In the realm of structural engineering, accurately predicting multiaxial fatigue life presents a formidable challenge, stemming from the complex interplay of stress and strain across multiple directions. This research introduces the Symbolic Regression-Neural Network (SR-NN) framework, a novel integration of symbolic regression-derived expressions with neural networks aimed at enhancing predictive accuracy in this field. Initiated by selecting salient features through SHAP-informed Recursive Feature Elimination, our approach effectively minimized dimensionality while pinpointing key feature groups. Symbolic regression, newly applied to guide neural network training in the prediction of alloy material fatigue life, facilitated the generation of meaningful expressions that describe the fatigue processes. These expressions were incorporated into the network’s loss function alongside MSE loss, refining the model’s learning dynamics. Our proposed SR-NN framework demonstrated substantial improvements over traditional models in rigorous testing, notably reducing MSE by 55.4% compared to RF and 45% against SVM models, underscoring the potential of merging symbolic regression with machine learning to tackle the inherent variability and complexity of fatigue behavior across diverse materials and loading conditions. This study highlights the transformative impact of symbolic regression in improving the interpretability and accuracy of predictive models within structural engineering.

中文翻译：

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神经网络与符号回归集成用于多轴疲劳寿命预测


在结构工程领域，由于多个方向上应力和应变的复杂相互作用，准确预测多轴疲劳寿命提出了艰巨的挑战。本研究引入了符号回归神经网络（SR-NN）框架，这是符号回归派生表达式与神经网络的新颖集成，旨在提高该领域的预测准确性。我们的方法首先通过 SHAP 通知的递归特征消除来选择显着特征，从而有效地最小化维度，同时精确定位关键特征组。新近应用于指导神经网络训练来预测合金材料疲劳寿命的符号回归，有助于生成描述疲劳过程的有意义的表达式。这些表达式与 MSE 损失一起被纳入网络的损失函数中，从而完善了模型的学习动态。我们提出的 SR-NN 框架在严格的测试中证明了对传统模型的显着改进，与 RF 相比，MSE 显着降低了 55.4%，与 SVM 模型相比，MSE 降低了 45%，强调了将符号回归与机器学习相结合以解决模型固有的可变性和复杂性的潜力。不同材料和负载条件下的疲劳行为。这项研究强调了符号回归在提高结构工程中预测模型的可解释性和准确性方面的变革性影响。