Modal decomposition from partial measurements

IF 1 4区 工程技术 Q4 MECHANICS Comptes Rendus Mecanique Pub Date : 2019-11-01 DOI:10.1016/j.crme.2019.11.011
Clément Jailin , Stéphane Roux
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引用次数: 1

Abstract

A data set over space and time is assumed to have a low-rank representation in separated spatial and temporal modes. The problem of evaluating these modes from a temporal series of partial measurements is considered. Each elementary instantaneous measurement captures only a “window” (in space) of the observed data set, but the position of this window varies in time so as to cover the entire region of interest and would allow for a complete measurement would the scene be static. A novel procedure, alternative to the Gappy Proper Orthogonal Decomposition (GPOD) methodology, is introduced. It is a fixed-point iterative procedure where modes are evaluated sequentially. Tested upon very sparse acquisition (1% of measurements being available) and very noisy synthetic data sets (10% noise), the proposed algorithm is shown to outperform two variants of the GPOD algorithm, with much faster convergence, and better reconstruction of the entire data set.

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部分测量的模态分解
假设空间和时间上的数据集在分离的空间和时间模式中具有低秩表示。考虑了从部分测量的时间序列中评估这些模态的问题。每个基本的瞬时测量只捕获观测数据集的一个“窗口”(在空间上),但是该窗口的位置随时间变化,以便覆盖整个感兴趣的区域,并且在场景是静态的情况下允许进行完整的测量。介绍了一种替代Gappy固有正交分解(GPOD)方法的新方法。它是一个不动点迭代过程,模态按顺序求值。在非常稀疏的采集(1%的测量值可用)和非常嘈杂的合成数据集(10%的噪声)上进行测试,所提出的算法优于GPOD算法的两种变体,具有更快的收敛速度,并且更好地重建整个数据集。
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来源期刊
Comptes Rendus Mecanique
Comptes Rendus Mecanique 物理-力学
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
12 months
期刊介绍: The Comptes rendus - Mécanique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … The journal publishes original and high-quality research articles. These can be in either in English or in French, with an abstract in both languages. An abridged version of the main text in the second language may also be included.
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