Recovery Algorithms For Compressive Sampling Of Structural Vibrational Signals Based On Joint Sparse Thoery

Compressive Sensing(CS)is a disruptive theory that has developed in the field of signal processing in the early 20 th century,which more and more experts and scholars in different fields begin to commit to study.Combining civil engineering and CS is bound to have a broad application prospec ts.Distributed Compressive Sensing(DCS)based on CS exploits the inter-correlation among different signals.There are three different Joint Sparsity Models(JSM)developed in DCS to further reduce the sampling rate.The Multiple Measurement Vectors(MMV)problem,also called joint sparse solution problem,is another frame that exploits the inter-correlation of signals that be consistent with JSM2 essentially.The purpose of this article is to study the exact JSM that best suits to the multichannel structu ral vibration signals and develop corresponding recovery algorithm for compressive signals.The main contents contain three parts.The theoretical framework of DCS and MMV are introduced,and emphasis is placed on the joint recovery algorithms.Si OMP,DCSSOMP,Texas DOI algorithm was selected and studied for each JSM of DCS,and the advantage of joint recovery compared to single signal is proved.In consideration of the characteristic of practical multichannel vibration signals,the second Joint Sparsity Model is regarded as the best JSM that suits for the compressive sampling of multichannel structural vibrational signals.Distributed Compressive Sensing Simultaneously Orthogonal Matching Pursuit(DCSSOMP)algorithm is a classical joint recovery algorithm t o solve JMS2.The DCSSOMP algorithm is improved to save huge computation time by change atomic selection formula,and the improved algorithm is applied to recover structure compressive sampling signals,combined with sub-sampling and Analog to Information Converter(AIC)sampling,then the feasibility of JSM2 and corresponding algorithm was verified.It has proved that the simultaneously sub-sampling performed as well as the non-simultaneously,and the AIC sampling performed worse than the sub-sampling.The article exploits the Subspace Augmented Multiple Signal Classification(SAMUSIC)algorithm of Multiple Measurement Vectors at last and make a comparison between the SMAUSIC and DCSSOMP algorithm.SMAUSIC performs much better than DCSSOMP when the noise d oesn't exist and the number of signals is large,while when the noise is huge,the two performs the same.And the time complexity of the two algorithm is also analyzed.Then,the SAMUSIC algorithm is also applied to recover practical compressive signals.