TY - JOUR
T1 - Uncertainty quantification of fatigue S-N curves with sparse data using hierarchical Bayesian data augmentation
AU - Chen, Jie
AU - Liu, Siying
AU - Zhang, Wei
AU - Liu, Yongming
N1 - Funding Information:
The work in this study was supported partially by fund from NSF ( 1536994 , 1537121 ). The support is greatly acknowledged. The authors also acknowledge the supports from the Connecticut Department of Transportation for providing the steel pieces taken from the Pearl Harbor Memorial Bridge.
Funding Information:
The work in this study was supported partially by fund from NSF (1536994, 1537121). The support is greatly acknowledged. The authors also acknowledge the supports from the Connecticut Department of Transportation for providing the steel pieces taken from the Pearl Harbor Memorial Bridge. Declarations of interest: none.
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/5
Y1 - 2020/5
N2 - A novel statistical uncertainty quantification (UQ) method for fatigue S-N curves with sparse data is proposed in this paper. Sparse data observation is very common in fatigue testing due to various reasons, such as time and budget constraints, availability of testing materials and resources. A brief review of existing UQ methods for fatigue properties with sparse data is given. Following this, a new method, called Hierarchical Bayesian data augmentation (HBDA) is proposed to integrate the hierarchical Bayesian modeling (HBM) and Bayesian data augmentation (BDA) to deal with sparse data problem specifically for fatigue S-N curves. The key idea is to use: (1) HBM for analyzing the variability of S-N curves both within one stress level and across stress levels; (2) BDA to build up a large-size sample of fatigue life data based on the observed sparse samples. Four strategies to estimate the probabilistic S-N curves with sparse data are proposed: (1) hierarchical Bayesian modeling (HBM) only, (2) Bayesian data augmentation (BDA) only, (3) posterior information from HBM used as prior information for BDA (HBM + BDA), and (4) augmented data from BDA used by HBM (BDA + HBM). The strategy (3) and (4) are named HBDA hereafter. Next, the four strategies are validated and compared using aluminum alloy data and laminate panel data from open literature. Convergence study and confidence estimation is performed, and it is shown that the HBDA methods (i.e., HBM + BDA or BDA + HBM) have better performance compared with the classical method and HBM/BDA alone. The performance gain is especially significant when the number of available data samples is small. Finally, the proposed methodology is applied to a practical engineering problem for fatigue property quantification of the demolished Pearl Harbor Memorial Bridge, where only limited samples are available for testing. Conclusions and future work are drawn based on the proposed study.
AB - A novel statistical uncertainty quantification (UQ) method for fatigue S-N curves with sparse data is proposed in this paper. Sparse data observation is very common in fatigue testing due to various reasons, such as time and budget constraints, availability of testing materials and resources. A brief review of existing UQ methods for fatigue properties with sparse data is given. Following this, a new method, called Hierarchical Bayesian data augmentation (HBDA) is proposed to integrate the hierarchical Bayesian modeling (HBM) and Bayesian data augmentation (BDA) to deal with sparse data problem specifically for fatigue S-N curves. The key idea is to use: (1) HBM for analyzing the variability of S-N curves both within one stress level and across stress levels; (2) BDA to build up a large-size sample of fatigue life data based on the observed sparse samples. Four strategies to estimate the probabilistic S-N curves with sparse data are proposed: (1) hierarchical Bayesian modeling (HBM) only, (2) Bayesian data augmentation (BDA) only, (3) posterior information from HBM used as prior information for BDA (HBM + BDA), and (4) augmented data from BDA used by HBM (BDA + HBM). The strategy (3) and (4) are named HBDA hereafter. Next, the four strategies are validated and compared using aluminum alloy data and laminate panel data from open literature. Convergence study and confidence estimation is performed, and it is shown that the HBDA methods (i.e., HBM + BDA or BDA + HBM) have better performance compared with the classical method and HBM/BDA alone. The performance gain is especially significant when the number of available data samples is small. Finally, the proposed methodology is applied to a practical engineering problem for fatigue property quantification of the demolished Pearl Harbor Memorial Bridge, where only limited samples are available for testing. Conclusions and future work are drawn based on the proposed study.
KW - Bayesian data augmentation
KW - Fatigue probabilistic S-N curve
KW - Sparse data
KW - hierarchical Bayesian model
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U2 - 10.1016/j.ijfatigue.2020.105511
DO - 10.1016/j.ijfatigue.2020.105511
M3 - Article
AN - SCOPUS:85078235239
SN - 0142-1123
VL - 134
JO - International Journal of Fatigue
JF - International Journal of Fatigue
M1 - 105511
ER -