Structural Damage Identification Based On Total Least Squares New Method

The structural damage identification method based on model updating is an important research topic in the field of civil engineering in recent years.Due to the complexity of engineering structure and the limitations of testing techniques,the ill-conditioned least squares problem is one of the key problems in the process of damage identification calculation.At this time,the noise contained in the data will lead to large error or even complete distortion of the calculation results.In order to solve the ill-conditioned least squares problem better,this paper combines the basic idea of total least squares with the basic idea of singular value truncation method,proposes a new total least square estimation method,and applies it to the calculation of structural damage identification.In the calculation of damage identification,the proposed method can better overcome the adverse effects of data noise and effectively improve the calculation accuracy and robustness.The main research contents are as follows:Based on the basic idea of total least squares estimation,a new total least squares method is proposed.For the case where there are errors in the coefficient matrix of the linear equations and the observation vector.Firstly,all the data errors are used in the normalized processing.They are all concentrated in the new coefficient matrix,and then the singular value truncation method is applied to solve the new equations,that is,the singular value decomposition of the new coefficient matrix is performed,and the smaller singular values are truncated,so as to effectively remove the data noise pollution.The results of the example show that the proposed method can effectively improve the accuracy and robustness of the solution.Aiming at the problem of singular value truncation threshold selection in the new least squares new method,an index determination method for determining the truncation threshold is proposed.The same example is used to compare the L curve inflection point observation method,the angle determination method and the index.The selection result of the judgment method shows the convenience and feasibility ofthe proposed index judgment method.The proposed method of total least squares is applied to the calculation of structural damage identification to reduce the error caused by data noise pollution on the damage identification result.In the calculation,the proposed total least squares new method is used multiple times,and the undamaged elements is selected according to the calculation result of each calculation,and the accuracy of the damage parameter is gradually improved.Taking the cantilever truss structure and the plate structure as examples,the numerical simulation of the proposed method is carried out.Taking a steel beam experiment as an example,the experimental data were verified by the proposed method.The results show that the proposed method is reasonable and feasible.