基于主动学习Kriging模型的矩独立灵敏度分析
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摘要
矩独立灵敏度指标反映模型的随便变量的不确定性对模型输出响应的概率统计的影响程度,其主要作用是甄别出重要的随机变量,是目前提高产品设计效率的一种辅助分析手段。矩独立灵敏度分析一般分为基于输出响应概率密度函数和基于输出响应累积分布函数两种。然而,由于其输出响应的分布函数在实际工程中难以获得,因此,其应用受到了极大限制。为此,首先利用克里金模型替代实际工程问题的输入输出关系,为提高计算效率,利用主动学习法对其克里金建模效率进行提高。其次,在其建立好的克里金代理模型基础上,利用Monte Carlo simulation(MCS)对两种矩独立灵敏度指标进行分析。最后,通过一个工程算例对所提方法进行验证,并以MCS方法为参考,说明所提方法的精度和效率。
Moment-independent sensitivity index reflects the impact degree of the uncertainty of input to the probability statistic of output response; its main function is to identify the important random variables. The sensitivity analysis is an auxiliary tool for improving the design efficiency of product. In general,moment-independent sensitivity index is classified as the probability density function-based and the cumulative distribution function-based sensitivity indices. However,due to difficult calculation of the distribution function of output response,it would actively discourage the application of moment-independent sensitivity analysis in practical engineering. In view of this,firstly,the Kriging surrogate model is employed in this paper to replace the relationship between input and output,and the modeling efficiency is improved by using the active learning mechanism in order to further improve the calculation efficiency. Secondly,based on the constructed Kriging model,the two moment-independent sensitivity indices are calculated by the given Monte Carlo simulation procedure. Finally,with the reference results calculated by MCS procedure,the efficiency and accuracy of the proposed method are verified by an engineering example.
Moment-independent sensitivity index reflects the impact degree of the uncertainty of input to the probability statistic of output response; its main function is to identify the important random variables. The sensitivity analysis is an auxiliary tool for improving the design efficiency of product. In general,moment-independent sensitivity index is classified as the probability density function-based and the cumulative distribution function-based sensitivity indices. However,due to difficult calculation of the distribution function of output response,it would actively discourage the application of moment-independent sensitivity analysis in practical engineering. In view of this,firstly,the Kriging surrogate model is employed in this paper to replace the relationship between input and output,and the modeling efficiency is improved by using the active learning mechanism in order to further improve the calculation efficiency. Secondly,based on the constructed Kriging model,the two moment-independent sensitivity indices are calculated by the given Monte Carlo simulation procedure. Finally,with the reference results calculated by MCS procedure,the efficiency and accuracy of the proposed method are verified by an engineering example.
引文
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[2]吴吉平,贺兵,胡威林.直线运动机构轨迹可靠性灵敏度分析[J].机械传动,2016(6):140-143.
[3]Wang W,Zhou C,Gao H,et al.Application of non-probabilistic sensitivity analysis in the optimization of aeronautical hydraulic pipelines[J].Structural&multidisciplinary optimization,2017(2):1-15.
[4]Borgonovo E,Tarantola S.Moment independent and variance-based sensitivity analysis with correlations:An application to the stability of a chemical reactor[J].International journal of chemical kinetics,2008,40(11):687-698.
[5]巩祥瑞,吕震宙,左健巍.两种基于方差的全局灵敏度分析W指标改进算法[J].航空学报,2016,37(6):1888-1898.
[6]王文选,高行山,周长聪.基于点估计的矩独立重要性测度分析方法[J].机械工程学报,2017,53(8):16-24.
[7]张崎,李兴斯.基于Kriging模型的结构可靠性分析[J].计算力学学报,2006,23(2):175-179.
[8]Liu Q,Homma T.A new computational method of a moment-independent uncertainty importance measure[J].Reliability engineering&system safety,2009,94(7):1205-1211.