Uncertainty Model Updating And Damage Identification Based On Frequency Response Function

Uncertainties always exist in engineering problems,and uncertain measurement data will inevitably lead to the uncertainty of the updated structural model,so the structural parameters obtained by the uncertainty model updating method are more reliable.At present,the modal parameters of structural vibration are the response of most uncertain model updating.Compared with modal parameters,the frequency response function of structural vibration contains more sufficient information of the structure and can reflect the dynamic characteristics of the structure more accurately.Combining measurement uncertainty and the advantages of frequency response function as model updating response,the stochastic and interval finite element model updating by adopting RBF(Radial Basis Function)model replacing finite element model in this thesis are respectively studied.In addition,in view of the wide application of finite element model updating in structural damage identification,the structural damage identification method based on model updating through frequency response function sensitivity analysis is studied in this thesis.The contents are as follows:(1)Considering uncertainty of test frequency response function and the influence of random uncertainty of parameters on structural response distribution,the stochastic model updating method based on frequency response function and RBF model is studied.Firstly,RBF model is constructed,and the frequency response function is transformed by wavelet transform and the low frequency wavelet coefficient is extracted as output,and the width of RBF model is optimized by coyote optimization algorithm.Secondly,the random measure of Bhattacharyya distance between two samples is introduced,and the response characteristic quantity of the finite element model is predicted by using parameter samples through the RBF model participating in the model updating.Then,the two-step and synchronous solution of the mean and standard deviation of the parameters to be updated is implemented respectively by the flower pollination algorithm with the goal of minimizing the Bhattacharyya distance.Finally,the feasibility of the proposed method is verified by plane and space truss structures,and the ideal results are obtained.(2)Considering that the practical application often lacks enough structural statistical information,and only the limit values of structural parameters and responses are needed,the interval model updating method based on frequency response function and RBF model is studied.Firstly,two objective functions to solve the parameters interval to be updated in two steps and one objective function to solve the parameters interval to be updated synchronously are established to evaluate the difference of distribution between two sample intervals.Secondly,a small samples representing the parameters interval are used to predict the response characteristic quantity of the finite element model through RBF model participating in model updating,and the response characteristic quantity intervals are evaluated by grey mathematics method.Then,the flower pollination algorithm is used to solve the midpoint and radius of the parameters interval to be updated in two steps and simultaneously.Finally,the feasibility of the proposed method is verified by numerical examples of aircraft wing structure and space truss structure and test example of simply supported beam,and the results show that it can effectively solve the problem of uncertainty model updating for small test samples.(3)To solve the problem of being difficult to get the correct convergence results through direct iteration due to the inherent limitations of the first-order approximation when the frequency response function sensitivity analysis method is used for damage identification,the structural damage identification method based on model updating by the frequency response function sensitivity fitting function is studied.Firstly,excitation points are selected according to the variation coefficient criterion of modal participation,and combining the frequency response effective independent method with the distance coefficient effective independent method,positions of measuring points are chosen.Secondly,a reasonable frequency point is selected by comprehensively considering the sensitivities of frequency response function to parameters to be updated and the correlation of frequency response function.Then,the sensitivity function of frequency response function with variation of parameters is fitted,and introducing new intermediate design parameters,the sensitivity equations of frequency response function with intermediate design parameters are established.Changes of updated parameters are solved through solving the changes of intermediate design parameters.Finally,the feasibility of the method is verified by a three-degree-of-freedom mass spring system and a two-dimensional truss structure.The results show that the method has higher computational efficiency and recognition accuracy,and effectively avoids the convergence problem caused by the numerical balance of sensitivity equations.