Many physics-based and surrogate models used in structural health monitoring are affected by different sources of uncertainty such as model approximations and simplified assumptions. Optimal structural health monitoring and prognostics are only possible with uncertainty quantification that leads to an informed course of action. In this article, a Bayesian neural network using variational inference is applied to learn a damage feature from a high-fidelity finite element model. Bayesian neural networks can learn from small and noisy data sets and are more robust to overfitting than artificial neural networks, which make it very suitable for applications such as structural health monitoring. Also, uncertainty estimates obtained from a trained Bayesian neural network model are used to build a cost-informed decision-making process. To demonstrate the applicability of Bayesian neural networks, an example of this approach applied to miter gates is presented. In this example, a degradation model based on real inspection data is used to simulate the damage evolution.

This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the displacement solution in the Cosserat frame. For the assumed deformed shape (both the midcurve and the cross-sectional orientation), the uniaxial value of strain in any given direction is obtained analytically, and this strain model is the basis used to predict the shape via an approximate local linearized solution strategy. Error analysis due to noise in measured strain values and in uncertainty in the proximal boundary condition is performed showing uniform convergence with increased sensor count.

Extracting damage-sensitive features plays an important role in all structural health monitoring applications, as it determines the metrics on which to base decision-making with regard to operation, maintenance, damage state, and so on. This article adopts the widely employed frequency response function, both its magnitude and phase, as the selected feature source and demonstrates how the damage types and locations are able to be classified by means of Bayesian recursive confidence updating. The features are estimated from the in situ acquired vibration data on a rotating machinery test-bed, and the probabilistic models that quantify feature uncertainty are the likelihood functions in a Bayesian framework, which informs the most plausible decisions based on the collected evidence. The damage classification effort in this article specifically calculates the posterior probability, considering the prior and likelihood of data observations; posterior probabilities are then fed back as prior probabilities in the next iteration as new test data are observed. There are three ball-bearing damage conditions applied to the rotary machine test-bed, and the correct model representing the correct damage types will be selected by the model with the maximum posterior confidence. Classification via posterior probability is shown in this article to outperform traditional likelihood evaluations, and the Bayesian recursive implementation distinguishes all three conditions in this work.