Research Of Structural Damage Identification Method Based On Generalized Flexibility

The method of structural damage identification based on the change of vibration parameters is a frontier topic in the field of civil engineering.In engineering practice,due to the limitation of testing technology,often only low-order modal data of structural vibration can be obtained.Therefore,it is very valuable to use low-order modal to identify structural damage.For this reason,the damage identification and sensor layout optimization method based on high order generalized flexibility are studied in this paper.In addition,in order to overcome the disadvantages of incomplete test data and measurement noise,a feedback singular value truncation method is proposed.The main research contents of this paper include:(1)The deduction process of general flexibility,first-order generalized flexibility and its sensitivity formula is briefly reviewed,and then a recursion calculation formula of generalized flexibility sensitivity is derived.Taking a four-storey frame structure as an example,it is shown that with the increase of the order of generalized flexibility,the negative effect of modal truncation on the calculation of generalized flexibility sensitivity becomes smaller and smaller.Using only the first two modes,a very accurate first or second-order generalized flexibility matrix can be obtained.(2)The method of damage identification based on generalized flexibility sensitivity with different order is studied in detail.It is found that the accuracy of damage assessment results is not increase with the increase of the order of generalized flexibility.The reason may be lie in that the condition number of the coefficient matrix of the generalized flexibility sensitivity equations is significantly increased with the increase of the order of generalized flexibility.This means that the ill condition of the equations is more serious with the increase of the order of generalized flexibility,which leads to the distorted identification results.Thus the generalized flexibility sensitivity with the first or second order is recommended for structural model updating or damage identification in engineering.(3)Aiming at the ill-conditioned equations in damage identification,this paperpresents a feedback truncated singular value method based on the conventional truncated singular value technology.The proposed method can overcome the adverse impacts of the data noise to a certain extent and improve the stability and accuracy of the identification results obviously.(4)Based on the generalized flexibility theory,an optimal sensor placement method is proposed in this paper.Firstly,according to the principle that the number of damage identification equations should be no less than the number of unknowns,the minimum number of sensor placement is determined.Then,according to the norm size of the generalized flexibility sensitivity matrix of each element,the key components in the structure are determined,and the optimal scheme of sensor placement is determined accordingly.The results show that this method can detect the key components effectively in the structure,and successfully identify the damaged elements in the structure under the interference of noise.