Integrating data-driven reduced order models with Kriging for efficient sensor placement and full-field prediction

This paper presents a two-stage methodology for efficient and accurate full-field displacement reconstruction using sparse online measurements derived from high-resolution Digital Image Correlation (DIC) data. The proposed approach integrates Modal Order Reduction and Kriging-based Uncertainty Quantification to address challenges associated with high-dimensional data analysis in structural dynamics.

In the offline stage, Adaptive Geometric Moment Descriptor (AGMD)-based shape features are used to compress the high-dimensional dataset, identify modal properties, and estimate residual covariance structures. In the online stage, a sparse set of optimally placed sensors, determined via QR decomposition with pivoting, is employed to infer full-field responses through Kriging interpolation, which also provides predictive variances for uncertainty quantification.

The methodology was demonstrated on a curved plate under random excitation. The results show strong correlations between measured and reconstructed fields using AGMDs and successfully identify multiple full-field vibration modes. In the online stage, the Kriging-predicted full-field responses, informed by an empirically estimated covariance structure from the offline dataset, exhibited better accuracy compared to predictions made using the Generalised Least Squares method (GLS). Validation on temporal sampling data achieved a coverage probability of 94.34% at 95% confidence intervals, highlighting the method’s reliability and robustness.