Research On Structural Damage Identification Method Based On Reciprocal Variable

Due to environmental and human factors,the structure will be damaged during operation.Over time,the damage may lead to a significant decrease in the performance of the structure or even destruction,and in severe cases,it may lead to unexpected loss of life and property.Therefore,it is necessary to monitor the structure in order to detect damage as early as possible and assess the health of the structure,so as to ensure the safe operation of the structure and avoid the occurrence of tragedy.Constructing a governing equation that is more sensitive to the damage degree is a key issue in damage identification.In structural optimization,the choice of design variables can change the form of Taylor expansion,which affects the accuracy of linear approximation based on Taylor expansion.According to the virtual work principle in structural mechanics,the displacement of beam,truss and rigid frame can be expressed as a linear combination of the reciprocal stiffness of each element.Therefore,for the damage identification of beam,truss and rigid frame,we introduce the concept of reciprocal variable.From the two aspects of statics and vibration mechanics,this thesis studies the influence of reciprocal variables on the accuracy of damage identification results,and preliminarily locates the location of structural damage by using static response and neural network technology.The main work of this thesis is as follows:（1）A structural damage identification method based on reciprocal variable and static response is proposed,and the damage identification results before and after introducing reciprocal variable are compared.The static displacement changes before and after structural damage are used to identify structural damage,and more displacement information is obtained by setting moving load,so as to reduce the number of sensors and overcome the difficulty of measuring some degrees of freedom in the structure.Considering the influence of noise,the anti noise ability of Tikhonov regularization method,truncated singular value method and non negative least square method is compared.（2）The reciprocal variable is introduced into the structural damage identification method based on flexibility matrix and the structural damage identification method based on generalized modal flexibility matrix respectively.The damage identification results before and after the introduction of reciprocal variable are compared.At the same time,considering that the accuracy of damage identification results can be improved by introducing a more effective damage solution model when the vibration mode is incomplete,the damage identification results of method 1（obtaining the modal normalization parameter value through the vibration mode expansion technology,and then solving the damage parameters）and method 2（taking the modal normalization parameter as the parameter to be solved together with the damage parameters）are compared.The influence of noise on damage identification results is also discussed.（3）A preliminary location method of structural damage based on BP neural network is proposed.According to the characteristics that the static displacement will change after structural damage,a BP neural network model is constructed to preliminarily locate the structural damage by using the static displacement after structural damage,so as to reduce the cost of subsequent damage solution.