基于贝叶斯理论的低循环疲劳寿命模型不确定性量化
收稿日期: 2016-10-08
修回日期: 2017-05-31
网络出版日期: 2017-06-02
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
Received date: 2016-10-08
Revised date: 2017-05-31
Online published: 2017-06-02
Supported by
National Natural Science Foundation of China (51675024,51305012,51375031);Aeronautical Science Foundation of China (2014ZB51)
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。
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 . DOI: 10.7527/S1000-6893.2017.220832
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.
[1] 胡殿印, 裴月, 王荣桥, 等. 涡轮盘结构概率设计体系的研究[J]. 航空学报, 2008, 29(5): 1144-1149. HU D Y, PEI Y, WANG R Q, et al. Research of probabilistic design system for turbine disk structure[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(5): 1144-1149 (in Chinese).
[2] 胡殿印, 裴月, 王荣桥, 等. 涡轮盘低循环疲劳的概率设计[J]. 推进技术, 2008, 29(4): 481-487. HU D Y, PEI Y, WANG R Q, et al. Probability design of low cycle fatigue for turbine disk[J]. Journal of Propulsion Technology, 2008, 29(4): 481-487 (in Chinese).
[3] 汤咏. 基于不确定性的航空发动机涡轮盘概率疲劳寿命预测模型[D]. 成都: 电子科技大学, 2013: 4-5. TANG Y. Fatigue life prediction model of aeroengine turbine disk based on uncertainty[D]. Chengdu: University of Electronic Science and Technology, 2013: 4-5 (in Chinese).
[4] BALDWIN J D, THACKER J G. A strain-based fatigue reliability analysis method[J]. Journal of Mechanical Design, 1995, 117(2): 229-234.
[5] ZHAO J, TANG J, WU H C. A reliability assessment method in strain-based fatigue life analysis[J]. Journal of Pressure Vessel Technology, 1998, 120(1): 99-104.
[6] 唐俊星, 陆山. 某涡轮盘低循环疲劳概率寿命数值模拟[J]. 航空动力学报, 2006, 21(4): 706-710. TANG J X, LU S. Numerical simulation of low cycle fatigue life of a turbine disk[J]. Journal of Aerospace Power, 2006, 21(4): 706-710 (in Chinese).
[7] BARGMANN H, RVSTENBERG I, DEVLUKIA J. Reliability of metal components in fatigue: A simple algorithm for the exact solution[J]. Fatigue & Fracture of Engineering Materials & Structures, 1994, 17(12): 1445-1457.
[8] 朱顺鹏, 黄洪钟, 甘露萍, 等. 基于模型不确定性量化的涡轮盘结构概率寿命预测[C]//中国运筹学会可靠性分会可靠性学术会议. 北京: 中国运筹学会, 2013: 261-269. ZHU S P, HUANG H Z, GAN L P, et al. Probabilistic life prediction for aircraft turbine disk based on model uncertainty quantification[C]//Reliability Academic Conference of the Reliability Branch of China Operational Research Society. Beijing: China Operational Research Society, 2013: 261-269 (in Chinese).
[9] ACEBAL R. Guide for the verification and validation of computational fluid dynamics simulation: AIAA-1998-0077[R]. Reston, VA: AIAA, 1998.
[10] KENNEDY M C, O’HAGAN A. Bayesian calibration of computer models[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2001, 63(3): 425-464.
[11] ANGEL U, SANKARAN M, THOMAS L P. Quanlification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty[J]. Realibity Engineering and System Safety, 2011, 96(9): 1114-1125.
[12] 高阳, 白广忱, 张瑛莉. 涡轮盘低循环疲劳寿命的概率分析[J]. 航空动力学报, 2009, 24(4): 804-809. GAO Y, BAI G C, ZHANG Y L. Probability analysis for the low cycle fatigue life of a turbine disk[J]. Journal of Aerospace Power, 2009, 24(4): 804-809 (in Chinese).
[13] 中国金属学会高温材料分会. 中国高温合金手册[M]. 北京: 中国质检出版社, 2012: 870-874. High Temperature Materials Branch of Chinese Society of Metals. China high temperature alloy handbook[M]. Beijing: China Zhijian Publishing House, 2012: 870-874 (in Chinese).
[14] SHANKAR S. Uncertainty qualification in fatigue damage prognosis[C]//Annual Conference of the Prognostics and Health Management Society, 2009: 1-13.
[15] CHAO M A, MATHÉ P, SCHLO?HAUER V, et al. Calibration and uncertainty quantification of gas turbines performance models: GT 2015-42392[R]. New York: ASME, 2015.
[16] 姚伟, 白广忱. 基于Fourier正交基神经网络的涡轮盘低循环疲劳可靠性分析[J]. 装备制造技术, 2014(10): 132-134. YAO W, BAI G C. Reliability analysis of low cycle fatigue of turbine disk based on Fourier orthogonal neural network[J]. Equipment Manufacturing Technology, 2014(10): 132-134 (in Chinese).
[17] 高阳, 白广忱, 陈冲. 基于RBF神经网络的涡轮盘疲劳可靠性分析[J]. 机械设计, 2009, 26(5): 8-14. GAO Y, BAI G C, CHEN C. Fatigue reliability analysis of turbine disk based on RBF neural network[J]. Journal of Machine Design, 2009, 26(5): 8-14 (in Chinese).
[18] 唐俊星, 陆山. 轮盘应变疲劳寿命可靠性分析方法[J]. 推进技术, 2005, 26(4): 344-347. TANG J X, LU S. Reliability analysis method for the strain fatigue life of a disk[J]. Journal of Propulsion Technology, 2005, 26(4): 344-347 (in Chinese).
[19] 傅惠民. 线性异方差回归分析[J]. 航空学报, 1994, 15(3): 295-302. FU H M. Linear variance regression analysis[J]. Acta Aeronautica et Astronautica Sinica, 1994, 15(3): 295-302 (in Chinese).
[20] GARNER R H, O’NEILL R V, MANKIN J B. A comparison of sensitivity and error analysis based on a stream ecosystem model[J]. Ecological Modelling, 1981, 12(3): 173-190.
[21] 孙艳伟, 把多铎, 王文川, 等. SWMM模型径流参数全局灵敏度分析[J]. 农业机械学报, 2012, 43(7): 43-49. SUN Y W, BA D D, WANG W C, et al. Global sensitivity analysis of runoff parameters of SWMM model[J]. Chinese Journal of Agricultural Machinery, 2012, 43(7): 43-49 (in Chinese).
[22] 钱文学, 尹晓伟, 何雪浤, 等. 压气机轮盘疲劳寿命影响参量的灵敏度分析[J]. 东北大学学报:自然科学版, 2006, 27(6): 677-680. QIAN W X, YIN X W, HE X H, et al. Sensitivity analysis of influential parameter on the fatigue life of compressor disk[J]. Journal of Northeastern University: Natural Science, 2006, 27(6): 677-680 (in Chinese).
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