·356 北京科技大学学报 2006年第4期 性，因而从工程应用角度来看，改进算法较传统算 45 法更可靠、更安全 4 一·改进方法 一传统方法 3 a TTCI值 参考文献 30 5 1]Provan J W.Probabilistic fracture mechanics and reliability. 2. Dordrecht:Martinus Nijhoff Publishers.1987 [2 Soprano A.Apicell A.Application of durability analysis to 1.0 glare aeronautical component.Int J Fatigue,1996(4):265 0.5 0 【童明波，郑=仲，王俊扬，等.飞机典型结构（紧固孔）原始 100020003000400050006000 疲劳质量研究.航空学报.198912)：595 飞行时间h 【4曹昌年，王志智，赵选民.紧固孔原始疲劳质量评定及符合 图5估计的TTC1分布概率密度比较(a,=127mm) 性检查.西北工业大学学报，1991)：15 Fig.5 Comparison of the estimated results (a,=1 27mm) 【习赵永翔.黄郁仲，高庆.铁道车辆☑50车轴钢的概率机械 性能.交通运输工程学报，20032)：11 (3)对每种参考裂纹水平下的TTCI值进行 【(胡仁伟，刘文器：结构原始疲劳质量分布确定方法的改进. 参数估计，从而得到EF$分布参数的方法，充分 北京航空航天大学学报，1999(1)：41 【刀熊振翔.插值多项式与插值样条.北京：国防工业出版社. 利用了裂纹扩展的信息，参数估计结果可靠随机 1995 性更小. [8 Li H X.Li L X.W ang J Y.Interpolation representation of (4)改进方法克服了样本数量带来的限制， feedforw and neural networks.Math Comput Modell,2008,37 很大程度上降低了分布参数的随机性，提高了估 (7,8):829 计结果的可靠性和有效性.同时，对传统方法的 [9 Chen Y.Kopp G A.Interpolation of wind-induced presaure time series with an artificial neural network.J Wind Eng Ind 改进没有增加计算的难度，相反计算更为简洁，适 Aerod小n,2002,90(6):589 合工程应用 L10 朱勇华.邰淑彩.孙韫玉。应用数理统计.武汉：武汉水利 (5)由于改进算法减小了传统算法的随机 电力大学出版社，1999 Advanced description method of the initial fatigue quality model YANG Moucun,NIE Hong School of Energy and Power Engineering.Najing University of Aemnautics and Astronautics,Nanjing 210016.China ABSTRACT An advanced description method of initial fatigue quality w as proposed,in which neural net- work interpolation is emplyed instead of Lagrange interpolation to compute the values of the time to crack initiation (TTCD and maximum likelihood estimation is used to estimate TTCI distribution parameters in- stead of mean rank estimation.Taking account into the randomicity encountered when only one group of TTCI values is used to estimate distribution parameters,several groups of TTCI distribution parameters were gained after maximum likelihood estimating for several groups of TTCI values corresponding to the given reference crack sizes.Then,equivalent initial flaw size distribut ion can be confimed based on the re- lations of several groups of TTCI distribut ion parameters.The fat igue test of some component and its initial fatigue quality analy sis show that the advanced method is feasible and reasonable. KEY WORDS fracture mechanics;initial fatigue quality (IFQ);parameter estimation;maximum likeli- hood estimation(MLE);neural netw ork;interpolation图 5 估计的 TTCI 分布概率密度比较( a r=1.27 mm) Fig.5 Comparison of the estimated results ( ar=1.27 mm) ( 3) 对每种参考裂纹水平下的 TTCI 值进行 参数估计, 从而得到 EIFS 分布参数的方法, 充分 利用了裂纹扩展的信息, 参数估计结果可靠, 随机 性更小. ( 4) 改进方法克服了样本数量带来的限制, 很大程度上降低了分布参数的随机性, 提高了估 计结果的可靠性和有效性.同时, 对传统方法的 改进没有增加计算的难度, 相反计算更为简洁, 适 合工程应用. (5) 由于改进算法减小了传统算法的随机 性, 因而从工程应用角度来看, 改进算法较传统算 法更可靠 、更安全. 参 考 文 献 [ 1] Provan J W.Probabilistic fractu re mechanics and reliabilit y . Dordrecht:Martinus Nijhoff Publishers, 1987 [ 2] Soprano A, Apicella A.Application of durability analysis t o glare aeronautical component.Int J Fatigue, 1996( 4) :265 [ 3] 童明波, 郑 仲, 王俊扬, 等.飞机典型结构( 紧固孔) 原始 疲劳质量研究.航空学报, 1989( 12) :595 [ 4] 曹昌年, 王志智, 赵选民.紧固孔原始疲劳质量评定及符合 性检查.西北工业大学学报, 1999( 1) :15 [ 5] 赵永翔, 黄郁仲, 高庆.铁道车辆 LZ50 车轴钢的概率机械 性能.交通运输工程学报, 2003( 2) :11 [ 6] 胡仁伟, 刘文 .结构原始疲劳质量分布确定方法的改进. 北京航空航天大学学报, 1999( 1) :41 [ 7] 熊振翔.插值多项式与插值样条.北京:国防工业出版社, 1995 [ 8] Li H X, Li L X, Wang J Y.Interpolation representation of f eedf orw ard neural networks.Math Comput Modell, 2003, 37 ( 7, 8) :829 [ 9] Chen Y, Kopp G A.Interpolation of w ind-induced pressu re time series with an artificial neural netw ork.J Wind Eng Ind Aerodyn, 2002, 90( 6) :589 [ 10] 朱勇华, 邰淑彩, 孙韫玉.应用数理统计.武汉:武汉水利 电力大学出版社, 1999 Advanced description method of the initial fatigue quality model Y ANG Moucun , NIE Hong S chool of Energy and Power Engineering, Nanjing Universit y of Aeronautics and Astronauti cs, Nanjing 210016, China ABSTRACT An advanced description method of initial fatigue quality w as proposed, in which neural net￾w ork interpolation is employed instead of Lag range interpolation to compute the values of the time to crack initiation ( TTCI) and maximum likelihood estimatio n is used to estimate TTCI distribution parameters in￾stead of mean rank estimatio n .Taking account into the randomicity encountered w hen only one g roup of TTCI values is used to estimate distribution parameters, several g roups of TTCI distribution parameters w ere g ained after maximum likelihood estimating fo r several g roups of TTCI values co rresponding to the g iven reference crack sizes .Then, equivalent initial flaw size distribution can be confirmed based on the re￾lations of several g roups of TTCI distribution parameters .The fatig ue test of some component and its initial fatigue quality analy sis show that the advanced method is feasible and reasonable. KEY WORDS fracture mechanics ;initial fatigue quality ( IFQ ) ;parameter estimation ;maximum likeli￾hood estimatio n ( M LE) ;neural netw ork ;interpolation · 356 · 北 京 科 技 大 学 学 报 2006 年第 4 期