Accelerated Data Assimilation in Structural Health Monitoring via Reduced-Order Statistical FEM
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.