基于任意多项式混沌的非线性复杂网络多尺度弹性的不确定性量化
Uncertainty Quantification of Multi-Scale Resilience in Nonlinear Complex Networks using Arbitrary Polynomial Chaos
摘要：
弹性是指系统在发生扰动时保持其原始功能的能力。在过去的几年里，我们的注意力主要集中在小规模的弹性，但我们的理解在大规模网络的弹性考虑组件之间的相互作用是有限的。尽管如此，最近在宏观和微观弹性模式的研究已经开发出分析工具，以分析拓扑结构和动态之间的关系，跨网络尺度。不确定性在大规模网络系统中的影响尚不清楚，特别是当不确定性在连接的节点之间级联时。为了量化网络分辨率（宏观到微观）的弹性不确定性，本文提出了一种任意多项式混沌（aPC）扩展方法来估计具有任意分布的参数不确定性的弹性。第一次，特别重要的是，我们能够识别节点失去弹性的概率，以及不同的模型参数如何导致这种风险。我们使用一个通用的网络双稳态系统来测试这一点，这将有助于从业者既了解宏观尺度的行为，又进行微观尺度的干预。
英文摘要：
Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network considering interactions between components is limited. Even though, recent research in macro and micro resilience pattern has developed analytical tools to analyze the relationship between topology and dynamics across network scales. The effect of uncertainty in a large-scale networked system is not clear, especially when uncertainties cascade between connected nodes. In order to quantify resilience uncertainty across the network resolutions (macro to micro),an arbitrary polynomial chaos (aPC) expansion method is developed in this paper to estimate the resilience subject to parameter uncertainties with arbitrary distributions. For the first time and of particular importance, is our ability to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk. We test this using a generic networked bi-stable system and this will aid practitioners to both understand macro-scale behaviour and make micro-scale interventions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
