2013
DOI: 10.1016/j.apm.2012.03.017
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A new algorithm for variance based importance analysis of models with correlated inputs

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Cited by 32 publications
(21 citation statements)
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“…Meanwhile, the correlated contribution S C i can be computed as S C i ¼ S i À S U i . Based on this idea, artificial neural network (ANN) [83], point estimation procedure [162] and SDR meta-model [163] have been introduced for computing S U i and S C i in the case of additive model.…”
Section: Dependent Casementioning
confidence: 99%
“…Meanwhile, the correlated contribution S C i can be computed as S C i ¼ S i À S U i . Based on this idea, artificial neural network (ANN) [83], point estimation procedure [162] and SDR meta-model [163] have been introduced for computing S U i and S C i in the case of additive model.…”
Section: Dependent Casementioning
confidence: 99%
“…Eq. (20) indicates that failure probability function P f ðθ G Þ can be expressed as the expectation of the function I F ðxÞf x ðxj θ G Þ=h x ðxj θ n Þ. Given a set of model input vector samples x ðjÞ ¼ ðx ðjÞ 1 ; x ðjÞ 2 ; :::; x ðjÞ m Þðj ¼ 1; 2; …; MÞ generated by the joint PDF h x ðxj θ n Þ, the failure probability function P f ðθ G Þ can be estimated by: …”
Section: Extended Monte Carlo Simulationmentioning
confidence: 97%
“…Among them, GSA is the most potential in engineering applications, and the indicators can also be called uncertainty importance measures [13] which have attracted lots of research interest in the literature. At present, a number of SA techniques with only aleatory uncertainty, such as a variancebased importance method [14][15][16][17][18][19] for single output or multiple output under a statistic or stochastic process, transformation invariance property and kinds of the moment-independent importance measures [20][21][22][23][24][25][26][27][28], the elementary effect method and the corresponding applications [29,30], the derivative-based method [31,32], the regional analysis techniques and their evolutions [33][34][35][36] and the parametric method [37][38][39], have been developed by different researchers. However, it is also essential for analysts to measure the contribution of distribution parameters to the probabilistic response such as the expectation function, standard deviation function and failure probability function (FPF) of the model output.…”
Section: Introductionmentioning
confidence: 99%
“…。例如,胡迎春等 [3] 利用局部灵敏度分析研究 了影响人工髋关节稳定性因素,结果表明人体骨头 密度对其影响最大。李祺等 [4] 采用灵敏度分析揭示 出各部件弹性对动态平台参考点柔度的影响,为其 结构的改进与优化设计提供了参考。全局灵敏度则 考虑输入变量在整个分布范围内对响应输出分布特 征的影响程度 [5][6][7] ,相对于局部灵敏度分析,全局灵 敏度能够充分地利用输入参数的统计信息,为设计 者提供更加合理的数据参考。例如,张扬等 [8] 将全 局灵敏度分析与动态代理模型相结合提出了一种多 参数多目标优化策略,并将其应用与汽车约束系统 的概念优化设计中。MA 等 [9] 介绍了多参数灵敏 度分析在复杂非线性系统稳健性优化设计中的 应用。 全局灵敏度又被称为重要性测度。 目前输入变量 的重要性测度一般分为基于方差的重要性测度 [10][11] 和矩独立的重要性测度 [12][13] 两类。基于方差的重要 性测度具有"全局性" 、 "可量化性"和"通用性" 的特征,能够反映输入参数对响应量方差的影响程 度, 是目前国内外比较常用的重要性测度分析手段。 后来的学者们对重要性测度提出了"矩独立性"要 求,BORGONOVO 等 [14][15][16][17] 所提出的矩独立重要性 测度能够考察输入参数的不确定性对响应量概率密 度函数的影响,该测度反映了输入参数对响应量在 整个分布范围内的影响程度,在目前得到了较广泛 的研究与应用。 由于模型响应量的概率密度函数不容易计算, LIU 等 [12] 在 Borgonovo 所提方法的基础上,将对模 型响应量概率密度函数的计算转换为对累积分布函 数的计算。此外,LIU 等提出了另一种矩独立重要 性测度,考虑了输入参数对响应量累积分布函数的 影响,为重要性测度指标的计算提供了新的思路。 从 LIU 等提出的方法可以看出,两种重要性测度指 标都需要计算响应量累积分布函数,换言之,对响 应量累积分布函数的计算直接影响到两种重要性测 度的精确性和计算效率。为改进重要性测度分析的 计算效率以提高其工程适用性和可实现性,本文基 于点估计提出了一种高效的计算方法对响应量的累 积分布函数进行估计,并利用嵌套点估计法计算得 到两种重要性测度指标。最后,通过工程实例对所 提理论与方法进行验证,证实所提方法的正确性与 工程实用性。 1 两种矩独立重要性测度 [18] 与 SEO [19] 对 ROSENBLUTH 提出的方 法 [20] 进行了改进,采用三点离散分布描述连续分…”
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