基于贝叶斯理论的低循环疲劳寿命模型不确定性量化

doi:10.7527/S1000-6893.2017.220832

固体力学与飞行器总体设计

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基于贝叶斯理论的低循环疲劳寿命模型不确定性量化

王荣桥^1,2,3, 刘飞¹, 胡殿印^1,2,3, 李达¹

1. 北京航空航天大学能源与动力工程学院, 北京 100083;
2. 先进航空发动机协同创新中心, 北京 100083;
3. 航空发动机结构强度北京市重点实验室, 北京 100083

收稿日期:2016-10-08 修回日期:2017-05-31 出版日期:2017-09-15 发布日期:2017-06-02
通讯作者: 胡殿印 E-mail:hdy@buaa.edu.cn
基金资助:
国家自然科学基金（51675024，51305012，51375031）；航空科学基金（2014ZB51）

Uncertainty quantification in low cycle fatigue life model based on Bayesian theory

WANG Rongqiao^1,2,3, LIU Fei¹, HU Dianyin^1,2,3, LI Da¹

1. School of Energy and Power Engineering, Beihang University, Beijing 100083, China;
2. Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100083, China;
3. Beijing Key Laboratory of Aero-Engine Structure and Strength, Beijing 100083, China

Received:2016-10-08 Revised:2017-05-31 Online:2017-09-15 Published:2017-06-02
Supported by:
National Natural Science Foundation of China (51675024,51305012,51375031);Aeronautical Science Foundation of China (2014ZB51)

摘要/Abstract

摘要：

为量化低循环疲劳寿命模型中的不确定性因素，利用贝叶斯理论，采用经典的模型校准形式确立了寿命模型的不确定性量化形式，并结合正态性检验对误差项进行验证；应用马尔可夫链-蒙特卡罗（MCMC）算法获得了模型参数后验分布的抽样样本，在小子样试验数据条件下确定了低循环疲劳寿命的95%不确定性区间，较好地覆盖了寿命的分散性；对参数样本进行了相关性分析，并将异方差回归概率模型与贝叶斯概率模型进行了比较。最后，利用Morris全局灵敏度分析方法获得了Manson-Coffin模型参数的全局灵敏度指标；同时，验证了在模型参数对先验信息敏感，或者说在先验信息影响极大的情况下，采用无信息先验处理方法的合理性。

关键词: 贝叶斯理论, 不确定性量化, 低循环疲劳, 概率模型, 全局灵敏度

Abstract:

To quantify the uncertainties in the model for low cycle fatigue life prediction, the classic model calibration method is applied using Bayesian theory, and the error term was verified by the normality test. Posterior distribution of the model parameter samples is obtained by Markov Chain-Monte Carlo (MCMC) simulation. An application is presented where a 95% interval of fatigue life prediction well describes the dispersity in real tests with small data samples. Correlation analysis of the samples of parameters is conducted to establish the heteroscedastic regression model. Comparison of the two models shows that the heteroscedastic regression model is questionable in uncertainty quantification performance. Morris global sensitivity analysis method is applied to quantify the sensitivity of the parameters in Manson-Coffin model, indicating that the non-informative prior is reasonable if posterior distribution is sensitive to the prior.

Key words: Bayesian theory, uncertainty quantification, low cycle fatigue, probabilistic model, global sensitivity

中图分类号:

王荣桥, 刘飞, 胡殿印, 李达. 基于贝叶斯理论的低循环疲劳寿命模型不确定性量化[J]. 航空学报, 2017, 38(9): 220832-220832.

WANG Rongqiao, LIU Fei, HU Dianyin, LI Da. Uncertainty quantification in low cycle fatigue life model based on Bayesian theory[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(9): 220832-220832.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于贝叶斯理论的低循环疲劳寿命模型不确定性量化

Uncertainty quantification in low cycle fatigue life model based on Bayesian theory

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