Structural Damage Identification Based On The Generalized Modal Flexibility Matrix

Damage identification methods based on static response parameters and vibration parameters are widely used in structural damage identification.More accurate results can be obtained by selecting more sensitive control equations.The frequency and mode of the structure are generally called structural vibration parameters.The control equation is constructed by measuring the vibration parameters before and after the structural damage,and then the damage position and degree of the structure are solved.Due to the difficulty in measuring the displacements of some nodes in the structure and the noisy data,the obtained physical parameters such as vibration parameters and displacements are incomplete and contain errors.These problems directly lead to the difficulty in obtaining accurate results for damage identification methods.In this paper,we mainly do the following work from the aspects of vibration mechanics and statics:1.Available from the knowledge of vibration mechanics,the unmeasured data is approximately represented by the measured data by the mode expansion method when the measurement information of modal parameters is not completed and a damage element prediction method is proposed.The possible damage location is determined by predicting the damage location and the control equation is reduced in dimension,so as to reduce the calculation amount.2.Based on the generalized modal flexibility matrix constructed by frequency and mode shape,the sensitivity of the matrix is derived by Nelson method and the damage identification control equation is established.In this paper,the least square QR decomposition method(LSQR)is used to solve the damage identification control equation,and on this basis,the iterative LSQR method is proposed to get more accurate results.3.In the practical measurement,the static displacement in statics are easy to obtain and higher accuracy in measurement.In this paper,the static response formula is used to deduce the control equation of statics.In order to extract more physical information of the structure,several displacement measurement experiments are used instead of the previous model expansion technology to overcome the difficulty of measuring some degrees of freedom in the structure.4.In this paper,the generalized modal flexibility matrix method and the multi-condition static response method are applied to several common building structures,which are composed of bar element and beam element respectively.The results of identification under the condition of incomplete measurement data and common noise level are more accurate than the previous methods.