This paper proposes a new stochastic model updating method to update structural models based on the improved cross-model cross-mode (ICMCM) technique. This new method combines the stochastic hybrid perturbation-Galerkin method with the ICMCM method to solve the model updating problems with limited measurement data and uncertain measurement errors. First, using the ICMCM technique, a new stochastic model updating equation with an updated coefficient vector is established by considering the uncertain measured modal data. Then, the stochastic model updating equation is solved by the stochastic hybrid perturbation-Galerkin method so as to obtain the random updated coefficient vector. Following that, the statistical characteristics of the updated coefficients can be determined. Numerical results of a continuous beam show that the proposed method can effectively cope with relatively large uncertainty in measured data, and the computational efficiency of this new method is several orders of magnitude higher than that of the Monte Carlo simulation method. When considering the rank deficiency, the proposed stochastic ICMCM method can achieve more accurate updating results compared with the cross-model cross-mode (CMCM) method. An experimental example shows that the new method can effectively update the structural stiffness and mass, and the statistics of the frequencies of the updated model are consistent with the measured results, which ensures that the updated coefficients are of practical significance.

中文翻译：

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基于改进的交叉模型交叉模式技术的随机模型更新新方法

提出了一种基于改进的交叉模型交叉模式（ICMCM）技术的结构模型随机更新方法。该新方法将随机混合扰动-Galerkin方法与ICMCM方法相结合，解决了测量数据有限和测量误差不确定的模型更新问题。首先，使用ICMCM技术，通过考虑不确定的测量模态数据，建立具有更新系数向量的新随机模型更新方程。然后，通过随机混合扰动-Galerkin方法求解随机模型更新方程，得到随机更新系数向量。之后，可以确定更新系数的统计特性。连续光束的数值结果表明，该方法可以有效地应对测量数据中较大的不确定性，并且该方法的计算效率比蒙特卡洛模拟方法高出几个数量级。当考虑秩不足时，与交叉模型交叉模式（CMCM）方法相比，所提出的随机ICMCM方法可以获得更准确的更新结果。实验实例表明，该方法可以有效地更新结构刚度和质量，更新后的模型频率统计结果与实测结果吻合，保证了更新后的系数具有实际意义。而且这种新方法的计算效率比蒙特卡洛模拟方法高出几个数量级。当考虑秩不足时，与交叉模型交叉模式（CMCM）方法相比，所提出的随机ICMCM方法可以获得更准确的更新结果。实验实例表明，该方法可以有效地更新结构刚度和质量，更新后的模型频率统计结果与实测结果吻合，保证了更新后的系数具有实际意义。而且这种新方法的计算效率比蒙特卡洛模拟方法高出几个数量级。当考虑秩不足时，与交叉模型交叉模式（CMCM）方法相比，所提出的随机ICMCM方法可以获得更准确的更新结果。实验实例表明，该方法可以有效地更新结构刚度和质量，更新后的模型频率统计结果与实测结果吻合，保证了更新后的系数具有实际意义。