In this paper, we provide a comprehensive definition and classification of various sources of uncertainty within the fields of structural dynamics, system identification, and structural health monitoring (SHM), with a primary focus on the latter. Utilizing the classical input-output system representation as a main contextual framework, we present a taxonomy of uncertainties, intended for consistent classification of uncertainties in SHM applications: (i) input uncertainty; (ii) model form uncertainty; (iii) model parameter/variable uncertainty; (iv) measurement uncertainty; and (v) inherent variability. We then critically review methods and algorithms that address these uncertainties in the context of key SHM tasks: system identification and model inference, model updating, accounting for environmental and operational variability (EOV), virtual sensing, damage identification, and prognostic health management. A benchmark shear frame model with hysteretic links is employed as a running example to illustrate the application of selected methods and algorithmic tools. Finally, we discuss open challenges and future research directions in uncertainty quantification for SHM.

Manual inspection and assessment of structures on a large scale is labour intensive and often infeasible, while data-driven machine learning techniques can fail to identify relevant failure mechanisms and suffer from poor generalization to previously unseen conditions, particularly when limited information is available. We propose a physics-informed variational autoencoder formulation for disentangled representation learning of confounding sources in the measurements with the aim of computing the posterior distribution of latent parameters of a physics-based model and predicting the response of a structure when limited measurements are available. The latent space of the autoencoder is augmented with a set of physics-based latent variables that are interpretable and allow for domain knowledge in the form of prior distributions and physics-based models to be included in the autoencoder formulation. To prevent the data-driven components of the model from overriding the known physics, a regularization term is included in the training objective that imposes constraints on the latent space and the generative model prediction. The feasibility of the proposed approach is evaluated on a synthetic case study.

The decreasing cost and improved sensor and monitoring system technology (e.g., fiber optics and strain gauges) have led to more measurements in close proximity to each other. When using such spatially dense measurement data in Bayesian system identification strategies, the correlation in the model prediction error can become significant. The widely adopted assumption of uncorrelated Gaussian error may lead to inaccurate parameter estimation and overconfident predictions, which may lead to suboptimal decisions. This article addresses the challenges of performing Bayesian system identification for structures when large datasets are used, considering both spatial and temporal dependencies in the model uncertainty. We present an approach to efficiently evaluate the log-likelihood function, and we utilize nested sampling to compute the evidence for Bayesian model selection. The approach is first demonstrated on a synthetic case and then applied to a (measured) real-world steel bridge. The results show that the assumption of dependence in the model prediction uncertainties is decisively supported by the data. The proposed developments enable the use of large datasets and accounting for the dependency when performing Bayesian system identification, even when a relatively large number of uncertain parameters is inferred.