Aiming at the small failure probability events and the strong non-linearity of limit state function in the fatigue reliability analysis of aero-engine Limited Life Parts (ELLP), a fatigue reliability analysis method based on the Auto Updating Monte Carlo Radius-Outside Adaptive Importance Sampling (AUMCROAIS) is proposed. In this method, the Monte Carlo Adaptive Importance Sampling (MCAIS) is used to approach the Most Probable Point (MPP) efficiently, then the polar coordinate sampling is employed by taking the approximate MPP as the sampling center. An active learning function is constructed to optimize the near-limit state function and sampling radius, so that the optimal sampling radius can be updated. The optimal sampling radius can be determined through continuous updating, accelerating the convergence of failure probability. This method improves the convergence speed of MPP points and ensures the accuracy of calculation. It solves the problem of reliability calculation of small failure probability events and strong non-linear limit state function. Finally, taking a compressor disk of an engine as an application, and the efficiency, robustness and simulation accuracy of the proposed method are verified by comparing with the traditional Monte Carlo Simulation (MCS) method, the Monte Carlo Radius-Outside Adaptive Importance Sampling (MCROAIS), and First-Order Reliability Method (FORM).
[1] U.S. Department of Transportation, Federal Aviation Administration. Guidance material for aircraft engine life limit parts requirement:Advisory Circular 33.70-1[R]. Washington, D.C.:FAA, 2009:30-50.
[2] VITTALS S, HAJELA P, JOSHI A. Review of approaches to gas turbine life management:AIAA-2004-4372[R]. Reston,VA:AIAA, 2004.
[3] BEACHKOFSKI B K, GRANDHI R V. Probabilistic system reliability for a turbine engine airfoil[C]//ASME Turbo Expo 2004:Power for Land, Sea, and Air. New York:ASME, 2004:171-179.
[4] MELIS M E, ZARETSKY E V,AUGUST R. Probabilistic analysis of aircraft gas turbine disk life and reliability[J]. Journal of Propulsion and Power, 1999, 15(5):658-666.
[5] GAO H, FEI C, BAI G. Reliability-based low-cycle fatigue damage analysis for turbine blade with thermo-structural interaction[J].Aerospace Science & Technology, 2016, 49:289-300.
[6] ZHU S P, LIU Q, PENG W, et al. Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks[J]. International Journal of Mechanical Sciences, 2018,142:502-517.
[7] ZHU S P, LIU Q, ZHOU J. Fatigue reliability assessment of turbine discs under multi-source uncertainties[J]. Fatigue & Fracture of Engineering Materials & Structures, 2018,4:1291-1305.
[8] HU D Y, MA Q H, SHANG L H,et al. Creep-fatigue behavior of turbine disc of superalloy GH720Li at 650℃ and probabilistic creep-fatigue modeling[J]. Materials Science & Engineering A, 2016,670:17-25.
[9] WANG R Q, LIU X, HU D Y, et al.Zone-based reliability analysis on fatigue life of GH720Li turbine disk concerning uncertainty quantification[J]. Aerospace Science and Technology, 2017,70:300-309.
[10] 李岩, 张曙光, 宫綦. 一种改进的航空发动机结构概率风险评估方法[J]. 航空学报, 2016, 37(2):597-608. LI Y,ZHANG S G,GONG Q. An improved probabilistic risk assessment method of structural parts for aeroengine[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(2):597-608(in Chinese).
[11] 陈志英, 谷裕, 周平, 等. 基于应力应变场强法的轮盘疲劳可靠性分析方法[J]. 推进技术, 2018,39(2):433-439. CHEN Z Y,GU Y,ZHOU P,et al. Fatigue reliability analysis of disk based on stress-strain field intensity method[J]. Journal of Propulsion Technology, 2018,39(2):433-439(in Chinese).
[12] 刘君强, 谢吉伟,左洪福,等.基于随机Wiener过程的航空发动机剩余寿命预测[J].航空学报,2015,36(2):564-574. LIU J Q, XIE J W, ZUO H F, et al. Residual lifetime prediction for aeroengines based on Wiener process with random effects[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(2):564-574(in Chinese).
[13] 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).
[14] 皮骏, 马圣, 贺嘉诚, 等. 遗传算法优化的SVM在航空发动机磨损故障诊断中的应用[J]. 润滑与密封, 2018, 43(10):95-103. PI J, MA S, HE J C,et al. Application of genetic algorithm optimized SVM in aeroengine wear fault diagnosis[J]. Lubrication Engineering, 2018, 43(10):95-103(in Chinese).
[15] TOMASSON E, SODER L. Improved importance sampling for reliability evaluation of composite power systems[J]. IEEE Transactions on Power Systems, 2017,32(3):2426-2434.
[16] LI L, LU Z Z. Interval optimization based line sampling method for fuzzy and random reliability analysis[J]. Journal of Applied Mathematics, 2014,38(13):3124-3135.
[17] XIONG B, TAN H F. A robust and efficient structural reliability method combining radial-based importance sampling and Kriging[J]. Science China Technological Sciences, 2018,61(5):724-734.
[18] MELCHERS R E. Search-based importance sampling[J]. Structural Safety,1990, 9:117-128
[19] AU S K, BECK J L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety, 1999, 21:135-158.
[20] SANKARAN M, PRAKASB L. Adaptive simulation for system reliability analysis of large structures[J].Computers and Stmctures,2000,77:725-734.
[21] 黄毅,王明政,颜寒,等. 快堆中心柱低周疲劳可靠性评价[J]. 原子能科学技术,2018,52(1):118-125. HUANG Y, WANG M Z, YAN H, et al. Low cycle fatigue reliability evaluation of central column in fast reactor[J]. Atomic Energy Science and Technology, 2018,52(1):118-125(in Chinese).
[22] 陈向前,董聪,闫阳.自适应重要抽样方法的改进算法[J]. 工程力学,2012,29(11):123-128. CHEN X Q, DONG C, YAN Y. Improved adaptive important sampling algorithm[J]. Engineering Mechanics, 2012,29(11):123-128(in Chinese).
[23] 马纪明,詹晓燕,曾声奎.基于自适应重要抽样的可靠性分析方法[J]. 北京航空航天大学学报,2011,37(9):1142-1150. MA J M, ZHAN X Y, ZENG S K. Reliability analysis method based on adaptive importance sampling[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011,37(9):1142-1150(in Chinese).
[24] 戴鸿哲,赵威,王伟.结构可靠性高效自适应重要抽样方法[J].力学学报,2011,4(6):1133-1140. DAI H Z, ZHAO W, WANG W. An efficient adaptive important sampling method for structural reliability analysis[J].Chinese Journal of Theoretical and Applied Mechanics, 2011,4(6):1133-1140(in Chinese).
[25] U. S. Department of Transportation, Federal Aviation Administration Airworthiness Standards. Aircraft engines:CFR 14 Part 33[S]. Washington, D.C.:FAA,2009:10-30.
[26] 吴学仁.飞机结构金属材料力学性能手册:静强度疲劳-耐久性[M].北京:航空工业出版社, 1997:30-35. WU X R.Handbook of mechanical prosperities of aircraft structural metals:Static strength/durability[M]. Beijing:Aviation Industry Press, 1997:30-35(in Chinese).
CJA