A Statistical Model Updating Method Of Beam Structure Subjected To Correlation Of Measured Data

In the design stage of engineering structure,the finite element model will have a big discrepancy with the measured data in the actual project.In order to reduce the error in the process of establishing the finite element model,the model should be updated.This paper summarizes some technical problems encountered in the domestic and foreign model updating based on previous research results,and has carried on the discussion about these problems.Taking full account of the effect of measurement error on the model updating effect in the actual measurement work,the following research contents are presented:(1)Under the premise of ignoring measurement error,a updated method for the deterministic beam structure is proposed based on the actual measurement data.The rotational degree of freedom of the structure is eliminated by static condensation.In actual measurement work the vertical displacement response of the structure is only needed.And combined with the theory of finite element,the governing equation of the structural element modifying factor is obtained.According to the calculation,the exact value of the element updating factor of the theoretical calculation model is consistent with the updating factor of the actual measurement structure,and the vertical displacement response of the theoretical calculation model is basically consistent with the vertical displacement response of the actual measurement structure,which verifies the reliability of the model modification method.(2)It is assumed that the updated parameter of the initial datum model is abnormal distribution.It takes the beam structure as the research object based on the non-orthogonal polynomials,the unit updating factor is expressed as the form of the four order perturbation expansion.The updating factor and its statistical characteristics of the corresponding structural units can be obtained combined with the global stiffness equation,and it can verify the reliability for stochastic modifying equation by direct Monte Carlo method.The change trends of the mean and mean square deviation of the updating factor can be consistent with the trend of the mean and mean variance of the direct Monte Carlo method with model updating.The vertical displacement response of the theoretical calculation model is basically consistent with the vertical displacement response of the actual measurement structure,which verifies the validity of the method.(3)Combined with the actual engineering situation,the error of the measuring node is divided into two parts.Taking into account the correlation between the two parts of the measurement error,two related random variables are transformed into two independent random variables by means of KL expansion.The exact control equation of element correction factor is obtained by four order perturbation stochastic finite element method,and then the probability distribution statistics of the structural element correction factor are analyzed.At the same time,the Carlo Monte method is used to compare and analyze the consistency between the theoretical calculation model and the practical engineering structure and the validity of the method.In the actual project,the consistency of the measurement data in the measurement results can ensure the accuracy of model updating and measurement data.