Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression

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1. Verfasser: Ghahari, Farid
Format: Preprint
Veröffentlicht: 2026
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author Ghahari, Farid
author_facet Ghahari, Farid
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_23101
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression
Ghahari, Farid
Numerical Analysis
Machine Learning
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.
title Mode-Shape Expansion Using Physics-Constrained Gaussian Process Regression
topic Numerical Analysis
Machine Learning
url https://arxiv.org/abs/2605.23101