Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST).
Understanding and comparisons of different sampling approaches for the Fourier Amplitudes Sensitivity Test (FAST).
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DOI：
10.1016/j.csda.2010.06.028
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发表时间：
2011-01-01
影响因子：
1.8
通讯作者：
Gertner G
中科院分区：
文献类型：
--
作者：
Xu C;Gertner G
傅立叶振幅灵敏度测试 (FAST) 是最流行的不确定性和灵敏度分析技术之一。它使用周期性采样方法和傅里叶变换将模型输出的方差分解为不同模型参数贡献的部分方差。到目前为止，FAST分析主要局限于模型参数主效应所贡献的部分方差的估计，而没有考虑到参数之间特定相互作用所贡献的部分方差。在本文中，我们从理论上证明，FAST 分析可用于使用不同抽样方法（即基于传统搜索曲线的抽样、简单随机抽样和随机平衡设计抽样）来估计由模型参数的主效应和交互效应贡献的部分方差。我们还分析计算了部分方差估计中的潜在误差和偏差。构建假设检验是为了减少抽样误差对部分方差估计的影响。我们的结果表明，与简单随机抽样和随机平衡设计抽样相比，基于搜索曲线的抽样估计的敏感性指数（特定模型输出的部分方差与方差之比）通常具有更高的精度，但低估程度更大。与简单随机抽样相比，随机平衡设计抽样通常可以为参数主效应贡献的部分方差提供更高的估计精度。高阶相互作用贡献的部分方差的理论推导以及不同采样方案下其相应估计误差的计算可以帮助我们更好地理解FAST方法，并为FAST的应用和进一步改进提供基础依据。
Fourier Amplitude Sensitivity Test (FAST) is one of the most popular uncertainty and sensitivity analysis techniques. It uses a periodic sampling approach and a Fourier transformation to decompose the variance of a model output into partial variances contributed by different model parameters. Until now, the FAST analysis is mainly confined to the estimation of partial variances contributed by the main effects of model parameters, but does not allow for those contributed by specific interactions among parameters. In this paper, we theoretically show that FAST analysis can be used to estimate partial variances contributed by both main effects and interaction effects of model parameters using different sampling approaches (i.e., traditional search-curve based sampling, simple random sampling and random balance design sampling). We also analytically calculate the potential errors and biases in the estimation of partial variances. Hypothesis tests are constructed to reduce the effect of sampling errors on the estimation of partial variances. Our results show that compared to simple random sampling and random balance design sampling, sensitivity indices (ratios of partial variances to variance of a specific model output) estimated by search-curve based sampling generally have higher precision but larger underestimations. Compared to simple random sampling, random balance design sampling generally provides higher estimation precision for partial variances contributed by the main effects of parameters. The theoretical derivation of partial variances contributed by higher-order interactions and the calculation of their corresponding estimation errors in different sampling schemes can help us better understand the FAST method and provide a fundamental basis for FAST applications and further improvements.
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DOI：
10.1034/j.1600-0870.1998.t01-2-00005.x
发表时间：
1998-05-01
影响因子：
2
作者：
Rodriguez-Camino, E;Avissar, R
通讯作者：
Avissar, R
影响因子：
8.1
作者：
Xu, Chonggang;Gertner, George Zdzislaw
通讯作者：
Gertner, George Zdzislaw
影响因子：
8.1
作者：
Helton, J. C.;Johnson, J. D.;Storlie, C. B.
通讯作者：
Storlie, C. B.
影响因子：
4.6
作者：
Sobol, IM
通讯作者：
Sobol, IM
影响因子：
1.5
作者：
KODA, M;MCRAE, GJ;SEINFELD, JH
通讯作者：
SEINFELD, JH