基于摄动法的不确定性有限元模型修正方法研究

开展了考虑不确定性的有限元模型修正方法的研究。基于摄动法推导了待修正参数均值和协方差矩阵的迭代格式,其中协方差的迭代格式包括是否考虑试验数据与修正参数之间相关性的两种形式。在理论研究基础上开展数值仿真研究,实现了不确定性有限元模型修正的摄动法,并研究了试验数据样本数量对修正误差的影响。仿真结果表明,该方法适用于解决系统参数与试验数据存在不确定性的模型修正问题,试验样本数量对待修正参数标准差的修正精度影响较大;忽略试验模态参数与待修正参数不确定性之间的相关性,能够避免计算二阶灵敏度矩阵,在保证修正结果准确性的前提下减少计算量。

A study on stochastic finite element model updating based on perturbation approach

A study on stochastic finite element model updating using perturbation method is conducted in this paper.The uncertain parameters to be updated are divided into the summation of mean value and a deviation term based on which the formulations for the stochastic model updating are derived, two kinds of updating equation for covariance matrix are formulated according to whether the correlation between the updating parameters and the measurements is considered.Based on stochastic model updating method, numerical simulations are conducted with a further study between the number of response samples and the accuracy of the method.Results show that the statistical characteristics of the uncertain parameters can be accurately identified though the iterations of the stochastic model updating method and the accuracy of the updated standard deviations of the parameters are affected by the number of samples.When the correlation between the uncertainties in the updating parameters and in the test data is ignored, higher order sensitivity matrix is not necessary to be calculated, which lead to a lower computational effort but promise results.