基于小样本机器学习加速有限元分析TiN/Ti多层涂层的动态冲击响应

詹研; 许柄权; 彭健; 王传彬

doi:10.11858/gywlxb.20251132

基于小样本机器学习加速有限元分析TiN/Ti多层涂层的动态冲击响应

doi: 10.11858/gywlxb.20251132

詹研^{1, 2,},
许柄权^{1, 2},
彭健^{1, 2,*, ,},
王传彬^{1, 2}

1.
武汉理工大学材料复合新技术全国重点实验室, 湖北武汉　430070
2.
湖北省先进复合材料技术创新中心, 湖北武汉　430070

基金项目: 基础加强计划重点基础研究项目（2022-JCJQ-ZD-172-00）

详细信息

作者简介:
詹　研（1996－），男，硕士研究生，主要从事有限元仿真防护涂层动态冲击研究. E-mail：479318892@qq.com

通讯作者:
彭　健（1986－），男，博士，研究员，博士生导师，主要从事低维材料、高熵材料、计算辅助新材料设计研究. E-mail：jian.peng@whut.edu.cn

中图分类号: O241; TB302; O521.9
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出版历程
- 收稿日期: 2025-07-16
- 修回日期: 2025-09-07
- 录用日期: 2025-10-11
- 网络出版日期: 2025-09-17
- 刊出日期: 2025-11-05

Accelerating Finite Element Analysis of Dynamic Impact Response of TiN/Ti Multilayer Coatings Based on Small Sample Machine Learning

ZHAN Yan^{1, 2
,},
XU Bingquan^{1, 2},
PENG Jian^{1, 2,*
, ,},
WANG Chuanbin^{1, 2}

1.
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, Hubei, China
2.
Hubei Provincial Advanced Composite Materials Technology Innovation Center, Wuhan 430070, Hubei, China

摘要

摘要: 服役于极端环境下的发动机高压涡轮叶片，因长期承受高温燃气携带的沙尘颗粒的高速撞击，使役寿命会大幅降低。TiN/Ti多层涂层凭借其高硬、高韧的特性成为叶片表面涂层的首选材料。然而，其抗冲蚀性能与其结构参数紧密相关，传统的实验试错法与有限元模拟往往耗时耗力。为了解决这一困境，提出了一个基于小样本机器学习（machine learning，ML）与有限元分析融合的TiN/Ti多层涂层设计框架。评估了多种回归算法，并优选出高斯过程回归模型，实现了涂层在动态冲击下的层内最大应力与基体最大塑性应变的高精度预测（决定系数R²分别为0.88和0.85）。结合残差与不确定性分析，进一步强化了模型的拟合能力。此外，通过SHAP（shapley additive explanations）模型分析揭示各特征对目标的影响。最终设计了8种新的结构与冲击条件下的涂层仿真模型，并验证了ML模型预测结果的准确性。该框架为高维参数空间下涂层抗冲击设计提供了数据高效、计算经济的解决方案。
- TiN/Ti多层涂层 /
- 机器学习 /
- 有限元分析 /
- 动态冲击
Abstract: Engine high-pressure turbine blades operating in extreme environments, such as deserts, are subjected to long-term high-velocity impacts from sand particles carried by hot combustion gases, significantly reducing their service life. Owing to its high hardness and toughness, the TiN/Ti multilayer coating has emerged as a preferred surface coating material for such blades. However, its erosion resistance is highly dependent on structural parameters, and traditional experimental trial-and-error methods and finite element simulations are often time-consuming and labor-intensive. To address this challenge, this study proposes a TiN/Ti multilayer coating design framework that integrates small-sample machine learning (ML) with finite element analysis. Multiple regression algorithms were evaluated, and Gaussian process regression (GPR) was selected for its superior performance, enabling high-accuracy prediction of the maximum intralayer stress and the maximum plastic strain in the substrate under dynamic impact conditions (with R² values of 0.88 and 0.85, respectively). The modelʼs fitting capability was further enhanced through residual and uncertainty analyses. Moreover, shapley additive explanations (SHAP) analysis was employed to elucidate the contribution of each feature to the target variables. Finally, eight new coating structures under varying impact conditions were designed and simulated to validate the predictive accuracy of the ML model. This framework offers a data-efficient and computationally economical solution for impact-resistant coating design in high-dimensional parameter spaces.
- TiN/Ti multilayer coating /
- machine learning /
- finite element analysis /
- dynamic impact

