A class of regeneration-constrained supervised deep learning methods for multi-channel structural vibration response reconstruction

Xueli Song, Fan Yang, Wen Yi, Aoqi Song, Tongyang Dao, Yuzhu Xiao, Supei Zheng, Rongpeng Li,
A class of regeneration-constrained supervised deep learning methods for multi-channel structural vibration response reconstruction,
Structures,
Volume 82,
2025,
110691,
ISSN 2352-0124,
https://doi.org/10.1016/j.istruc.2025.110691.
(https://www.sciencedirect.com/science/article/pii/S2352012425025081)
Abstract: Vibration responses in structural health monitoring systems often experience data loss during acquisition. Compared to random or continuous loss in single-sensor responses, simultaneous failure of multiple sensors can block information across channels, posing a greater challenge. Most existing studies have focused on adapting deep learning models from other fields or integrating limited physical information, which inevitably neglects their intrinsic properties, leading to reduced reconstruction accuracy. Therefore, developing a unified artificial constraint to guide models in capturing these intrinsic properties remains an unresolved issue. To address this, we propose a class of regeneration-constrained supervised deep learning methods, which encode intrinsic structural properties as a regeneration prior, integrated into the loss function using the generalized Lagrange multiplier method, guiding models to learn these properties. The regeneration constraint is theoretically proven to be a necessary condition for obtaining the optimal reconstruction model. A joint convolutional neural network (CNN)-transformer model is also designed for verification. Experiments on field acceleration data from the Canton Tower and Hardanger Bridge show that the proposed prior improves reconstruction accuracy across metrics, including mean squared error, relative error, and coefficient of determination. The proposed prior also mitigates overfitting, improves generalization, and is robust to noise and hyperparameter variation.
Keywords: Deep learning; Structural health monitoring; Response reconstruction; Supervised learning; Loss function