Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
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DOI：
10.1007/s00348-016-2127-7
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发表时间：
2016-03-01
影响因子：
2.4
通讯作者：
Rowley, Clarence W.
中科院分区：
文献类型：
--
作者：
Dawson, Scott T. M.;Hemati, Maziar S.;Rowley, Clarence W.
动态模态分解（DMD）提供了一种从流体数据集中提取有意义的动态信息的实用方法。像任何数据处理技术一样，DMD的有用性受到其从噪声损坏的数据中提取真实和准确动态特征的能力的限制。在这里，我们分析地表明DMD对传感器噪声有偏倚，并量化这种偏倚如何取决于数据的大小和噪声水平。我们提出了三种可用于消除这种偏差的DMD修改：(1)使用已知噪声特性直接校正已识别的偏差，(2)结合时间上向前和向后执行DMD的结果，以及(3)总最小二乘启发算法。我们讨论了每种算法的相对优点，并在一系列合成、数值和实验数据集上展示了这些修改的性能。我们进一步将我们改进的DMD算法与最近文献中提出的其他变体进行了比较。
Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here, we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (1) a direct correction of the identified bias using known noise properties, (2) combining the results of performing DMD forwards and backwards in time, and (3) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in the recent literature.