A multi-fidelity surrogate model for structural health monitoring exploiting model order reduction and artificial neural networks

Stochastic approaches to structural health monitoring (SHM) are often inevitably limited by computational constraints. For instance, for Markov chain Monte Carlo algorithms relying upon computationally expensive finite element models it is almost infeasible to sample the probability distribution of the structural state. To provide instead real-time procedures, this work proposes a non-intrusive surrogate modeling strategy, leveraging model order reduction and artificial neural networks. By relying upon a multi-fidelity (MF) framework, a composition of deep neural networks (DNNs) is devised to map damage and operational parameters onto time-dependent sensor recordings. Such an effective strategy is able to exploit datasets characterized by different fidelity levels without any prior assumption, allowing to blend a small high-fidelity (HF) dataset with a large low-fidelity (LF) dataset, ultimately alleviating the computational burden of supervised training while ensuring the accuracy of the approximated quantities of interest. The resulting surrogate model is made of an LF-DNN, which mimics sensor recordings in the undamaged condition, and of a long short-term memory HF-DNN, which adaptively refines the approximation with the effect of damage. An HF finite element model and an LF reduced order model are adopted offline to generate labeled training data of different fidelity, respectively in the presence or absence of a structural damage. Results relevant to an L-shaped cantilever beam and a portal frame railway bridge prove that the procedure efficiently provides remarkably accurate approximations, outperforming their single-fidelity counterparts. The capability of the MF-DNN to be exploited for SHM purposes is finally shown within an automated Bayesian procedure, aimed at updating the probability distribution of the structural state conditioned on sensor recordings, in the presence of operational variability and measurement noise.