基于联合稀疏理论的结构振动压缩采样信号的恢复算法

发布时间：2018-04-02 10:49

本文选题：结构振动压缩采样信号　切入点：分布式压缩感知　出处：《哈尔滨工业大学》2017年硕士论文

【摘要】：压缩感知(Compressive Sensing,CS)是20世纪初发展起来的在信号处理领域具有颠覆性的一种理论,越来越多学科领域的专家学者开始致力于CS的研究。将土木工程和压缩感知结合,势必也会有广阔的应用前景。分布式压缩感知(Distributed Compressive Sensing,DCS)在CS的基础上研究多个通道信号之间的相关性,发展了三种不同的联合稀疏模型,进一步降低了采样率。而多观测向量(Multiple Measurement Vectors,MMV)问题被称作联合稀疏求解问题,是另外一种研究信号间相关性的框架,本质与JSM2一致。本文的研究目的是研究适用于多通道结构振动信号的联合稀疏模型并且发展相应的压缩信号恢复算法。主要内容包含以下三个方面。本文介绍了分布式压缩感知、多观测向量的框架以及相应的联合恢复算法。针对DCS的三种联合稀疏模型,分别选择SiOMP、DCSSOMP、Texas DOI恢复算法进行研究,验证联合恢复相较于单通道信号的优势。然后结合实际的多通道结构振动信号的特点,确定第二种联合稀疏模型(Joint Sparsity Model 2,JSM2)作为适用于多通道结构振动压缩感知信号的模型。JSM2所用的分布式压缩感知同步正交匹配追踪(DCS Simultaneously Orthogonal Matching Pursuit,DCSSOMP)算法是一种经典的联合恢复算法。本文改变了DCSSOMP算法的原子选择公式从而大幅节约运算的时间,然后结合下采样(sub-sampling)以及AIC(Analog to Information Converter)采样,将改进的DCSSOMP算法应用于实际的结构压缩采样信号的联合恢复当中,验证了该稀疏模型和恢复算法对振动信号联合恢复可行性。文章验证了同步下采样和非同步下采样恢复效果是一致的,而AIC采样则在联合重构效果上略逊于下采样。本文最后研究了多观测向量问题中的比较新颖的基于增广子空间的多重信号分类(Subspace Augmented Multiple Signal Classification,SAMUSIC)算法,对比了SAMUSIC算法以及DCSSOMP算法的性能。证明了在无噪声且当信号个数比较多时,SAMUSIC算法是远优于DCSSOMP算法的,而在信号噪声比较大的情况下,SAMUSIC算法与DCSSOMP算法的恢复性能一致,同时也分析了两者的时间复杂度。最后将SAMUISC算法应用到实际结构压缩采样信号的联合重构中。
[Abstract]:Compressed-sensing (CSC) is a subversive theory in the field of signal processing developed in the early 20th century. More and more experts and scholars in more and more disciplines are beginning to devote themselves to the research of CS. Distributed compressed sensing Compressive sensing (DCS) studies the correlation between multiple channel signals based on CS, and develops three different joint sparse models. The multi-observation vector multiple Measurement VectorsMVD problem is called the joint sparse solution problem, which is another framework to study the correlation between signals. The purpose of this paper is to study the joint sparse model for multi-channel structure vibration signal and develop the corresponding compression signal recovery algorithm. The main contents include the following three aspects. Distributed compression awareness, The frame of multi-observation vector and the corresponding joint recovery algorithm. For the three joint sparse models of DCS, we select the SiOMPI DCS SSOMP DOI recovery algorithm to study. Verify the advantages of joint recovery over single channel signals. Then combine the characteristics of actual multi-channel structural vibration signals, Determine the second joint sparse model Sparsity Model 2 JSM2 as a model for vibration compression sensing of multi-channel structures .JSM2. The distributed compressed sensing synchronous orthogonal matching tracking (DCS Simultaneously Orthogonal Matching pursuit DCSSOMP) algorithm is a classic combination. In this paper, the atomic selection formula of DCSSOMP algorithm is changed to save the time of operation. Then, combining the sub-sampling and AIC(Analog to Information sampling, the improved DCSSOMP algorithm is applied to the joint recovery of the actual compressed sampling signals. It is proved that the sparse model and the restoration algorithm are feasible for the joint restoration of vibration signals. The effect of synchronous down-sampling and non-synchronous down-sampling recovery is proved to be consistent in this paper. AIC sampling is slightly inferior to lower sampling in joint reconstruction. Finally, a novel subspace Augmented Multiple Signal classification algorithm based on augmented subspace for multi-observation vector problem is studied in this paper. The performances of SAMUSIC algorithm and DCSSOMP algorithm are compared. It is proved that the SAMUSIC algorithm is much better than the DCSSOMP algorithm when there is no noise and when the number of signals is large, and the recovery performance of SAMUSIC algorithm is the same as that of DCSSOMP algorithm under the condition of high signal noise. At the same time, the time complexity of the two methods is analyzed. Finally, the SAMUISC algorithm is applied to the joint reconstruction of compressed sampling signals with actual structure.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU317

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