腐蚀条件下基于残差修正的飞机结构寿命灰色马氏链预测
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摘要
针对在役飞机结构腐蚀检修数据样本量小且随机波动性大的特点,首先基于灰色理论建立遭受腐蚀损伤的飞机结构使用寿命预测模型。其次为提高模型预测精度,引入马氏链转移方程对残差进行修正,得到飞机结构腐蚀寿命的灰色马氏链预测模型。最后对收集的某航空公司经典机型机队11架飞机后货舱隔框结构的腐蚀检修数据进行算例分析。预测结果表明:这类隔框结构在机龄约为15a时达到2级腐蚀状态,使用寿命相应终止。按结构维修手册要求需对其进行更换,经过残差修正的灰色马氏链预测值与实际值的平均相对误差为0.44%,明显低于未修正的灰色预测平均相对误差1.64%,达到工程问题的预测精度要求,而且预测结果与民航飞机结构腐蚀维修经验基本吻合,说明所建模型可用于腐蚀条件下的在役飞机结构寿命预测。
Due to the limited sample sizes and random fluctuations of actual structure corrosion data of aircrafts in service,a lifetime prediction model of corroded aircraft structure was built based on grey theory.A Markov transfer equation was introduced to modify the residual error in order to improve the prediction accuracy of above model.The corrosion maintenance data of frame structure in cargo of a fleet containing 11 aircrafts with same classic type were collected to make the numerical analysis.The results show that the frame structure should be replaced according to the maintenance manuals because it will reach the second corrosion state in the age of 15 years,which means this kind of frame structure will be failure.The average relative error between predicted value of improved grey Markov model and actual value is 0.44%,obviously lower than that of uncorrected gery model 1.64%,and meets the requirements of engineering accuracy.Moreover,the predicted result bsaed on the model conforms to the actual outcomes of aircraft frame structure in civil aviation,which indicates that proposed model can be used to predict the lifetime for aircraft structure in service in corrosion environment.
Due to the limited sample sizes and random fluctuations of actual structure corrosion data of aircrafts in service,a lifetime prediction model of corroded aircraft structure was built based on grey theory.A Markov transfer equation was introduced to modify the residual error in order to improve the prediction accuracy of above model.The corrosion maintenance data of frame structure in cargo of a fleet containing 11 aircrafts with same classic type were collected to make the numerical analysis.The results show that the frame structure should be replaced according to the maintenance manuals because it will reach the second corrosion state in the age of 15 years,which means this kind of frame structure will be failure.The average relative error between predicted value of improved grey Markov model and actual value is 0.44%,obviously lower than that of uncorrected gery model 1.64%,and meets the requirements of engineering accuracy.Moreover,the predicted result bsaed on the model conforms to the actual outcomes of aircraft frame structure in civil aviation,which indicates that proposed model can be used to predict the lifetime for aircraft structure in service in corrosion environment.
引文
[1]陈群志,康献海,刘健光,等.军用飞机腐蚀防护与日历寿命研究[J].中国表面工程,2010,23(4):1-6.
[2]HARLOW D G,WEI R P.Probability approach for prediction of corrosion and corrosion fatigue life[J].American Institute of Aeronautics and Astronautics Journal,1994,32(10):2073-2079.
[3]王晓光,何宇廷,张海威,等.预应力腐蚀对2A12-T4铝合金疲劳寿命的影响[J].腐蚀与防护,2013,34(6):475-478.
[4]GRUENBERG K M,CRAIG B A,HILLBERRY B M,et al.Predicting fatigue life of pre-corroded 2024-T3aluminum[J].International Journal of Fatigue,2004,26(6):629-640.
[5]WALDE K V,HILLBERRY B M.Characterization of pitting damage and prediction of remaining fatigue life[J].International Journal of Fatigue,2008(30):106-118.
[6]SRIAMAN M R,PIDAPATI R M.Life prediction of aircraft aluminum subjected to pitting corrosion under fatigue condition[J].Journal of Aircraft,2009,46(4):1253-1259.
[7]XIANG Y,LIU Y.EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens[J].Engineering Fracture Mechanics,2010,77(8):1314-1324.
[8]耿德平,宋庆功.航空材料腐蚀疲劳研究进展[J].腐蚀与防护,2011,32(3):206-209.
[9]刘治国,李旭东,穆志韬,等.航空铝合金材料腐蚀坑形状特征[J].腐蚀与防护,2014,35(2):128-132.
[10]张蕾,刘慧丛,朱立群,等.局部修复对典型环境中飞机外部结构件腐蚀的影响及腐蚀当量关系修正[J].腐蚀与防护,2014,35(8):833-837.
[11]刘延利,钟群鹏,王宇魁.铝合金预腐蚀与疲劳性能灰色模型研究[J].北京航空航天大学学报,2001,27(2):129-132.
[12]刘成臣,徐胜,王浩伟,等.基于灰色模型和神经网络的铝合金腐蚀预测对比[J].装备环境工程,2013,10(3):27-31.
[13]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2005.
[14]刘刚,朱金福.基于灰色新陈代谢马尔可夫模型的飞行事故预测[J].中国安全科学学报,2007,17(5):17-21.
