Study Of Recovery Algorithms For Sub-sampling Vibration Of Structures

Compressed Sensing(CS)theory was developed in recent years as new theory and framework for data acquisition and data processing, and it drew attention from multidisciplinary areas immediately. In the field of structural health monitoring, CS also has important theoretical value and potential applications. For example, CS can potentially replace conventional high-frequency data acquisition system to easily sample guided ultrasonic wave; when CS is used for wireless sensor networks, it can reduce energy consumption in data collection, transmission and processing, which prolongs the life of wireless sensor networks. This paper will study the recovery algorithms based on sub-sampling scheme, and the performance of the algorithms to recover structural vibration signal. The main contents are as following.Firstly, the theoretical framework of Compressed Sensing is introduced, and emphasis is placed on the recovery algorithms. The recently raised SDP( Semidefinite Programming) algorithm, which is based on continuous dictionary is evaluated by processing real vibration signals, and the merits and shortcomings of this algorithm are analyzed.OMP(Orthogonal Matching Pursuit)algorithm is a classic greedy algorithm. This algorithm is more efficient than those based on continuous atom library, as it needs less iterations. An adaptive OMP algorithm is proposed in this paper. In this algorithm, the signal’s sparsity is firstly obtained through iterative steps, and then OMP algorithm is employed to recover the signal. By choosing an appropriate atomic library density multiples, the accuracy of the recovered signals is further improved. Compared to the SDP algorithm in terms of recovery accuracy and efficiency, the improved OMP has equal accuracy but more efficiency, implicating better chance for application.A simpler and easier way to control interval sub-sampling scheme is proposed in this paper. Considering the different compression sampling schemes, recovery performance of the improved OMP algorithm is investigated.Besides, the applicability of recovery algorithms to signals with real complexibility is studied. Through processing more types of signals and increasing the complexibility of signals, the performance of the two algorithms, i.e, SDP algorithm and improved OMP algorithm are compared to evaluate their potential for real vibrational signal recovery.