Research On Bayesian Compression Sampling Considering The Correlation Of Prediction Errors

In this paper,Bayesian compressive sensing method considering error correlation and its application in structural health monitoring are studied.In sparse Bayesian learning modelling,this method takes into account the correlation between the prediction error in Bayesian compressive sensing algorithm to perfect the original method in theory.Then a novel Bayesian compressive sensing method was established to consider the prediction error correlation,one-dimensional signal and two-dimensional image signal are utilized to compare and validate the proposed method.The main research contents are as follows:(1)The first chapter introduces the content and significance of structural health monitoring and compressive sensing.This chapter shows that Bayesian compressive sensing method has the advantage of quantifying uncertainty in the process of signal decompression.(2)In chapter 2,a novel Bayesian compressive sensing method considering the prediction error correlation is established.Firstly,the traditional sparse Bayesian learning method is introduced,and the error modeling of the traditional method is adjusted so that the predictive error correlation introduced by the compression matrix in the signal compression process can be considered.Then,the new correlation model is applied to BCS-MPE algorithm.So the new algorithm BCS-MPE~* is obtained.And the relevant theoretical calculation formula of the new algorithm BCS-MPE~* is deduced.In addition,in order to apply the new error modeling method to approximate sparse signals,the new prediction error model was combined with the BCS-IPE algorithm,which marginalizes the probability of error precision parameters,to obtain the new algorithm BCS-IPE~*.The relevant theoretical calculation formulas of the new algorithm BCS-IPE~* were derived.Finally,the action mechanism of the new prediction error model is analyzed by eigenvalue decomposition.(3)Chapter 3 shows BCS-MPE~* algorithm and BCS-IPE~* algorithm and verifies them.Based on one-dimensional sparse signals and approximate sparse signals under different compression rates and degrees of sparsity,the performance of the Bayesian compressive sensing algorithm proposed in this paper considering prediction error correlation is calculated.The results of BCS-MPE and BCS-MPE~*,BCS-IPE and BCS-IPE~* are compared respectively,verifying the superiority of the new method presented in this paper.Finally,the applicability of the new method under complex signals is further verified based on structural monitoring signals and two-dimensional image signals respectively.(4)In chapter 4,two kinds of multi-task sparse Bayesian learning model is proposed considering the prediction error correlation,one uses different precision of the prediction error parameters between different tasks,the other shares the same precision of prediction error parameters between different tasks.The theoretical derivation of the two methods is given,and the realization of the corresponding algorithm is presented.The related performance verification is carried out on the onedimensional synthetic signal and the actual structural health monitoring signal.