[15]CALEYO F,VELZQUEZ J C,VALOR A,et al.Markov chain modelling of pitting corrosion in underground pipelines[J].Corrosion Science,2009,51(9):2197-2207.
[16]杨灿生,黄国忠,陈艾吉,等.基于灰色-马氏链理论的建筑施工事故预测研究[J].中国安全科学学报,2011,21(10):102-106.
[17]徐建新,杨杰.煤矿百万吨死亡率动态无偏灰色马氏链预测[J].中国安全科学学报,2012,22(3):122-127.
[18]陈钊,徐阿猛.基于灰色马尔科夫模型的钻孔瓦斯流量预测[J].中国安全科学学报,2014,22(3):79-85.
[19]李大伟,徐浩军,刘东亮,等.改进的灰色马尔科夫模型在飞行事故率预测中的应用[J].中国安全科学学报,2009,19(9):53-58.
[20]甘旭升,端木京顺,田井远.基于灰色马尔科夫模型的严重飞行事故频数预测[J].空军工程大学学报(自然科学版),2004,5(1):18-22.
[21]刘数,王燕,胡凤阁.对灰色预测模型残差问题的探讨[J].统计与决策,2008(1):9-11.
[22]陈奎,张天云,卢柏林,等.基于马尔科夫的灰色残差GM(1,1)模型在塑料老化行为预测中的应用[J].重庆大学学报,2014,37(5):71-76.
[23]AC-121-65航空器结构持续完整性大纲[S].
[2]HARLOW D G,WEI R P.Probability approach for prediction of corrosion and corrosion fatigue life[J].American Institute of Aeronautics and Astronautics Journal,1994,32(10):2073-2079.
[3]王晓光,何宇廷,张海威,等.预应力腐蚀对2A12-T4铝合金疲劳寿命的影响[J].腐蚀与防护,2013,34(6):475-478.
[4]GRUENBERG K M,CRAIG B A,HILLBERRY B M,et al.Predicting fatigue life of pre-corroded 2024-T3aluminum[J].International Journal of Fatigue,2004,26(6):629-640.
[5]WALDE K V,HILLBERRY B M.Characterization of pitting damage and prediction of remaining fatigue life[J].International Journal of Fatigue,2008(30):106-118.
[6]SRIAMAN M R,PIDAPATI R M.Life prediction of aircraft aluminum subjected to pitting corrosion under fatigue condition[J].Journal of Aircraft,2009,46(4):1253-1259.
[7]XIANG Y,LIU Y.EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens[J].Engineering Fracture Mechanics,2010,77(8):1314-1324.
[8]耿德平,宋庆功.航空材料腐蚀疲劳研究进展[J].腐蚀与防护,2011,32(3):206-209.
[9]刘治国,李旭东,穆志韬,等.航空铝合金材料腐蚀坑形状特征[J].腐蚀与防护,2014,35(2):128-132.
[10]张蕾,刘慧丛,朱立群,等.局部修复对典型环境中飞机外部结构件腐蚀的影响及腐蚀当量关系修正[J].腐蚀与防护,2014,35(8):833-837.
[11]刘延利,钟群鹏,王宇魁.铝合金预腐蚀与疲劳性能灰色模型研究[J].北京航空航天大学学报,2001,27(2):129-132.
[12]刘成臣,徐胜,王浩伟,等.基于灰色模型和神经网络的铝合金腐蚀预测对比[J].装备环境工程,2013,10(3):27-31.
[13]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2005.
[14]刘刚,朱金福.基于灰色新陈代谢马尔可夫模型的飞行事故预测[J].中国安全科学学报,2007,17(5):17-21.
[15]CALEYO F,VELZQUEZ J C,VALOR A,et al.Markov chain modelling of pitting corrosion in underground pipelines[J].Corrosion Science,2009,51(9):2197-2207.
[16]杨灿生,黄国忠,陈艾吉,等.基于灰色-马氏链理论的建筑施工事故预测研究[J].中国安全科学学报,2011,21(10):102-106.
[17]徐建新,杨杰.煤矿百万吨死亡率动态无偏灰色马氏链预测[J].中国安全科学学报,2012,22(3):122-127.
[18]陈钊,徐阿猛.基于灰色马尔科夫模型的钻孔瓦斯流量预测[J].中国安全科学学报,2014,22(3):79-85.
[19]李大伟,徐浩军,刘东亮,等.改进的灰色马尔科夫模型在飞行事故率预测中的应用[J].中国安全科学学报,2009,19(9):53-58.
[20]甘旭升,端木京顺,田井远.基于灰色马尔科夫模型的严重飞行事故频数预测[J].空军工程大学学报(自然科学版),2004,5(1):18-22.
[21]刘数,王燕,胡凤阁.对灰色预测模型残差问题的探讨[J].统计与决策,2008(1):9-11.
[22]陈奎,张天云,卢柏林,等.基于马尔科夫的灰色残差GM(1,1)模型在塑料老化行为预测中的应用[J].重庆大学学报,2014,37(5):71-76.
[23]AC-121-65航空器结构持续完整性大纲[S].