Chen Hui, Huang Bin, Tee Kong Fah, Lu Bo
School of Civil Engineering & Architecture, Wuhan University of Technology, Wuhan 430070, China.
Wuhan Institute of Technology, College of Post and Telecommunication, Wuhan 430074, China.
Sensors (Basel). 2021 May 10;21(9):3290. doi: 10.3390/s21093290.
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.
本文提出了一种基于改进的跨模型跨模态（ICMCM）技术的新型随机模型更新方法，用于更新结构模型。该新方法将随机混合摄动 - 伽辽金方法与ICMCM方法相结合，以解决测量数据有限且测量误差不确定情况下的模型更新问题。首先，利用ICMCM技术，通过考虑不确定的测量模态数据，建立一个具有更新系数向量的新型随机模型更新方程。然后，采用随机混合摄动 - 伽辽金方法求解该随机模型更新方程，从而得到随机更新系数向量。随后，可以确定更新系数的统计特性。连续梁的数值结果表明，该方法能够有效应对测量数据中相对较大的不确定性，且该新方法的计算效率比蒙特卡罗模拟方法高几个数量级。当考虑秩亏时，与跨模型跨模态（CMCM）方法相比，所提出的随机ICMCM方法能够获得更准确的更新结果。一个实验实例表明，该新方法能够有效更新结构的刚度和质量，并且更新后模型频率的统计结果与测量结果一致，这确保了更新系数具有实际意义。
