Surface roughness plays a critical role and has effects in, e.g., fluid dynamics or contact mechanics. For example, to evaluate fluid behavior at different roughness properties, real-world or numerical experiments are performed. Numerical simulations of rough surfaces can speed up these studies because they can help collect more relevant information. However, it is hard to simulate rough surfaces with deterministic or structured components in current methods. In this work, we present a novel approach to simulate rough surfaces with a Gaussian process (GP) and a noise model because GPs can model structured and periodic elements. GPs generalize traditional methods and are not restricted to stationarity so they can simulate a wider range of rough surfaces. In this paper, we summarize the theoretical similarities of GPs with auto-regressive moving-average processes and introduce a linear process view of GPs. We also show examples of ground and honed surfaces simulated by a predefined model. The proposed method can also be used to fit a model to measurement data of a rough surface. In particular, we demonstrate this to model turned profiles and surfaces that are inherently periodic.

Surface roughness plays a critical role and has effects in, e.g., fluid dynamics or contact mechanics. For example, to evaluate fluid behavior at different roughness properties, real-world or numerical experiments are performed. Numerical simulations of rough surfaces can speed up these studies because they can help collect more and relevant information. However, it is hard to simulate rough surfaces with deterministic or structured components in current methods. In this work, we present a novel approach to simulate rough surfaces with Gaussian processes (GPs) because they have been capable of modeling structured or periodic elements in recent studies. Compared to traditional methods, GPs are not restricted to stationarity so they can simulate a wider range of rough surfaces. They are also able to interpolate invalid points in surface measurements. In this paper, we also summarize theoretical similarities of GPs with auto-regressive moving-average processes and introduce a linear process view of GPs. We particularly show that GPs can be used to model turned rough surfaces with only stationary assumptions from data.