Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression
For structural dynamics engineers needing full-field mode shapes from limited sensors, this method improves reconstruction accuracy by enforcing physical consistency.
This paper develops a physics-constrained Gaussian process regression method to reconstruct full-field structural mode shapes from sparse sensor data, achieving more accurate and reliable expansions than standard GPR.
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.