Neural network integrated with symbolic regression for multiaxial fatigue life prediction

Abstract

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.