Compressed sensing techniques for arbitrary frequency-sparse signals in structural health monitoring
Compressed sensing techniques for arbitrary frequency-sparse signals in structural health monitoring
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DOI：
10.1117/12.2048276
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发表时间：
2014-03
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通讯作者：
Z. Duan;Jie Kang
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作者：
Z. Duan;Jie Kang
结构健康监测需要采集大量的样本数据，有时需要采集高频振动数据，以检测结构的损伤。收集数据的昂贵成本是一个巨大的挑战。最近提出的压缩感知方法可以大大减少采样，这是一种应对挑战的方法。压缩感知理论需要稀疏信号，这意味着信号可以很好地近似为来自已知离散基或字典的几个元素的线性组合。结构振动信号可以在DFT域中分解为几个正弦线性组合。不幸的是，在大多数情况下，分解的正弦曲线的频率在该域中是任意的，这可能不精确地位于离散DFT基或字典上。在这种情况下，信号将失去其稀疏性，这使得恢复性能显着下降。提高信号稀疏性的一种方法是增加字典的大小，但存在一个折衷：密集的DFT字典将增加字典中元素之间的相干性，这反过来又降低了恢复性能。在这项工作中，我们介绍了三种方法的任意频率信号恢复。第一种方法是连续基追踪（CBP），它通过引入插值步骤来重建连续基。第二种方法是半定规划（SDP），它在连续的基础上搜索最稀疏的信号，而不建立任何字典，使一个非常高的恢复精度。第三种方法是谱迭代硬阈值（SIHT），它是基于冗余DFT字典和一个受限的子空间联合信号模型，抑制密集的正弦信号。通过数值模拟对这三种方法进行了研究。利用有限元模型模拟结构振动信号，并对信号进行压缩测量，进行信号恢复。对这三种方法的性能进行了比较，并对振动信号压缩采样测试系统的设计提出了进一步的研究方向。
Structural health monitoring requires collection of large number sample data and sometimes high frequent vibration data for detecting the damage of structures. The expensive cost for collecting the data is a big challenge. The recent proposed Compressive Sensing method enables a potentially large reduction in the sampling, and it is a way to meet the challenge. The Compressed Sensing theory requires sparse signal, meaning that the signals can be well-approximated as a linear combination of just a few elements from a known discrete basis or dictionary. The signal of structure vibration can be decomposed into a few sinusoid linear combinations in the DFT domain. Unfortunately, in most cases, the frequencies of decomposed sinusoid are arbitrary in that domain, which may not lie precisely on the discrete DFT basis or dictionary. In this case, the signal will lost its sparsity, and that makes recovery performance degrades significantly. One way to improve the sparsity of the signal is to increase the size of the dictionary, but there exists a tradeoff: the closely-spaced DFT dictionary will increase the coherence between the elements in the dictionary, which in turn decreases recovery performance. In this work we introduce three approaches for arbitrary frequency signals recovery. The first approach is the continuous basis pursuit (CBP), which reconstructs a continuous basis by introducing interpolation steps. The second approach is a semidefinite programming (SDP), which searches the sparest signal on continuous basis without establish any dictionary, enabling a very high recovery precision. The third approach is spectral iterative hard threshold (SIHT), which is based on redundant DFT dictionary and a restricted union-of-subspaces signal model, inhibiting closely spaced sinusoids. The three approaches are studied by numerical simulation. Structure vibration signal is simulated by a finite element model, and compressed measurements of the signal are taken to perform signal recovery. Comparison of the performance of the three approaches is made, and future work on design of compressive sampling testing system for vibration signal is proposed.