Kernelised Bayesian transfer learning for population-based structural health monitoring

Population-based structural health monitoring is the process of utilising information from a group of structures in order to perform and improve inferences that generalise to the complete population. A significant challenge in inferring a general representation for structures is that feature spaces will be inconsistent for a wide variety of populations and datasets. This scenario, where the dimensions of the feature spaces for each structure are different, occurs for a variety of reasons. Firstly, the group of structures themselves may be a heterogeneous population, where differences occur due to topology, leading to inconsistency in modal-based features. Secondly, feature spaces may be inconsistent across the population due to differences in the raw data (i.e. different sample frequencies etc.) and feature extraction processing. In this context, where feature spaces are inconsistent between different structure in a population, a general model that describes their behaviours becomes challenging to infer. This issue is because dimensionality reduction must be performed such that each domain’s feature set projects to a consistent shared latent space where a model can be inferred. This paper introduces a technique, kernelised Bayesian transfer learning, that seeks to learn a projection matrix and kernel embedding that map to a latent space where a discriminative classifier can be inferred in a Bayesian manner, using variational inference. This algorithm allows a general discriminative classifier to be inferred across a population where the feature spaces for each structure are inconsistent. A numerical case study is presented, demonstrating the effectiveness of this approach and for providing a discussion of its implications for population-based structural health monitoring.