Surface data imputation with stochastic processes

Spurious measurements in surface data are common in technical surfaces. Excluding or ignoring these spurious points may lead to incorrect surface characterization if these points inherit features of the surface. Therefore, data imputation must be applied to ensure that the estimated data points at spurious measurements do not strongly deviate from the true surface and its characteristics. Traditional surface data imputation methods rely on simple assumptions and ignore existing knowledge of the surface, yielding in suboptimal estimates. In this paper, we propose using stochastic processes for data imputation. This approach, which originates from surface simulation, allows for the straightforward integration of a priori knowledge. We employ Gaussian processes for surface data imputation with artificially generated missing features. Both the surfaces and the missing features are generated artificially. Our results demonstrate that the proposed method fills the missing values and interpolates data points with better alignment to the measured surface compared to traditional approaches, particularly when surface features are missing.

Feature Characterization for Profile Surface Texture

Conventional field parameters for surface measurement use all data points, while feature characterization focuses on subsets extracted by watershed segmentation. This approach enables the extraction of specific features that are potentially responsible for the function of the surface or are a direct reflection of the manufacturing process, allowing for a more accurate assessment of both aspects. Feature characterization with the underlying watershed segmentation for areal surface topographies has been standardized for over a decade and is well established in industry and research. In contrast, feature characterization for surface profiles has been standardized recently, and the corresponding standard for watershed segmentation is planned to be published in the near future. Since the standards do not provide guidelines for implementation, this paper presents an unambiguous algorithm of the watershed segmentation and the feature characterization for surface profiles. This framework provides the basis for future work, mainly investigating the relationship between feature parameters based on feature characterization and the function of the surface or manufacturing process. For this purpose, recommendations for the configuration and extensions of the toolbox can also be developed, which could find their way into the ISO standards.

Model of rough surfaces with Gaussian processes

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.