基于密度权重的可靠性灵敏度分析方法
收稿日期: 2013-03-28
修回日期: 2013-05-17
网络出版日期: 2013-05-20
基金资助
航空科学基金（2011ZA53015）
Reliability Sensitivity Analysis Method Based on Weight Index of Density
Received date: 2013-03-28
Revised date: 2013-05-17
Online published: 2013-05-20
Supported by
Aeronautical Science Foundation of China(2011ZA53015)
为了提高可靠性灵敏度求解数字模拟法的效率，提出了一种变量空间确定性低偏差均匀抽样与样本点处联合概率密度函数构造权重相结合的方法，来估计可靠性灵敏度。该方法通过均匀样本点处联合概率密度函数的权重保证了可靠性灵敏度的估计值收敛于真值，而由低偏差抽样代替原问题中的联合概率密度抽样则可以保证更低的误差阶以及在小失效概率条件下抽得的样本有更高的可能性落入失效域，从而保证了所提方法具有更高的收敛速度。另外，所提方法可以采用与独立变量相同的步骤来估计相关变量情况下的可靠性灵敏度，计算简便，适用范围广。算例充分证明了所提方法的优越性。
吕召燕 , 吕震宙 , 李贵杰 , 唐樟春 . 基于密度权重的可靠性灵敏度分析方法[J]. 航空学报, 2014 , 35(1) : 179 -186 . DOI: 10.7527/S1000-6893.2013.0259
In order to improve the efficiency of digital simulation in approximating reliability sensitivity, a method is proposed which works by generating deterministic and low-discrepancy samples uniformly in the design space and applying the value of joint probability density function as a weight index at any sample. The weight indexes ensure the estimated values of the reliability sensitivity are converged to the true values. This way of getting points by low-discrepancy sampling instead of depending on a variable's probability density can ensure smaller error bounds and a higher possibility for the samples to fall into failure domain, so that the convergence speed becomes much higher for small failure probability events. Additionally, the steps to calculate the reliability sensitivity with related variables are the same as those with independent variables, which is another advantage that makes the method simpler and easily applicable. Several examples in this paper demonstrate the advantages of the proposed method sufficiently.
[1] Wu Y T, Monhant Y S. Variable screening and ranking using sampling based sensitivity measures[J]. Reliability Engineering and System Safety, 2006, 91(6): 634-647.
[2] Wu Y T. Computational methods for efficient structural reliability and reliability sensitivity analysis[J]. AIAA Journal, 1994, 32(8): 1717-1723.
[3] Schueller G I, Stix R. A critical appraisal of methods to determine failure probabilities[J]. Structural Safety, 1987, 4(4): 293-309.
[4] Melchers R E. Importance sampling in structural system[J]. Structural Safety, 1989, 6(1): 3-10.
[5] Ibrahim Y. Observations on applications of importance sampling in structural reliability analysis[J]. Structural Safety, 1991, 9(4): 269-281.
[6] Au S K, Beck J L. Estimation of small failure probabilities in high dimensions by subset simulation[J]. Probabilistic Engineering Mechanics, 2001, 16(4): 263-277.
[7] Au S K. On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment[D]. California: California Institute of Technology, 2001.
[8] Au S K. Reliability-based design sensitivity by efficient simulation[J]. Computers & Structures, 2005, 83(14): 1048-1061.
[9] Schuller G I, Pradlwarter H J, Koutsourelakis P S. A critical appraisal of reliability estimation procedures for high dimensions[J]. Probabilistic Engineering Mechanics, 2004, 19(4): 463-473.
[10] Schuller G I, Pradlwarter H J, Koutsourelakis P S. A comparative study of reliability estimation procedures for high dimension[C]//16th ASCE Engineering Mechanics Conference, 2003.
[11] Ditlevsen O, Olesen R, Mohr G. Solution of a class of load combination problems by directional simulation[J]. Structural Safety, 1987, 4(2): 95-109.
[12] Ditlevsen O, Melchers R E, Gluver H. General multi-dimensional probability integration by directional simulation[J]. Computers & Structures, 1990, 36(2): 355-368.
[13] Jinsuo N, Ellingwood B R. Directional methods for structural reliability analysis[J]. Structural Safety, 2000, 22(3): 233-249.
[14] Dai H Z, Wang W. Quasi-Monte Carlo method for structural reliability analysis[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(4): 666-671. (in Chinese) 戴鸿哲, 王伟. 结构可靠性分析的拟蒙特卡罗方法[J]. 航空学报, 2009, 30(4): 666-671.
[15] Feng M, Ghosn M. Modified subset simulation method for reliability analysis of structural systems[J]. Structural Safety, 2011, 33(4): 251-260.
[16] Fang G C, Lu Z Z, Wei P P. Modified subset simulation method for reliability and reliability sensitivity analysis of structural system[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(8): 1440-1447. (in Chinese) 房冠成, 吕震宙, 魏鹏飞. 结构系统可靠性及可靠性灵敏度分析的改进子集模拟法[J]. 航空学报, 2012, 33(8): 1440-1447.
[17] Hao W R, Lu Z Z, Tian L F. A novel method for analyzing variance based importance measure of correlated input variables[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(9): 1637-1643. (in Chinese) 郝文锐, 吕震宙, 田龙飞. 基于方差的相关输入变量重要性测度分析新方法[J]. 航空学报, 2011, 32(9): 1637-1643.
[18] Echard B, Gayton N, Lemaire M, et al. A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models[J]. Reliability Engineering and System Safety, 2013, 111: 232-240.
[19] Li G J, Lu Z Z, Wang P. Sensitivity analysis of non-probability reliability of uncertain structures[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(3): 501-507. (in Chinese) 李贵杰, 吕震宙, 王攀. 结构非概率可靠性灵敏度分析方法[J]. 航空学报, 2012, 33(3): 501-507.
[20] Mohsen R, Mahmoud M, Mehdi A M. A new efficient simulation method to approximate the probability of failure and most probable point[J]. Structural Safety, 2012, 39: 22-29.
[21] Yuan X K, Lu Z Z, Yue Z F. Bootstrap confidence interval of quantile function estimation for small samples[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(10): 1842-1849. (in Chinese) 袁修开, 吕震宙, 岳珠峰. 小样本下分位数函数的Bootstrap置信区间估计[J]. 航空学报, 2012, 33(10): 1842-1849.
[22] Niederreiter H. Random number generation and quasi-Monte Carlo methods[M]. Philadelphia: SIAM, 1992.
[23] Halton J H. On the efficiency of certain quasi-random sequences of points in evaluation multi-dimensional integrals[J]. Nurnerische Mathematik, 1960, 2(1): 84-90.
/
| 〈 |
|
〉 |
CJA