Bayesian Markov chain Monte Carlo Framework for uncertainty quantification and propagation in non-Gaussian digital roughness mapping

Author

• Prithbey Dey
• David Lee Enke, Missouri University of Science and TechnologyFollow

Abstract

Non-Gaussian surface profiles generated during turning strongly influence the functional performance of engineering components, including contact mechanics, lubrication behavior, and wear resistance. Furthermore, the stochastic nature of machined surfaces introduces both aleatory and epistemic uncertainties, necessitating roughness characterization and prediction under uncertainty. However, uncertainty-aware approaches are rarely integrated into spatial roughness modeling, particularly for the characterization of non-Gaussian surfaces. To bridge this gap, this study introduces a Bayesian uncertainty quantification and propagation framework for digital roughness mapping of arithmetic mean roughness (𝑅𝑎) within a non-Gaussian descriptor domain defined by skewness (𝑅𝑠𝑘) and kurtosis (𝑅𝑘𝑢). While significant inter-trial variability is inherent in precision machining, conventional homoscedastic assumptions often underrepresent trial-to-trial uncertainty. Therefore, a heteroscedastic Markov Chain Monte Carlo (MCMC) posterior predictive sampling framework guided by knowledge-informed priors is developed to quantify and propagate this uncertainty through synthetic data generation for subsequent spatial modeling and prediction. Spatial point-pattern analysis and semi variogram modeling are employed to characterize spatial autocorrelation, heterogeneity, and dependence within the convex non-Gaussian descriptor domain. Group-wise leave-one-out cross-validation (LOOCV) indicates that universal kriging achieves better predictive performance compared with ordinary kriging, highlighting the benefit of incorporating machining parameters as deterministic trend components alongside descriptor domain spatial dependence. Most importantly, Bayesian synthetic data generation resolves prediction failures encountered in empirical-data-driven kriging interpolation, enabling robust and reliable prediction across the entire 𝑅𝑠𝑘–𝑅𝑘𝑢 domain. This framework establishes a robust, knowledge-driven, and uncertainty-aware methodology for 2D non-Gaussian digital roughness mapping, providing a foundation for decision-support applications in intelligent precision manufacturing.

Recommended Citation

P. Dey and D. L. Enke, "Bayesian Markov chain Monte Carlo Framework for uncertainty quantification and propagation in non-Gaussian digital roughness mapping," Knowledge-Based Systems, vol. 352, article no. 116960, Elsevier BV, Sep 2026.

The definitive version is available at https://doi.org/10.1016/j.knosys.2026.116960

Department(s)

Engineering Management and Systems Engineering

Keywords and Phrases

Precision machining; Bayesian inference; Markov chain Monte Carlo; Uncertainty quantification and propagation; Kriging; Digital roughness mapping

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Elsevier B. V., All rights reserved.

Publication Date

9 September 2026