Atomic Norm Minimization for Modal Analysis From Random and Compressed Samples
Atomic Norm Minimization for Modal Analysis From Random and Compressed Samples
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DOI：
10.1109/tsp.2018.2793907
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发表时间：
2018-04-01
影响因子：
5.4
通讯作者：
Wakin, Michael B.
中科院分区：
文献类型：
--
作者：
Li, Shuang;Yang, Dehui;Wakin, Michael B.
模态分析是估计系统模态参数的过程，例如其固有频率和模式形状。模态分析的一种应用是结构性健康监测（SHM），其中传感器网络可用于从物理结构（例如建筑物或桥梁）中收集振动数据。基于无线传感器网络中收集的数据，对开发SHM的自动化技术的兴趣越来越大。但是，为了节省电源并延长电池寿命，希望最大程度地减少必须在这种传感器网络中收集和传输的数据量。在本文中，我们强调了一个事实，即模态分析可以作为原子规范最小化（ANM）问题进行表述，该问题可以有效地解决，在某些情况下可以完美地恢复结构的模式形状和频率。我们调查了一个可以在物理传感器网络中考虑的广泛采样和压缩策略，并为这些压缩方案的样本复杂性提供了界限，以便通过ANM恢复结构的模式形状和频率。我们论文的主要贡献是建立对模态分析的样本复杂性的结合，并随机时间压缩，在这种情况下，我们证明，随着传感器的数量的增加，每个传感器所需的样品数量实际上可以减少。在统一采样的情况下，我们还将原子规范降解问题扩展到了多个测量矢量设置。
Modal analysis is the process of estimating a system's modal parameters, such as its natural frequencies and mode shapes. One application of modal analysis is in structural health monitoring (SHM), where a network of sensors may be used to collect vibration data from a physical structure, such as a building or bridge. There is a growing interest in developing automated techniques for SHM based on data collected in a wireless sensor network. In order to conserve power and extend battery life, however, it is desirable to minimize the amount of data that must be collected and transmitted in such a sensor network. In this paper, we highlight the fact that modal analysis can be formulated as an atomic norm minimization (ANM) problem, which can be solved efficiently and in some cases recover perfectly a structure's mode shapes and frequencies. We survey a broad class of sampling and compression strategies that one might consider in a physical sensor network, and we provide bounds on the sample complexity of these compressive schemes in order to recover a structure's mode shapes and frequencies via ANM. A main contribution of our paper is to establish a bound on the sample complexity of modal analysis with random temporal compression, and in this scenario we prove that the required number of samples per sensor can actually decrease as the number of sensors increases. We also extend an atomic norm denoising problem to the multiple measurement vector setting in the case of uniform sampling.