利用改进交叉模型交叉模态的随机模型修正方法

Stochastic model updating method using the improved cross-model cross-mode technique

将混合摄动-伽辽金方法和改进的交叉模型交叉模态技术相结合,提出了一种随机模型修正方法。该方法有效缓解了模型修正过程中测量数据有限和测量误差不确定的影响。考虑到实测模态数据具有不确定性,基于改进的交叉模型交叉模态方法,建立了一个新的描述结构随机参数和随机响应关系的模型修正方程。利用混合摄动-伽辽金方法求解该随机修正方程,进而得到结构随机修正参数的统计特征。简支梁的数值结果表明,该方法在测量数据不确定性较大时仍能保持很高的修正精度,同时计算效率比蒙特卡罗模拟方法高出一个数量级。在测量模态数据较少的情况下,该方法比单独的混合摄动-伽辽金修正方法修正效果好,且比交叉模型交叉模态法的修正精度更高。框架试验的结果表明,该方法可以同时修正结构的刚度和质量,修正后的结构参数与预设工况基本吻合,同时能复现结构的测量模态,从而验证了所提方法的有效性。

In this paper,a new stochastic model updating method is proposed,which combines the random hybrid perturbation-Galerkin method with the improved cross-model cross-mode technique.This method effectively alleviates the impaction of limited measurement data and uncertain measurement errors on model updating.Considering the uncertainty of the measured modal data,a new stochastic updating equation with update coefficient vector is established based on the improved cross-model cross-mode meth⁃od.Using the hybrid perturbation-Galerkin method to solve the stochastic updated equation,the update coefficient vector is ob⁃tained.The statistical characteristics of the update coefficients can then be determined.The numerical results of the simply support⁃ed beam show that the proposed method can effectively deal with the relatively large uncertainty in the actual measurement data,and shows relatively strong stability in the case of different modal combinations,and has a higher computational efficiency than the Monte Carlo method.Considering the rank deficit,the improved cross-model cross-mode method proposed in this paper can get better updating results than the cross-model cross-mode method.The experimental results of the frame show that the new method can simultaneously modify the stiffness and the quality of the structure,and the updated model can be used to obtain modal data consistent with the measured results,thus verifying the effectiveness of the proposed method.