Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression

• URL: http://arxiv.org/abs/2605.23101v1
• Date: Thu, 21 May 2026 23:33:59 GMT
• Title: Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression
• Abstract summary: This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data.<n>The proposed method overcomes existing limitations in GP-based prediction, providing more accurate and reliable expanded mode shapes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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