Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression

2026-05-21

AI Summary

Traditional Gaussian process regression often yields physically inconsistent results when reconstructing full-field modal shapes from sparse sensor data. This work proposes a physics-constrained single-output Gaussian process framework (CONS-SOGP), which, for the first time, embeds mass orthogonality constraints directly into Gaussian process regression. By jointly optimizing independent modal kernels and an orthogonality penalty term, the method achieves high-fidelity modal expansion while preserving physical plausibility. Leveraging marginal likelihood derivation and gradient-based hyperparameter optimization, CONS-SOGP demonstrates significantly improved performance over existing Gaussian process approaches in numerical experiments on multi-degree-of-freedom structures, yielding more accurate and reliable reconstructions of modal shapes.

Abstract

This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty quantification, standard formulations often yield physically inconsistent mode-shape reconstructions under sparse sensing conditions. A Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework is derived that utilizes independent modal kernels while coupling the optimization via a mass-orthogonality penalty. The paper presents derivations for the marginal likelihood, hyperparameter gradients, and penalty coupling. Numerical verification on a multi-degree-of-freedom structure demonstrates that the proposed method overcomes existing limitations in GP-based prediction, providing more accurate and reliable expanded mode shapes.

Problem

• mode-shape expansion
• sparse sensor data
• physical consistency
• Gaussian Process Regression
• structural dynamics

Innovation

• Physics-Constrained Gaussian Process
• Mode-Shape Expansion
• Mass-Orthogonality Penalty
• Sparse Sensor Data
• Structural Dynamics