Multivariate Probabilistic Collocation Method for Effective Uncertainty Evaluation With Application to Air Traffic Flow Management
Multivariate Probabilistic Collocation Method for Effective Uncertainty Evaluation With Application to Air Traffic Flow Management
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DOI：
10.1109/acc.2013.6580833
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发表时间：
2013-06
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影响因子：
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通讯作者：
Yi Zhou;D. Ramamurthy;Y. Wan;Sandip Roy;C. Taylor;C. Wanke
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文献类型：
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作者：
Yi Zhou;D. Ramamurthy;Y. Wan;Sandip Roy;C. Taylor;C. Wanke
现代大型基础设施系统具有典型的复杂结构和动力学，需要大量的模拟来评估其性能。概率配置方法（PCM）已被开发出来，可以有效地模拟参数不确定性下的系统性能。特别是，它允许仅使用有限数量的模拟来对不确定参数和系统性能测量/输出之间的映射进行降阶表示；原始系统的结果表示在可能的参数值范围内被证明是准确的。在本文中，我们将单变量 PCM 的形式分析扩展到多变量情况，其中多个不确定参数可能是独立的，也可能不是独立的。具体来说，我们提供了允许多元 PCM 精确预测原始系统输出平均值的条件。我们还探索了多元 PCM 在交叉统计预测、与最小均方估计量的关系、大维参数集的计算可行性以及基于样本的解决方案近似方面的其他功能。在本文的最后，我们演示了多元 PCM 在评估天气不确定性下的空中交通系统性能中的应用。
Modern large-scale infrastructure systems have typical complicated structure and dynamics, and extensive simulations are required to evaluate their performance. The probabilistic collocation method (PCM) has been developed to effectively simulate a system's performance under parametric uncertainty. In particular, it allows reduced-order representation of the mapping between uncertain parameters and system performance measures/outputs, using only a limited number of simulations; the resultant representation of the original system is provably accurate over the likely range of parameter values. In this paper, we extend the formal analysis of single-variable PCM to the multivariate case, where multiple uncertain parameters may or may not be independent. Specifically, we provide conditions that permit multivariate PCM to precisely predict the mean of original system output. We also explore additional capabilities of the multivariate PCM, in terms of cross-statistics prediction, relation to the minimum mean-square estimator, computational feasibility for large dimensional parameter sets, and sample-based approximation of the solution. At the end of the paper, we demonstrate the application of multivariate PCM in evaluating air traffic system performance under weather uncertainties.