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.

针对概率疲劳S - N，本文提出了一种概率物理指导神经网络（PPgNN）。曲线估计。提出的模型克服了现有的参数回归模型和用于疲劳数据分析的经典机器学习模型的局限性。与显式回归类型模型（例如幂定律拟合）相比，PPgNN具有灵活性，并且在不同压力水平，平均压力或其他因素下对功能类型没有施加限制。一个独特的好处是，所提出的方法在机器学习模型中包含了已知的物理/知识约束；与传统的机器学习模型（例如神经网络模型）相比，该方法可以产生准确且物理上一致的结果。此外，PPgNN在训练过程中同时使用了故障数据和跳动数据，该过程使用新提出的损失函数对跳动数据进行编码，与仅使用数值点数据的某些现有模型进行比较时，它是有益的。得出了一个数学公式，其中包括不同类型的物理约束，可以处理平均值，方差和导数/曲率约束。公开文献中的一些疲劳数据集小号- ñ曲线测试用于模型演示和模型验证。接下来，所提出的网络体系结构被扩展为包括多因素（例如，平均应力，腐蚀，频率效应等）疲劳数据分析。结果表明，提出的PPgNN可以作为疲劳数据的一般拟合和不确定性量化的灵活，鲁棒模型。本文提供了一种可行的方法，将已知的物理/知识纳入基于神经网络的机器学习中。这是通过适当设计网络拓扑并限制神经网络的偏见和权重来实现的。通过比较带有和不带有物理指导的神经网络模型的结果，说明了所提出的以物理指导的疲劳数据分析学习的好处。没有物理指导的神经网络模型，S - N曲线斜率和疲劳寿命随应力水平降低而单调增加。使用具有编码的先验物理知识的物理学指导的学习模型可以避免此问题。