Interpretable machine learning (ML) has become a popular tool in the field of science and engineering. This research proposed a domain knowledge combined with ML method to increase interpretability while ensuring the accuracy of ML models and verifies the generality of the ML approach in fatigue crack growth (FCG) modelling. LZ50 steel single edge notch tension (SENT) specimens were tested for short crack (SC) growth rate and microstructure characterization under various R-controls. Based on the test results, the SC growth process was divided into 3 stages: microstructural short crack (0–145 μm), physical short crack (145–1000 μm), and long crack (1000 μm–fracture). Following the analysis of 8 semi-empirical FSCG rate equations with different driving forces, 6 impact variables that may affect the FCG rate characteristics were identified. Random forest and Pearson correlation analysis were used to investigate the influence of each feature on the FCG rate and the relationships among the features. The main influential features for the short crack symbolic regression (SCSR) model were found to be |ΔK–ΔK_at|, Δγ_xy, |a–a_t|, and e^α(1−R). After considering these 4 input features, the predicted FSCG rate equation generated by the SR model has a concise mathematical structure. Finally, an elastic net multiple linear regression method was proposed to determine the parameters of the predicted equation, while retaining the physical characteristics of each parameter. The SCSR model for SC demonstrated good prediction performance on various metallic materials.

Graphical Abstract

中文翻译：

---

用于模拟疲劳短裂纹扩展行为的可解释机器学习方法

可解释的机器学习（ML）已成为科学和工程领域的流行工具。本研究提出了将领域知识与机器学习方法相结合，以提高可解释性，同时确保机器学习模型的准确性，并验证了机器学习方法在疲劳裂纹扩展（FCG）建模中的通用性。在各种R控制下，测试了 LZ50 钢单刃缺口拉伸 (SENT) 样本的短裂纹 (SC) 扩展速率和微观结构特征。根据测试结果，SC生长过程分为3个阶段：微观结构短裂纹（0-145μm）、物理短裂纹（145-1000μm）和长裂纹（1000μm-断裂）。通过对 8 个具有不同驱动力的半经验 FSCG 速率方程进行分析，确定了 6 个可能影响 FCG 速率特征的影响变量。采用随机森林和Pearson相关分析研究各特征对FCG率的影响以及各特征之间的关系。发现短裂纹符号回归（SCSR）模型的主要影响特征是 |Δ K –Δ K _{a t} |、Δ γ _xy、| a – a _t | 和e ^{α (1− R )}。考虑这 4 个输入特征后，SR 模型生成的预测 FSCG 速率方程具有简洁的数学结构。最后，提出一种弹性网多元线性回归方法来确定预测方程的参数，同时保留每个参数的物理特征。 SC 的 SCSR 模型对各种金属材料表现出良好的预测性能。

图形概要