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<p>This study presents an enhanced hybrid superposition approximation model with scaling-variable confidence for machining prediction applications. Building upon existing scaling function-based variable confidence approximation frameworks, our methodology incorporates three key innovations: (1) Implementation of gene expression programming for precise scaling function fitting; (2) Integration of a superposition accuracy controller to ensure systematic error regulation; (3) Development of a Bayesian framework for quantitative assessment of model contribution weights. The proposed model was rigorously validated through H62 brass complex surface milling experiments, employing a dual-validation approach combining 18 simulation trials and 9 physical tests to establish comprehensive high/low precision training datasets. Average prediction error of the proposed method is less than 5% for power, roughness, and hardness in H62 brass milling, outperforming traditional Kriging and Co-Kriging models. Notably, this performance enhancement was attained without significant structural modifications to the baseline modeling architecture, confirming the method's robustness and practical applicability in precision machining parameter optimization.</p> Graphical abstract <p></p>

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Prediction of power, surface roughness and Vickers hardness in CNC complex surface milling processes based on a hybrid superposition scaling reliability approximate model (HSU-MFM)

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Yang Yang,
  • YiQing Chen,
  • Yuan Wang

摘要

This study presents an enhanced hybrid superposition approximation model with scaling-variable confidence for machining prediction applications. Building upon existing scaling function-based variable confidence approximation frameworks, our methodology incorporates three key innovations: (1) Implementation of gene expression programming for precise scaling function fitting; (2) Integration of a superposition accuracy controller to ensure systematic error regulation; (3) Development of a Bayesian framework for quantitative assessment of model contribution weights. The proposed model was rigorously validated through H62 brass complex surface milling experiments, employing a dual-validation approach combining 18 simulation trials and 9 physical tests to establish comprehensive high/low precision training datasets. Average prediction error of the proposed method is less than 5% for power, roughness, and hardness in H62 brass milling, outperforming traditional Kriging and Co-Kriging models. Notably, this performance enhancement was attained without significant structural modifications to the baseline modeling architecture, confirming the method's robustness and practical applicability in precision machining parameter optimization.

Graphical abstract