Xudong Jian

Zhilu Lai, Wei Liu, Xudong Jian et al.

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or mechanical structures), which are typically high-dimensional in nature. In the scope of physics-informed machine learning, this paper proposes a framework -- termed Neural Modal ODEs -- to integrate physics-based modeling with deep learning for modeling the dynamics of monitored and high-dimensional engineered systems. Neural Ordinary Differential Equations -- Neural ODEs are exploited as the deep learning operator. In this initiating exploration, we restrict ourselves to linear or mildly nonlinear systems. We propose an architecture that couples a dynamic version of variational autoencoders with physics-informed Neural ODEs (Pi-Neural ODEs). An encoder, as a part of the autoencoder, learns the abstract mappings from the first few items of observational data to the initial values of the latent variables, which drive the learning of embedded dynamics via physics-informed Neural ODEs, imposing a modal model structure on that latent space. The decoder of the proposed model adopts the eigenmodes derived from an eigen-analysis applied to the linearized portion of a physics-based model: a process implicitly carrying the spatial relationship between degrees-of-freedom (DOFs). The framework is validated on a numerical example, and an experimental dataset of a scaled cable-stayed bridge, where the learned hybrid model is shown to outperform a purely physics-based approach to modeling. We further show the functionality of the proposed scheme within the context of virtual sensing, i.e., the recovery of generalized response quantities in unmeasured DOFs from spatially sparse data.

Xudong Jian, Kiran Bacsa, Gregory Duthé et al.

Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural networks (GNNs), transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures. The transformer module decomposes multi-degrees-of-freedom (MDOF) structural dynamic measurements into single-degree-of-freedom (SDOF) modal responses, facilitating the identification of natural frequencies and damping ratios. Concurrently, the GNN captures the structural configurations and identifies mode shapes corresponding to the decomposed SDOF modal responses. The proposed model is trained in a purely physics-informed and unsupervised manner, leveraging modal decomposition theory and the independence of structural modes to guide learning without the need for labeled data. Validation through numerical simulations and laboratory experiments demonstrates its effectiveness in accurately decomposing dynamic responses and identifying modal properties from sparse structural dynamic measurements, regardless of variations in external loads or structural configurations. Comparative analyses against established modal identification techniques and model variations further underscore its superior performance, positioning it as a favorable approach for population-based structural health monitoring.

Xudong Jian, Charikleia Stoura, Simon Scandella et al.

Damage identification is a core task in structural health monitoring. In practice, however, its reliability is often compromised by confounding non-damage effects, such as variations in excitation and environmental conditions, which can induce changes comparable to or larger than those caused by structural damage. To address this challenge, this study proposes a self-supervised label-free disentangled representation learning framework for robust vibration-based structural damage identification. The proposed framework employs an autoencoder with two latent representations to learn directly from raw vibration acceleration signals. A self-supervised invariance regularization, implemented via Variance-Invariance-Covariance Regularization (VICReg), is imposed on one latent representation using baseline data where structural damage is assumed constant but operational and environmental conditions vary. In addition, a frequency-domain constraint is introduced to enforce agreement between the power spectral density reconstructed from the latent representation and that computed from the corresponding input time series. Together, these mechanisms promote disentanglement, enabling the learned representation to be sensitive to damage-related characteristics while remaining invariant to nuisance variability. The framework is trained in a fully end-to-end and label-free manner, requiring no prior information on damage, excitation, or environmental conditions, making it well-suited for real-world applications. Its effectiveness is validated on two distinct real-world vibration datasets, including a bridge and a gearbox. The results demonstrate robustness to operational variability, strong generalization capability, and good performance in both damage detection and quantification.

Kiran Bacsa, Wei Liu, Xudong Jian et al.

This study investigates the behavior of Causal Convolutional Neural Networks (CNNs) with quasi-linear activation functions when applied to time-series data characterized by multimodal frequency content. We demonstrate that, once trained, such networks exhibit properties analogous to Finite Impulse Response (FIR) filters, particularly when the convolutional kernels are of extended length exceeding those typically employed in standard CNN architectures. Causal CNNs are shown to capture spectral features both implicitly and explicitly, offering enhanced interpretability for tasks involving dynamic systems. Leveraging the associative property of convolution, we further show that the entire network can be reduced to an equivalent single-layer filter resembling an FIR filter optimized via least-squares criteria. This equivalence yields new insights into the spectral learning behavior of CNNs trained on signals with sparse frequency content. The approach is validated on both simulated beam dynamics and real-world bridge vibration datasets, underlining its relevance for modeling and identifying physical systems governed by dynamic responses.

Hanshuo Wu, Xudong Jian, Christos Lataniotis et al.

Bridges, as critical components of civil infrastructure, are increasingly affected by deterioration, making reliable traffic monitoring essential for assessing their remaining service life. Among operational loads, traffic load plays a pivotal role, and recent advances in deep learning - particularly in computer vision (CV) - have enabled progress toward continuous, automated monitoring. However, CV-based approaches suffer from limitations, including privacy concerns and sensitivity to lighting conditions, while traditional non-vision-based methods often lack flexibility in deployment and validation. To bridge this gap, we propose a fully automated deep-learning pipeline for continuous traffic monitoring using structural health monitoring (SHM) sensor networks. Our approach integrates CV-assisted high-resolution dataset generation with supervised training and inference, leveraging graph neural networks (GNNs) to capture the spatial structure and interdependence of sensor data. By transferring knowledge from CV outputs to SHM sensors, the proposed framework enables sensor networks to achieve comparable accuracy of vision-based systems, with minimal human intervention. Applied to accelerometer and strain gauge data in a real-world case study, the model achieves state-of-the-art performance, with classification accuracies of 99% for light vehicles and 94% for heavy vehicles.

Mingyuan Zhou, Xudong Jian, Ye Xia et al.

Structural health monitoring (SHM) has experienced significant advancements in recent decades, accumulating massive monitoring data. Data anomalies inevitably exist in monitoring data, posing significant challenges to their effective utilization. Recently, deep learning has emerged as an efficient and effective approach for anomaly detection in bridge SHM. Despite its progress, many deep learning models require large amounts of labeled data for training. The process of labeling data, however, is labor-intensive, time-consuming, and often impractical for large-scale SHM datasets. To address these challenges, this work explores the use of self-supervised learning (SSL), an emerging paradigm that combines unsupervised pre-training and supervised fine-tuning. The SSL-based framework aims to learn from only a very small quantity of labeled data by fine-tuning, while making the best use of the vast amount of unlabeled SHM data by pre-training. Mainstream SSL methods are compared and validated on the SHM data of two in-service bridges. Comparative analysis demonstrates that SSL techniques boost data anomaly detection performance, achieving increased F1 scores compared to conventional supervised training, especially given a very limited amount of labeled data. This work manifests the effectiveness and superiority of SSL techniques on large-scale SHM data, providing an efficient tool for preliminary anomaly detection with scarce label information.