representation and Data Compression of Full-Field Displacement Maps for Structural Modal Analysis and Damage Identification

## TL;DR

This paper introduces a method to compress and analyze full-field displacement data from structural tests, improving damage detection accuracy and efficiency.

## Contribution

A novel low-rank representation method is proposed for compressing and analyzing displacement maps in structural testing.

## Key findings

- The first 20 principal components capture mode shape and damage characteristics of displacement fields.
- The first six modes provide robust damage localization results.
- The method retains both global and local shape features while compressing data.

## Abstract

Stereo-digital image correlation (DIC) is promising in structural vibration testing due to its advantages of non-contact, full-field, and high-spatial resolution. However, thousands of full-field displacement maps generated by stereo-DIC hamper its practical applications. Furthermore, with the evaluated mode shapes, how to accurately reveal the embedded/hidden damage positions without a reference dataset is another critical problem. For the purpose of resolving those issues, a complete method is proposed, consisting of (1) an adaptive kernel function construction method for low-rank-representing the full-field displacement maps while retaining both global and local shape features, (2) an enhanced frequency domain decomposition approach for noise-robust mode shape estimation based on the kernel functions, and (3) extracting and fusing local shape features of multiple mode shapes for more accurate damage localization. Finally, numerical and experimental case studies are investigated to verify the effectiveness and accuracy of the proposed low-rank representation method in modal parameters and damage identification. In addition, it is found that the mode shape and damage characteristics of displacement fields can be captured by the first 20 principal components, and the first six modes provide robust damage localization results.