Abstract While Structural Health Monitoring (SHM) has been widely studied, its reliability in real-world applications remains challenged by pronounced operational variability, particularly when system behavior changes discretely between operating regimes. Such methods generally rely on baseline comparisons; however, under multiple operating regimes, the baseline becomes distributed across several distinct regions, each associated with a specific regime. This multi-baseline behavior complicates anomaly detectability, as variations induced by changing operating conditions may mask the subtle changes caused by structural degradation. The challenge is particularly pronounced for systems exhibiting regime-dependent behavior, where transitions between approximately stationary conditions occur frequently and are difficult to isolate. To address this, an efficient probabilistic multi-model framework is proposed, in which each operating regime is represented by a locally Vector Autoregressive (VAR) model. A Bayesian formulation is adopted to account for parameter uncertainty explicitly and to enable sequential updating, allowing the regime models to adapt as additional data become available—an important feature for early-stage SHM. New observations are evaluated against the ensemble of regime-specific VAR models using the marginal likelihood, enabling assessment of statistical consistency with the learned reference behavior. Persistently low consistency is interpreted as indicative of anomalies, which may reflect structural changes or evolving degradation. The proposed method is demonstrated using vibration data from gearboxes onboard a Crew Transfer Vessel operating under multiple regimes. Despite the limitations and uncertainties inherent to early-phase SHM, the framework successfully identifies deviations from the learned reference behavior within consistent operating conditions, demonstrating its potential for SHM under realistic, time-varying operation.
Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification, which makes them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.
G. Singini, Samuel Manda· Frontiers in Applied Mathema...· 0 citations
Integrating sensor measurements with complex numerical models for structural health monitoring holds great promise because both sources provide complementary and potentially high-fidelity sources of information. However, effectively assimilating data into computationally intensive models presents substantial challenges. Among these are noisy and potentially sparse data, simplifications and uncertainties in the computational model and strong nonlinearities that pose challenges to traditional assimilation approaches. While Bayesian updating offers a principled approach to data assimilation under uncertainty, it requires considerable numerical effort that is often not acceptable, in particular, if frequent and fast updates are required.
The present work takes [1] as a starting point, where a statistical version of the Finite Element method (statFEM) has been introduced. The main ingredients of statFEM are a propagation of uncertainty through a Finite Element model and (empirical) Bayesian updating that explicitly accounts for model misspecification. Subsequent work also considers Ensemble Kalman filtering as an alternative to linear Bayesian updating [2] and demonstrated its applicability in structural health monitoring contexts [3].
Here, we investigate the limits of updating methods, as presented in [1] or [4], and present a comparative computational analysis against alternative strategies such as Ensemble Kalman filtering for standard benchmark problems. In order to accelerate the prior computations, we employ surrogate models and further integrate adaptive sampling techniques. As a case study, we model aging material properties as spatially correlated random fields and assimilate noisy simulated measurements of structural responses. This allows us to demonstrate the efficient computation of stochastic priors and their assimilation via both the original statFEM and ensemble-based methods. Finally, we discuss the propagation of cracks and its implications for load-bearing capacity assessment within the data assimilation framework.
[1] Girolami, M., Febrianto, E., Yin, G., & Cirak, F. (2021). The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions. Computer Methods in Applied Mechanics and Engineering, 375, 113533.
[2] Duffin, C., Cripps, E., Stemler, T., & Girolami, M. (2021). Statistical finite elements for misspecified models. Proceedings of the National Academy of Sciences, 118(2), e2015006118.
[3] Muralidhar, N. K., Gräßle, C., Rauter, N., Mikhaylenko, A., Lammering, R. & Lorenz, D. A. (2023). Damage identification in fiber metal laminates using Bayesian analysis with model order reduction, Computer Methods in Applied Mechanics and Engineering, 403, 115737.
[4] Narouie, V., Wessels, H., Cirak, F., & Römer, U. (2025). Mechanical state estimation with a Polynomial-Chaos-Based Statistical Finite Element Method. Computer Methods in Applied Mechanics and Engineering, 441, 117970.
