矩独立重要性分析的Kriging代理模型方法
收稿日期: 2015-07-10
修回日期: 2015-09-06
网络出版日期: 2015-09-10
基金资助
国家自然科学基金（51305350)；陕西省自然科学基金（2013JM6011)；西北工业大学基础研究基金（3102014JCQ01045)
A Kriging surrogate model method for moment-independent importance analysis
Received date: 2015-07-10
Revised date: 2015-09-06
Online published: 2015-09-10
Supported by
National Natural Science Foundation of China (51305350); Natural Science Foundation of Shaanxi Province (2013JM6011); Foundation Research Funds of Northwestern Polytechnical University (3102014JCQ01045)
结构重要性分析是结构不确定性分析的重要研究内容之一。作为一种矩独立的重要性测度指标，基于失效概率的重要性测度能够有效地反映输入变量的不确定性对结构失效概率的影响。然而，相比于其他形式的重要性测度，对基于失效概率的矩独立重要性测度进行高效准确的求解仍然存在一定的困难。基于此，结合Kriging代理模型提出了一种高效的矩独立重要性分析的新方法。所提方法首先通过较少的实验设计样本构建能够充分近似真实输入输出响应函数的Kriging代理模型，进而通过数值模拟策略对所构建的Kriging模型进行分析，最终求解得到各个输入变量基于失效概率矩独立重要性测度的主效应和总效应，给出各个输入变量对于失效概率的影响程度排序。相比于现有方法，所提方法由于引入Kriging代理模型极大地降低了对响应函数的计算次数，同时保证了重要性分析的计算精度。两个工程应用实例结果表明了所提方法在计算效率和计算精度方面的优势，体现了所提方法良好的适用性。
赵海龙 , 岳珠峰 , 刘伟 . 矩独立重要性分析的Kriging代理模型方法[J]. 航空学报, 2016 , 37(7) : 2234 -2241 . DOI: 10.7527/S1000-6893.2015.0248
Structural importance analysis is one of the research focuses on the fields of structural uncertainty analysis. As a kind of moment-independent importance measure index, the failure probability-based importance measure attracts attention of the researchers for the reason of that it can be used to effectively reflect the influence of the input uncertainties on the failure probability. However, compared with other kinds of importance measure indices, there are still some difficulties to accurately and efficiently estimate the failure probability-based moment-independent importance measure. In this context, a highly efficient method for moment-independent importance analysis is proposed. The proposed method firstly constructs a Kriging surrogate model with a slight number of experimental design samples to fully approximate the actual input-output response function. Then, the numerical simulation strategy is adopted to carry out the importance measure analysis of the constructed Kriging model. Finally, the main effect and total effect indices of the failure probability-based importance measure for each input variables can be obtained, the effect ranking order of each input variables on the failure probability can be provided as well. Compared with the existing methods, because of the introduction of Kriging surrogate model, the calculating times of the actual response function are greatly decreased and the computing accuracy is guaranteed as well. The application results of two engineering examples illustrate the superiorities of the proposed method in the aspect of calculating efficiency and accuracy, and indicate its excellent applicability.
[1] ZIO E. Reliability engineering:Old problems and new challenges[J]. Reliability Engineering and System Safety, 2009, 94(2):125-141.
[2] CASTILLO E, MINGUEZ R, CASTILLO C. Sensitivity analysis in optimization and reliability problems[J]. Reliability Engineering and System Safety, 2008, 93(12):1788-1800.
[3] LU Z, SONG J, SONG S, et al. Reliability sensitivity by method of moments[J]. Applied Mathematical Modelling, 2010, 34(10):2860-2871.
[4] LU Z, ZHOU C, SONG Z, et al. Subset simulation-based method for cumulative distribution function sensitivity of output response in random environment[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2012, 226(11):2770-2790.
[5] SALETLLI A. Sensitivity analysis for importance assessment[J]. Risk Analysis, 2002, 22(3):3-18.
[6] MCKAY M D. Nonparametric variance-based methods of assessing uncertainty importance[J]. Reliability Engineering and System Safety, 1997, 57(3):267-279.
[7] SOBOL I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and Computers in Simulation, 2001, 55(1):271-280.
[8] SALTELLI A. Making best use of model evaluations to compute sensitivity indices[J]. Computer Physics Communications, 2002, 145(2):280-297.
[9] CUI L, LU Z, ZHAO X. Moment-independent importance measure of basic random variable and its probability density evolution solution[J]. Science China Technological Sciences, 2010, 53(4):1138-1145.
[10] LI L, LU Z, FENG J, et al. Moment-independent importance measure of basic variable and its state dependent parameter solution[J]. Structural Safety, 2012, 38:40-47.
[11] BORGONOVO E. A new uncertainty importance measure[J]. Reliability Engineering and System Safety, 2007, 92(6):771-784.
[12] WEI P, LU Z, YUAN X. Monte Carlo simulation for moment-independent sensitivity analysis[J]. Reliability Engineering and System Safety, 2013, 110:60-67.
[13] WEI P, LU Z, HAO W, et al. Efficient sampling methods for global reliability sensitivity analysis[J]. Computer Physics Communications, 2012, 183(8):1728-1743.
[14] KLEIJNEN J P C. Kriging metamodeling in simulation:A review[J]. European Journal of Operational Research, 2009, 192(3):707-716.
[15] KAYMAZ I. Application of Kriging method to structural reliability problems[J]. Structural Safety, 2005, 27(2):133-151.
[16] ECHARD B, GAYTON N, LEMAIRE M. AK-MCS:An active learning reliability method combining Kriging and Monte Carlo simulation[J]. Structural Safety, 2011, 33(2):145-154.
[17] ZHAO H, YUE Z, LIU Y, et al. An efficient reliability method combining adaptive importance sampling and Kriging metamodel[J]. Applied Mathematical Modelling, 2015, 39(7):1853-1866.
[18] JIN R, CHEN W, SUDJIANTO A. An efficient algorithm for constructing optimal design of computer experiments[J]. Journal of Statistical Planning and Inference, 2005, 134(1):268-287.
[19] 张磊刚, 吕震宙, 陈军. 基于失效概率的矩独立重要性测度的高效算法[J]. 航空学报, 2014, 35(8):2199-2206. ZHANG L G, LU Z Z, CHEN J. An efficient method for failure probability-based moment-independent importance measure[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(8):2199-2206(in Chinese).
[20] 罗阳军, 高宗战, 岳珠峰, 等. 随机-有界混合不确定性下结构可靠性优化设计[J]. 航空学报, 2011, 32(6):1058-1066. LUO Y J, GAO Z Z, YUE Z F, et al. Reliability-based optimization design for structures with stochastic and bounded parameter uncertainties[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(6):1058-1066(in Chinese).
/
| 〈 |
|
〉 |
CJA