Neural network approaches for real-time fatigue life estimation by Surrogating the rainflow counting method

Fatigue life estimation is critical for ensuring the safety and reliability of systems under cyclic loading. Traditional rainflow counting methods require exhaustive traversal of load histories, making them computationally expensive for real-time applications. To address this issue, this present study leverages the increasing demand for efficient high-cycle fatigue (HCF) life estimation methods, combining neural network surrogate modeling with physical principles to enhance both accuracy and computational speed. The Euler neural network (ENN) and the Runge-Kutta 4th-order neural network (RK4NN) for fatigue life estimation are proposed. These approaches are validated by comparing the results of rainflow counting with wind turbine damage ratios, demonstrating the accuracy achieves errors within 15 % for over 74 % of cases in the numerical stability range. Moreover, the RK4NN displayed superior generalization and fitting capacities across varied load conditions, effectively capturing early-stage damage growth while avoiding overfitting with the mean squared error 1.99 × 10⁻³⁶. Additionally, the ENN and the RK4NN achieved the acceleration ratio of 19.53 × and 19.38 × respectively in comparison with the modified rainflow counting method (RCM). These findings underscore the practical value of the surrogate models in improving the real-time responsiveness and computational efficiency of fatigue life estimation frameworks, particularly in digital twin applications for industrial systems.