Damage Identification Method Of Beam Structures Using Biased Estimation

Beam structure is one of the most common structural forms in engineering,and its working state is related to the safety of the whole structure.Once damage occurs in the beam structure,it is necessary to identify the damage in time.Among the existing damage identification methods,finite element model(FEM)updating is one of the most common methods.However,the ill-posed least squares problem caused by data errors is common in FEM updating.At this point,a small error will result in poor accuracy or even complete distortion of the FEM updating results.When the traditional least squares estimation(LSE)is used to solve ill-conditioned equations,the accuracy of the calculated results is not very good,even completely distorted.In view of this,this paper mainly studies the damage identification method of beam structure using model updating based on biased estimation.The proposed methods can overcome the problem of noise pollution in the calculation process and obtain more stable and accurate calculation results.The main contents include:Firstly,based on the static test data of beam structure,this paper proposes a damage identification method based on truncated singular value decomposition(TSVD).The main advantage of the proposed method is that it can obtain the robust and accurate results from the ill-posed linear equations due to measurement noise.The influences of the truncation threshold value and the error level on the calculation result are discussed in detail.In addition,the second calculation using the singular value truncation method by another loading state is proposed in order to further improve the accuracy of the calculation.The numerical experiments show that the proposed method is reasonable and feasible,and has better anti-noise performance than the least squares method.When the noise level is less than 10%,the accurate enough results can be obtained.It was found that the proposed method is promising for structural damage identification.Secondly,based on the modal parameters of the dynamic test of the beam structure,the enhanced ridge estimation(ERE)method is proposed in this paper.It is used to overcome the adverse influence of measurement errors in modal data to obtain accurate and robust damage assessment results.The presented algorithm consists ofthree steps.Firstly,the linear system of damage evaluation equations is solved for the first time by the common ridge estimate(RE)to obtain the rough result.Secondly,a new diagonal correction matrix that will be used in the enhanced ridge estimate is designed according to the result by the first RE.Thirdly,the linear system of damage evaluation equations is solved again by the ERE to obtain more accurate results.A beam structure is used as a numerical example to demonstrate the effectiveness of the proposed method.The results show that the ERE has greatly improved accuracy over the common RE.Structural damages can be successfully detected by the proposed method even if 10% data noise is added.It was found that the proposed method may be very useful for structural damage assessment and other similar engineering problems.Finally,this paper summarizes the proposed method based on biased estimation for damage detection of beam structures,analyses some defects and shortcomings in the current research,and makes a prospect for further research.