M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions
M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions
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DOI：
10.1016/j.matcom.2018.10.010
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发表时间：
2019-05
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影响因子：
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通讯作者：
Junfei Xie;Yan Wan;K. Mills;J. Filliben;Yu Lei;Zongli Lin
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作者：
Junfei Xie;Yan Wan;K. Mills;J. Filliben;Yu Lei;Zongli Lin
高维不确定输入参数系统的输出性能统计评估对于在不确定环境下运行的大型复杂系统的鲁棒实时决策任务至关重要。我们开发了一个整合多元概率配置方法（M-PCM）和正交分数因子设计（OFFD）的框架，以实现有效和可扩展的输出统计估计。在这篇文章中,我们证明,当每个不确定参数的程度不超过3和高维系统的普遍假设下不确定输入参数之间的相互作用可以忽略不计超越特定的顺序,综合M-PCM-OFFD方法打破了诅咒的维度正确输出意味着估计通过最大限度地减少模拟的数量从2 2 m 2日志2 (m + 1) m的系统映射不确定输入参数。此外，在M-PCM仿真集中所有相同大小的子集中，所得到的减小尺寸的仿真集对仿真器的数值截断误差的鲁棒性最强。该分析还为offd的最优性提供了新的有见地的正式解释。
The evaluation of output performance statistics for systems of high-dimensional uncertain input parameters is crucial for robust real-time decision-making tasks of large-scale complex systems that operate in an uncertain environment. We develop a framework that integrates Multivariate Probabilistic Collocation Method (M-PCM) and Orthogonal Fractional Factorial Design (OFFD) to achieve an effective and scalable output statistics estimation. In this paper, we prove that when the degree of each uncertain parameter does not exceed 3 and under the widely held assumption for high-dimensional systems that the interactions among uncertain input parameters are negligible beyond certain order, the integrated M-PCM–OFFD method breaks the curse of dimensionality for correct output mean estimation by maximally reducing the number of simulations from 2 2 m to 2 log 2 (m+ 1) for a system mapping of m uncertain input parameters. In addition, the resulting reduced-size simulation set is the most robust to numerical truncation errors of simulators among all subsets of the same size in the M-PCM simulation set. The analysis also provides new insightful formal interpretations of the optimality of OFFDs.