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Within structural health monitoring, the capture and use of acoustic emission is a popular technique for the localisation of damage. In particular, approaches that view localisation as a problem of spatial mapping have performed well when applied to structures containing inhomogeneities such as complex geometrical features or the composition of multiple materials. The maps first require a series of artificial acoustic emission events to be generated across a test specimen, resulting in a mapping that represents difference-in-time-of arrival (dTOA) information. Despite their success, the application of dTOA maps has generally been restricted to applications that can be characterised by Euclidean distance measures. For spherical geometries such as a bearing raceway, this geometrical definition is not representative of the domain. This paper therefore proposes a novel extension to the spatial mapping approach for spherical domains, allowing acoustic emission localisation on a spherical roller bearing. The presented methodology firstly poses the generation of dTOA mappings as a problem of Gaussian process regression. Through a Bayesian framework, the source location likelihood of a real acoustic emission event is then assessed across the surface of the structure. Under the standard Gaussian process convention, the assumption is made that inputs to the kernel can be represented as a function of Euclidean distance. However, as bearings exist in a spherical space, the Euclidean distance will ignore the topological constraints of the bearing and is therefore not an appropriate measure. To bypass this issue, a reduced-rank approach is taken that expresses the covariance function as an approximate eigendecomposition. This approach allows the inputs to be projected onto an eigenbasis, satisfying both the conditions of a valid covariance function, as well as the topological constraints imposed by the geometry of the bearing. The proposed method is then applied to localise AE on a spherical roller bearing that is designed to replicate planetary support bearings that are found in wind turbine gearboxes.
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