A physically consistent framework for fatigue life prediction using probabilistic physics-informed neural network

Machine learning has drawn growing attention from the areas of fatigue, fracture, and structural integrity. However, most current studies are fully data-driven and may contradict the underpinning physical knowledge. To address this issue, we propose a physically consistent framework for fatigue life prediction that uses a probabilistic physics-informed neural network (PINN) to incorporate the physics underpinning the fatigue mechanism. Particularly, we consider the scatter of the fatigue life using a probabilistic neural network with the output to parametrize the fatigue life distribution. Then use neural networks' inherent backpropagation capabilities to automatically compute the derivatives that represent the physical knowledge. Finally, construct a composite loss function to encode the derivatives with certain physical constraints and uses a negative log-likelihood function to consider both failure data and run-out data. This enforces the network training process to learn a continuous function that describes the stress-life relationship satisfying both experimental data and physical knowledge. We demonstrate the proposed framework with sensitivity analysis and a comparison to the fully data-driven neural networks and the conventional statistical methods using the fatigue test data of three different materials. The results show that the proposed framework has a robust performance to effectively reflect the underlying physical knowledge and prevent overfitting issues. The findings provide a better understanding of neural networks’ application to fatigue life prediction and suggest that one should be cautious when using a fully data-driven approach in scientific applications.