Enhancing Bayesian model updating in structural health monitoring via learnable mappings

TL;DR

This work presents a hybrid approach to structural health monitoring that fuses a learnable feature extractor with a feature-oriented surrogate to perform fast, data-driven Bayesian updating of health parameters.A multi-fidelity surrogate (combining POD-Galerkin ROM and HF FOM) generates large labeled datasets offline, which train a Siamese autoencoder-based feature extractor and a surrogate that maps parameters to low-dimensional features via MTF-encoded images.During online monitoring, an MCMC sampler uses the learned features to evaluate a Gaussian likelihood, achieving accurate parameter estimates with substantial computational speed-ups compared to conventional MF-only methods, demonstrated on three synthetic structures.The results show improved localization and quantification of damage, reduced posterior uncertainty, and real-time updating capabilities, highlighting the practical potential for rapid SHM decision-making.Future directions include integrating latent-variable probabilistic frameworks and digital twin concepts to cope with model-form uncertainties and enable real-time, decision-support SHM.

Abstract

In the context of structural health monitoring (SHM), the selection and extraction of damage-sensitive features from raw sensor recordings represent a critical step towards solving the inverse problem underlying the identification of structural health conditions. This work introduces a novel approach that employs deep neural networks to enhance stochastic SHM methods. A learnable feature extractor and a feature-oriented surrogate model are synergistically exploited to evaluate a likelihood function within a Markov chain Monte Carlo sampling algorithm. The feature extractor undergoes pairwise supervised training to map sensor recordings onto a low-dimensional metric space, which encapsulates the sensitivity to structural health parameters. The surrogate model maps structural health parameters to their feature representation. The procedure enables the updating of beliefs about structural health parameters, eliminating the need for computationally expensive numerical models. A preliminary offline phase involves the generation of a labeled dataset to train both the feature extractor and the surrogate model. Within a simulation-based SHM framework, training vibration responses are efficiently generated using a multi-fidelity surrogate modeling strategy to approximate sensor recordings under varying damage and operational conditions. The multi-fidelity surrogate exploits model order reduction and artificial neural networks to speed up the data generation phase while ensuring the damage-sensitivity of the approximated signals. The proposed strategy is assessed through three synthetic case studies, demonstrating high accuracy in the estimated parameters and strong computational efficiency.

Figures (16)

• Figure 1: Graphical abstraction of the proposed methodology.
• Figure 2: Scheme of the MF-DNN surrogate model: red nodes denote the input/output quantities; blue nodes refer to the learnable components of the surrogate model; hat variables denote quantities obtained from neural network approximations. Figure adapted from art:Torzoni_MF.
• Figure 3: Flowchart of the MF-DNN surrogate modeling strategy.
• Figure 4: Learnable feature extractor and feature-oriented surrogate: flowchart of the sequential training process. Red nodes refer to the input/output quantities and blue nodes denote the corresponding computational blocks. $\text{N\spaceN}_\text{ENC}$ is the feature extractor, $\text{N\spaceN}_\text{DEC}$ is the decoder branch, and $\text{N\spaceN}_\text{SUR}$ is the feature-oriented surrogate model. $\I(\mathbf{x}^\text{HF})$ denotes the input mosaic, $\widehat{\I}(\mathbf{h})$ denotes the reconstructed mosaic, and $\boldsymbol{\theta}$ is the vector of parameters for which we aim to update the belief. $\mathbf{h}(\I)$ is the low-dimensional feature representation of $\I(\mathbf{x}^\text{HF})$ provided by $\text{N\spaceN}_\text{ENC}$, and $\widehat{\mathbf{h}}(\boldsymbol{\theta})$ is the corresponding approximation provided by $\text{N\spaceN}_\text{SUR}$.
• Figure 5: Scheme of the MCMC procedure to update the posterior probability distribution of the structural state. Red nodes refer to the input/output quantities and blue nodes denote the corresponding computational blocks.