A data centric approach to generative modelling of rough surfaces: An application to 3D-printed Stainless Steel

The emergence of 3D printing technologies for stainless steel enables steel struc-tures with almost arbitrarily complex geometries to be manufactured. A common design preference for steel structures is that they arethin-walled, to reduce weight and limit the requirement for raw material. The mechanical properties of thin-walled structures are principally determined by their geometry; however, 3D-printed steel components exhibit geometric variation beyond that which was intended, due to the welding process involved, at a scale that is non-negligible with respect to the thickness of the wall. The cumulative impact of geometric variation is to alter the macro-scale mechanical properties of a printed component, such as deformation under load. An important challenge is therefore to predict the (random) macro-scale mechanical properties of a component, before it is manufactured. To address this, we trained a generative probabilistic model for rough surfaces defined on smooth manifolds to an experimentally-obtained dataset consisting of samples of 3D-printed steel. Combined with finite element simulation of components under load, we were able to produce detailed probabilistic predictions of the mechanical properties of a 3D-printed steel component. The main technical challenge was to transfer information from the training dataset to the hypothetical component, whose notional geometry may be described by a different manifold. Our proposed solution was to employ spatial random field models which can be characterised locally using a differential operator, and to leverage the correspondence between the Laplacian on the training and the test manifolds to facilitate the transfer of information.