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Precision Measurements and Parametric Models of Vertebral Endplates
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Data-driven spatial metamodeling for non-Gaussian digital roughness mapping in precision machining.

Prithbey Raj Dey1, David Enke2

  • 1Department of Engineering Management and Systems Engineering, Missouri University of Science and Technology, 600 W 14th St, Rolla, MO, 65409, USA. prdfyb@mst.edu.

Scientific Reports
|June 1, 2026
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Summary

Precision machining creates complex surfaces. This study introduces a new method using geospatial analysis and kriging to map surface roughness, considering non-Gaussian characteristics for better quality control.

Keywords:
Digital Roughness MappingKrigingNon-Gaussian SurfacePrecision MachiningSpatial Metamodeling

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Area of Science:

  • Manufacturing Engineering
  • Surface Metrology
  • Data Science

Background:

  • Turning processes generate non-Gaussian surface topographies characterized by skewness and kurtosis.
  • Accurate surface roughness modeling is crucial for predicting tribology and functional performance but is challenged by process variability and limited integration of non-Gaussian parameters.
  • Existing models often neglect the spatial variability and non-Gaussian nature of machined surfaces.

Purpose of the Study:

  • To develop a novel data-driven metamodeling framework, Spatial Non-Gaussian Roughness Metamodeling (SNGRM), for spatial mapping of arithmetic mean roughness ([Formula: see text]).
  • To integrate geospatial analysis and kriging interpolation to explicitly account for non-Gaussian surface conditions defined by skewness ([Formula: see text]) and kurtosis ([Formula: see text]).
  • To advance the multivariate characterization of non-Gaussian machined surfaces by incorporating machining parameters.

Main Methods:

  • Implementation of a data-driven metamodeling framework (SNGRM) utilizing geospatial analysis and kriging interpolation.
  • Application of ordinary kriging to capture spatial variability within the skewness-kurtosis domain.
  • Advancement using universal kriging, incorporating machining parameters as external drift to model systematic roughness variations.

Main Results:

  • Universal kriging demonstrated superior predictive performance compared to ordinary kriging.
  • The framework effectively captures both non-Gaussian spatial variability and deterministic trends influenced by machining parameters.
  • SNGRM successfully integrates empirical machining data, retaining measurement variability for robust spatial interpolation of [Formula: see text].

Conclusions:

  • The proposed SNGRM framework provides a rigorous, data-driven approach for digital roughness mapping in precision machining.
  • Jointly incorporating non-Gaussian spatial characteristics and machining parameters enables reliable spatial interpolation of [Formula: see text] with quantified uncertainty.
  • This metamodeling approach enhances the understanding and prediction of surface quality in turning operations.