<p>Laser surface polishing is widely employed to improve surface integrity and reduce surface roughness in nickel-based superalloys such as Inconel 718. However, many existing predictive approaches remain largely empirical and often provide limited physical interpretability or uncertainty quantification. In this study, a physics-constrained Gaussian Process (GP) framework is developed by integrating Buckingham Π-based dimensional analysis with probabilistic machine learning to establish a physically interpretable representation of laser surface polishing behaviour. The proposed framework incorporates dimensionless descriptors associated with thermal diffusion, transport scaling, energy input, and simplified thermophysical effects to characterize the relationships between processing conditions and post-processed surface roughness. The model achieved a training coefficient of determination (R²) of 0.998 and a 5 × 5 repeated cross-validation R² of 0.985 ± 0.022, demonstrating strong predictive consistency within the investigated process domain. Permutation feature importance analysis identified thermal diffusion length scaling and diffusion-related transport descriptors as the most influential variables within the developed framework, indicating a strong association between thermal transport behaviour and roughness evolution. In particular, the thermal diffusion length descriptor (Π₅) exhibited the highest predictive importance, while the diffusion-normalized transport parameter (Π₃) demonstrated a clear inverse relationship with surface roughness in the dimensionless scaling analysis. These results suggest that diffusion-controlled transport effects play a more significant role in determining polishing performance than energy input magnitude alone within the investigated processing window. To enhance practical applicability, uncertainty-aware optimization maps were constructed to identify low-roughness operating regions characterized by both improved surface quality and high predictive confidence. A simplified thermal interpretation was further employed to qualitatively relate the observed dimensionless trends to established thermal transport and surface redistribution phenomena reported in the laser polishing literature. Although the proposed framework does not explicitly solve thermo-fluid melt-pool equations or temperature-dependent material behaviour, it provides a computationally efficient, physically interpretable, and uncertainty-aware methodology for process understanding, parameter selection, and data-efficient optimization of laser surface engineering processes. The limitations associated with literature-derived datasets, effective thermophysical property assumptions, and material-specific calibration are also discussed.</p><p></p>

Physics-constrained dimensionless Gaussian process modelling of laser surface polishing in inconel 718

期刊论文
发表日期：

2026年6月17日

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Aswin Karkadakattil

摘要

Laser surface polishing is widely employed to improve surface integrity and reduce surface roughness in nickel-based superalloys such as Inconel 718. However, many existing predictive approaches remain largely empirical and often provide limited physical interpretability or uncertainty quantification. In this study, a physics-constrained Gaussian Process (GP) framework is developed by integrating Buckingham Π-based dimensional analysis with probabilistic machine learning to establish a physically interpretable representation of laser surface polishing behaviour. The proposed framework incorporates dimensionless descriptors associated with thermal diffusion, transport scaling, energy input, and simplified thermophysical effects to characterize the relationships between processing conditions and post-processed surface roughness. The model achieved a training coefficient of determination (R²) of 0.998 and a 5 × 5 repeated cross-validation R² of 0.985 ± 0.022, demonstrating strong predictive consistency within the investigated process domain. Permutation feature importance analysis identified thermal diffusion length scaling and diffusion-related transport descriptors as the most influential variables within the developed framework, indicating a strong association between thermal transport behaviour and roughness evolution. In particular, the thermal diffusion length descriptor (Π₅) exhibited the highest predictive importance, while the diffusion-normalized transport parameter (Π₃) demonstrated a clear inverse relationship with surface roughness in the dimensionless scaling analysis. These results suggest that diffusion-controlled transport effects play a more significant role in determining polishing performance than energy input magnitude alone within the investigated processing window. To enhance practical applicability, uncertainty-aware optimization maps were constructed to identify low-roughness operating regions characterized by both improved surface quality and high predictive confidence. A simplified thermal interpretation was further employed to qualitatively relate the observed dimensionless trends to established thermal transport and surface redistribution phenomena reported in the laser polishing literature. Although the proposed framework does not explicitly solve thermo-fluid melt-pool equations or temperature-dependent material behaviour, it provides a computationally efficient, physically interpretable, and uncertainty-aware methodology for process understanding, parameter selection, and data-efficient optimization of laser surface engineering processes. The limitations associated with literature-derived datasets, effective thermophysical property assumptions, and material-specific calibration are also discussed.