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Article

Achieving High Hardness and Uniformity in Fe-Based Amorphous Coatings for Enhanced Wear Resistance via Explainable Machine Learning

1
Defense Innovation Institute, Academy of Military Sciences, Beijing 100071, China
2
State Key Laboratory of Advanced Marine Materials, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Coatings 2026, 16(2), 199; https://doi.org/10.3390/coatings16020199
Submission received: 14 January 2026 / Revised: 29 January 2026 / Accepted: 2 February 2026 / Published: 5 February 2026
(This article belongs to the Special Issue Advanced Corrosion- and Wear-Resistant Coatings)

Abstract

High-Velocity Air-Fuel (HVAF) spraying of Fe-based amorphous coatings involves strong nonlinear coupling among multiple process parameters, while practical optimization is severely constrained by limited experimental data and poor model interpretability. To address these challenges, a systematic data-driven optimization framework integrating the Denoising Diffusion Probabilistic Model (DDPM)-based data augmentation with explainable machine learning is proposed. Coating microhardness and hardness uniformity were jointly selected as target properties to capture both performance level and spatial reliability. Three generative models—Generative Adversarial Network (GAN), Variational Autoencoder (VAE), and DDPM—were comparatively evaluated using statistical matching and distribution-consistency metrics, revealing that DDPM most faithfully reproduces the intrinsic statistical characteristics of real HVAF process data. We benchmarked ten representative regression algorithms covering classical statistical learning, ensemble methods, and deep learning paradigms, with GBR demonstrating the highest predictive accuracy and stability. The inclusion of 10% DDPM-generated samples further improved the predictive precision of the GBR model. SHapley Additive exPlanations (SHAP) quantitatively identified spraying distance as the dominant parameter governing coating hardness, while elucidating the coupled effects of multiple parameters on hardness uniformity. By interpolatively expanding the process parameter space, a two-stage screening strategy identified 98 high-performance parameter combinations. Experimental validation confirmed that the optimal parameter set simultaneously achieved higher hardness and improved uniformity compared with the original best condition, resulting in a 13.6% reduction in wear rate.
Keywords: amorphous alloy coating; thermal spraying; explainable machine learning; data augmentation; hardness uniformity amorphous alloy coating; thermal spraying; explainable machine learning; data augmentation; hardness uniformity

Share and Cite

MDPI and ACS Style

Zhang, E.; Ma, C.; Yuan, J.; Yan, S.; Zhang, Z.; Jing, Z.; Zhang, B. Achieving High Hardness and Uniformity in Fe-Based Amorphous Coatings for Enhanced Wear Resistance via Explainable Machine Learning. Coatings 2026, 16, 199. https://doi.org/10.3390/coatings16020199

AMA Style

Zhang E, Ma C, Yuan J, Yan S, Zhang Z, Jing Z, Zhang B. Achieving High Hardness and Uniformity in Fe-Based Amorphous Coatings for Enhanced Wear Resistance via Explainable Machine Learning. Coatings. 2026; 16(2):199. https://doi.org/10.3390/coatings16020199

Chicago/Turabian Style

Zhang, Enhao, Cong Ma, Jiachi Yuan, Shuang Yan, Zhibin Zhang, Zhiyuan Jing, and Binbin Zhang. 2026. "Achieving High Hardness and Uniformity in Fe-Based Amorphous Coatings for Enhanced Wear Resistance via Explainable Machine Learning" Coatings 16, no. 2: 199. https://doi.org/10.3390/coatings16020199

APA Style

Zhang, E., Ma, C., Yuan, J., Yan, S., Zhang, Z., Jing, Z., & Zhang, B. (2026). Achieving High Hardness and Uniformity in Fe-Based Amorphous Coatings for Enhanced Wear Resistance via Explainable Machine Learning. Coatings, 16(2), 199. https://doi.org/10.3390/coatings16020199

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