Lucas Hermann, Saddam Hijazi, C. Gräßle et al.· e-Journal of Nondestructive...· 0 citations
Understanding temporal dynamics in complex systems often requires identifying abrupt structural changes, known as change points in multivariate time series. Traditional vector autoregressive (VAR) models have been widely used for modeling dependencies across time, yet their parameter space grows quadratically with the number of variables, leading to computational and estimation challenges in high‐dimensional settings. The recently proposed network autoregressive (NAR) modeling framework offers a computationally efficient alternative by reducing parameter complexity through a network‐based representation. However, existing NAR models either assume homogeneous temporal behavior across all nodes, overlooking node‐specific dynamics that frequently arise in environmental and socio‐economic systems, or do not allow for structural breaks. In this work, we propose
NLDNAR‐CP
, a novel change point detection method within a node‐specific NAR framework that accommodates heterogeneous temporal dependencies across variables. The proposed approach efficiently detects multiple structural breaks while preserving scalability to high‐dimensional networks. We demonstrate the method's superior empirical performance through extensive simulations and a real‐world environmental application.
Environmental monitoring networks increasingly record pollutant levels as curves observed over time at fixed stations. Yet, exposure and risk assessment often require predicting these curves, with their uncertainty, at unmonitored locations. Conventional smooth-basis methods for such spatially correlated functional data, including spline-based kriging, tend to over-smooth acute, high-frequency episodes such as pollution peaks. We propose a parsimonious wavelet-based Bayesian hierarchical model that anchors a single, shared Mat\'ern correlation matrix at each resolution level, avoiding the parameter inflation of coefficient-specific spatial processes. Adaptive sparsity is enforced through a spatially informed regularized horseshoe prior, allowing the model to borrow strength across neighboring locations. At the same time, a non-centered parameterization ensures stable inference under the No-U-Turn Sampler. In simulation studies across distinct signal-to-noise regimes, incorporating spatial dependence substantially stabilizes reconstruction under severe noise relative to strictly independent models. Applied to PM$_{10}$ concentrations from Mexico City and benchmarked against ordinary kriging for functional data and a hierarchical Bayesian wavelet alternative, the model captures acute pollution events and, beyond improving point prediction, delivers sharper and better-calibrated credible intervals at unobserved locations.
Alvaro Alexander Burbano-Moreno, Alex Rodrigo dos Santos Sousa, L. Hotta· 0 citations
The Causal Regime Bayesian (CaReBayes) forecasting framework is proposed, which integrates regime detection, causal discovery, and Bayesian forecasting within a unified approach and produces regime-dependent causal graphs that summarize candidate structural relationships in the system, enhancing interpretability.
Structural Health Monitoring (SHM) aims to enhance infrastructure reliability by reducing unnecessary inspections, minimizing downtime, and preventing failures. However, noise in sensor data remains a persistent challenge, often arising from sensor degradation, environmental variability, or transmission errors. This noise is typically non-stationary and can follow time-varying patterns that affect the reliability of observations. Partially Observable Markov Decision Processes (POMDPs) provide a framework for optimizing inspection and maintenance policies to achieve cost-effective decision-making without compromising safety. Yet, POMDP formulations often rely on bounding assumptions such as access to high-quality, noise-free observations, and standard models typically do not update this assumption during operation. This simplification overlooks the complex nature of noise in monitoring data, causing belief updates to become overconfident and leading to suboptimal, locally optimal maintenance policies. To address this, the study proposes a Noise-aware Observation-Integrated POMDP (NOI-POMDP) framework that explicitly incorporates the noise-generating process as a dynamic and learnable component of the observation model (Fig. 1). The SHM agent updates beliefs from noisy observations while the underlying NOI-POMDP explicitly represents how time-varying sensor noise affects state information, enabling adaptive belief updates and improving long-run decision quality. The methodology is demonstrated through a beam SHM case study where structural condition is identified using vibration-based features derived from sensor measurements. Across simulated deterioration processes and varying noise patterns, the NOI-POMDP framework demonstrates improved decision quality compared to conventional fixed-noise POMDP formulations. Results show increased policy robustness under severe noise variability and improved state estimation accuracy, leading to balanced inspections and lower long-term lifecycle costs while maintaining safety constraints.
Junyi Li, E. Tronci· e-Journal of Nondestructive...· 0 citations