HTML全文

图 1 TiN/Ti多层涂层的有限元模型

Figure 1. Finite element model of TiN/Ti multilayer coating

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图 2 相关性分析热图

Figure 2. Heatmap of correlation analysis

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图 3 不同算法针对目标建模精度（R²）的对比

Figure 3. Comparison of target modeling accuracy (R²) for different algorithms

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图 4 6种不同算法建模结果的对比

Figure 4. Comparison of modeling results from six different algorithms

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图 5 以层内最大应力为目标的GPR超参数优化建模结果及分析

Figure 5. Modeling results and analysis of GPR hyperparameter optimization targeting the maximum stress within a layer

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图 6 以基体最大塑性应变为目标的GPR超参数优化建模结果及分析

Figure 6. Modeling results and analysis of GPR hyperparameter optimization targeting maximum plastic strain of the matrix

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图 7 SHAP蜂巢图

Figure 7. SHAP honeycomb plot results

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图 8 SHAP依赖图

Figure 8. SHAP dependency graph

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图 9 机器学习模型预测结果与真实值的对比

Figure 9. Comparison of machine learning model predictions with actual values

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图 10 涂层内部最大应力云图

Figure 10. Maximum stress cloud map inside the coating

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图 11 基体最大塑性应变云图

Figure 11. Maximum plastic strain cloud map of the matrix

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表 1 原始数据集

Table 1. Original dataset

Feature					Target
α/(°)	v/(m·s⁻¹)	h/μm	N	$ \lambda $	σ_max/GPa	ε_max
15	100	24	8	4	1.65	0.11
30	100	24	8	4	2.66	0.16
45	100	24	8	4	3.51	0.21
60	100	24	8	4	4.01	0.22
75	100	24	8	4	4.37	0.24
90	100	24	8	4	4.54	0.25
90	75	24	8	2	2.72	0.18
90	100	24	8	2	3.53	0.25
90	125	24	8	2	5.21	0.44
90	150	24	8	2	7.84	0.68
90	100	12	2	4	8.64	0.33
90	100	16	2	4	7.65	0.32
90	100	20	2	4	6.84	0.31
90	100	24	2	4	5.68	0.29
90	100	24	2	4	5.67	0.29
90	100	24	6	4	5.12	0.28
90	100	24	8	4	4.52	0.25
90	100	24	12	4	3.99	0.23
90	100	24	8	2	3.53	0.25
90	100	24	8	4	4.52	0.26
90	100	24	8	11	5.89	0.35
90	100	24	8	19	6.36	0.47

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表 2 TiN/Ti多层涂层有限元建模结构参数及冲击条件设定

Table 2. Finite element modeling of TiN/Ti multilayer coating structural parameters and impact condition settings

Case	α/(°)	v/(m·s⁻¹)	h/μm	N	$ \lambda $
C1	30	100	24	48	2
C2	60	100	24	48	2
C3	90	100	24	48	2
C4	30	200	24	48	2
C5	60	200	24	48	2
C6	90	200	24	48	2
C7	90	200	24	24	2
C8	90	200	24	12	2

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表 3 Ti6Al4V、TiN、Ti和Al₂O₃的基本参数

Table 3. Basic parameters of Ti6Al4V, TiN, Ti, and Al₂O₃

Material	ρ/(kg·m⁻³)	E/GPa	ν
Ti6Al4V	4 428	113.8	0.34
TiN	5 400	480.0	0.27
Ti	4 500	110.0	0.33
Al₂O₃	3 970	344.0	0.20

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表 4 基体Ti6Al4V与Ti的J-C本构参数

Table 4. J-C constitutive parameters of the matrix Ti6Al4V and Ti

Material	A/MPa	B/MPa	n₀	C	$ {\dot{\varepsilon }}_{0} $/s^–1	D₁	D₂	D₃	D₄	D₅
Ti6Al4V	1 098	1 092	0.93	0.014	1	–0.090	0.27	0.48	0.014	3.87
Ti	309	80	0.16	0.060	1	0.145	0.33	0.48	0.004	3.90

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表 5 8组涂层层内最大应力与基体最大塑性应变的真实值与预测值对比结果

Table 5. Comparison between the predicted and actual values of the maximum intralayer stress and the maximum plastic strain in the substrate for eight coating groups

Case	σ_max/GPa		ε_max
Case	True value	Predicted value	True value	Predicted value
C1	2.83	2.76	0.012 6	0.013 4
C2	3.42	3.51	0.017 4	0.018 9
C3	3.56	4.15	0.020 8	0.022 6
C4	6.12	6.19	0.018 4	0.019 7
C5	9.02	9.12	0.019 6	0.021 8
C6	11.41	12.52	0.023 4	0.026 1
C7	14.56	15.32	0.024 8	0.027 2
C8	17.37	16.81	0.029 9	0.030 3

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