Heteroscedastic Gaussian Processes for Localising Acoustic Emission

Abstract

As interest continues to grow in developing more informative structural health monitoring systems, the capture and use of acoustic emission data has emerged as a popular technique for localising damage. The basis of a number of these approaches is the construction of difference-in-time-of-arrival (dTOA) maps, which is a spatial mapping that characterises the expected dTOA information for a given sensor pair across the surface of a test structure. In this approach, a series of artificial acoustic emission sources are first generated across the structure, where the arrival time at a number of surface-mounted sensors can be recorded. For each sensor pair, dTOA values can then be extracted, allowing a spatial mapping to be learned.

In recent work, the use of Gaussian process regression for constructing dTOA maps has been demonstrated, offering a number of benefits such as interpolation across space and a probabilistic interpretation of predictions, naturally enabling uncertainty quantification. One assumption made under the standard Gaussian process framework is that the noise associated with each observation is constant across the input space. In the case of dTOA values mapped across a structure, as the distance between a measurement and a sensor pair increases, there will be an increasing uncertainty. This effect results in the emergence of a spatially dependent noise process, rendering a uniform noise model sub-optimal. This chapter therefore presents the use of a heteroscedastic Gaussian process model for learning dTOA maps, where it is demonstrated that the input-dependent noise process can be suitably captured. Future acoustic emission events can then be localised by maximising the likelihood of the corresponding dTOA values. The methodology is applied to a complex structure, showing an improved localisation performance in comparison to the homoscedastic model.