Uncertainty Finite Element Model Updating Method Based On Polynomial Chaotic Expansion

In recent years,the methods of finite element model updating have been deeply studied and developed.Among them,the uncertainty model updating has been widely concerned because it takes into account the influence of various uncertain factors and conforms to the practical engineering application.However,the uncertainty model updating needs to obtain the probability or interval distribution of parameters or structural responses,and the updating process is relatively complex and the calculation is relatively large.The application of Polynomial Chaotic Expansion(PCE)theory in the quantification of structural uncertainty and the uncertainty model updating is studied in the thesis.The main contents are as follows.The theory of polynomial chaotic expansion is briefly introduced.The process of model building is introduced,and the calculation formula of the statistical moment of structural response is deduced.Finally,taking a three-dimensional truss structure as an example,the natural frequency uncertainty of truss structure is quantified,and the calculated results are compared with those by the traditional Monte Carlo Simulation(MCS),which verifies the advantages of polynomial chaotic expansion in the calculation of statistical moments and the possibility of its application in the quantification of structural uncertainty and the updating of uncertainty model.Aiming at the problem of large computation in the process of random model updating,Kullback Leibler divergence(KLD),which is used to measure the correlation degree of probability distribution,is regarded as the objective function of model updating,and the mean value and standard deviation of the parameters are updated simultaneously.Kriging model is used to replace finite element model in the process of model construction,while the statistical moment of structural response(mean value and standard deviation)is calculated quickly by polynomial chaotic expansion model.Harris hawks optimization is selected to iteratively optimize the parameters to be updated.The results show that the KL divergence is the objective function without adjusting the mean value and standard deviation weight of the parameters,and reducing the subjective factors.The polynomial chaotic expansion can avoid the influence of the calculation accuracy of statistical moment on the updating result due to the number of sample points or uneven distribution of samples,and can improve the overall updating accuracy and updating efficiency.Aiming at the problems of random uncertainty and cognitive(interval)uncertainty in response and finite element models of engineering structures,a mixed uncertainty model updating method based on probability box is proposed.The Kriging-PCE model is constructed to quickly calculate the statistical moment of structural response.In the updating process,the random uncertainty of parameters is dealt with by probability theory,and the cognitive uncertainty of parameters is dealt with by interval model.Above two kinds of uncertainties are uniformly described by probability box.The upper and lower bounds of the structural response probability box of the model are updated respectively to obtain the upper and lower bounds of the cumulative probability distribution of the uncertain parameters.The Zhongshan Bridge model is used to verify the proposed method.The results show that this method can not only reduce the requirement of accurate probability distribution in the updating of stochastic uncertainty model,but also can avoid the problem of missing information caused by considering parameter distribution in interval analysis,which is more convenient for engineering application.