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提出了一种基于随机抽样技术与距离判别分析的结构有限元随机模型修正(SMU)方法,并将其应用到GARTEUR飞机模型的有限元模型修正过程中。传统的模型修正方法以灵敏度分析及优化分析方法为核心,对有限元模型的输入参数进行修正。而本文的随机模型方法充分考虑了有限元建模过程与试验测量中普遍存在的不确定性,利用Monte Carlo抽样方法进行大量的随机抽样实验,完成不确定性从输入参数向输出特征的传递分析;在参数修正过程中,利用距离判别分析计算试验与仿真两个数据集之间的统计学差异,并通过迭代程序逐步修正输入参数使仿真数据逐步收敛于测量数据;利用径向基函数,在修正过程中引入代理模型,在保证精度的同时大大降低了随机模型修正的计算量。利用MCS.Patran的二次开发语言PCL开发了随机抽样实验的相关程序,并可以自动收集数据用于参数修正的迭代运算。通过普遍认可的三级确认准则对GARTEUR有限元模型可靠性进行了确认分析,结果表明提出的随机模型修正方法具有可行性和工程应用价值。
A structural finite element stochastic model updating (SMU) method based on stochastic sampling technique and distance discriminant analysis is proposed and applied to the finite element model updating process of GARTEUR aircraft model. The traditional method of model correction uses sensitivity analysis and optimization analysis as the core, and modifies the input parameters of the finite element model. However, the stochastic model method in this paper fully takes into account the ubiquitous uncertainties in the process of finite element modeling and experimental measurement. A large number of random sampling experiments are conducted by Monte Carlo sampling to complete the transfer of uncertainty from input parameters to output characteristics In the process of parameter correction, the statistical difference between the two datasets of experiment and simulation was calculated by distance discriminant analysis, and the simulation data was gradually converged to the measured data by iteratively modifying the input parameters. By using radial basis function, Introducing the agent model in the process of correction, the computational complexity of stochastic model correction is greatly reduced while ensuring the accuracy. PCL, the secondary development language of MCS.Patran, developed the relevant procedures of random sampling experiment and can automatically collect data for iterative computation of parameter correction. The reliability of the GARTEUR finite element model was verified by the generally accepted three-level validation criteria. The results show that the proposed stochastic model correction method is feasible and applicable.