基于失效概率的全局灵敏度分析可以度量各个基本随机变量的不确定性对失效概率的影响程度，对如何降低结构的失效概率具有指导意义。基于交叉熵方法和空间分割提出一种新全局可靠性灵敏度分析方法。该方法采用交叉熵法自适应的确定重要抽样密度函数，有效地回避了传统重要抽样中设计点位置和个数求解的困难。基于评估失效概率所使用的样本，利用空间分割方法计算各个输入随机变量的全局可靠性灵敏度指标，能够提高样本的利用率和计算效率。文中利用一个数值算例和两个工程算例验证了所提方法的计算效率和精度。
Failure-probability-based sensitivity analysis is capable to measure the effects of uncertainties of input variables on failure probability, and can provide guidance on how to reduce the failure probability of a structure. In this paper, a new method is proposed to estimate the global reliability sensitivity indices, based on cross entropy method and space partition. The proposed method adaptively determines the important sampling density function by cross entropy method, avoiding the issue of determining the positions and number of the design points. Based on the identical set of samples used to estimate failure probability, the global reliability sensitivity index of each input random variable is calculated by the space partition method, which significantly improves the utilization of the samples and computational efficiency. A numerical and two engineering examples are used to illustrate the accuracy and efficiency of the proposed method.
[1] SALTELLI A. Sensitivity analysis for importance assessment[M]. New Dersey:Wiley, 2002:579-590.[2] 吕震宙, 宋述芳, 李洪双, 等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京:科学出版社, 2009:6-8. LU Z Z, SONG S F, LI H S, et al. Reliability and sensitivity analysis of structure and mechanism[M]. Beijing:Science Press, 2009:6-8(in Chinese).[3] SALTELLI A. Global sensitivity analysis:The primer[M]. New Dersey:Wiley, 2004:1-42.[4] HELTON J C, DAVIS F J. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems[J]. Reliability Engineering & System Safety, 2003, 81(1):23-69.[5] SALTELLI A, MARIVOET J. Non-parametric statistics in sensitivity analysis for model output:A comparison of selected techniques[J]. Reliability Engineering & System Safety, 1990, 28(2):229-253.[6] IMAN R L, HORA S C. A robust measure of uncertainty importance for use in fault tree system analysis[J]. Risk Analysis, 1990, 10(3):401-406.[7] SOBOL I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics & Computers in Simulation, 2001, 55(1-3):271-280.[8] BORGONOVO E. A new uncertainty importance measure[J]. Reliability Engineering & System Safety, 2007, 92(6):771-784.[9] 吕震宙, 李璐祎, 宋述芳, 等. 不确定性结构系统的重要性分析理论与求解方法[M]. 北京:科学出版社, 2015:1-8. LU Z Z, LI L Y, SONG S F, et al. The important analysis theory and the solution method of the uncertainty structure system[M]. Beijing:Science Press,2015:1-8(in Chinese).[10] CUI L J, LU Z Z, ZHAO X P. Moment-independent importance measure of basic random variable and its probability density evolution solution[J]. Science China Technological Sciences, 2010, 53(4):1138-1145.[11] LI L, LU Z Z, FENG J, et al. Moment-independent importance measure of basic variable and its state dependent parameter solution[J]. Structural Safety, 2012, 38(38):40-47.[12] BORGONOVO E, CASTAINGS W, TARANTOLA S. Model emulation and moment-independent sensitivity analysis:An application to environmental modelling[J]. Environmental Modelling & Software, 2012, 34(8):105-115.[13] WEI P F, LU Z Z, HAO W R, et al. Efficient sampling methods for global reliability sensitivity analysis[J]. Computer Physics Communications, 2012, 183(8):1728-1743.[14] 任超, 李洪双. 基于失效概率的全局重要性测度分析的交叉熵方法[J]. 西北工业大学学报, 2017, 35(3):536-544. REN C, LI H S. Cross-entropy method for failure probability based global importance measure analysis[J]. Northwestern Polytechnical University, 2017, 35(3):536-544(in Chinese).[15] RUBINSTEIN R Y. Optimization of computer simulation models with rare events[J]. European Journal of Operational Research, 1997, 99(1):89-112.[16] RUBINSTEIN R Y. The cross-entropy method for combinatorial and continuous optimization[J]. Methodology & Computing in Applied Probability, 1999, 1(2):127-190.[17] ZHAI Q, YANG J, ZHAO Y. Space-partition method for the variance-based sensitivity analysis:Optimal partition scheme and comparative study[J]. Reliability Engineering & System Safety, 2014, 131(6):66-82.[18] PLISCHKE E. An adaptive correlation ratio method using the cumulative sum of the reordered output[J]. Reliability Engineering & System Safety, 2012, 107:149-156.[19] LI C, MAHADEVAN S. An efficient modularized sample-based method to estimate the first-order Sobol' index[J]. Reliability Engineering & System Safety, 2016, 153:110-121.[20] PLISCHKE E, BORGONOVO E, SMITH C L. Global sensitivity measures from given data[J]. European Journal of Operational Research, 2013, 226(3):536-550.[21] 李洪双, 马远卓. 结构可靠性分析与随机优化设计的统一方法[M]. 北京:国防工业出版社, 2015:129-139. LI H S, MA Y Z. Unified methods for structure reliability analysis and stochastic optimization design[M]. Beijing:National Defense Industry Press, 2015:129-139(in Chinese).[22] ZHOU C, LU Z, YUAN X. Use of relevance vector machine in structural reliability analysis[J]. Journal of Aircraft, 2013, 50(6):1726-1733.
CJA