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Grey-box Modelling for Structural Health Monitoring: Physical Constraints on Machine Learning Algorithms



The use of machine learning algorithms for structural health monitoring remains a powerful and active area of research as the technology and availability of data evolve together. The amount of interest reflects the fact that many tasks in SHM processes rely on regression, clustering or classification, which are naturally handled by machine learners. Within the authors’ research group alone, among many examples, regression via neural networks and Gaussian processes have been used for dealing with confounding influences in monitoring data, and clustering methods like Gaussian mixture models and more advanced variants have been used to group data according to operating/environmental and damage condition. In the work that is particularly relevant to the example used in this paper, Gaussian process regression has been used to attempt to model the loads experienced by a structure in operation from (for example) acceleration measurements taken at accessible locations away from where the load is applied. These regression models work well to reproduce measured strains on data unseen by the algorithm, however, they are limited by their dependence on training data (such a model requires training data across all possible operating conditions) and a lack of physical interpretability. Currently the authors are working on means of enhancing machine learning algorithms with physical insight. If one considers an entirely physics-based model as a white-box model, and a purely data-driven machine learning model as a black-box, then the work here is about the development of grey-box models. In this paper the idea of building physical constraints into a Gaussian process regression model is considered. By building knowledge of the physics at work into the kernel, one can ensure that the model predictions are, in the least, physically possible. This paper demonstrates how one can build knowledge of boundary conditions of a vibrating structure into the covariance matrix and how this can improve a GP’s predictive capability.


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