使用增强灵敏度的多项式混乱扩展来量化混乱系统的时间平均数量的不确定性量化
Kyriakos D Kantarakias1, George Papadakis1
1Department of Aeronautics, Imperial College London, London SW7 2AZ, United Kingdom.
Physical review. E
|May 17, 2024
概括
本研究引入了灵敏度增强的泛化多项式混沌扩展 (se-gPC),以有效量化混乱系统中的随机参数效应. 这种新的方法提供了计算效率和准确性,优于现有技术.
科学领域:
- 动态系统和混沌理论
- 计算数学 计算数学 计算数学
- 随机分析 随机分析
背景情况:
- 混乱系统通常受到多个不确定的参数的影响.
- 量化这些随机参数对系统行为的影响至关重要.
- 现有的不确定性量化方法在计算上可能很昂贵.
研究的目的:
- 开发一种有效的方法来量化多个随机参数对混乱系统中时间平均数量的影响.
- 引入和验证增强灵敏度的泛化多项式混沌扩展 (se-gPC).
主要方法:
- 使用增强灵敏度的泛化多项式混乱扩展 (se-gPC).
- 在频率域中导出影子操作员的助理,以计算灵敏度.
- 将副操作符与通用多项式混乱 (gPC) 合起来,以量化不确定性.
主要成果:
- se-gPC方法有效量化了随机参数的影响.
- 计算成本是独立于其基本形式的随机变量的数量.
- 库拉莫托-西瓦辛斯基方程的结果与蒙特卡洛模拟结果有很好的一致性.
- 这种方法显著优于像斯莫利亚克方程这样的稀疏网格方法.
结论:
- se-gPC提供了一种高效准确的方法,用于在混乱系统中量化不确定性.
- 该方法的效率使其适用于具有众多随机参数的复杂动态系统.
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