Probabilistic physics-guided machine learning for fatigue data analysis

A Probabilistic Physics-guided Neural Network (PPgNN) is proposed in this paper for probabilistic fatigue S-N curve estimation. The proposed model overcomes the limitations in existing parametric regression models and classical machine learning models for fatigue data analysis. Compared with explicit regression-type models (such as power law fitting), the PPgNN is flexible and does not impose restrictions on function types at different stress levels, mean stresses, or other factors. One unique benefit is that the proposed method includes the known physics/knowledge constraints in the machine learning model; the method can produce both accurate and physically consistent results compared with the classical machine learning model, such as neural network models. In addition, the PPgNN uses both failure and runout data in the training process, which encodes the runout data using a new proposed loss function, and is beneficial when compared with some existing models using only numerical point value data. A mathematical formulation is derived to include different types of physics constraints, which can deal with mean value, variance, and derivative/curvature constraints. Several data sets from open literature for fatigue S-N curve testing are used for model demonstration and model validation. Next, the proposed network architecture is extended to include multi-factor (e.g., mean stress, corrosion, frequency effect, etc.) fatigue data analysis. It is shown that the proposed PPgNN can serve as a flexible and robust model for general fitting and uncertainty quantification of fatigue data. This paper provides a feasible way to incorporate known physics/knowledge in neural network-based machine learning. This is achieved by properly designing the network topology and constraining the neural network's biases and weights. The benefits for the proposed physics-guided learning for fatigue data analysis are illustrated by comparing results from neural network models with and without physics guidance. The neural network model, without physics guidance, produces results contradictory to the common knowledge, such as a monotonic decrease of S-N curve slope and a monotonic increase of fatigue life variance as the stress level decreases. This problem can be avoided using the physics-guided learning model with encoded prior physics knowledge.