Session: 03-01-01: General Topics of Aerospace Materials

Paper Number: 104976

104976 - Probabilistic Fatigue Data Analysis Using Physics-Guided Mixture Density Networks 

The relationship between materials' probabilistic fatigue lives (N) and applied stresses (S) is critical for the safe-life design processes considering reliability. Those relationships are usually presented in the form of probabilistic S-N (P-S-N) curves. Furthermore, a fatigue life prediction under general random loadings requires the analysis of the probabilistic fatigue damage accumulation at various stress levels. Thus, a reliable fatigue data analysis and uncertainty quantification method plays a significant role in engineering designs and analyses.

This paper proposes a Physics-guided Mixture Density Network (PgMDN) model for probabilistic fatigue data analysis. It integrates a Mixture Density Network for probabilistic modeling and physics knowledge as regularizations. This model can handle arbitrary distribution of data (e.g., strongly non-Gaussian, multi-mode, and truncated distributions). The physics knowledge from parameters and their partial derivatives is used as equality/ inequality constraints. The training of physics-guided machine learning is formulated as a constrained optimization problem. The constrained optimization problem is transformed to an unconstrained one using a dynamic penalty function algorithm to train the neural network with the commonly used backpropagation algorithm. The required training data size can be reduced with the physics constraints, and the overfitting problem can be mitigated. Finally, this paper applies the PgMDN in the engineering problem for fatigue stress-life curve estimation.

Good results of fatigue data fitting can be obtained using the proposed PgMDN model. The physics constraints (i.e., slope and curvature constraints on the P-S-N curves) are satisfied with the guidance of the physics knowledge. The data at low strain levels where the S-N curves tend to be flat can be appropriately fitted due to the flexibility of the mixture distribution.

Some discussions are given to illustrate the effectiveness of incorporating the physics knowledge when data are sparse, the improvement of the dynamic penalty function method compared with the static method, and the benefits achieved from the distribution mixture compared with a single Gaussian distribution.

Presenting Author: Yongming Liu Arizona State University

Presenting Author Biography: Yongming Liu is a professor of aerospace and mechanical engineering with the School for Engineering of Matter, Transport and Energy at Arizona State University. He heads the Prognostic Analysis and Reliability Assessment Laboratory (PARA).

His research interests range from fatigue and fracture of engineering materials and structures, probabilistic computational mechanics, risk assessment and management to multi-physics damage modeling and structural durability, multi-scale uncertainty quantification and propagation, imaging-based experimental testing, diagnostics and prognostics.

Authors:

Jie Chen Northwestern University
Yongming Liu Arizona State University